June 2011 

NASA/CR–2011-217157 

Compression After Impact Experiments and 

Analysis on Honeycomb Core Sandwich Panels 

with Thin Facesheets 

Thomas D. McQuigg 

National Institute of Aerospace, Hampton, Virginia 
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June 2011 

NASA/CR–2011-217157 

Compression After Impact Experiments and 

Analysis on Honeycomb Core Sandwich Panels 

with Thin Facesheets 

Thomas D. McQuigg 

National Institute of Aerospace, Hampton, Virginia 
Available from: 

NASA Center for AeroSpace Information 

7115 Standard Drive 

Hanover, MD 21076-1320 

443-757-5802 

Acknowledgments 

I would like to make the following acknowledgements of the valuable support I received 

for this research. First, thank you to my graduate advisor, Dr. Rakesh Kapania, for many 

years of support and mentorship. Thanks to my Ph.D. Committee: Dr. Mayuresh Patil, 

Dr. Gary Seidel, Dr. Stephen Scotti, and Dr. Sandra Walker, for their encouragement and 

advice. Additional thanks to Dr. Scotti and Dr. Walker, for serving as my NASA mentors 

during my time there. Thanks to Dr. Wade Jackson and Dr. James Ratcliffe for lending 

their expertise in experiments and analysis, as well as the use of their excellent model. 

Also, thanks to Dr. Tom Haynie and Dr. Mark Hilburger for the use of, and instruction 

on, some of the auxiliary instrumentation used in the experiments. Finally, I would like to 

extend my sincere gratitude to NASA Langley Research Center and the National Institute 

of Aerospace, both of Hampton, Virginia, for their financial support of my research, and 

the use of their world-class resources.

This report was submitted as a Dissertation to the Faculty of the Virginia Polytechnic Institute 

and State University in partial fulfillment of the requirements for the degree of Doctor of 

Philosophy in Aerospace Engineering. 

Trade names and trademarks are used in this report for identification only. Their usage does not 

constitute an official endorsement, either expressed or implied, by the National Aeronautics and 

Space Administration. 
Compression After Impact Experiments and Analysis on

Honeycomb Core Sandwich Panels with Thin Facesheets

Thomas Dale McQuigg

(ABSTRACT)

A better understanding of the effect of impact damage on composite structures is necessary to give the engineer an ability to design safe, efficient structures. Current composite

structures suffer severe strength reduction under compressive loading conditions, due to even

light damage, such as from low velocity impact. A review is undertaken to access the current

state-of-development in the areas of experimental testing, and analysis methods. A set of

experiments on Nomex honeycomb core sandwich panels, with thin woven fiberglass cloth

facesheets, is described, which includes detailed instrumentation and unique observation

techniques. These techniques include high speed video photography of compression after

impact (CAI) failure, as well as, digital image correlation (DIC) for full-field deformation

measurements. The effect of nominal core density on the observed failure mode is described.

A finite element model (FEM) is developed to simulate the experiments performed in the

current study. The purpose of this simulation is to predict the experimental test results, and

to confirm the experimental test conclusions. A newly-developed, commercial implementation of the Multicontinuum Failure Theory (MCT) for progressive failure analysis (PFA) in

composite laminates, Helius:MCT, is included in this model. The inclusion of PFA in the

present model gives it the new, unique ability to account for multiple failure modes. In addition, significant impact damage detail is included in the model as a result of a large amount

of easily available experimental test data. A sensitivity study is used to assess the effect of

each damage detail on overall analysis results. Mesh convergence of the new FEM is also

discussed. Analysis results are compared to the experimental results for each of the 32 CAI

sandwich panel specimens tested to failure. The failure of each specimen is accurately predicted in a high-fidelity, physics-based simulation and the results highlight key improvements

in the understanding of honeycomb core sandwich panel CAI failure. Finally, a parametric

study highlights the strength benefits compared to mass penalty for various core densities.

Contents

1 Introduction 1

1.1 Overview of Impact Damage in Composites . . . . . . . . . . . . . . . . . . . 1

1.2 Impact Damage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

1.2.1 Impact Damage in Composite Laminates . . . . . . . . . . . . . . . . 5

1.2.2 Impact Damage in Sandwich Composites . . . . . . . . . . . . . . . . 7

1.2.3 Considerations for the Experimental Study of

Impact Damage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

1.3 Compression After Impact Experiments . . . . . . . . . . . . . . . . . . . . . 13

1.3.1 CAI Testing of Composite Laminates . . . . . . . . . . . . . . . . . . 14

1.3.2 CAI Testing of Composite Sandwich Constructions . . . . . . . . . . 17

1.4 CAI Modeling and Strength Prediction for

Sandwich Constructions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

1.4.1 Experimentally Based CAI Strength Prediction . . . . . . . . . . . . 19

1.4.2 Analytic Solutions of CAI Response . . . . . . . . . . . . . . . . . . . 20

1.4.3 Finite Element Models for CAI Response . . . . . . . . . . . . . . . . 23

1.4.4 Modeling of Honeycomb Core . . . . . . . . . . . . . . . . . . . . . . 27

1.5 Progressive Failure Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

1.6 Overview of the Present Work . . . . . . . . . . . . . . . . . . . . . . . . . . 34

2 Impact Damage and CAI Tests of PXX Series Materials 36

2.1 Materials and Test Coupons . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

vii
2.2 Impact Damage Evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

2.2.1 Static Indentation Tests . . . . . . . . . . . . . . . . . . . . . . . . . 39

2.2.2 Drop Tower Impact Survey . . . . . . . . . . . . . . . . . . . . . . . . 45

2.3 Compression After Impact Experiments . . . . . . . . . . . . . . . . . . . . . 52

2.3.1 Apparatus and Instrumentation . . . . . . . . . . . . . . . . . . . . . 53

2.3.2 CAI Failure of PXX Series Coupons . . . . . . . . . . . . . . . . . . . 58

2.3.3 Full-field Displacement Measurements Using DIC . . . . . . . . . . . 64

2.4 Conclusions from Impact Damage and CAI Tests of PXX Series Materials . . 68

3 Impact Damage and CAI Tests of 3PCF-XX and 6PCF-XX Series

Materials 70

3.1 Materials and Test Coupons . . . . . . . . . . . . . . . . . . . . . . . . . . . 71

3.2 Impact Damage Evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . 74

3.2.1 Static Indentation Tests . . . . . . . . . . . . . . . . . . . . . . . . . 74

3.2.2 Drop Tower Impact Survey . . . . . . . . . . . . . . . . . . . . . . . . 78

3.3 Compression After Impact Experiments . . . . . . . . . . . . . . . . . . . . . 87

3.3.1 Apparatus and Instrumentation . . . . . . . . . . . . . . . . . . . . . 87

3.3.2 CAI Failure of 3PCF-XX and 6PCF-XX Series Coupons . . . . . . . 90

3.3.3 Full Field Displacement Measurements using DIC . . . . . . . . . . . 97

3.4 Conclusions from Impact Damage and CAI Tests of 3PCF-XX and 6PCF-XX

Series Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103

4 CAI Analysis Using Existing Models 105

4.1 General Theory for CAI Prediction . . . . . . . . . . . . . . . . . . . . . . . 106

4.1.1 Classical Laminate Theory . . . . . . . . . . . . . . . . . . . . . . . . 106

4.1.2 Composite Laminates in Finite Element Analysis . . . . . . . . . . . 112

4.1.3 Honeycomb Core as an Orthotropic Continuum . . . . . . . . . . . . 116

4.1.4 Honeycomb Core Non-Linear Out-of-Plane Response . . . . . . . . . 121

4.2 FEM with Spring Element Core . . . . . . . . . . . . . . . . . . . . . . . . . 122

viii
4.2.1 Explanation of Model Components and Inputs . . . . . . . . . . . . . 123

4.2.2 CAI Analysis Results for Spring Element Core Model . . . . . . . . . 126

4.3 FEM with Solid Orthotropic Element Core . . . . . . . . . . . . . . . . . . . 129

4.3.1 Explanation of Model Components and Inputs . . . . . . . . . . . . . 129

4.3.2 CAI Analysis Results for Solid Element Core Model . . . . . . . . . . 134

4.4 Conclusions from CAI Analysis Using Existing

Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137

5 Development of a New Model for CAI Analysis 139

5.1 Progressive Failure Analysis Theory . . . . . . . . . . . . . . . . . . . . . . . 140

5.1.1 Multicontinuum Theory . . . . . . . . . . . . . . . . . . . . . . . . . 141

5.1.2 MCT Failure Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . 145

5.1.3 Material States for Woven Composite Laminates During PFA . . . . 148

5.2 Introduction to Proposed FEM for CAI Analysis . . . . . . . . . . . . . . . . 149

5.2.1 Geometry, Boundary Conditions and Finite Elements . . . . . . . . . 151

5.2.2 Honeycomb Core Implementation using UMAT . . . . . . . . . . . . 154

5.2.3 Impact Damage Modeling . . . . . . . . . . . . . . . . . . . . . . . . 156

5.3 Mesh Pattern and Convergence . . . . . . . . . . . . . . . . . . . . . . . . . 167

5.3.1 Mesh Convergence: Coupon Width Direction (eX) . . . . . . . . . . 167

5.3.2 Mesh Convergence: Coupon Load Direction (eY ) . . . . . . . . . . . 170

5.3.3 Mesh Convergence: Coupon Thickness Direction (eZc) . . . . . . . . 172

5.3.4 Additional Notes from the Mesh Convergence Study . . . . . . . . . . 174

5.4 FEM Sensitivity Studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175

5.4.1 Sensitivity to Impact Damage Definition . . . . . . . . . . . . . . . . 176

5.4.2 Sensitivity to Core Damage Depth Definition . . . . . . . . . . . . . . 180

5.4.3 Sensitivity to Element Stiffness Degradation . . . . . . . . . . . . . . 182

5.4.4 Final Notes on the FEM’s Sensitivities . . . . . . . . . . . . . . . . . 184

5.5 Conclusions from the Development of the New FEM for CAI Analysis . . . . 186

ix
6 Analysis of Test Coupons and Other CAI Analysis Results 188

6.1 Analysis of CAI Response of PXX Series

Panels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 189

6.1.1 PXX Analysis Inputs . . . . . . . . . . . . . . . . . . . . . . . . . . . 190

6.1.2 PXX Analysis Results . . . . . . . . . . . . . . . . . . . . . . . . . . 193

6.2 Analysis of CAI Response of 3PCF-XX Series

Panels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 199

6.2.1 3PCF-XX Analysis Inputs . . . . . . . . . . . . . . . . . . . . . . . . 199

6.2.2 3PCF-XX Analysis Results . . . . . . . . . . . . . . . . . . . . . . . 202

6.3 Analysis of CAI Response of 6PCF-XX Series

Panels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 206

6.3.1 6PCF-XX Analysis Inputs . . . . . . . . . . . . . . . . . . . . . . . . 207

6.3.2 6PCF-XX Analysis Results . . . . . . . . . . . . . . . . . . . . . . . 209

6.4 Parametric Study of CAI Response with Various Core Densities . . . . . . . 215

6.4.1 Discussion of Core Crush Property Variance with

Core Density . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 216

6.4.2 Results of the Parametric Study . . . . . . . . . . . . . . . . . . . . . 218

6.5 Conclusions from the Results of Using the New FEM for CAI Analysis . . . 220

7 Conclusions and Future Work 222

7.1 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 224

7.1.1 Experimental Testing Conclusions . . . . . . . . . . . . . . . . . . . . 225

7.1.2 Analysis Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . 228

7.2 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 231

Bibliography 234

A Additional Results of CAI Experiments 246

x
List of Figures

2.1 PXX series honeycomb core sandwich panel material. . . . . . . . . . . . . . 37

2.2 PXX series sandwich panel coupons for testing. . . . . . . . . . . . . . . . . 39

2.3 Apparatus used for static indentation of PXX series material coupons. . . . . 40

2.4 Semi-hemispherical tip used for static indentation, 0.5 in. diameter. . . . . . 40

2.5 PXX series material coupon with resulting damage from static indentation. . 41

2.6 Results of static indentation testing on PXX series materials: resultant force

vs. applied displacement measured at Location 2. . . . . . . . . . . . . . . . 42

2.7 Results of static indentation testing on PXX series materials: resultant force

vs. applied displacement measured at Locations 4 and 5. . . . . . . . . . . . 44

2.8 Drop tower apparatus used for impacting PXX series material coupons. . . . 45

2.9 Results of drop tower impact testing on PXX series materials: dent depth vs.

impact energy. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

2.10 Results of drop tower impact testing on PXX series materials: dent diameter

vs. impact energy. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

2.11 Results of drop tower impact testing on PXX series materials: maximum

impact force vs. impact energy. . . . . . . . . . . . . . . . . . . . . . . . . . 47

2.12 Results of drop tower impact testing on PXX series materials: impact length

vs. impact energy. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

2.13 Results of drop tower impact testing on PXX series materials: impact force

vs. time for Panel 1, Location 3. . . . . . . . . . . . . . . . . . . . . . . . . . 48

xi
2.14 Results of drop tower impact testing on PXX series materials: impact force

vs. time for Panel 1, Location 4. . . . . . . . . . . . . . . . . . . . . . . . . . 49

2.15 PXX series material coupon with resulting damage from drop tower impact,

Panel 1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

2.16 PXX series material coupon with resulting damage from drop tower impact,

Panel 2. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

2.17 PXX series material coupon with resulting damage from drop tower impact,

front of Panel 3. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52

2.18 PXX series material coupon with resulting damage from drop tower impact,

rear of Panel 3. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53

2.19 Load frame and coupon mounting apparatus used for CAI testing. . . . . . . 54

2.20 Location of strain gages for CAI testing of PXX series material coupons (all

dimensions in inches). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

2.21 Planform drawing of test frame loading platen which shows of DCDT locations

used for CAI testing (all dimensions in inches). . . . . . . . . . . . . . . . . . 56

2.22 Auxiliary apparatus for CAI testing of PXX series coupons with video instrumentation (above) and Vic-3D digital cameras (below). . . . . . . . . . . . . 57

2.23 Speckled PXX series material coupon for Vic-3D instrumentation of CAI testing. 58

2.24 Results of CAI testing of PXX series materials: typical measured resultant

force vs. applied. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59

2.25 PXX series material coupon during CAI testing, post-failure, showing results

of indentation propagation failure mode. . . . . . . . . . . . . . . . . . . . . 59

2.26 Results of CAI testing of PXX series materials: time lapse images taken

throughout test. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60

2.27 Results of CAI testing of PXX series materials: time lapse images taken from

high speed camera during failure. . . . . . . . . . . . . . . . . . . . . . . . . 61

2.28 Results of CAI testing of PXX series materials: CAI failure stress and strain

vs. impact energy. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62

xii
2.29 Results of CAI testing of PXX series materials: typical reaction force vs. strain

measured by various methods. . . . . . . . . . . . . . . . . . . . . . . . . . . 63

2.30 Results of CAI testing of PXX series materials: typical reaction force vs. strain

measured by individual gages. . . . . . . . . . . . . . . . . . . . . . . . . . . 63

2.31 Results of CAI testing of PXX series materials: typical reaction force vs.

displacement measured by individual DCDT. . . . . . . . . . . . . . . . . . . 64

2.32 Results of CAI testing of PXX series materials: three dimensional DIC imaging

of PXX test coupon at 75% of failure load, out-of-plane deformation shown. 65

2.33 Results of CAI testing of PXX series materials: three dimensional DIC imaging of PXX test coupon after indentation propagation failure, out-of-plane

deformation shown. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66

2.34 Results for DIC measurements: dent growth in coupon width direction for

PXX test coupons. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67

2.35 Results for DIC measurements: dent growth in coupon load direction for PXX

test coupons. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67

2.36 Results for DIC measurements: dent depth increase in coupon load direction

for PXX test coupons. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68

3.1 3PCF-XX (top) and 6PCF-XX (bottom) series honeycomb core sandwich

panel material. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71

3.2 3PCF-XX (top right) and 6PCF-XX (top left) series material coupons for

testing, with top load bearing end (middle) and side views (bottom. . . . . . 73

3.3 Static indentation of 3PCF-XX (right) and 6PCF-XX (left) series sandwich

coupons. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75

3.4 Results of static indentation of 3PCF-XX series material coupons: residual

dents. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76

3.5 Results of static indentation of 3PCF-XX series material coupons: resultant

force vs. applied displacement. . . . . . . . . . . . . . . . . . . . . . . . . . . 76

xiii
3.6 Results of static indentation of 6PCF-XX series material coupons: residual

dents. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77

3.7 Results of static indentation of 6PCF-XX series material coupons: resultant

force vs. applied displacement. . . . . . . . . . . . . . . . . . . . . . . . . . . 78

3.8 Drop tower apparatus used for impact survey of 3PCF-XX and 6PCF-XX

series material coupons. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79

3.9 Results of drop tower impact testing on 3PCF-XX and 6PCF-XX series materials: variation of the dent depth vs. the impact energy. . . . . . . . . . . . 80

3.10 Results of drop tower impact testing on 3PCF-XX and 6PCF-XX series materials: variation of the dent diameter vs. the impact energy. . . . . . . . . . 81

3.11 Results of drop tower impact testing on 3PCF-XX and 6PCF-XX series materials: variation of the maximum impact force vs. the impact energy. . . . . 81

3.12 Results of drop tower impact testing on 3PCF-XX and 6PCF-XX series materials: variation of the impact length vs. the impact energy. . . . . . . . . . 82

3.13 Results of drop tower impact testing on 3PCF-XX and 6PCF-XX series materials: variation of the core damage width vs. the impact energy. . . . . . . 82

3.14 Results of drop tower impact testing on 3PCF-XX and 6PCF-XX series materials: variation of the core damage depth vs. the impact energy. . . . . . . 83

3.15 Results of drop tower impact testing on 3PCF-XX and 6PCF-XX series materials: variation of the total dent depth for 3PCF-XX materials vs. the impact

energy. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83

3.16 Results of drop tower impact testing on 3PCF-XX and 6PCF-XX series materials: variation of the total dent depth for 6PCF-XX materials vs. the impact

energy. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84

3.17 Results of drop tower impact testing on 3PCF-XX series materials: residual

dents. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85

3.18 Results of drop tower impact testing on 6PCF-XX series materials: residual

dents. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86

xiv
3.19 Results of drop tower impact testing on 6PCF-XX series materials: core damage shown through destructive evaluation. . . . . . . . . . . . . . . . . . . . 87

3.20 Load frame and coupon mounting apparatus used for CAI testing with 3PCFXX (left) and 6PCF-XX (right) coupons installed. . . . . . . . . . . . . . . . 88

3.21 Location of strain gages for CAI testing of 3PCF-XX and 6PCF-XX series

material coupons (all dimensions in inches). . . . . . . . . . . . . . . . . . . 89

3.22 Auxiliary apparatus for CAI testing of 3PCF-XX and 6PCF-XX series coupons

with high speed Phantom cameras and necessary lighting systems. . . . . . . 90

3.23 Results of CAI testing of 3PCF-XX and 6PCF-XX series materials: failure

modes of indentation propagation for 3PCF-XX series coupons (left) and crack

propagation in 6PCF-XX coupons (right). . . . . . . . . . . . . . . . . . . . 92

3.24 Results of CAI testing of 6PCF-XX series materials: time lapse images taken

throughout test. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93

3.25 Results of CAI testing of 3PCF-XX and 6PCF-XX series materials: time lapse

images taken from high speed camera during failure for 3PCF-XX (right) and

6PCF-XX (left) materials. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94

3.26 Results of CAI testing of 3PCF-XX and 6PCF-XX series materials: failure

stress vs. impact energy. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96

3.27 Results of CAI testing of 3PCF-XX and 6PCF-XX series materials: failure

strain vs. impact energy. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96

3.28 Example 3D representation of the indentation propagation failure mode for a

3PCF-XX series CAI test coupon. . . . . . . . . . . . . . . . . . . . . . . . . 98

3.29 Example 2D representation of the indentation propagation failure mode for a

3PCF-XX series CAI test coupon. . . . . . . . . . . . . . . . . . . . . . . . . 98

3.30 Example 3D representation of the crack propagation failure mode for a 6PCFXX series CAI test coupon. . . . . . . . . . . . . . . . . . . . . . . . . . . . 99

3.31 Example 2D representation of the crack propagation failure mode for a 6PCFXX series CAI test coupon. . . . . . . . . . . . . . . . . . . . . . . . . . . . 99

xv
3.32 Results from DIC Measurements: dent growth in coupon width direction for

3PCF-XX test coupons. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100

3.33 Results from DIC Measurements: dent growth in coupon load direction for

3PCF-XX test coupons. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101

3.34 Results from DIC measurements: dent depth increase for 3PCF-XX test

coupons. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101

3.35 Results from DIC measurements: dent growth in coupon width direction for

6PCF-XX test coupons. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102

3.36 Results for DIC measurements: dent growth in coupon load direction for

6PCF-XX test coupons. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102

3.37 Results from DIC measurements: dent depth increase for 6PCF-XX test

coupons. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103

4.1 Cellular in-plane geometry of hexagonal cell honeycomb core. . . . . . . . . . 118

4.2 Solid element core crush constitutive model. . . . . . . . . . . . . . . . . . . 122

4.3 Spring element core sandwich panel CAI FEM with boundary conditions. . . 123

4.4 Spring element core crush constitutive model. . . . . . . . . . . . . . . . . . 125

4.5 Spring element core FEM results: Typical reaction force vs. applied displacement with and without effect of including initial core damage. . . . . . . . . 126

4.6 Sample spring element core FEM results: indentation propagation failure

mode with out-of-plane displacement indicated by colored contours (blue indicates maximum negative displacement). . . . . . . . . . . . . . . . . . . . . 127

4.7 Sample spring element core FEM results: reaction force vs applied displacement for sample analyses on PXX series panels. . . . . . . . . . . . . . . . . 128

4.8 Solid element core sandwich panel CAI FEM with boundary conditions. . . . 130

4.9 Sample solid element core FEM results: typical reaction force vs. applied

displacement. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133

4.10 Damaged core elements (left) and damaged facesheet elements (right) in the

solid element core model example. . . . . . . . . . . . . . . . . . . . . . . . . 133

xvi
4.11 Sample solid element core FEM results: reaction force vs applied displacement,

model did not include simulated impact damage in the facesheets. . . . . . . 135

4.12 Sample solid element core FEM results: failure stress vs. impact energy with

(WFD) and without simulated facesheet impact damage (NFD). . . . . . . . 136

5.1 New CAI model: FEM Geometry. . . . . . . . . . . . . . . . . . . . . . . . . 152

5.2 New CAI model: FEM node points (highlighted in red) for boundary conditions of symmetry (left), simulated potting (center), and applied displacement

(right). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152

5.3 Idealized core crush response use to define non-linear constitutive core behavior of 3PCF Nomex core. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156

5.4 New CAI analysis model: close-up view of indented region of FEM. . . . . . 158

5.5 Examples of core damage from destructive microscopy of 3PCF-XX (left) and

6PCF-XX (right) series materials. . . . . . . . . . . . . . . . . . . . . . . . . 159

5.6 New CAI analysis model: damaged core region example. . . . . . . . . . . . 160

5.7 Examples of facesheet damage from microscopy of PXX (left) and 3PCF-XX

(right) series materials. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161

5.8 Example of matrix cracking as a result of impact damage observed by optical

microscopy. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161

5.9 New CAI analysis model:facesheet element regions representing areas of observed IFF (left) and fiber fracture (right), prior to any compressive load

analysis steps. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162

5.10 Mesh convergence study results: CAI failure load vs. number of elements (eX). 169

5.11 Mesh convergence results: % change in CAI failure load vs. number of elements (eX). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 170

5.12 Mesh convergence results: CAI failure load vs. number of elements (eY). . . 171

5.13 Mesh convergence results: % change in CAI failure load vs. number of elements (eY). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172

5.14 Mesh convergence results: CAI failure load vs. number of elements (eZc). . . 173

xvii
5.15 Mesh convergence results: % change in CAI failure load vs. number of elements (eZc). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 174

6.1 PXX analysis results: reaction force vs. applied displacement for analysis of

PXX series test coupons. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 194

6.2 Demonstration of correct failure mode prediction for example analysis of PXX

series material coupons using the new FEM for CAI analysis. . . . . . . . . . 195

6.3 PXX analysis results: comparison of PXX test coupon analysis failure strength

to experimental test results. . . . . . . . . . . . . . . . . . . . . . . . . . . . 196

6.4 PXX analysis results: dent growth in the coupon width direction (x-direction)

predicted from FEA of PXX test coupons. . . . . . . . . . . . . . . . . . . . 197

6.5 PXX analysis results: dent growth in the coupon load direction (y-direction)

predicted from FEA of PXX test coupons. . . . . . . . . . . . . . . . . . . . 198

6.6 PXX analysis results: maximum dent depth growth predicted from FEA of

PXX test coupons. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 198

6.7 3PCF-XX analysis results: reaction force vs. applied displacement for analysis

of 3PCF-XX series test coupons. . . . . . . . . . . . . . . . . . . . . . . . . . 202

6.8 3PCF-XX analysis results: comparison of 3PCF-XX test coupon analysis failure strength to experimental test results. . . . . . . . . . . . . . . . . . . . . 204

6.9 3PCF-XX analysis results: dent growth in the coupon width direction (xdirection) predicted from FEA of 3PCF-XX test coupons. . . . . . . . . . . . 205

6.10 3PCF-XX analysis results: dent growth in the coupon load direction (ydirection) predicted from FEA of 3PCF-XX test coupons. . . . . . . . . . . . 205

6.11 3PCF-XX analysis results: maximum dent depth growth predicted from FEA

of 3PCF-XX test coupons. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 206

6.12 6PCF-XX analysis results: reaction force vs. applied displacement for analysis

of 6PCF-XX series test coupons. . . . . . . . . . . . . . . . . . . . . . . . . . 209

6.13 Demonstration of crack propagation failure mode for example analysis of

6PCF-XX series material coupons using the new FEM for CAI analysis. . . . 211

xviii
6.14 6PCF-XX analysis results: comparison of 6PCF-XX test coupon analysis failure strength to experimental test results. . . . . . . . . . . . . . . . . . . . . 213

6.15 6PCF-XX analysis results: dent growth in the coupon width direction (xdirection) predicted from FEA of 6PCF-XX test coupons. . . . . . . . . . . . 214

6.16 6PCF-XX analysis results: dent growth in the coupon load direction (ydirection) predicted from FEA of 6PCF-XX test coupons. . . . . . . . . . . . 214

6.17 6PCF-XX analysis results: maximum dent depth growth predicted from FEA

of 6PCF-XX test coupons. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 215

6.18 Core crush strength of Nomex honeycomb shown varying with nominal core

density, and the data fit calculated for use with the parametric study analyses. 217

6.19 Core crush modulus of Nomex honeycomb shown varying with nominal core

density, and the data fit calculated for use with the parametric study analyses. 218

6.20 Parametric study results: failure strength vs. nominal core density associated

with continuum core properties. . . . . . . . . . . . . . . . . . . . . . . . . . 219

6.21 Parametric study results: percentage strength increase vs. normalized mass

increase. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 219

A.1 Additional results of CAI testing of PXX series materials: residual dent depth

vs. impact energy. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 247

A.2 Additional results of CAI testing of PXX series materials: residual dent diameter vs. impact energy. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 247

A.3 Additional results of CAI testing of 3PCF-XX and 6PCF-XX series materials:

residual dent depth for impacts on coupons used for CAI testing of 3PCF-XX

and 6PCF-XX series materials. . . . . . . . . . . . . . . . . . . . . . . . . . 249

A.4 Additional results of CAI testing of 3PCF-XX and 6PCF-XX series materials:

residual dent diameter for impacts on coupons used for CAI testing of 3PCFXX and 6PCF-XX series materials. . . . . . . . . . . . . . . . . . . . . . . . 251

xix
List of Tables

2.1 Results of static indentation testing on PXX series materials: damage measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

4.1 Spring core element FEM analysis: engineering constants used for layers of

PXX series sandwich panel facesheets. . . . . . . . . . . . . . . . . . . . . . 124

4.2 Spring core element FEM results: failure metrics. . . . . . . . . . . . . . . . 128

4.3 Sample solid core element FEM analysis: engineering constants used for orthotropic continuum representation of Nomex honeycomb core. . . . . . . . . 132

4.4 Sample solid core element FEM analyses: inputs used for demonstration. . . 134

4.5 Sample solid element core FEM results: failure metrics. . . . . . . . . . . . . 135

5.1 Nominal input values for MATLAB function for Abaqus input file creation

used during the sensitivity studies. . . . . . . . . . . . . . . . . . . . . . . . 177

5.2 Detailed sensitivity results of 3PCF-02 test coupon model to residual dent

maximum depth definition. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179

5.3 Sensitivity study results for various MATLAB function inputs. . . . . . . . . 179

5.4 Sensitivity study results, core damage region depth input. . . . . . . . . . . . 181

5.5 Sensitivity study results for element stiffness degradation inputs. . . . . . . . 184

6.1 E-glass/Epoxy woven fabric lamina material properties used in the CAI analysis of PXX series test coupons. . . . . . . . . . . . . . . . . . . . . . . . . . 191

6.2 E-glass/Epoxy woven fabric lamina strengths used in the CAI analysis of PXX

series test coupons. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191

xx
6.3 3PCF Nomex honeycomb core orthotropic engineering constants used in the

CAI analysis of PXX and 3PCF-XX series test coupons. . . . . . . . . . . . 191

6.4 MATLAB program inputs for creation of ABAQUS input files to run analyses

of PXX series test coupons. . . . . . . . . . . . . . . . . . . . . . . . . . . . 192

6.5 PXX analysis results: failure load, strength and strain for analysis of PXX

series test coupons. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 196

6.6 S2-glass/Epoxy woven fabric lamina material properties used in the CAI analysis of 3PCF-XX and 6PCF-XX series test coupons. . . . . . . . . . . . . . . 200

6.7 S2-glass/Epoxy woven fabric laminate strengths used in the CAI analysis of

3PCF-XX and 6PCF-XX series test coupons. . . . . . . . . . . . . . . . . . . 201

6.8 MATLAB program inputs for creation of ABAQUS input files to run analyses

of 3PCF-XX series test coupons. . . . . . . . . . . . . . . . . . . . . . . . . . 201

6.9 3PCF-XX analysis results: failure load, strength and strain for analysis of

3PCF-XX series test coupons. . . . . . . . . . . . . . . . . . . . . . . . . . . 203

6.10 6PCF Nomex honeycomb core orthotropic engineering constants used in the

CAI analysis of 6PCF-XX series test coupons. . . . . . . . . . . . . . . . . . 207

6.11 MATLAB program inputs for creation of Abaqus input files to run analyses

of 6PCF-XX series test coupons. . . . . . . . . . . . . . . . . . . . . . . . . . 208

6.12 6PCF-XX analysis results: failure load, strength and strain for analysis of

6PCF-XX series test coupons. . . . . . . . . . . . . . . . . . . . . . . . . . . 212

A.1 Additional results of impact survey of PXX series materials: panel 1 damage

metrics. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 246

A.2 Additional results of impact survey of PXX series materials: panel 2 damage

metrics. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 246

A.3 Additional results of impact survey of PXX series materials: panel 3 damage

metrics. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 248

A.4 Additional results of CAI testing of PXX series materials: impact damage

metrics. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 249

xxi
A.5 Additional results of CAI testing of PXX series materials: CAI failure metrics. 250

A.6 Additional results of CAI testing of 3PCF-XX and 6PCF-XX series materials:

3PCF-XX static indentation results. . . . . . . . . . . . . . . . . . . . . . . . 251

A.7 Additional results of CAI testing of 3PCF-XX and 6PCF-XX series materials:

6PCF-XX static indentation results. . . . . . . . . . . . . . . . . . . . . . . . 251

A.8 Additional results of CAI testing of 3PCF-XX and 6PCF-XX series materials:

impact survey results describing the residual damage for 3PCF-XX materials. 252

A.9 Additional results of CAI testing of 3PCF-XX and 6PCF-XX series materials:

impact survey results describing the force and length of impact for 3PCF-XX

materials. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 253

A.10 Additional results of CAI testing of 3PCF-XX and 6PCF-XX series materials:

impact survey results describing the residual damage for 6PCF-XX materials. 254

A.11 Additional results of CAI testing of 3PCF-XX and 6PCF-XX series materials:

impact survey results describing the force and length of impact for 6PCF-XX

materials. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 255

A.12 Additional results of CAI testing of 3PCF-XX and 6PCF-XX series materials:

results for impacts on 3PCF-XX coupons used for CAI testing. . . . . . . . . 255

A.13 Additional results of CAI testing of 3PCF-XX and 6PCF-XX series materials:

results for impacts on 6PCF-XX coupons used for CAI testing. . . . . . . . . 256

A.14 Additional results of CAI testing of 3PCF-XX and 6PCF-XX series materials:

results for failure of 3PCF-XX series panels during CAI testing. . . . . . . . 257

A.15 Additional results of CAI testing of 3PCF-XX and 6PCF-XX series materials:

results for failure of 6PCF-XX series panels during CAI testing. . . . . . . . 258

xxii
List of Symbols

(e) Supercript meaning element

∗ Superscript indicated effective property

1 Local cooridinate or axis, fiber direction

2 Local cooridinate or axis, transverse direction

3 Local cooridinate or axis, out-of-plane direction

A Matrix component

B Matrix component

C Component of the lamina stiffness matrix

D Matrix component

E Extensional Young’s modulus

F Forces

FS Shear flexibility

G Shear modulus

H Total laminate thickness

I Stress invariant, used with subscript to identify

xxiii
Kh Hourglass stiffness

M Composite laminate moment resultant

N Composite laminate normal stress resultant

R Principle radii of curvature

S Component of the lamina compliance matrix

U Displacements

V Composite laminate transverse stress resultant

V ol Volume of region

W ‘Waviness’ coefficient

Γ Hourglass mode

Φ Rotations

Π Total potential energy

Θ, Λ, Γ Finite element deformation modes

Ξ Deformed coordinates along the laminate midsurface

α Equation coefficient

C ̄ Component of the transformed (global coordinates) lamina stiffness matrix

S ̄ Component of the transformed (global coordinates) lamina compliance matrix

δ Delta operator, variation

γ Shear components of the shear tensor

γ

o Shear strain component at the composite laminate midsurface

xxiv
κ

o Curvature component at the composite laminate midsurface

λ Eigenvalue

[C] Constitutive matrix

[N] Finite element shape functions

∂ Indicates partial derivative

φf Fiber volume fraction

φm Matrix volume fraction

φf ill/mat Superconstituent volume fraction (fill tow fiber/matrix and ply matrix pockets)

φf ill Fill tow volume fraction (fill tow fiber/matrix)

φmat Laminate matrix pockets tow volume fraction

φwarp Warp tow volume fraction (warp tow fiber/matrix)

σ Extensional components of the stress tensor

σ

f

C Compressive fiber strength

σ

m

C Compressive matrix strength

σ

f

S12 In-plane fiber shear strength

σ

m

S12 In-plane matrix shear strength

σ

m

S23 Transverse matrix shear strength

σ

f

T Tensile fiber strength

σ

m

T Tensile matrix strength

xxv
τ Shear components of the stress tensor

θ Ply orientation angle with respect to the global coordinate system

υ Poisson’s ratio

ε Extensional components of the strain tensor

ε

o Extensional strain component at the composite laminate midsurface

ξ Coordinates along the laminate reference surface

{} Strain tensor

{σ} Stress tensor

a Equation coefficient

c Subscript or superscript meaning composite property

d Maximum dent diameter

eX Number of elements in the global model x-direction

eY Number of elements in the global model y-direction

eZc Number of elements in the global model z-direction, core region only

f Subscript or superscript meaning fiber constituent property

hmax Maximum dent depth

i Subscript indicating tensor placement, or superscript indicating mode

ij Subscripted indices indicating tensor placement

m Subscript or superscript meaning matrix constituent property

n Maximum integer value in summation

xxvi
o, p, q Element local Cartesian coordinates

x Global cooridinate or axis

y Global cooridinate or axis

z Global cooridinate or axis, distance from the laminate midsurface

xxvii
Chapter 1

Introduction

1.1 Overview of Impact Damage in Composites

An aerospace vehicle will probably sustain some type of impact loading during its lifetime,

whether during fabrication, maintenance or in some phase of in-service operation. The

resulting damage from impact may result in residual strength loss in airframe structures which

can be potentially life threatening. A well known example of the potential tragic consequences

of impact damage to an airframe can be seen in the 2003 events of the Space Shuttle Columbia

disaster. Camarda [1] noted that new design and analysis methods were proposed as a result

of this tragedy, and the emphasis on understanding impact damage in aerospace structures

was renewed. This emphasis on impact damage has led to experiments and analysis like the

work that will be presented in the current research on low velocity impact damage. Although

the mechanics are different from the preceding example, understanding low speed impact

damage is also of critical importance. Vehicles today are increasingly built from composite

structures, such as honeycomb core sandwich panels, which often feature thin, laminated

facesheets. In the literature review which follows in the present chapter, structures such as

these will be shown to be susceptible to large residual strength reductions due to damage

which may not be readily apparent. Research on impact damage in composite structures

has largely focused on experiments. Analysis of this problem has not been as thoroughly

1
Chapter 1. Introduction

performed, which means that design efficiency often suffers because of the complexity and

lack of understanding associated with this damage.

A comprehensive review of the work prior to 1999 on the subject of damage tolerance

in composite materials was written by Tomblin et al. [2] for the U.S. Department of Transportation (DOT) Federal Aviation Administration (FAA) Office of Aviation Research. The

researchers noted that the problem of impact damage in composites had already received

a wide array of treatment, but the effect of this damage on the mechanical response and

residual strength on sandwich composite components has not been as thoroughly developed.

This FAA report summarized impact damage on composite laminates and sandwich panels

and noted the differences in damage modes between the two classes of materials. Some of

these differences will be discussed later in the literature review. They noted, sources of localized damage resulting from low to medium velocity impacts, are similar to both types

of materials and include damage during manufacturing, assembly, and handling (e.g. tool

drops) and in-service operation (e.g. hail or bird strikes). Other sources of damage include

materials, fabrication, and processing defects, but the results of this type of damage is not

the focus of the current research and will not be covered in the literature review.

The incentive for the FAA to establish a document on damage tolerance in composites

was to ascertain an approach for future designs to meet government safety requirements for

airframe certification. In this pursuit, the report by Tomblin et al. [2] describes two critical

standards which were considered in the present research. First, the authors established relationships between representative damage sizes to design load requirements. Second, a five

step methodology for describing composite airframe damage tolerance is explained. (This

approach was later formally adopted as guidance for development and certification of composite structures by the FAA [3].) The relationships between damage sizes and design load

requirements are as follows. The smallest level damage is defined as that which is below

the Allowable Damage Limit (ADL) threshold. This sometimes undetectable damage is also

known as Barely Visible Impact Damage (BVID), a common term in the study of composite

impact damage. An airframe is required to withstand this type of damage over the op2
Chapter 1. Introduction

erational lifetime of the vehicles without repair at no decrease in ultimate load capability.

Tomblin et al. [2] next define a damage level, the Critical Damage Threshold (CDT), up to

which the damage is viewable, but may not be found except by periodic inspection. Aircraft

are required to be able to withstand damage up to CDT while undergoing multiple loadings

between specified inspection intervals and at least one lifetime limit load. Damage beyond

the CDT is defined as readily apparent to the operator of the vehicle (such as bird strike

or engine burst) and a vehicle must be able to safely finish its present flight after such an

impact event.

Tomblin et al. [2] went on to propose the following five step methodology for describing

the damage tolerance of a structure. First, damage formation in a specific sandwich structure

subject to low-velocity impact must be investigated experimentally. During this process,

the impact energy and velocity, and the impactor shape and diameter are chosen based on

previous studied work. The damage induced should then be studied and quantified. The

report suggests that this data can be used for semi-empirical model development. In the

second step, sandwich panel coupons are tested for residual strength. The report notes

that residual strength can be compared to damage size or impact energy level. In the

third task, damaged sandwich panels are subjected to fatigue loading, which is important in

characterizing types of damage up to the CDT. Next, in step four, a model for predicting

impact damage development and residual strength degradation should be developed. During

this process, they recommend that a number of analytical, numerical, and semi-empirical

models should be considered. It is expected that no one model can account for all types and

amounts of damages, or all materials and sandwich configurations. The fifth and final state

of the recommended methodology for determining damage tolerance is component, and then

full-scale testing and verification of the model results.

The following review of the literature relevant to the current research will cover subjects related to damage resistance or damage tolerance. Damage resistance is a measure of

a material or structure’s ability to withstand impact damage without sustaining damage.

Experiments including quasi-static indentation and impact testing are used to study a com3
Chapter 1. Introduction

ponent’s ability to withstand damage. With the data these experiments generate, damage

modes can be measured and described and new materials can be designed based on the

information learned. Analysis models can also be used to examine a component’s damage

resistance. Damage tolerance, on the other hand, is the study of a component’s ability to

carry design loads while damaged. Experimental testing of damaged components as well

as analytic models can be used to characterize their residual strength and failure modes.

Compression after impact (CAI) loading is the most used method of measuring damage tolerance in a composite material or structure. The largest reductions in residual strength, due

to impact damage, occur under compression loading, due to instabilities introduced by this

damage.

Through a better understanding of both damage resistance and damage tolerance,

safer and more efficient airframes and other structures can be designed and built. The

literature review begins in the following section with some highlights in the area of damage

resistance. These topics are related to the current research as they serve to establish the

damage expected and the evaluation techniques used. The remainder of the literature review

will focus on topics of damage tolerance. First, samples of the work done by experimental

testing are discussed to define the types of damage relevant to CAI and the failure modes

unique to this loading condition. Next, the current state of the analysis efforts which have

focused on the CAI problem is given. Some of the techniques and assumptions discussed are

used extensively in the present research, while others are not used. Finally, an area of research

new to analysis techniques used for considering CAI will be discussed. This area of research

is progressive failure analysis of laminated composites and will be a major component of the

model proposed in the current work.

1.2 Impact Damage

Tomblin et al. [2] suggested that the major purpose of the study of impact damage is

to identify airframe load path critical structures and materials, damage modes, detectable

4
Chapter 1. Introduction

damage sizes, and strength limiting sizes. It is especially important to determine the damage

levels that are detectable and at what load levels that damage results in strength reduction

to the material or structure. The study of impact damage allows for the design of critical

load bearing components in which damage can be detected before failure can occur. It can be

rightly pointed out that impact damage in composite laminates and sandwiches have unique

damage modes and should be studied separately. The following section first briefly outlines

impact damage in laminates and impact damage in sandwich constructions. Then, various

damage evaluation techniques are described, some of which were later used in the current

research.

1.2.1 Impact Damage in Composite Laminates

Cantwell and Morton [4] identified several failure mechanisms due to impact in fiber reinforced polymer (FRP) composite laminates, including fiber-matrix debonding, fiber pull-out,

intralaminar matrix cracking, matrix deformation, delamination, and fiber fracture. Fibermatrix debonding occurs when the stress in the interphase region of a fiber reinforced polymer

material exceeds the local strength allowing a crack to form. This type of debond depends

on fiber surface treatment prior to manufacture and can actually reduce the stress raising

effect of impact damage because fiber sliding becomes a principal energy absorbing mechanism. Intralaminar matrix cracking is partly responsible for the large areas of damage found

following an impact of a fiber reinforced matrix material. This type of cracking can involve

large cracks parallel to the fibers in either the matrix or interphase regions of a composite. Plastic matrix deformation occurs in fiber reinforced matrix materials when the matrix

yield strength is reached. The ability of the matrix to plastically deform can actually be

quite beneficial to reducing stress raising effects and blunting cracks that form at damage.

However, due to the high strain rates involved with impact, the dynamic yield strength is

usually much higher than measured at near static conditions and the material’s toughness

is reduced. Interlaminar delaminations occur at ply interfaces and during impact the most

severe cases of this type of damage have been shown to occur at locations of large differences

5
Chapter 1. Introduction

in the orientations of the adjacent plies to the interlaminar region. In cases of impact these

regions of delamination are usually linked by a series of intralaminar matrix cracks which

incline between delaminations at 45 degrees. Impacts can also create localized fiber fracture

in a composite laminate material. Fiber cracks are most likely to be detrimental to a material’s tensile loading capability and in general are less detrimental than matrix damage to a

composite material’s compressive strength. It has also been shown that this type of damage

dominates in thin laminates, whereas matrix damage is more common in thicker laminates.

The failure mechanisms described are applicable to both unidirectional and woven

fabric FRP laminates. In the current research, only plain woven fabric plies are considered.

An example of an experimental investigation on the response of a woven fiberglass reinforced

matrix (GFRP) laminate to low velocity impact loading was presented by Hosur, Karim, and

Jeelani [5]. The authors reported the effects of single and repeated impacts on GFRP with

and without Kevlar stitching as reinforcements. They noted that delaminations are the major

cause of failure in impact damaged laminates and that stitching can be used to arrest their

development. However, the authors found that penetration was a more likely damage mode

in stitched panels, as most of the resulting damage was contained to the impact location. In

the study, stitched panels were able to sustain more repeated impacts than unstitched ones.

Hosur et al. [6] also considered the hybridization of laminates with glass and carbon fibers

reinforcing the laminate matrix. The authors noted that improved load carrying capability

during impact could be achieved with only minor reductions in stiffness.

Since S2-glass woven fabric material is considered in the current research, an example

of impact damage on this type of material is considered in the work by Baucom et al. [7].

The authors examined and compared traditional 2D weaves, as well as 3D weaves. 3D weaves

involve laminate organization where tows are woven through the thickness direction. This

effectively eliminates traditional plies. Scanning electron microscopy was used to obtain high

resolution images of the resulting damage. The authors reported traditional impact damage

in woven laminates for the 2D weaves (e.g. matrix and fiber cracks, delamination, etc.) which

was reduced in the 3D weaves. The 3D woven materials also absorbed more energy before

6
Chapter 1. Introduction

penetration of the laminate.

In addition to stitching, other factors which play an important role in the damage

from low velocity impacts on composite laminates include geometric effects, such as thickness

and curvature. An example of these effects can be found in an experimental and analytical

study of the effects of panel curvature on the impact response of composite laminates was

presented by Ambur et al. [8]. The authors presented an analytic solution for the response

of flat and curved panels to impact loading using small deflection and first order shear theory

which appeared to accurately predict the experimental response. Experimental and analytic

data suggested that curvature has a significant impact on the impact response of composite

laminates and damage development. Contact force, in general, was found to decrease with

increasing curvature radius, while a limit point instability exists for tests of a certain panel

curvature radius and impact load force that results in a reduction in contact force due to

panel buckling.

1.2.2 Impact Damage in Sandwich Composites

In composite sandwich constructions with FRP facesheets, each of the impact failure mechanisms mentioned by Cantwell et al. [4] for composite laminates can be found in the facesheets.

Tomblin et al. [2] also mentioned several types of impact damage unique to sandwich composites, facesheet-core delamination, core crush, and puncture. Other examples of data from

impact damage studies on sandwich composites can be found in various FAA reports and

will be summarized in the present section. Tomblin et al. [9] also studied scaling of impact

damage and residual strength from coupon level tests to component or full scale structures.

The results noted that the residual strengths obtained from coupon level component testing

can be validly compared to the large level tests. They do, however, note that larger specimens distribute the impact energy and thus sustain less impact damage for a given impact

energy.

An example of a thorough impact damage study on sandwich composites can be found

in a recent work by Raju et al. [10]. In this study, the authors conducted impact testing on

7
Chapter 1. Introduction

coupons with dimensions of roughly 8.5 in. by 10.5 in. using hemispherically shaped indentors

with 1 and 3 in. diameter tips. The smaller tip was found to produce facesheet penetration,

as well as regions of highly crushed core material that extended through the thickness of the

panels. On the other hand, the larger indentor tip produced small deflections of the facesheet

and only a small layer of core damage below the facesheet, but the damage extended over a

large area of the panel.

Raju et al. [10] also identified a series of damage progression that can be applied to

other impact damage studies of composite materials, including those later described in this

work. The first type of damage they identified for the lowest levels of impact energy is the

initiation of facesheet and core damage. This includes the onset of core crush and plastic

deformation of the facesheet which may be accompanied by local constituent damage and

failure. Second, the damage propagates through the facesheet (by subsequent constituent or

bonding failure) and the core (by crushing). In the third stage, the facesheet may fracture

for some sandwich constructions, especially with thick core, while the core may just consolidate for thinner cores. Extreme damage becomes apparent in the fourth stage as complete

facesheet penetration occurs and the core completely consolidates. Finally, in the fifth and

most extreme stage of impact damage for a material, damage is initiated in the backside

facesheet.

Raju et al. [10] noted other parameters associated with carrying out the impacts

that may be of importance. They showed that the peak force recorded by the impactor

for a given impact load will vary with size of the indentor, amount of core crush, and the

boundary conditions associated with the panel being impacted. Damage trends, including

size and amount, were also shown to vary with these variables. Tomblin et al. [11] observed

the effects of panel curvature on the properties of impact damage in composite sandwich

structures. It was found that when the radius of curvature of a panel was decreased, resulting

in increased global bending stiffness, the local contact stiffness near an impact was decreased.

This resulted in increased amounts of impact damage when impacted with a sharp tip and

decreased amounts of damage when impacted with a blunt impact tip. The effects of panel

8
Chapter 1. Introduction

curvature were also discussed by Shyprykevich et al. [12] and Moody et al. [13].

An analytical approach to studying the impact damage in composite sandwich structures was presented by Ambur and Cruz [14]. A local-global approach was used to analyze

the effect of several sandwich construction variables on the contact force, displacement, and

surface strains on the contacted facesheet, as well as resulting damage. Facesheet thickness was found to be the primary factor influencing the resulting damage of those studied.

Another analytic approach to modeling the results of low-velocity impact loading was undertaken by Foo et al. [15]. This group modeled the onset of facesheet delamination and

fiber fracture, core yield at the impact location, and the propagation of the damage under

additional loading. The results of the analytical study were compared to energy based methods and the authors concluded that the impact response of the sandwich panel could be

successfully modeled by considering its energy absorption during impact loading.

The use of static indentation as an alternative to low velocity impact when evaluating

the damage mechanisms of sandwich panel constructions was considered by Singh et al. [16].

The researchers evaluated damage in the BVID range and below in aluminum honeycomb

core sandwich panels with 8-ply quasi-isotropic GFRP facesheets. The types of damage found

using quasi-static indentation was similar to low-velocity impact damage. The researchers

considered three different aluminum honeycomb core materials, four quasi-isotropic facesheet

lay-ups, and one and three inch diameter semi-hemispheric indentation tips. Delamination

was observed more often in the interply interfaces closest to the core despite the specific

layup of the specimen. The data presented showed that core density had the largest effect

on the size of the resulting damage. Stiffer cores resulted in more facesheet delaminations,

smaller crushed core regions, and smaller residual dents.

1.2.3 Considerations for the Experimental Study of

Impact Damage

Several experiments will be described later in Chapters 2 and 3. The design of these experiments takes into account the work and advice of several researchers. Important components

9
Chapter 1. Introduction

of impact testing include the selected impact mass and velocity, the boundary conditions

of the impact specimen, the geometry of the impact specimen as well as the impacting tip

of the impact mass, and finally, the methods for detecting and characterizing the resulting

damage. As the focus of this work was on the compression after impact experiment and

modeling results, this section is intended to be an overview and by no means is meant to

encapsulate the range of variables an experimentalist must consider when undertaking the

study of damage characteristics and damage resistance in composites.

An excellent example of the experimental techniques associated with the study of

impact damage in composites can be seen in the work by Tomblin et al. [17]. A well

developed drop tower impact apparatus which allows for the variation of impactor mass and

end geometry is shown in their work. Other critical components include a rebound catch

mechanism and a high speed data acquisition system. In addition, it is important to consider

the boundary conditions associated with the panel being impacted. The key measurements

during impact testing are impact load, and impactor displacement and velocity. The resulting

data that can be considered includes impact force vs. time, impact force vs. displacement,

peak impact force vs. impact energy, peak impactor displacement vs. impact energy, and

impact duration vs. impact energy.

The influence of the mass of the projectile on the resulting impact damage in composites was considered by Cantwell and Morton [18] in both high and low speed impacts

for a single diameter of impacting tip. The authors showed that for a given impact energy,

the mass of the impactor has a significant effect on the damage in a composite structure.

They concluded that greater mass meant more concentrated damage in a specimen, while

lower masses actually produced larger areas of damage. Specimen sizing was also studied

by Cantwell [19] in an attempt to understand its effect on the resulting damage for a given

impact velocity. He found that the thickness of a specimen had a large effect on the resulting

damage, while the length and/or width of the panel did not have an appreciable effect. In a

subsequent work, Cantwell and Morton [20] studied the geometry of impact specimens and

found that impact resulted in damage initiation at the point of contact for short beams,

10
Chapter 1. Introduction

while damage initiation began at the lower surface due to beam flexure for longer specimens.

The authors also showed that circular specimens tend to absorb more energy and result in a

lower damage level for similar impact energy levels.

Some other measurements of interest include planar damage area vs. impact energy

and maximum residual indentation vs. impact energy. Several methods for detecting, measuring and describing damage that may be present in a given composite material or structure

are available. In their study of high velocity impacts on CFRP materials, Cantwell and Morton [21] described several methods, including X-radiography, ultrasonic C-scanning, optical

microscopy and thermal deplying. X-radiography and ultrasonic C-scanning have the advantage of being non-destructive. Therefore, the experimentalist can use these techniques to

examine specimens which may then be used in additional experimentation, such as compression after impact. C-scans are useful for giving the user an idea of the in-plane damaged area

of the coupon and X-ray images are useful for identifying matrix cracking and delamination;

however, neither can clearly show the location and mode of fiber fracture. Optical microscopy

and thermal deplying have the disadvantage of destroying the subject being viewed, though

they yield greater information about the damaged area of interest. Individual locations and

modes of fiber fracture and delaminations can be identified using the destructive techniques.

In a later work, Cantwell and Morton [4] discussed other benefits and penalties which

exist for each of the methods discussed previously. For instance, some ultrasonic C-scan

methods involve the immersion of the subject in a bath of water. This immersion can be

detrimental to the composite if voids exist in the laminate or sandwich composite which may

retain the fluid once the scan is complete. In addition, for large components or full-scale tests

an immersion of the subject may not be practical due to the large volume of water required.

Also, C-scans are most suited to the detection of delamination type fracture and cannot detect

fiber fracture, matrix cracking or micro-mechanical damage. X-ray imagery improves upon

this by not placing the subject in an environment detrimental to its mechanical properties.

In addition, considerably smaller defects can be observed if a fine enough X-ray film is used.

This type of inspection is too tedious for routine production and service damage detection,

11
Chapter 1. Introduction

but can be used for high-resolution damage characterization if the point of inspection is

known. Thermal deplying involves the heat treatment of the specimen until the matrix

degrades and a razor can be used to separate the plies. This technique is especially useful for

examining ply by ply fiber crack location in impact damage composites, but is less effective

for examining matrix dependent failure. Optical microscopy can yield detection of all types

of damage, but is tedious and labor intensive. It can also be difficult to detect matrix defects

without the aid of an imposed dye.

There are still more techniques for damage detection that should be considered. Perhaps the simplest non-destructive technique is visual inspection. This is especially the case

for detection of damage due to impact because of the localized dent. Simple inspection of

the dent can yield quantitative information that can reveal valuable information about an

impact site. Thermography, acoustic emission, eddy currants, fiber optics, holography, Moir ́e

interferometry and various other methods also exist for non-destructive evaluation of impact

damage in composites. Also, scanning electron microscopy is a third destructive technique.

More information on each of these techniques can found in Ref. [4].

Additional non-destructive techniques were used by Tomblin et al. [11] including tap

testing and mechanical impedance analysis. Mechanical tap testing involves the collection of

force magnitude and impact duration data at locations across the undamaged and damaged

regions of the specimen. The duration of the response is subject to the local mechanical

properties of the specimen so that the response will be different at damaged and undamaged

locations. This type of damage evaluation can also be done acoustically by measuring the

acoustic response of the panel at each location tapped. Mechanical impedance analysis is

effective as well due to the reduction in impedance of a sandwich structure due to flaws

or impact damage that may be present in the material. A newer non-destructive damage

detection technique has been developed by Yang et al. [22] using thermal wave techniques

for debonding damage. This type of imaging was shown to be useful in two typical adhesive

structures for general defect location and sizing, although some noise reduction techniques

are necessary to make the techniques feasible.

12
Chapter 1. Introduction

It should be noted that no one technique is perfect for visualizing or assessing all

types of damage at an impact location and during any study of impact damage several

methods should be employed to obtain the requisite information. Although non-destructive

techniques of assessing damage characteristics, locations, and sizes are essential if evaluating

before further testing, such as in the case of CAI, a previously mentioned work by Raju et

al. [10] showed that the results of these techniques can be misleading. For example for some

combinations of material property, sandwich constructions, and applied indentation, the size

of the residual dent was found to be less than that recorded by the result of ultrasonic C-scan.

Both non-destructive and destructive impact damage evaluation techniques were used in the

current research. The techniques used are discussed in Chapters 2 and 3 of the present work.

1.3 Compression After Impact Experiments

Residual strength of impact damaged specimens can be measured in response to tensile,

compressive and shear loading conditions. In addition, fatigue loading is often of interest

and examples of results are available in research by Tomblin et al. [11] and Shyprykevich et

al. [12]. However, the out of plane displacement of sandwich panel components associated

with impact damage as shown in various impact tests, result in significant stress raising and

instabilities during compressive loading making compression after impact (CAI) the primary

tool of residual strength determination. This is especially true in the presence of shear

strength driven interply delaminations for composite laminates. In the case of composite

sandwich structures, out-of-plane deformation from impact damage can cause additional

core crushing during compressive loading and ultimately, unique sandwich panel CAI failure

modes. For this reason, CAI strength cannot, in general, be approximated by open hole

compressive strength tests, where the open hole is of similar size to CAI strength.

Tomblin et al. [23] showed that CAI residual strength is higher for a similar size

damage location in sandwich panels since impact damage does not extend through the entire

core and does not affect the un-impacted facesheet for low velocity impacts. However, the

13
Chapter 1. Introduction

CAI strength of a composite laminate found in material property data sheets (e.g. Ref.

[24]) is usually worse than the open hole compressive specimen with the hole of an equal

size. This is due to the fact that the listed CAI strength is a limit value that corresponds

to large amounts of damage, which is usually repaired or the component is replaced upon

inspection. Damage amounts equal to or less than BVID are still significant, but cannot be

estimated from the listed values for CAI strength or open hole strength. The creation of

CAI strength values through statistical analysis will be further explained in references to the

work by Nettles and Jackson [25], later in this chapter.

A good general overview of the CAI test procedure can be found in the work of Tomblin

et al [17]. In general, CAI testing involves the placement of a material coupon under an end

loaded uniaxial compressive load. Clamped conditions are simulated at the load application

ends of the specimen, and some fixtures may stabilize the panel from buckling by simulating

simply supported conditions along the non-load application coupon sides. Typically, the

impact damage is located in the center of the test coupon, and strain gages are placed to each

side of the damaged location as well as on the undamaged facesheet in the case of sandwich

constructions. Multiple strain gages may be used if a strain distribution is desired. Also,

force resultant is usually recorded, as well as applied displacement information. CAI residual

strength results are usually presented as a function of impact energy, but can also be presented

versus other damage measures such as planar damage or maximum indentation. Failure in

material coupons in the following section will be shown to vary based on the materials, and

types and amount of impact, among other variables. These results of previous work will

again be segregated between composite laminate and sandwich constructions because of the

unique features of the two types of materials. Test procedures and corresponding testing

standards will be further discussed in Chapters 2 and 3.

1.3.1 CAI Testing of Composite Laminates

The characteristics of CAI failure was shown by Rhodes et al. [26] for thick rectangular

flat laminates. Initially, panels were surveyed for impact damage characteristics at various

14
Chapter 1. Introduction

impact load levels. Non-destructive and destructive techniques were used to characterize the

damage, including C-scans, visually, and by sectioning. Impact levels of interest were then

chosen for CAI tests. Three compressive failure modes were observed including delamination

propagation, local short-wave buckling, and local shear crippling failure. Material systems

involving unidirectional tape and woven fabric were studied and no appreciable difference in

the resulting residual strength for a similar impact damage level was found. The residual

strengths are significantly lower for damaged laminates than for un-impacted panels even for

coupons with impact damage that is not readily apparent to visual inspection.

Starnes et al. [27] studied and compared the effect of impact damage to the effects of

an open hole in GFRP composite laminated plates under compression loading. The authors

did their own study on the impact characteristics of the plates they considered using a survey

of impact velocities, followed by non-destructive and destructive evaluation methods of the

impact locations. The authors also studied the effect of impacts on compressive strength

when the impacts were done on panels already under compressive loads. The authors found

that many of the panels failed for a given impact velocity at compressive loads much lower

than the loads a panel would achieve if the panel were impacted prior to compression.

Stiffeners of various geometries have been studied as a means of increasing the damage tolerance of composite plates by arresting the propagation of impact damage during

compressive loading. Typical cross sections of stiffeners include open sections, such as blade

stiffeners, and close sections, including hat stiffeners. Williams et al. [28] conducted a series

of experiments on composite laminate plate with stiffeners of blade and hat configuration

with impact damage in a variety of locations on and around the stiffeners to characterize how

each damage location uniquely affects the panel’s strength. Demuts et al. [29] also considered stiffeners in CAI testing of composite laminates in the form of multi-rib and multi-spar

designs. The authors found that impacts in a variety of damage locations can cause significant reductions in residual strength whether or not damage was visibly apparent, even in

stiffened panels. Also, it was determined that in multi stiffener designs multiple impacts of

one impact level in adjacent bays of a panel separated by stiffeners can cause a more drastic

15
Chapter 1. Introduction

strength reduction than a single impact of much higher energy level.

During various studies of the CAI response of un-stiffened and stiffened composite

laminate plates, some of which were mentioned, it was found that the damage tolerance

of the composite system depended, in part, on the epoxy resin used. Williams et al. [30]

suggested that this was due to its effect on delamination buckling. A significant CAI failure

model in laminates were delaminations, initially present as impact damage, which propagate

transversely to the applied loading direction until global panel failure. Resin ductility and

ultimate strength are identified as two key mechanical properties that can indicate the ability

of a resin system to raise the damage tolerance of a laminate. A sufficiently high shear

modulus has also been identified as another important design criterion of damage tolerant

systems due to these CAI tests.

Although the previously mentioned material examined the CAI response of composite

laminates made from unidirectional material plies, recently woven fabric material systems

have become of interest. An example of a CAI study on the response of woven fiber reinforced

composite laminates was done by Yan et al. [31]. The authors noted the following damage of

their GFRP panels due to impact damage: a matrix crack along the fill direction, a matrix

crack along the warp direction, delamination at the impact area, and additional matrix

and fiber cracks within the impact area. Delaminations appeared particularly in the ply

interface regions farthest from the side of impact. CAI tests of the specimens found that

failure occurred by propagation of the delamination regions and the fill direction matrix

crack. The authors also presented a detailed finite element model (FEM) and numerical

analysis to predict CAI strength of these laminates by explicitly modeling the woven material

geometry within a representative volume element. The authors concluded that delaminations

due to impact resulted in a critical reduction in the buckling strength of the panels under

compressive load. Analytic results like this one help researchers understand and implement

the failure mechanisms in earlier experimental work in structural analysis.

16
Chapter 1. Introduction

1.3.2 CAI Testing of Composite Sandwich Constructions

Rhodes [32] [33] studied impact and CAI failure in composite sandwich panels at NASA

Langley Research Center several decades ago. He utilized the same technique that he, as

well as other researchers, had been successful with, in the CAI testing of composite laminates.

First, specimens were surveyed to determine the impact velocities and corresponding energies

of interest. Rhodes found that the areas of delamination in sandwich panels were much

smaller than laminate plates impacted similarly. However, areas of crippled honeycomb core

were present beneath the impact areas. Rhodes observed only a sharp well defined facesheet

crack as the resulting failure mode of compression testing these specimens. The facesheets

of Rhodes’ panels were thicker than those that would later be characterized by other authors

discussed here.

McGowan and Ambur [34] studied and compared the response of impact damaged

sandwich panels under compressive loading where the impact was performed prior to, and

during compressive loading. Some impact loadings of composite structures can occur during

in-service operation while the composite airframe is loaded, which makes understanding this

type of impact damaged compressive response invaluable. The authors point out that while

the compressive failure response of panels impacted under the two conditions (loaded and

unloaded) does not differ; the initialization of damage is sensitive to this difference. Panels

which were impacted while loading were observed to have much higher levels of damage and

above an applied compressive threshold would fail instantly.

Recently, an example of an experimental study by Raju et al. [10] studied the CAI

strength in honeycomb core sandwich panels with both GFRP and CFRP facesheets with

damage at various impact energy levels from two different size indentors. The authors made

several conclusions about the relationship of CAI strength to sandwich construction, including a dependence on dent diameter and core thickness. It was determined that a thicker core

produced a higher CAI strength for a given impact energy. Also, three failure mechanisms

were observed, which are common to several other CAI studies. First, some panels failed

by strength failure across the width initiating at the damage location. Second, some panels

17
Chapter 1. Introduction

failed by indentation propagation mechanism, and finally in a third class of failure the indentation propagation is started but then is arrested and facesheet strength failure follows for

the remaining width of the specimen. The authors also noted that in CAI strength, often a

small residual dent with core crushing can result in a more catastrophic reduction in residual

strength of the panel than if the panel contained a through-the-thickness hole of the same

diameter.

Tsang and Lagace [35] conducted an interesting experimental study on composite

sandwiches to separate the influences of core damage and facesheet damage and thus determine each factor’s effect on the compressive failure mode of the sandwich. They showed

that core damage had to be present to instigate the dimple propagation failure mode seen

in this and other experimental studies, but the presence of facesheet damage accelerated

this failure mode. They also showed that facesheet layup determined the final shape of the

resulting facesheet crack propagation. Finally, the researchers concluded that both facesheet

and core failure modes would need to be included in any CAI failure modeling techniques to

accurately represent the sandwich panel’s response.

Sandwich panel coupon geometry has also been studied with respect to CAI strength.

Moody et al. [36] studied the effect on specimen width with respect to CAI strength with

BVID. The researchers determined that a larger specimen width resulted in an increased

CAI strength of the panel and also found that the resulting failure mode varied. Tomblin et

al. [9] concluded that wide specimens could exhibit arresting mechanisms to core controlled

failure leading to a facesheet strength failure. This result was also mentioned in Ref. [10].

Moody et al. [13] also investigated the effect of sandwich panel curvature on CAI strength

and concluded CAI strength was independent of panel curvature for panels with radius of

curvature on the order of 1 meter (39.3 in.).

Tomblin et al. [11] studied thin-facesheet sandwich panels with both honeycomb core

and foam core. They reported two types of failure modes, both related to dimple propagation.

In one mode the dimple propagated to failure and in the other the dimple was arrested and

crack growth resulted in ultimate specimen failure. They found that the crack growth mode

18
Chapter 1. Introduction

appeared in the thinner two ply per facesheet specimens, while the dimple propagation mode

occured in thicker 4-ply facesheet specimens. This resulted in the conclusion that facesheet

stiffness controlled the failure mode. This was somewhat different from previous results which

show dimple propagation as the primary failure mode of thin-facesheet sandwich panels and

other studies with have shown that the dimple propagation does not occur in thick facesheets. For instance, kink-band failure, a special type of crack growth mode, was found to

be the dominate failure mode in thick facesheet composite sandwich panels in research by

Edgren et al. [37] which involved sandwich constructions using facesheets consisting of 8-

and 16-ply lay-ups.

1.4 CAI Modeling and Strength Prediction for

Sandwich Constructions

A wide variety of methods have been used for the analysis of impact damaged sandwich panels

and the prediction of CAI strength. Moody and Vizzini [38] provided a summary of the stateof-the-art in the field until 2000. They summarized the work of various researchers in the field

of CAI response of thin facesheet sandwich panels, some of which will be mentioned in the

following section. Also, various techniques, including idealization of core crushing response,

and inclusion of damage by reduced stiffness were discussed. The relevance and similarity

to the state-of-the-art-today, over 10 years later, indicates the complexity that modeling of

CAI response undertakes and the value an accurate and robust model would present.

1.4.1 Experimentally Based CAI Strength Prediction

In the absence of reliable CAI strength prediction models, the design of safe to use composite

materials in impact damage susceptible structural component has relied upon high safety

margins or strength “knock downs” to account for the drastic reductions of strength due to

damage observed in experimental data. One approach to obtaining CAI strength predictions

is to rely exclusively on CAI failure experiments to create a statistical material strength value.

19
Chapter 1. Introduction

An example of the development of this type of tool was presented by Nettles and Jackson

[25]. The authors presented experimental results on the damage resistance and tolerance of

an aluminum honeycomb core sandwich material. With the data presented, they defined an

A-basis and B-basis residual compressive strength curve to fit to the data. These types of

curve can then be used to define an acceptable and reliable margin of safety.

Since experimentally determining the damage tolerance of every component designed

is neither resourceful nor cost effective, modeling and analysis to predict failure have become

an increasingly important focus of CAI studies. Experimentally based design criterion such

as the method presented in this section attempt to reduce the safety margins required in

load critical structural components. Unfortunately, they do not reduce the reliance on expensive and time consuming experimental testing. Although all models and analysis require

experimental validation, numerical, analytical, and finite element models can limit this cost

to the design process.

1.4.2 Analytic Solutions of CAI Response

Analytic solutions have been used by various authors to predict the CAI failure of thin

facesheet sandwich panels. Some of these solutions are very detailed and numerical results

are complex and time consuming. Others have developed simple expressions for CAI strength

prediction based on simple inputs. An earlier analytic solution using a single parameter model

with experimental validation was put forth by Kassapoglou and Abbot [39]. The authors

assume that delamination is the predominant damage produced by the impact and driver of a

compression load related failure. However, their methodology ignores the effect of a residual

dent which can have a significant effect on damage progression and ultimate failure in thin

face-sheet sandwich panels. Around the same time, Lie [40] presented a simple methodology

for determining the impact response and CAI response of thin-facesheet honeycomb core

sandwich panels using analytic models implemented using FORTRAN code. He presented

a buckling solution for predicting CAI strength which was cost efficient to implement, but

significantly underestimated the strength of the panels. A comparison of these two models

20
Chapter 1. Introduction

reveals significant differences in the failure mode modeled for similar sandwich constructions

panels. Subsequent models have continued to focus on a single damage propagation model

and little effort has been expended to analytically study the competition between failure

modes in sandwich panels, or the panel construction variables from which they result. Rather,

attention is paid to experimental methods for picking the failure mode to model, and then

analytically studying limited specific cases. The methods proposed in the current work will

seek to expand upon this by including multiple failure modes within a single model to truly

understand their nature by analytic means.

An analytic solution was used by Minguet [41] to predict dimple propagation failure

mode in thin-facesheet sandwich construction, by considering the effect of the residual dent

and associated core damage on CAI strength. A continuum core model was implemented by

assuming its response as a series of springs whose response could be presented as a series of

harmonic functions. Through this approach, the mechanical properties of the core could be

represented as a 6 by 6 stiffness matrix. Only the out of plane movement of the damaged

facesheet, modeled by Classical Laminate Theory, was considered, while the undamaged

facesheet’s response was fixed in the out-of-plane direction. Core damage and propagation

was represented as an assumed idealized version of a flatwise compression test response

of a honeycomb core; this technique would be carried over into succeeding models. The

resulting model, implemented in FORTRAN, over-predicted the CAI strength of the limited

experimental data point presented in the paper. The CAI strength prediction could be

calibrated to the experimental results by adjusting the stress carried by the core after crush

failure. Minguet’s model has proved to be complex in implementation and computationally

intensive. The fidelity of subsequent analytic models has been reduced for computational

efficiency, while still retaining many of Minguet’s core ideas.

Tsang [42] offered a revision to the Minguet continuum core model that included

an elastic foundation core. The Tsang model was described by two parameters used as a

fit for the displacement and stress distribution in the through-the-thickness direction. This

reduced reliance on the assumption that the behavior of a hexagonal honeycomb comb cellular

21
Chapter 1. Introduction

structure could be simulated as an orthotropic solid. A detailed experimental impact damage

and CAI study of thin facesheet composite sandwich panel was presented. The resulting

dimple propagation failure mode was simulated using the sandwich model with the two

parameter core. It was found that the lack of accounting for facesheet damage and failure

propagation contributed to an under-prediction of growth of the initial indentation and overprediction of the final CAI strength. Currently, the representation of a cellular honeycomb

structure as a continuum solid has received more attention, which will be discussed later in

the present chapter. However, other authors continued to simplify the Minguet model.

Xie and Vizzini [43] [44] offered a further revised version of the Minguet model with

a simple one-parameter representation of the non-linear core crushing response. The out of

plane stress acting on the core is simply monitored until the core crush strength is exceeded.

Once this occurs, the reaction force of the core is set to zero. It was shown that his model

successfully captures the correct propagation of core damage. The authors concluded that

the level of safety of a composite structure could be expressed mathematically with respect

to a critical far field stress based on an experimental calibration at a known sensor location.

The authors also assumed that the significance of facesheet damage was negligible to the

dimple propagation failure mechanism in thin facesheet sandwich panels and did not include

initial or progressive facesheet failure. Noteworthy assumptions in this model include the

negligible effect of the undamaged facesheet as well as the core shear stiffness on sandwich

panel response.

An example of an alternate approach to the indentation propagation problem was used

by Staal et al. [45]. The authors presented an elastic stability solution based on the buckling

characteristics of a thin, indented plate on an elastic foundation. For this approach, the

plate was represented as a beam of infinite width. During the development of the expression

for this beam, an Euler buckling term presents itself and a critical Euler buckling stress can

be defined to represent the local buckling failure that occurs during CAI of thin facesheet

sandwich panels. They compared the results of this expression to finite element eigenvalue

buckling analysis, using both solid 3D and plane stress 2D elements, and made the following

22
Chapter 1. Introduction

conclusions. A critical damage length exists for a given loading direction panel length (or

beam length in a 2D case) and a given damage depth. At damage lengths above critical,

failure was based on facesheet instability, whereas for damage below critical, core crushing

response dominates the response. The conclusions are validated by experimental results,

which show that the CAI failure strength approaches a minimum with increasing damage

size.

1.4.3 Finite Element Models for CAI Response

Other researchers have turned to finite element modeling (FEM) as a means of including

more realistic damage (e.g. core crushing) while still limiting implementation complexity

and computational time. Ratcliffe and Jackson [46] have expanded on the work and input of

Minguet, Tsang, and Xie through a simple FEM which includes a shell element represented

face-sheet and a non-linear spring element model for the elastic support provided by the core.

Impact damage in this model was modeled as a geometric dent included in the facesheet and

a region of damaged core elements based on the idealized core crush response of damaged

honeycomb core. However, during their work they found that the included ”damaged” spring

element core region resulted in a gradual global failure which was dissimilar to the case study

experimental results they presented as well.

The spring core model is a simple finite element implementation of the assumptions

used by Xie and Vizzini [43] [44] and previous similar analytic models. It is computationally

efficient and successfully simulates the dimple propagation failure mode in thin facesheet

composite sandwich panels. Other authors have considered the spring core model as well.

One example is the implementation of this type of FEM by Castani ́e et al. [47], which

includes limited experimental validation. McQuigg et al. [48] presented a thorough CAI

investigation of panels similar to the type Jackson and Ratcliffe had attempted to model and

were able to use the spring core model to accurately predict the CAI strength of some of

these panels. The authors chose not to use the damaged spring core elements because of the

detrimental effect to the speed at which failure was predicted to occur based on the results

23
Chapter 1. Introduction

in Jackson and Ratcliffe’s paper as well as their own analyses. More detail will be provided

about the spring core model and CAI strength predictions made using the spring core model

in Chapter 4.

Hwang and Lacy [49] also considered the analytic work of Minguet and others and

created a FEM approach for predicting the CAI strength of similar honeycomb core panels. Non-destructive techniques were used to estimate material property degradation due to

the initial impact damage and honeycomb core crush tests were used to obtain a non-linear

transverse core behavior for implementation. Results were correlated with experimental CAI

tests of panels with minimal facesheet damage. The expected CAI strengths were consistently under-predicted by the model for these panels. The authors also briefly considered

facesheet failure during CAI strength prediction with their FEM model using a maximum

stress criterion for individual elements. This was effective for predicting the onset of facesheet

failure, but was not able to model progressive facesheet failure. The authors [50] continued

studying the incorporation of facesheet damage in their model by comparing CAI strength

prediction results with experimental results.

Another group of researchers made use of the implementation efficiency of modern

commercially available finite element analysis (FEA) software to create a much higher fidelity

FEM. Czabaj et al. [51] presented a high fidelity FEM approach to CAI strength prediction by using a complex model which included geometrically accurate representations of a

honeycomb core. The geometrically accurate region was located in the region of expected

failure only, and the rest of the core was modeled with solid orthotropic elements to increase

the computational efficiency of the model. In addition to predicting the CAI strength, the

researchers also wished to correctly model the sandwich panel’s response to quasi-static indentation and found that the accurate geometric depiction of the core provided an improved

response to this loading condition over a smeared property solid isotropic core model. The

transverse response of the core was modeled after an idealized flatwise core compression

experimental result, a common CAI strength prediction technique. The resulting model provided an excellent match to experimental quasi-static indentation data from tests on the

24
Chapter 1. Introduction

sandwich constructions they sought to model. It however over-predicted the CAI strength

prediction, although the authors acknowledge the need to develop a method of modeling

progressive facesheet damage.

Two earlier attempts at an FEM for analysis of sandwich panel CAI response using

a solid core model was presented by Shyprykevich et al. [12]. Before discussing each model,

one based on ANSYS FEA software and the other on ABAQUS FEA software, the authors

summarized the degraded properties associated with impact damage as degradation of flexural facesheet stiffness for planar facesheet damage and transverse core properties for observed

core crushing. The solid element core FEM using the ABAQUS FEA environment presented

by the authors included the following aspects of impact damage: a damaged facesheet region,

a damaged core region, and an initial geometry dent. The profiles of each of these regions

were based on experimentally determined geometry. The transverse properties of the core

were based on an idealization of the stress-strain curve resulting from flatwise compression

tests of initial damaged and initially undamaged honeycomb core material. These idealized

core properties were assumed to average through-the-thickness response of the core, so only

one element was used through the thickness. Failure was assumed to be dominated by transverse core crushing only, and so no facesheet fracture was modeled although the authors did

note that some of the results suggest it might be necessary to include such failure mode.

To correlate the ABAQUS results with experimental tests, the authors attempted to compare facesheet strains to previous experimental results at specific locations on the damage

facesheet in the path of the dimple propagation. The effect of stiffness reduction in the area

of initial damage on the strain results at these locations was presented. Failure was predicted in their model using comparisons of the strain distributions in the modeled damaged

facesheet with experimental results.

The authors [12] also presented a similar model where the FEA was done in the

ANSYS software environment. A similar core crushing mechanism was included in the model

to simulate failure. Core damage was included in the model as a void with the assumption

that damaged core can carry no load. Delamination of the facesheet was included in the model

25
Chapter 1. Introduction

in the area of facesheet damage. (Cantwell and Morton [4] mentioned that delamination is not

a primary damage mode in impact testing on thin facesheet sandwich panels, so delamination

of the facesheets is not included as impact damage in the proposed model described in the

current research.) The results of this model were again compared to experimental strain

gages measurement taken in the path of the core indentation propagation. Knee points

in the experimental stress versus strain curves were considered to be the moment where

the indentation propagation reaches that particular strain gage. Several cases of lightly

impacted sandwich panels were considered and the core crush strength included in the nonlinear core model was varied to calibrate the FEM predicted strain curves at each location

to the experimentally found curves. Overall, predictions in both the ABAQUS and ANSYS

models for residual strength were found to be poor unless calibrated with correlation to

experimental data. In addition, both models had difficulty handling very small initial dents

in the facesheet.

Xie and Vizzini [52] also presented a finite element which utilized a solid core to

approximate the three dimensional orthotropic response of the honeycomb core of a sandwich

panel. The researchers again focused on local strain at locations in the path of the advancing

crushed core region, by comparing experimentally determined local strain versus applied far

field stress to FEA strain results at the same location in the model. The researchers assumed

that the far field stress at a critical location in the path of the core crush region propagation

was the determining factor in the residual strength. Therefore, failure was assumed when

the stress at the particular location reached the level indicated by experiments at failure,

instead of allowing the model to propagate damage to failure to determine CAI strength.

The researchers only included the core crush mechanism in the region of the sandwich panel

closest to the initial damage location.

Xie and Vizzini [53] also studied the effect of delamination damage in the FEM model.

Although they found this type of damage to have a marginal effect on CAI strength, they did

note that it tended to slightly delay damage propagation because of the increased deformation allowed delaying indentation propagation. Another example of a solid-core model was

26
Chapter 1. Introduction

presented by Schubel et al. [54], but the authors considered thicker facesheets in both an experimental and FEM evaluation. In the thicker facesheets, damage was largely constrained to

delamination, and CAI failure was dominated by delamination driven local buckling, rather

than any core crush mechanism.

1.4.4 Modeling of Honeycomb Core

It has been shown in the present literature review that the method used to model the honeycomb core response during CAI loading can be critical to the accuracy and efficiency of

the model used. The present section will discuss modeling techniques used for various honeycomb core response characteristics, some of which will be included in the proposed model

of the present work. Other examples are provided to validate the assumptions used in their

implementation. A well known reference on the subject of cellular solids, such as hexagonal

pore honeycomb structures is the book by Gibson and Ashby [55]. The authors provide

a method of calculating the effective homogenized material properties of honeycomb core

based on the two dimensional bending response of cell walls. This theory will be covered

in detail, later in Chapter 4. An alternate approach to calculating honeycomb core effective

properties is presented in a series of papers by Hohe et al. [56] [57] [58]. For hexagonal cell

honeycombs, the results are similar between the two methods. The following section provides

some examples where these methods have been considered and the results found have been

validated by experiments. First linear elastic in-plane properties are considered, then the

non-linear core crush response is explained.

In-plane properties of hexagonal cell honeycomb core structures have been predicted

from analyses by various authors. Chen and Ozaki [59] studied the effect of core thickness

on the elastic modulus using a numerical approximation by the finite element method. It

was found that under plane strain conditions, the in-plane elastic modulus of the honeycomb

calculated closely approximated the result without this assumption. This result demonstrated

the independence of the in-plane properties on the cell wall height (i.e. core thickness). A set

of equations was proposed to predict all the in-plane elastic properties given cell geometry for

27
Chapter 1. Introduction

a specific honeycomb. The results of this were checked against FEM results and found to be

in agreement. Hu and Yu [60] analyzed the dynamic in-plane crushing strength of hexagonal

cell honeycomb by considering the explicit geometry associated with such a structure.

The known mechanical properties of Nomex paper have been used in finite element

modeling of explicit cellular honeycomb structures to determine the linear orthotropic behavior of the honeycomb structure Foo et al. [61]. The authors recognized the extensive

computational cost of modeling cellular structures in large models and attempted to predict

the orthotropic properties and verify them with appropriate experiments. The in-plane properties were predicted very closely, while the accuracy of the predicted transverse modulus was

less. The reduction of the out-of-plane modulus’s value as the number of cells included in the

specimen was increased was shown experimentally, while this dependence was not mirrored

in the analysis.

The transverse non-linear response of hexagonal cell honeycomb core due to an out-ofplane crushing load has been incorporated into various CAI strength prediction models in an

idealized form. A good explanation of honeycomb core crushing behavior using experimental

and numerical results was presented by Aktay et al. [62]. They showed the stages of core

crush in Nomex and Aluminum honeycomb cores, including buckling initiation, progressive

folding, and finally densification using experimental examples. Two numerical models were

implemented, one depicting the detailed core structure, and the other with homogenized

material properties. The homogenized model used a semi-adaptive coupling (SAC) technique

to eliminate failed elements and replace them with discrete particle elements defined by a

plastic compression law. The SAC model agreed closely with experimental results and was

significantly more computationally efficient then the micromechanical model.

Gornet et al. [63] also showed that the linear behavior of a Nomex honeycomb core

structure could be determined from an analysis considering the geometry and Nomex paper mechanical properties available from the manufacturer. Using a finite element method

analysis of a representative single cell that can reproduce the entire honeycomb geometry

by a series of translations, it was shown that the full 3D results could be found for any

28
Chapter 1. Introduction

cell size, Nomex density, and thickness. The non-linear transverse crushing response of the

honeycomb structure could then also be found by an Euler buckling analysis of the finite

element model. The resulting core crush strength from analysis was predicted consistently

lower than the experimentally found values, though. Heimbs [64] also considered the out

of plane crushing response of honeycomb core structures using a detailed FEM model. The

author acknowledged the over-prediction of the strength results of similar models and investigated the inclusion of geometric imperfections in the honeycomb cell wall structure. He

found in his investigation that the inclusion of imperfections allowed for better predictions

of core crushing strength and non-linear response.

A recent analysis of the out-of-plane crushing response of honeycomb core sandwich

panels by buckling was carried out experimentally and numerically by Kaman et al. [65].

The authors considered various materials, core densities, and cell sizes. In honeycomb cores

with paper materials similar to Nomex, they identified three failure modes due to crushing, experimentally, including local buckling, folding failure, and a cracking of the material.

Buckling resulted in the most severe reduction in load carrying ability and was preceded by

cracking, if present. The critical buckling load was found to significantly increase with cell

wall thickness and corresponding core density.

The homogenization of honeycomb core response has been well covered in the literature and is validated by experimental results. It is important that this was considered

because in the proposed model in the current research, the honeycomb core will be modeled

as homogenized continuum with an assumed linear elastic orthotropic response defined by

engineering constants. Also, a non-linear core crush response is included in the proposed

model, which is based on an idealization of the results of a flatwise compression test. The

characteristic results of this type of test and associated idealization are discussed in Chapter 4. The assumptions considered when these modeling techniques are used was shown in

the literature review (e.g. Aktay et al. [62], Gornet et al. [63], Heimbs [64], etc.) to be

well-founded, and they are considered essential to the computational efficiency of the model.

They have has also been used in models outside of CAI strength prediction successfully, such

29
Chapter 1. Introduction

as simulation of dynamic crushing response using LS-DYNA by Feraboli et al. [66]. In fact,

use of this assumption has been done successfully for decades (one example found in the

literature by Abd El-Sayed et al. [67] dates to 1979).

1.5 Progressive Failure Analysis

The present research includes an implementation of progressive damage modeling in the

facesheets of the sandwich panel finite element model. The facesheets are modeled as a

composite laminate. Although the analysis of composite laminate stress and strains is well

understood and accomplished through common, accepted methods, the analysis and prediction of fiber reinforced composite failure is less well understood. Many methods exist, but

there is no universally accepted criterion. As explained by D ́avila et al. [68], this is due to

the varied nature of discrete damage events in a fiber reinforced laminate and high degree

of variability in laminate construction. The type of damage events which are pertinent to

the present research were previously discussed in the sections concerning impact damage in

composite laminates and sandwich panels.

In addition to the degree of variation in the types of damage and orientation possible, the treatment of the analysis and prediction of the formation and propagation of this

damage varies with scale of the idealization. The three scales identified by D ́avila et al. [68]

are the micro scale, the meso scale, and the structural scale. In the micro scale, typically

representative volume elements formulations are used to predict localized damage, such as

matrix cracking or fiber-matrix interface failures. Meso-scale models are popular for being

both more computationally advantageous than micromechanics models, as well as more detailed and accurate than structural scale models. Structural scale models institute through

thickness cracks (i.e. hard discontinuities) in the model based on critical energy release rates

or other methods. These types of damage events in composites are strongly dependent on

laminate construction and structural level analysis methods do not take into account the

sub-scale interactions which are critical in accurately predicting the propagation of these

30
Chapter 1. Introduction

cracks. A meso-scale model is used in the present research.

Two distinct types of meso-scale models are identified by D ́avila et al. [68] and

discussed with respect to their advantages and disadvantages. Currently, the most common

method for discrete damage analysis in composites is continuum damage mechanics (CDM)

models. CDM generally assume homogenous, orthotropic plies and corresponding damage

modes. When analysis predicts a damage event, a soft discontinuity is imposed in the form of

a stiffness reduction to the damaged material. The failure criteria and material degradation

used are often associated with a particular mode of failure. Other damage phenomenon,

such as fiber-matrix disbond and fiber kinking are taken into account through techniques

such as co-current analysis of a micromechanics model and in situ strengths, respectively. A

second meso-scale model is discrete damage mechanics (DDM), where hard discontinuities

are placed in the model through the extended finite element method. The authors argue that

this newer class of composite damage analysis improves upon the diffused nature of damage

inherent to a CDM approach, such as over-propagation of inter-fiber fracture (IFF).

Two important components of any laminate strength analysis are, that they are close

to physical reality, and they are simple enough for computationally efficient implementation

in engineering design work, espoused Puck and Sch ̈urmann [69]. The authors consider the following to be the most significant characteristics of any fracture criteria: (1) two independent,

but simultaneously fracture criteria for fiber and matrix failure; (2) the transverse tensile and

compressive strengths must act independently of each other; (3) continuous stiffness degradation; and (4) consideration of the specific IFF mode. The authors also succinctly describe

the requirements of a progressive failure analysis (PFA) which applies to the method of implementation in the current research. Stress and strains must first be analyzed ply by ply. In

the present research this will be done through the use of classical laminate theory (CLT). A

fracture criterion is applied to single plies. A degradation model must then be utilized which

includes the effects of material fractures which may not lead to ultimate laminate failure.

Finally, the previously mentioned requirements of the PFA must be implemented iteratively

through the use of a computer program. The latter three requirements will be discussed

31
Chapter 1. Introduction

presently, and additional details are presented in Chapter 5, as they pertain to the present

research.

A highlight of the work by Puck and Sch ̈urmann [70] for the World Wide Failure

Exercise (WWFE) included heavy investigation of IFF fracture mechanisms, with special

focus on the orientation of matrix cracks and the consideration of stress with respect to the

fracture plane. An important observation from this investigation was the importance of the

consideration of brittle fracture characteristics in failure analysis of composites. The wellknown work of Hashin [71] included a brittle failure criterion for fiber reinforced composite

laminates. Fracture is predicted by a combination of normal and shear stresses which are

included in the quadratic formulated Hashin failure criterion. The Hashin failure criterion

is used to predict the onset of damage in an implementation of PFA based on the work of

Lapczyk and Hurtado [72]. Damage evolution is evaluated by a criteria based on the fracture

energy dissipated by damage to the composite laminate. Complications which traditionally

arise during numerical implementation of progressive damage models are addressed. A crack

band model as well as a viscous regularization scheme is suggested to alleviate problems with

mesh sensitivity and convergence, respectively. An implementation of this work can be found

in the commercial finite element code ABAQUS [73]. Although the authors noted that all

parameters used to define this model have physical meaning, in practice these parameters

are difficult to obtain experimentally and have limited availability in literature.

Attempts to account for the effects of micro-mechanics in CDM models have led to

the use of multi-continuum theories (MCT), such as the MCT developed by Garnich and

Hansen [74]. Garnich et al. recognized that the continuum assumption used by general

elasticity was insufficient for constituent level analysis of composite laminates and developed

the idea of multicontiuum, since it works better with the micromechanics of such materials. A

failure criterion for composite laminates which makes use of MCT was later developed in the

work by Mayes and Hansen [75]. Mayes and Hansen point out that most composite failure

criterion, such as Hashin’s, attempt to predict composite failure using composite average

stress and strain states, and homogenous laminate properties. A micromechanical model

32
Chapter 1. Introduction

instead utilizes individual constituent properties and can use them to determine failure as

well as interaction between the constituents and relationships of individual constituent failure

with laminate response. It should be pointed out that the implementation of MCT involves

the use of average constituent stress and strain states, rather than individual values. Also,

the accuracy of a failure model implemented using MCT depends upon the accuracy and

validity of the experimentally obtained strength values for the constituent materials. The

main benefit of MCT is that it allows robust progressive failure analysis of a composite

laminate through the use of soft discontinuities. When constituent level failure occurs within

a model, the model structure remains intact and the resulting redistribution of load in the

model can easily be evaluated. The MCT failure theory by Mayes et al. was implemented by

Firehole Composites, Inc. in their commercially available software Helius:MCT. A custom

version of this software is used in the present research.

Schumacher and Key [76] expounded on the details and merits of multicontinuum

theory (MCT) and associated failure models. MCT provides the analyst with not only the

traditional smeared composite average material stress and strain fields but also provides the

matrix average stress and strain and fiber average stress and strain. The purpose of this

additional information is to add additional accuracy in failure mode modeling in composite

materials. As characteristic of CDM formulated composite laminate failure criterions, MCT

failure criterion involves the reduction of the material stiffness in the finite element based on

a degradation model. Ideally, when implemented numerically, the material will be degraded

gradually, especially with respect to IFF. Knops and B ̈ogle [77] presented a significant example of the implementation of gradual composite failure using CLT which was validated by

empirical evidence. The authors noted a substantial improvement in laminate failure analysis when using a gradual failure analysis calibrated and verified by experimental results.

Composite progressive failure analysis involving MCT failure theory through the use of Firehole Composites’ software, Helius:MCT in the present research will be further developed in

Chapter 5. A user’s manual and several examples and tutorials are available from Firehole

Compsites to describe the commercial use of Helius:MCT.

33
Chapter 1. Introduction

1.6 Overview of the Present Work

In the present document, a body of research consisting of experiments and analysis on the

CAI response of thin facesheet honeycomb core sandwich panels is presented. Chapter 1

has introduced the topic and outlined literature which is relevant to the research topic. In

Chapters 2 and 3 which follow, a set of experiments on three sets of sandwich panel material systems will be described. Static indentation and impact using a drop tower apparatus

was used to assess the damage resistance of these materials and the characteristics of this

damage was observed using non-destructive and destructive evaluation techniques. The measurements taken and observations recorded were then used to select the impact energy levels

of interest. These levels are primarily those which result in damage which may be only

barely visible. A set of CAI experiments was then completed on each material system using

a variety of instrumentation to capture the response of each test coupon during compressive

loading and at failure. Unique insight is provided to describe the failure modes observed

using high speed photography and digital image correlation. The influence of the density of

the honeycomb core sandwich panels on the resulting failure mode is presented in the results

of this experimental study. The experimental results presented in Chapters 2 and 3 will be

used to validate the new FEM which is the focus of the remainder of the present research.

Chapter 4 is used to discuss the basics of composite laminate theory and the shell

theory which is used in ABAQUS. The early stages of model development are then described.

This process begins with demonstration of previous analysis efforts, including a spring element core model and a solid element core model. A brief analysis was completed using models

of select experimental test coupons to demonstrate the effectiveness of these models and the

techniques they make use of which are carried over to the new model that is developed in the

present work. Carrying forward, the major development of the new FEM is the inclusion of

a method of progressive failure analysis in the facesheets using an implementation of MCT

failure theory. A detailed look at MCT and associated failure theory is provided in Chapter

5. The remainder of Chapter 5 details the development of the new FEM. First, the geometry and boundary conditions of the new model are described. Next, detailed information

34
Chapter 1. Introduction

concerning the inclusion of impact damage in the FEM is given. The chapter concludes with

observations from the mesh convergence study which was completed, as well as analysis of

the model to sensitivity of the inputs which were used in the creation of every ABAQUS

input file used in the present research with the newly developed FEM.

With the new model for CAI analysis described, results which have been obtained

using the new FEM are described in Chapter 6. Results are included from analyses of each

of the 32 test coupons which underwent CAI testing from the three sandwich panel material

systems described in Chapters 2 and 3. In addition, further analysis results are given for a

parametric study of the effect of varying core density on the CAI strength and failure mode.

The parametric study results are used as the final validation of both experimental and analysis conclusions on the effect of honeycomb core density on the CAI response of the sandwich

panels studied. Finally, the conclusions of the current research are given in Chapter 7. The

major contributions of the present research to the state-of-the-art of the understanding of

the compression after impact response of composite honeycomb core sandwich panels are as

follows. First, a detailed set of experimental tests have been completed which determine both

the impact damage response and the CAI characteristics of three sandwich panel material

systems. In particular, the core density of the sandwich panel is shown to be the sole contributing factor to the CAI failure mode and resulting CAI strength. Second, a new, detailed,

computationally-efficient, physics-based FEM is developed to confirm the experimental test

results and validate the conclusions made. New contributions to CAI modeling are made in

the areas of damage fidelity included in the CAI model, and the included composite laminate

PFA. It is shown that each of the impact damage traits included has a significant effect on

the CAI model results. The model matches the experimental test results at least as well

as current models in all areas, and in many cases makes improvements. More importantly,

increased confidence in CAI modeling is achieved, since the new model is validated with more

experimental data than seen previously in CAI analysis work.

35
Chapter 2

Impact Damage and CAI Tests of

PXX Series Materials

In Chapter 1, selections from the literature relevant to the study of impact damage and compression after impact (CAI) response of honeycomb core sandwich panels with thin facesheets

were summarized. In Chapter 2, a set of experiments on a similar sandwich panel material

system is presented. The tests include studies of the impact response of this material using static indentation and drop tower impact, as well as the CAI tests to coupon failure.

Information about the material system and coupons used, the impact damage evaluation

test apparatus, instrumentation, and results, and the CAI apparatus, instrumentation, and

results is given. Many of the techniques shown in this chapter are used in the tests which

will be presented in Chapter 3. Also, the results found were used in comparisons to current

models studied in Chapter 4 during the development of the new finite element model for

analysis of CAI failure in honeycomb core sandwich panels. Experimental test results from

this chapter and Chapter 3 are compared to analysis in Chapter 6.

36
Chapter 2. Impact Damage and CAI Tests of PXX Series Materials

2.1 Materials and Test Coupons

A series of compression after impact (CAI) experiments was performed on a commercial

sandwich panel material system consisting of thin glass fiber reinforced polymer facesheets

and Nomex hexagonal honeycomb core that is readily available to the consumer. The set

of material coupons used for CAI testing were designated P01 through P12 although only

10 coupons were tested in compression and will be referred in general in this document as

PXX series materials. These materials were manufactured by AAR Composites and can be

ordered for commercial applications. Each facesheet of the sandwich construction consisted

of two plies of style 7781 plain woven E-glass fabric with 40% epoxy resin content. The plies

were directionally aligned in the 0odirection and the nominal cured thickness for a single

face-sheet was 0.020 in. The honeycomb core had a 1 in. thickness, with a 0.125 in. cell

size, and a density of 3.0 lb/ft3. The PXX series material is shown in Fig. 2.1, where the

translucent property of the thin GFRP face-sheets allows for viewing of the core underneath.

This property also allows for improved visual inspection for damage and manufacturing

imperfection that may be present in the material.

Figure 2.1: PXX series honeycomb core sandwich panel material.

37
Chapter 2. Impact Damage and CAI Tests of PXX Series Materials

AAR Composites lists the following material property data for this material, which

is given the company designation ATR-FP-101F2. The GFRP facesheets have the following

nominal properties. The warp (0) direction and fill (90) direction strength and modulus are

listed as 60.0 ksi and 3.0 Msi, respectively, for compressive loading, and 54.0 ksi and 3.0

Msi, respectively, for tensile loading. The in-plane shear strength and modulus are 13.0 ksi

and 0.400 Msi, respectively. The in-plane Poisson’s ratio is 0.140 and the interlaminar shear

strength is 3.5 ksi. The Nomex honeycomb core properties are listed as tested on a 0.5 inch

thick specimen. The out-of-plane strength and moduli are 270 psi and 20 ksi, respectively.

The shear strengths are listed as 140 psi for the L direction (ribbon direction), and 74 psi for

the W direction. The shear modulus are listed as 4.5 and 2.5 ksi for the L and W directions,

respectively [78].

Test coupons were prepared from the PXX series material at the nominal size of 6

in. by 6 in. The test coupons are shown in Fig. 2.2. These coupons were used in all of

the tests described in the next sections. To avoid premature coupon failure for the uniaxial

compression tests, special considerations for load introduction were made. At the top and

bottom (the load bearing ends of each coupon) a section of core material was removed from

between the facesheets. This section had dimensions of the width (6 in.) and thickness (1

in.) of the coupon and it extended in the loading direction approximately 0.5 in. A clay

“potting” material with a higher stiffness than the honeycomb core it replaced was used to

fill this void. The purpose of this was to increase the surface area for load transfer between

the compression test frame and the coupon. In addition, the potting limited the out of plane

bending and brooming (i.e. severe matrix cracking causing separation of fibers) of the coupon

facesheets’ load direction edges, due to the applied compression load. The potting on the

ends of each coupon was ground to straight and level, to a tolerance of 0.001 in.

38
Chapter 2. Impact Damage and CAI Tests of PXX Series Materials

Figure 2.2: PXX series sandwich panel coupons for testing.

2.2 Impact Damage Evaluation

Two sets of preliminary experimental tests were used to characterize the damage for a particular impact energy level. The two types of testing used were static indentation and impact

testing using a drop tower. The results of these tests were used to select the energy levels

for the impacts to coupons for CAI testing. The energy levels of interest for the PXX series

materials were representative of low velocity impacts which would cause light damage to

the impacted sandwich panel. The range of damage included barely visible impact damage

(BVID) and extended to clearly visible damage. The testing procedures, apparatus, instrumentation, and results for static indentation and drop impact on PXX series materials will

be described in the following sections.

2.2.1 Static Indentation Tests

A brief damage study was conducted on the PXX series panels using static indentation instead

of impact. Static indentation is a controlled, easily repeatable method of causing damage in

composite sandwich panels. In this research, it was used to gain an initial understanding of

the types of damage which would appear in the panels for various energy levels. Although

39
Chapter 2. Impact Damage and CAI Tests of PXX Series Materials

the types of damage from static indentation are comparable to impact damage, this method

produces more damage for a given energy level than a low velocity impact. Thus, it is

considered a conservative method of estimating damage resistance in a given material. The

hydraulic testing machine used is shown in Fig. 2.3. The 0.5 in. diameter hemispherical tip

used for indentation is shown in Fig. 2.4. A 1.0 in. diameter tip was also used in initial

damage evaluations.

Figure 2.3: Apparatus used for static indentation of PXX series material coupons.

Figure 2.4: Semi-hemispherical tip used for static indentation, 0.5 in. diameter.

40
Chapter 2. Impact Damage and CAI Tests of PXX Series Materials

Several indentations of the PXX series material were conducted. The resulting static

indentation PXX series material coupon with close ups of the four dents with which data was

recorded is shown in Fig. 2.5. For each indentation, the panel was clamped on all four edges

using a frame which allowed the rear facesheet of the sandwich panel to be unsupported.

This type of boundary condition was used in all subsequent tests. The frame is shown in Fig.

2.3, next to the hydraulic indentor, without a panel mounted. Loading was displacement

controlled and applied at a rate of 0.05 inches per minute. Displacement and force was

measured at the time of each indentation and the results are discussed here.

Figure 2.5: PXX series material coupon with resulting damage from static indentation.

41
Chapter 2. Impact Damage and CAI Tests of PXX Series Materials

Location 1 of the static indentation panel is not discussed because data was not

recorded during a brief indentation of that location. Several repeated indentions were conducted at Location 2, each with a higher maximum force than the last. First, indentation

was done until the resultant force was roughly 50 lbs. and then the indentation tip was

completely removed. Subsequently, the same location was loaded to 100 lbs. and then an

attempt was made to load to 150 lbs., but the facesheet failed prior to that mark being obtained and the force resultant dropped considerably. As additional displacement was applied

the force resultant began to rise again before the static indentation tip was removed from

application. During the third load application, just under 0.5 ft-lb. of work was completed,

as determined as the area under the force vs. displacement curve calculated using Simpson’s

Rule. The force vs. displacement results for Location 2 can be seen in Fig. 2.6.

Figure 2.6: Results of static indentation testing on PXX series materials: resultant force vs. applied

displacement measured at Location 2.

The effect of the damage present at the location from previous indentation reduces

the initial force for a given indentation for subsequent loadings, which can be seen in Fig.

42
Chapter 2. Impact Damage and CAI Tests of PXX Series Materials

2.6. The appearance of facesheet cracks begin with the sudden drop in force which occurs

at about 0.08 inches of displacement during “Indentation 3” in the figure. They are oriented

parallel to the warp and fill tows in the woven facesheets and create a cross centered at the

indentation center. The presence of crushed core located directly beneath the indentation

center is assumed due to the appearance of a residual dent when the load is removed from

the sandwich panel. After the final indentation at Location 2, the residual dent measured

0.05 inches deep and 0.78 inches in diameter. The complete results of the static indentation

test of PXX series materials can be seen in Table 2.1. In the table, “N/A” stands for “not

applicable” and refers to the fact that facesheet fracture was not reached for those indentation

test. “N/M” stands for “not measured” and refers to the fact that the measurement was not

taken.

Table 2.1: Results of static indentation testing on PXX series materials: damage measurements

Locations 3 and 4 were indented to 0.1 and 0.2 inches, respectively, with the 0.5 in.

indentation tip. The maximum force achieved for each of these indentations was similar

to indentation three at Location 2. However, the appearance of the force vs. displacement

result at Locations 3 and 4 more closely resemble indentation one at Location 2 for lower

indentation levels. This further illustrates the difference between an indentation on a pristine

sandwich panel versus an indentation at a previously damaged location. It also suggests that

significant damage exists in the sandwich panel even after indentation at low load levels. The

force vs. displacement result for Location 4 is shown in Fig. 2.7, for illustration. Finally, a

1.0 in. diameter hemispherical tip was used for indentation at Location 5. At the time this

43
Chapter 2. Impact Damage and CAI Tests of PXX Series Materials

test was completed, the 1.0 in. diameter tip was being evaluated for impact of compression

after impact panels and this static indentation was necessary for comparison. It should be

noted that a much higher maximum force was reached and a higher amount of work was

needed to fracture the facesheet at Location 5 with this indentation tip, suggesting that

higher impact energies could be considered for impacts with the 1.0 in. diameter tip. The

force vs. displacement result for Location 5 is also shown in Fig. 2.7. It was concluded

that for the PXX material system, very low energy levels (less then 10 ft-lbs.) would be

considered for impact testing, including energy levels of less than 2 ft-lbs. for impacts with

the smaller tip.

Figure 2.7: Results of static indentation testing on PXX series materials: resultant force vs. applied

displacement measured at Locations 4 and 5.

44
Chapter 2. Impact Damage and CAI Tests of PXX Series Materials

2.2.2 Drop Tower Impact Survey

A survey of impact damage using a mass dropped from a tower was used to gain information

about the damage resistance properties of the PXX series sandwich material. The purpose of

the impact survey was to determine the characteristic damage at various impact energy levels,

and to make a decision about which impact energy levels would be used for compression after

impact tests. A PXX series material coupon was clamped on all four edges in the special

test fixture, shown in Fig. 2.3 previously, with no support under the opposite facesheet; this

boundary condition is considered to be characteristic of a real world structural impact. The

test fixture was then clamped to a stout steel table at the point of impact beneath the drop

tower, shown in Fig. 2.8.

Figure 2.8: Drop tower apparatus used for impacting PXX series material coupons.

45
Chapter 2. Impact Damage and CAI Tests of PXX Series Materials

The drop tower consisted of a blue metal tube several yards in length mounted vertically. A pulley system was mounted to the tube to raise and set the drop height of the mass

which would impact the sandwich panel coupon. Once in place, the impactor was dropped

with a draw string attached to a mechanical release. Upon impact, the mass would rebound

from the coupon and a cover could be slid into place over the specimen to keep the mass from

striking a second time. Impacts were conducted with both a 0.5 in. and a 1.0 in. diameter

hemispherical tip and the weight of the impactor was measured to be 2.7565 lb. and 2.7570

lb. with the 0.5 in. diameter tip and the 1.0 in. diameter tip, respectively. The impactor

with the 0.5 in. tip mounted and 1.0 in. tip shown can also be seen in Fig. 2.8. The drop

height for a given impact energy level was then calculated by dividing the desired impact

energy level by the weight of the impactor. The drop height could be set using the impact

tower apparatus to the nearest sixteenth of an inch.

Once an impact on a PXX series material coupon was conducted, the residual dent

was measured in terms of its maximum depth and diameter. Each dent was nearly circular

although some eccentricities were seen. An attempt was made to consistently determine

the largest axis from which to measure the diameter. In addition to this information, the

impact force was recorded electronically with respect to time so that impact length could

also be determined. The impact length is defined as the time (in seconds) from the moment

the impactor strikes the sandwich panel coupon, to when the impactor completely rebounds

from the surface. In addition, measured and visual (qualitative) observations were made

about the location and characteristics of other types of damage present, including cracking

or penetration of the impacted facesheet. Results versus impact energy for residual dent

depth, residual dent diameter, maximum impact force, and impact length are shown in Figs.

2.9, 2.10, 2.11, and 2.12, respectively.

A characteristic impact force vs. time plot, for a low velocity impact on a PXX

series sandwich panel, has a bell curve shape for low impact energy levels. At a certain

threshold energy level, impacts above the threshold will cause significant facesheet damage

which results in one or more through-the-thickness cracks that are oriented in the direction

46
Chapter 2. Impact Damage and CAI Tests of PXX Series Materials

Figure 2.9: Results of drop tower impact testing on PXX series materials: dent depth vs. impact

energy.

Figure 2.10: Results of drop tower impact testing on PXX series materials: dent diameter vs. impact

energy.

Figure 2.11: Results of drop tower impact testing on PXX series materials: maximum impact force

vs. impact energy.

47
Chapter 2. Impact Damage and CAI Tests of PXX Series Materials

Figure 2.12: Results of drop tower impact testing on PXX series materials: impact length vs. impact

energy.

of the warp and fill tows forming either a slit or cross centered at the location of the impact.

The force vs. time curve for this type of energy level shows a sudden drastic drop in impact

force indicating that the facesheet failure absorbs a large amount of the impact energy. It

was also noted that during impacts which resulted in a facesheet fracture, the impactor

rebounded considerably less than it would have, had the facesheet not been compromised,

like at lower energy levels. An example of the recorded force vs. time with and without the

facesheet fracture is shown in Fig. 2.13 and 2.14, respectively.

Figure 2.13: Results of drop tower impact testing on PXX series materials: impact force vs. time

for Panel 1, Location 3.

48
Chapter 2. Impact Damage and CAI Tests of PXX Series Materials

Figure 2.14: Results of drop tower impact testing on PXX series materials: impact force vs. time

for Panel 1, Location 4.

Other types of damage noted include facesheet discoloration which suggests matrix

cracking, facesheet delamination, or facesheet to core disbond could have occurred. A major

difference between static indentation and impact testing is that much more discoloration

was seen prior to facesheet fracture during low velocity impact testing; however, facesheet

fracture occurred at much higher energy levels for impact testing, as well. This suggests that

the high strain rate associated with impact results in higher amounts of localized damage

and may explain why static indentation is a more conservative estimate of damage formation

for a given energy level. The data collected also shows that the low velocity impacts resulted

in larger residual dent diameter, but shallower dent depth. Three coupons were used for

the impact survey. They are shown in Figs. 2.15, 2.16, 2.17, and 2.18 with close ups of the

resulting damage at each point of impact. It should be noted that due to limited material

availability, multiple impact sites are found on a given coupon for the impact survey. The

effect of the panel boundary conditions and nearby prior impacts is going to vary slightly

from impact location to impact location. For this reason, impact damage was also studied

in the impacts done on CAI coupons, prior to CAI testing, for comparison. This data will

be presented in the next section.

49
Chapter 2. Impact Damage and CAI Tests of PXX Series Materials

Figure 2.15: PXX series material coupon with resulting damage from drop tower impact, Panel 1.

Once the information taken during the impact survey of the PXX series sandwich

material was reviewed, a decision was made about which damage levels would be the most

interesting for CAI testing. During the impact survey, energy levels were considered from

0.5 to 2.5 ft-lbs. at 0.5 ft-lb. increments for the 0.5 in. diameter impact tip and from 1.0 to

50
Chapter 2. Impact Damage and CAI Tests of PXX Series Materials

Figure 2.16: PXX series material coupon with resulting damage from drop tower impact, Panel 2.

6.0 ft-lbs. at 1.0 ft-lb. increments for the 1.0 in. diameter impact tip. The impact damage

from the 0.5 in. diameter tip was found to be more severe for lower impact energies and is

also considered more representative of an impact made by a tool drop during inspection or

installation of a sandwich panel airframe, which low velocity impacts simulate. Therefore,

impacts using the 1.0 in. diameter impact tip were not considered for CAI coupons, for

the most part, although one coupon was tested with damage from this impact tip. Also,

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Chapter 2. Impact Damage and CAI Tests of PXX Series Materials

Figure 2.17: PXX series material coupon with resulting damage from drop tower impact, front of

Panel 3.

the barely visible impact damage (BVID) range for the PXX series material effectively ends

with a facesheet fracture, due to the highly visible nature of the cross like cracks that were

noted. Therefore, energy levels above 2.0 ft-lbs. were not considered for CAI testing of

these materials. Energy levels of 0.5, 1.0, 1.5, and 2.0 ft-lb. were chosen for impacting CAI

coupons of PXX series materials.

2.3 Compression After Impact Experiments

Several test methods were considered when the CAI tests described in this section were

designed. ASTM standard test methods (STM) were consulted, but an ASTM STM for

compressive residual strength of sandwich constructions has not currently been adopted. The

ASTM STM for compressive residual strength of composite plates does describe a procedure

and special test fixture for simple plates with centrally located impact damage [79]. This

reference was consulted for strain gage placement and allowable failure modes. The ASTM

STM for edge-wise compressive strength (undamaged) of sandwich constructions was also

considered [80]. This test method was consulted for sizing of the damaged panels, since

52
Chapter 2. Impact Damage and CAI Tests of PXX Series Materials

Figure 2.18: PXX series material coupon with resulting damage from drop tower impact, rear of

Panel 3.

the increased bending stiffness of sandwich constructions should preclude the use of the test

fixture described in Ref. [79]. In the next section, the apparatus and instrumentation used

for compression after impact (CAI) testing of PXX series sandwich panel coupons will be

completely described. The results of testing will also be presented.

2.3.1 Apparatus and Instrumentation

A servo-hydraulically actuated MTS load frame with a 100-kip maximum load was used for

the CAI tests of PXX series sandwich coupons. The sandwich panel coupons were clamped

at the top and bottom, placed on top of a small manually adjustable bearing and mounted

on the MTS load frame between its two square loading platens. On the load frame, the top

platen remained fixed, while the lower platform was also adjustable. The adjustable bearing

and lower loading platen could be used to adjust the position of the sandwich panel coupon

53
Chapter 2. Impact Damage and CAI Tests of PXX Series Materials

with a small load applied to facilitate a uniform compressive loading condition free from

significant bending moments. Compressive loading was displacement controlled and applied

through hydraulically actuated movement of the lower platen at a rate of 0.02 in. per minute,

slow enough to be considered quasi-static for a given measurement point. The load frame

and a mounted CAI coupon installed within the apparatus are shown in Fig. 2.19.

Figure 2.19: Load frame and coupon mounting apparatus used for CAI testing.

The following instrumentation was used for each CAI test of the PXX series material

coupons. The applied displacement and the measured reaction force were recorded from the

load head of the MTS test frame. Far field strain in the direction of loading was recorded

on the front and rear facesheets of each CAI coupon throughout testing. In general, five

strain gages were placed on the specimen as shown in Fig. 2.20; however, occasionally a

strain gage malfunctioned and this was noted when it occurred. At least three of the strain

gages numbered 1 through 4 in Fig. 2.20 were necessary to assure coupon alignment within

the loading apparatus. Also, three direct current displacement transducers (DCDT) were

mounted to monitor the displacement at several locations between the loading platens. The

DCDTs can be seen in Fig. 2.19 and their location is described in Fig. 2.21. These three

instruments could then be used as auxiliary instrumentation to monitor any applied bending

54
Chapter 2. Impact Damage and CAI Tests of PXX Series Materials

or to enhance the applied displacement information recorded at the load frame head.

Figure 2.20: Location of strain gages for CAI testing of PXX series material coupons (all dimensions

in inches).

Several types of auxiliary instrumentation were used throughout CAI testing. Each

test was recorded visually with a high definition video recording system monitoring the front

and rear of each specimen. Also, ambient temperature and humidity were noted for each

specimen. In addition, high speed footage using a Phantom camera system [81] was taken of a

selection of panels which included one panel damaged at each impact energy level considered,

as well as an initially undamaged specimen. Another set of panels which also included one

damaged panel at each selected impact energy level was prepared for measurement during

CAI testing by digital image correlation of digital images using a VIC3D system [82]. The

CAI apparatus with various instrumentation configurations is shown in Fig. 2.22.

55
Chapter 2. Impact Damage and CAI Tests of PXX Series Materials

Figure 2.21: Planform drawing of test frame loading platen which shows of DCDT locations used

for CAI testing (all dimensions in inches).

The image correlation software allows for collection of full three-dimensional displacements associated with the region of interest during testing. The software can then be used

to calculate strains for the region of interest. For the purpose of this testing, the entire front,

damaged facesheet, visible between the clamps at the top and bottom of the coupon, was the

field of interest. The mounted strain gages must be removed from the field of interest due

to optical distortion. In preparation for measurements by digital image correlation (DIC),

the entire front facesheet is spray-painted white after the strain gages have been mounted.

Afterwards, fields of unique black speckles are added based on the size of the field of view, the

displacements expected, and the digital cameras. Two digital cameras are used to capture

two synchronous images from which the software can recognize and correlate each unique

speckle. Once the system is in place and calibrated, displacement measurements can be made

56
Chapter 2. Impact Damage and CAI Tests of PXX Series Materials

Figure 2.22: Auxiliary apparatus for CAI testing of PXX series coupons with video instrumentation

(above) and Vic-3D digital cameras (below).

using each image pair and information obtained through calibration, such as camera location

with respect to target, and various optical image distortion parameters. More information

can be obtained on image correlation theory in the resource by Sutton, Orteu, and Schreier

[83]. A speckled CAI coupon can be seen in Fig. 2.23.

57
Chapter 2. Impact Damage and CAI Tests of PXX Series Materials

Figure 2.23: Speckled PXX series material coupon for Vic-3D instrumentation of CAI testing.

2.3.2 CAI Failure of PXX Series Coupons

Coupons of PXX series sandwich constructions were centrally impacted on one facesheet

using a drop tower impactor, with a 0.5 in. diameter hemispherical shaped tip, at predetermined energy levels of 0.5, 1.0, 1.5, and 2.0 ft-lb. Two coupons were damaged with

impacts at each energy level. One further coupon was damaged with a low velocity impact of

2.0 ft-lb. using a 1.0 in. diameter impact tip. The resulting damage from low velocity impact

was similar to the results of the impact damage survey discussed previously. Data on the

resulting residual dents in each specimen is available in Appendix A. These coupons and two

other, undamaged coupons were tested to failure under displacement controlled compressive

loading conditions. The typical force vs. displacement response, as collected from the test

frame load head for a CAI test of PXX series materials, is shown in Fig. 2.24.

The force-displacement behavior is linear until panel failure is observed, at which time

there is a sudden drop in the reaction force. The global failure is sudden and results in a

58
Chapter 2. Impact Damage and CAI Tests of PXX Series Materials

Figure 2.24: Results of CAI testing of PXX series materials: typical measured resultant force vs.

applied.

catastrophic reduction in the load carrying capability of the panel, as seen by a drop of nearly

40% in the reaction force. Damage in the failed sandwich panel is noted only in the initially

damaged facesheet for CAI specimens. The failed specimen has a region of local buckling,

extending transverse to the direction of applied load, from the residual dent initially left by

the low velocity impact each coupon was subjected to, shown in Fig. 2.25. Note also, the

transverse facesheet crack at the center of the locally buckled facesheet.

Figure 2.25: PXX series material coupon during CAI testing, post-failure, showing results of indentation propagation failure mode.

59
Chapter 2. Impact Damage and CAI Tests of PXX Series Materials

Video photography allowed the effective capture of the failure mode for these panels.

High definition real time cameras monitored each panel so that the following characteristics

could be closely documented. For coupon P11, a PXX series coupon initially impacted with

a 0.5 in. diameter impact tip with impact energy of 0.5 ft-lb., the small residual dent can

be clearly seen in the front facesheet in the recorded video even before loading takes place.

Initially, during the linear response of the panel to compressive loading, the residual dent

which resulted from low velocity impact can be seen to grow larger, as illustrated by the

frames from this video presented in Fig. 2.26.

Figure 2.26: Results of CAI testing of PXX series materials: time lapse images taken throughout

test.

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Chapter 2. Impact Damage and CAI Tests of PXX Series Materials

The video of the P11 panel is about 3 minutes and 30 seconds long and begins just

prior to load application. Growth of the residual dent cannot be seen until about 2 minutes

into the video. By 2 minutes and 30 seconds, the residual dent is still circular, but its

increased depth from the initial dent is readily apparent. Between 2 minutes 30 seconds and

3 minutes and 10 seconds, the dent becomes more elliptical as it begins to expand further

along its axis perpendicular to the direction of loading. Failure occurs between 3:10 and 3:11

in the real time video, illustrating the sudden nature of failure.

High speed video photography is necessary to capture the rapid, unstable propagation

of dent resulting from local buckling of the facesheet. The Phantom version 7 video system

captured and stored images at a rate of 10,000 Hz. Several frames were selected from a high

speed video capture of the indentation propagation failure and are shown in Fig. 2.27. With

this footage, the unstable propagation of the region of large out-of-plane displacement can

easily be seen. Also, the facesheet crack that appears at the mid-point of the locally buckled

region of the front facesheet of this coupon can clearly be seen propagating near the front of

the advancing indented region.

Figure 2.27: Results of CAI testing of PXX series materials: time lapse images taken from high

speed camera during failure.

Nominal failure stress, calculated from the measured resultant force divided by the

nominal cross sectional facesheet area of each coupon, and average measured far-field failure

strain from the five strain gages on each panel were reported for each coupon tested. The

results are shown in Fig. 2.28. The complete results of nominal failure stress and failure

strain for CAI tests of PXX series materials can be found in Appendix A. The failure strength

of PXX sandwich material is shown to drop dramatically even for lightly impact damaged

61
Chapter 2. Impact Damage and CAI Tests of PXX Series Materials

specimens. This is illustrated by a 5-10 ksi drop in failure strength for coupons which were

impact damaged at 1.0 ft-lb. energy levels, from the pristine coupon’s strength. The drop

of failure strength is shown to decrease in severity with further increasing levels of damage.

For specimens damaged at 2.0 ft-lb. energy levels the failure strength is shown to decrease

less than a further 5 ksi.

Figure 2.28: Results of CAI testing of PXX series materials: CAI failure stress and strain vs. impact

energy.

With various instrumentations available during these CAI tests, multiple measures of

failure strain exist for this series of materials. An example of measured resultant force vs.

various strain measurements is shown in Fig. 2.29. The measurement types include averages

of gages 1-4 and average of all five strain gages, strain calculated from DCDT average divided

by nominal coupon length, and applied displacement recorded divided by nominal coupon

length. It is interesting to note failure strain measured by averages of strain gages 1-4 and

5 gage averages differ slightly. The fifth gage, being located on the undamaged facesheet

but directly adjacent to the damaged region is usually farthest from the average. A typical

plot of strain measured by each gage on a coupon is shown in Fig. 2.30 and it illustrates

the previous point. It can be noted that the DCDT strain and applied displacement strain

continue to increase after failure, while strain gage averaged strain measurements severely

drop after failure (along with the resultant force). This is due to the loss of load carrying

capability of the failed facesheet. The difference in load carried by the failed and intact

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Chapter 2. Impact Damage and CAI Tests of PXX Series Materials

facesheet can also be seen by the difference in the drop in strain measured in gages 1 and

2 vs. gages 3 and 4, which is shown in Fig. 2.30. DCDT displacement measurements are

typically uniform, shown in Fig. 2.31, and their average seldom depends on the DCDT used.

Figure 2.29: Results of CAI testing of PXX series materials: typical reaction force vs. strain

measured by various methods.

Figure 2.30: Results of CAI testing of PXX series materials: typical reaction force vs. strain

measured by individual gages.

63
Chapter 2. Impact Damage and CAI Tests of PXX Series Materials

Figure 2.31: Results of CAI testing of PXX series materials: typical reaction force vs. displacement

measured by individual DCDT.

2.3.3 Full-field Displacement Measurements Using DIC

A three dimensional (3D) digital image correlation (DIC) system, VIC-3D [82], was used for

full-field shape and deformation measurement of a select set of the PXX experimental test

coupons during CAI testing. Sutten et al. [83] espoused on the history, current state of

the art, theory and practical consideration of DIC for full-field shape, deformation, and also,

motion measurement. DIC is possible through advanced digital cameras and image matching

software. For deformation measurements in three dimensions a stereo-vision camera system

consisting of two cameras mounted to a tripod on a rigid cross-member with a between

camera pan angle of roughly 30o, measured from a vertex located at the specimen center.

Test coupons were spray-painted white and then speckled with a random pattern of black

paint dots. The area of interest of the current research was only the front, impact-damaged

facesheet of the test coupons. Since the aperture of the digital cameras is reduced to improve

the depth of field, auxiliary lighting is used during these tests. The test apparatus used during

DIC instrumentation of PXX series experimental tests was shown in Fig. 2.22. The three

dimensional imaging capability of the stereo vision DIC system is shown in Fig. 2.32 for a

PXX series test coupon loaded to 75% of ultimate. Figure 2.33 shows the same test coupon

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Chapter 2. Impact Damage and CAI Tests of PXX Series Materials

after failure where the indentation indicated by the color-marked out-of-plane deformation

is propagated to the ends of the coupon in the width direction. The crack in the center of

the indentation is the cause of the distortion in Fig. 2.33.

Figure 2.32: Results of CAI testing of PXX series materials: three dimensional DIC imaging of PXX

test coupon at 75% of failure load, out-of-plane deformation shown.

A DIC system was used in the present research to monitor the deformation of the

initial dent present in each impact damaged test coupon subject to end-loaded uni-axial

compression. Previously, time lapse images taken from videography of a sample test were used

to show how this dent deforms as a result of the coupon’s loading. The images captured using

the DIC cameras were analyzed using VIC-3D software [82] and the results were visualized

using MATLAB software [84]. This visualization allowed the measurement of the residual

dent at various load levels for four PXX series CAI test coupons: P12, P05, P07, andP09.

These coupons were damaged with low velocity impacts prior to compression loading at

impact energy levels of 0.5, 1.0, 1.5, and 2.0 ft-lbs., respectively. The measurements used in

65
Chapter 2. Impact Damage and CAI Tests of PXX Series Materials

Figure 2.33: Results of CAI testing of PXX series materials: three dimensional DIC imaging of PXX

test coupon after indentation propagation failure, out-of-plane deformation shown.

the results presented here were taken at zero load, as well as at 50%, 75%, 90% and 100%

(just prior to failure) of the coupon’s failure load. It should be noted that the zero load

measurements taken using the DIC system vary, marginally, from those taken on the same

coupon prior to compression testing by hand measurement.

The results for size of each coupon’s indentation, from measurements taken at each

of the stated increments, in the coupon width direction, are shown in Fig. 2.34. The corresponding results for the dent growth in the coupon load direction are shown in Fig. 2.35.

These results confirm the observations taken from the time lapse images mentioned previously. The indentation grows in size in a stable fashion prior to global coupon failure. This

growth is seen predominantly in the X-direction or coupon width direction. The majority of

this growth takes place after the test coupon has been loaded to 50% of its eventual failure

load. It can be seen in these results that the indentation of each panel grows to maximum

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Chapter 2. Impact Damage and CAI Tests of PXX Series Materials

size of 1.5 in. or greater in three out of the four test cases measured with the DIC systems.

This represents stable indentation growth to a remarkable 25% of the coupon’s width (6.0

in.) or greater.

Figure 2.34: Results for DIC measurements: dent growth in coupon width direction for PXX test

coupons.

Figure 2.35: Results for DIC measurements: dent growth in coupon load direction for PXX test

coupons.

The indentation also grows in depth throughout the coupon’s compressive loading.

67
Chapter 2. Impact Damage and CAI Tests of PXX Series Materials

This result is not seen as well through the time lapse images, so the measurements taken using

the DIC system provide further usefulness, in this regard. The results for indentation growth

for the coupons observed using the DIC system are shown in Fig. 2.36. The indentations

are shown to grow significantly in size from 50% of the eventual failure load until coupon

failure. The indentation depth growth must result in further crushing of the honeycomb core

beneath the initial indentation. In most of the cases measured, this additional core crush is

more than double the initial indentation depth measured.

Figure 2.36: Results for DIC measurements: dent depth increase in coupon load direction for PXX

test coupons.

2.4 Conclusions from Impact Damage and CAI Tests

of PXX Series Materials

In the present chapter, a series of tests to determine the impact and CAI response of PXX

series was presented. Typical response of this type of material to static indentation, impact

from a drop tower apparatus, and compression loading after impact were given. CAI tests

were completed on panels with damage from impacts at energy levels below 2 ft-lbs, as chosen by the damage formation evaluation completed using static indentation and the impact

68
Chapter 2. Impact Damage and CAI Tests of PXX Series Materials

survey. A large reduction in residual compression strength at the smallest damage levels was

seen. Further reduction, but of lower magnitude, was found for increasing damage levels.

The indentation propagation failure mode of these panels was clearly indicated by time lapse

photography, and was further quantified by measurements from DIC data.

69
Chapter 3

Impact Damage and CAI Tests of

3PCF-XX and 6PCF-XX Series

Materials

Previously, in Chapter 2, a set of experiments on the impact damage and CAI response

of a material system consisting of a honeycomb core sandwich panel with thin facesheets

was presented. Two further sets of materials will be considered in Chapter 3. In Chapter

2, the apparatus, instrumentation, and procedures used for each these tests was explained

in detail. Most of the equipment and techniques described previously have been re-used,

although some changes were made as a result of the lessons learned. In the present chapter,

the reader will be referred to Chapter 2 for further detail, except where changes made for the

current set of experiments are noted in detail. In Chapter 6, the results of the experimental

study discussed in Chapters 2 and 3 will be used to validate a new finite element model for

analysis of CAI failure in honeycomb core sandwich panel coupons.

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Chapter 3. Impact Damage and CAI Tests of 3PCF-XX and 6PCF-XX Series

Materials

3.1 Materials and Test Coupons

A second set of compression after impact (CAI) experiments was performed on two series

of materials fabricated specifically for this research initiative by AAR Composites. Each

of these new material systems were fabricated with woven, glass fiber reinforced polymer

(GFRP) facesheets and Nomex hexagonal honeycomb core. The designation given to each of

these new material systems was based on the density of the Nomex honeycomb core included

in each of the new material systems. 3PCF-XX series material coupons contain a Nomex

core with 3 lb. per cu. ft. density and 6PCF-XX series materials contain a Nomex core with

6 lb. per cu. ft. density. Other material properties are shared by the two material systems.

Both cores are 0.75 in. thick and have a 0.125 in. nominal cell size. The 3PCF-XX and

6PCF-XX sandwich materials are shown in Fig. 3.1. The core gives the 3PCF-XX material

a yellow hue through the translucent facesheets, while the 6PCF-XX series panels are green

for the same reason.

Figure 3.1: 3PCF-XX (top) and 6PCF-XX (bottom) series honeycomb core sandwich panel material.

71
Chapter 3. Impact Damage and CAI Tests of 3PCF-XX and 6PCF-XX Series

Materials

The facesheets of both the 3PCF-XX and the 6PCF-XX material systems consisted

of two plies each of style 6781 woven S2-glass fabric cloth with 35% epoxy resin content. The

type of resin present was MTM45-1. The facesheets of these two sandwich panel systems

were again thin gage as they consisted of two plies, and the nominal facesheet thickness was

again 0.02 in. However, in addition to being fabricated from a higher grade S2 fiberglass,

the facesheet plies of these new material systems were oriented with ply directions of 0oand

45o. The overall sandwich panel was a symmetric [0/45/CORE/45/0] construction for both

material systems.

The type of woven S2 glass cloth plies used in the facesheets of these two materials

systems has the following material properties according to a National Institute for Aviation

Research Qualification Material Property Data Report [85]. The warp (0o) direction strength

and moduli are listed as 81.46 ksi and 4.22 Msi, respectively, for tensile loading, and 83.43

ksi and 4.22 Msi, respectively, for compressive loading. The fill (90o) direction strength and

moduli are listed as 80.50 ksi and 4.07 Msi, respectively, for compressive loading, and 69.07

ksi and 4.02 Msi, respectively, for tensile loading. The in-plane shear strength and modulus

are 5.45 ksi and 0.550 Msi, respectively. The in-plane Poisson’s ratio is 0.138.

The Nomex honeycomb core properties for the 3PCF-XX material systems are listed

as tested on a 0.5 inch thick specimen. The out-of-plane strength and modulus is 270 psi

and 20 ksi, respectively. The shear strengths are listed as 140 psi for the L direction (ribbon

direction) and 74 psi for the W direction. The shear moduli are listed as 4.5 and 2.5 ksi for

the L and W directions, respectively. For the 6PCF-XX material system, the higher density

Nomex honeycomb core properties are as follows from tests on samples of 0.5 in. thickness.

The out-of-plane crush strength and modulus are 925 psi and 60 ksi, respectively. The shear

strengths are 330 psi and 170 psi for the L and W directions, respectively. The shear moduli

are 13.0 and 6.5 for the L and W directions, respectively. The data presented here is available

from HexCel Composites, Inc. [86].

Test coupons for impact and CAI testing of 3PCF-XX and 6PCF-XX materials were

prepared similarly to the PXX series coupons, though they were fabricated slightly smaller

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Chapter 3. Impact Damage and CAI Tests of 3PCF-XX and 6PCF-XX Series

Materials

at the nominal size of 5.5 in. by 5.5 in. based on source material limitations. Examples of the

test coupons are shown in Fig. 3.2. A new potting method was also introduced for the new set

of coupons. A section of core material was removed from between the facesheets at the load

bearing ends of each coupon. This section had dimensions of the width (6 in.) and thickness

(0.75 in.) of the coupon and it extended in the loading direction approximately 0.5 in. Instead

of traditional clay “potting” material, a piece of wood was cut to tight tolerances and set in

place of the removed core material with an epoxy resin. The purpose of this was to decrease

the out-of-plane deflection of the facesheets due to contraction during curing of the potting

material. This allowed for more desirable load transference to the coupon, and yielded a more

successful compressive failure test of undamaged coupons. This is important for comparing

CAI failure strength. This new potting method was also successful at prohibiting brooming

of the coupon edges. The potting on the ends of each coupon was again ground to straight

and level to a tolerance of 0.001 in.

Figure 3.2: 3PCF-XX (top right) and 6PCF-XX (top left) series material coupons for testing, with

top load bearing end (middle) and side views (bottom.

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Chapter 3. Impact Damage and CAI Tests of 3PCF-XX and 6PCF-XX Series

Materials

3.2 Impact Damage Evaluation

Two sets of preliminary experimental tests were used to characterize damage formation in

these two materials for a range of impact energy levels. The two types of testing used were

static indentation and impact testing using a drop tower. The results of these tests were used

to select the energy levels for the impacts to coupons for CAI testing. The energy levels of

interest for the 3PCF-XX and 6PCF-XX series materials were representative of low velocity

impacts which would cause low to moderate damage to the impacted sandwich panel. The

highest levels of damage included complete facesheet penetration and core crushing through

greater than 50% of the coupons thickness. The range of damage included barely visible

impact damage (BVID) and extended to clearly visible damage. The testing procedures,

apparatus, instrumentation, and results for static indentation and drop impact on 3PCF-XX

and 6PCF-XX series materials will be described in the following sections.

3.2.1 Static Indentation Tests

A brief damage study was conducted on the 3PCF-XX and 6PCF-XX series panels using

static indentation. Static indentation is a controlled, easily repeatable method of causing

damage in composite sandwich panels. In this research, it was used to gain an initial understanding of the types of damage which would appear in the panels for various energy levels.

Although the types of damage from static indentation are comparable to damage from an

impact, this method produces more damage for a given energy level then a low velocity

impact and is considered to be a conservative method of estimating damage resistance in

a given material. The hydraulic testing machine used was shown in Fig. 2.3 and the 0.5

in. diameter hemispherical tip used for indentation was shown in 2.4. Static indentation of

3PCF-XX and 6PCF-XX series sandwich coupons is shown in Fig. 3.3.

Indentations of 3PCF-XX and 6PCF-XX series materials were conducted while the

coupons were clamped on all four edges using a metallic frame which allowed for the coupon

to be suspended with the rear, undamaged facesheet unsupported. This test frame is the

74
Chapter 3. Impact Damage and CAI Tests of 3PCF-XX and 6PCF-XX Series

Materials

same as discussed previously in use with PXX series coupons, and can be seen in Fig. 3.3.

One coupon of each material was used for static indentation and several indentations were

made in each coupon. The quasi-static loading was displacement controlled and applied at a

rate of 0.05 inch per minute. Both the displacement and the force was measured at the time

of each indentation and the results are discussed here.

Figure 3.3: Static indentation of 3PCF-XX (right) and 6PCF-XX (left) series sandwich coupons.

Five static indentations were made into a 3PCF-XX material coupon to investigate

the coupon’s response. The results of static indentation are shown in photographs in Fig.

3.4. The static indentation test at Location 1 on the coupon was used to find the resultant

force measured at facesheet fracture. Facesheet fracture occurred at roughly 170 lbs. It is

interesting to note that fracture does not result in a cross pattern of cracks aligned with the

woven fiber tows like in PXX series materials shown in Fig 2.5. Instead fiber and matrix

fracture saturate the entire point of loading creating a uniform damaged appearance. Damage

prior to facesheet failure also results in asterisk shaped discolorations at the location of the

residual dent.

The force vs. displacement results for all five static indentation tests can be seen

in Fig. 3.5. Facesheet fracture occurred in tests at Location 1 and Location 5 and can

be seen as a sudden drop in resultant force while the applied displacement is still being

increased. Tests were also conducted to 50, 100, and 150 lbs. nominally, for Locations 2, 3,

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Chapter 3. Impact Damage and CAI Tests of 3PCF-XX and 6PCF-XX Series

Materials

Figure 3.4: Results of static indentation of 3PCF-XX series material coupons: residual dents.

Figure 3.5: Results of static indentation of 3PCF-XX series material coupons: resultant force vs.

applied displacement.

and 4, respectively. The detailed results can be found in Appendix A. 3PCF-XX materials

which had similar core (except smaller thickness) to PXX materials, but higher strength and

modulus facesheet material, were able to withstand greater force before facesheet fracture,

76
Chapter 3. Impact Damage and CAI Tests of 3PCF-XX and 6PCF-XX Series

Materials

but deflected less for a given applied load. This meant that the panels were stiffer in response

to impact loading and impacts of equal energy would result in higher measured resultant force

from 3PCF-XX materials than PXX series materials.

Six static indentation tests were completed on a 6PCF-XX series material coupon to

make initial evaluations on its response to out-of-plane concentrated loads. The resulting

dents and damage can be seen in Fig. 3.6. Force vs. displacement results for these indentation

tests are shown in Fig. 3.7. The first indentation was again used to determine the load and

energy required for facesheet fracture. Failure occurred at 205.1 lbs. and 0.101 in. of

indentation. By integration, the energy absorbed was found to be 0.891 ft-lb. The resulting

damage found in this material is similar to damage in 3PCF-XX materials, at similar energy

levels. In addition to indentations made to facesheet failure at Locations 1 and 5, indentations

were made to 50, 100, 150 and 180 lbs. at Locations 2, 3, 6, and 4, respectively. A table of

the complete results recorded for each of these indentations can be found in Appendix A.

Figure 3.6: Results of static indentation of 6PCF-XX series material coupons: residual dents.

77
Chapter 3. Impact Damage and CAI Tests of 3PCF-XX and 6PCF-XX Series

Materials

Figure 3.7: Results of static indentation of 6PCF-XX series material coupons: resultant force vs.

applied displacement.

3.2.2 Drop Tower Impact Survey

An impact damage survey using a mass dropped from a tower was again used to find the properties of resulting impact damage and to measure the response due to impact of 3PCF-XX

and 6PCF-XX series material coupons. The purpose of the impact survey was to determine

the characteristic damage at various impact energy levels and to make a decision about which

impact energy levels would be used for compression after impact tests. A material coupon

was clamped on all four edges in the special test fixture, shown under the drop tower in Fig.

3.8, with no support under the opposite facesheet as done in other tests. The test fixture

was then clamped to a stout steel table at the point of impact beneath the drop tower.

The drop tower used for the experiments described in the current chapter consisted

of a metal tube several yards in length, mounted vertically. An electronic pulley system was

mounted to the tube to raise and set the drop height of the mass which would impact the

sandwich panel coupon. Once in place the impactor was dropped with the press of a button

which activated a mechanical release. Upon impact the mass would rebound from the coupon

and a mechanical catch would spring into place automatically to catch the impactor before it

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Chapter 3. Impact Damage and CAI Tests of 3PCF-XX and 6PCF-XX Series

Materials

could strike the coupon a second time. Impacts were conducted with a 0.5 in. hemispherical

tip and the weight of the impactor with the tip attached was measured to be 2.4855 lb.

The drop height for a given impact energy level was then calculated by dividing the desired

impact energy level by the weight of the impactor. The drop height could be set using the

impact tower apparatus to the nearest tenth of an inch.

Figure 3.8: Drop tower apparatus used for impact survey of 3PCF-XX and 6PCF-XX series material

coupons.

Once an impact on a 3PCF-XX or 6PCF-XX series material coupon was conducted,

the residual dent was measured in terms of its maximum depth and diameter just as in the

impact survey of PXX materials. After the coupons were visually examined, they were later

carefully dissected with through-thickness cuts through the center of each of the indentations

in order to assess the condition of the honeycomb core beneath the indentation. Maximum

thickness and width of the crushed core region (measured from the bottom of the dented

facesheet) was measured using inspection by optical microscope. In addition to this information, the impact force was recorded electronically with respect to time so that impact length

79
Chapter 3. Impact Damage and CAI Tests of 3PCF-XX and 6PCF-XX Series

Materials

could also be determined. The impact length is the time in seconds from when the impactor

comes into contact with the sandwich panel specimen, to when it rebounds completely. In

addition, measured and visual qualitative observations were made about the location and

characteristics of other types of damage present, including cracking or penetration of the

impacted facesheet. Results versus impact energy for residual dent depth, residual dent diameter, maximum impact force, and impact length are shown in Fig. 3.9, 3.10, 3.11, and

3.12, respectively. Results for comparisons of crushed core diameter (width), crushed core

depth, and total damage depth comparisons for both 3PCF-XX and 6PCF-XX materials are

shown in Fig. 3.13, 3.14, 3.15, and 3.16, respectively. The complete results of the impact

survey of 3PCF-XX and 6PCF-XX series materials, including damage descriptions, can be

found in Appendix A.

Figure 3.9: Results of drop tower impact testing on 3PCF-XX and 6PCF-XX series materials:

variation of the dent depth vs. the impact energy.

Impacts on 3PCF-XX and 6PCF-XX materials with energies ranging from 1 to 9

ft-lbs. were surveyed. The higher energies became of interest during review of background

literature because this type of damage had not been considered by other researchers studying

CAI strength prediction in thin facesheet sandwich panels. For the 3PCF-XX material, when

impacted at 8 ft-lb. the impactor completely impacted the first facesheet and became lodged

80
Chapter 3. Impact Damage and CAI Tests of 3PCF-XX and 6PCF-XX Series

Materials

Figure 3.10: Results of drop tower impact testing on 3PCF-XX and 6PCF-XX series materials:

variation of the dent diameter vs. the impact energy.

Figure 3.11: Results of drop tower impact testing on 3PCF-XX and 6PCF-XX series materials:

variation of the maximum impact force vs. the impact energy.

in the sandwich panel. Since this was well beyond the damage levels of major impact, 9

ft-lb. was not considered. 3.5 ft-lb. was considered instead for the ninth impact location on

the specimen. Facesheet fracture occurred at 4 ft-lbs for both types of panels. This can be

seen in Fig. 3-9 where the dent depth suddenly becomes much larger with increasing impact

81
Chapter 3. Impact Damage and CAI Tests of 3PCF-XX and 6PCF-XX Series

Materials

Figure 3.12: Results of drop tower impact testing on 3PCF-XX and 6PCF-XX series materials:

variation of the impact length vs. the impact energy.

Figure 3.13: Results of drop tower impact testing on 3PCF-XX and 6PCF-XX series materials:

variation of the core damage width vs. the impact energy.

energy. The maximum impact force also increases with impact energy until impact levels

at which facesheet fracture occurs, and then reaches a maximum. Impact length is longer

for impacts where fracture occurred due to the decreased rebound speed as more energy is

absorbed by the panel, contributing to damage. Core damage was considered in detail for

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Chapter 3. Impact Damage and CAI Tests of 3PCF-XX and 6PCF-XX Series

Materials

Figure 3.14: Results of drop tower impact testing on 3PCF-XX and 6PCF-XX series materials:

variation of the core damage depth vs. the impact energy.

Figure 3.15: Results of drop tower impact testing on 3PCF-XX and 6PCF-XX series materials:

variation of the total dent depth for 3PCF-XX materials vs. the impact energy.

3PCF-XX and 6PCF-XX panels. Figure 3.13 and shows that the width of the damaged core

region is higher for 3PCF-XX panels then for 6PCF-XX, in general. Also, the maximum

thickness of the crushed core region is higher for damage regions in 3PCF-XX materials.

The conclusion can be made from these results that the higher strength and stiffness of the

83
Chapter 3. Impact Damage and CAI Tests of 3PCF-XX and 6PCF-XX Series

Materials

Figure 3.16: Results of drop tower impact testing on 3PCF-XX and 6PCF-XX series materials:

variation of the total dent depth for 6PCF-XX materials vs. the impact energy.

6PCF-XX material’s core has a significant effect on the impact resistance of the sandwich

panel. It is also interesting to note that the depth of the core crush region beneath the

indented facesheet stays about the same for all levels of impact energy.

Several types of damage are present in the impact locations on the 3PCF-XX series

materials shown in Fig. 3.17, and the 6PCF-XX materials shown in Fig. 3.18. At very

low impact energy levels, 1 to 3 ft-lb. for 3PCF-XX, and 1 to 2 ft-lb. for 6PCF-XX,

there is a slight discoloration of the facesheet and almost imperceptible residual dents in the

facesheet, which are shown graphically in Figs. 3.9 and 3.10. These levels are considered

barely visible impact damage (BVID) as they would be difficult to find even during routine

inspection, especially if the facesheets were coated with paint. The maximum impact energy

level associated with BVID is about 3 ft-lb. for both sets of materials; although, for the

less stiff 3PCF-XX materials it may extend marginally higher. At higher energy levels, the

facesheet fracture is very noticeable. At levels of 6 ft-lb. and higher, there is practically an

open hole in the facesheet. Photographs of damage cross sections, taken after cuts were made,

show that significant core damage is also present for panels with this amount of facesheet

damage. An example of this evaluation is shown in Fig. 3.19, but a photograph was not

84
Chapter 3. Impact Damage and CAI Tests of 3PCF-XX and 6PCF-XX Series

Materials

readily available for damage levels higher than 5 ft-lb. At higher energy levels, the core

damage present includes large amounts of tearing and bears little resemblance to the original

hexagonal cellular structure.

Figure 3.17: Results of drop tower impact testing on 3PCF-XX series materials: residual dents.

The data collected, as a result of the impact survey of 3PCF-XX and 6PCF-XX series

sandwich panels, helped establish the energy levels of interest for various CAI test coupons.

Higher energy levels for impacts than used in the PXX series tests would naturally be of

interest since the BVID range of these panels extended to higher levels. Also, higher levels of

85
Chapter 3. Impact Damage and CAI Tests of 3PCF-XX and 6PCF-XX Series

Materials

Figure 3.18: Results of drop tower impact testing on 6PCF-XX series materials: residual dents.

damage were of interest, since they have seen less prior attention by researchers studying CAI

strength prediction analysis. During the impact survey, impact energy levels of 1 to 9 ft-lbs.

were considered for both sets of materials. Energy levels of 1, 3, 5, and 7 ft-lbs. were chosen

for impacts on CAI coupons of 3PCF-XX and 6PCF-XX series materials using the 0.5 in.

diameter hemispherical impact tip. Three coupons with impacts from each energy level would

86
Chapter 3. Impact Damage and CAI Tests of 3PCF-XX and 6PCF-XX Series

Materials

Figure 3.19: Results of drop tower impact testing on 6PCF-XX series materials: core damage shown

through destructive evaluation.

be tested for each set of material coupons. In addition, undamaged panels would be tested

for comparison of CAI residual strength to initial compression strength. It was expected

that 3PCF-XX and 6PCF-XX panels would have nearly identical undamaged compressive

strength, since this result depends upon the material strengths of the facesheets, of which

the two material systems are identical.

3.3 Compression After Impact Experiments

Several test method standards, mentioned in Chapter 2, were considered when the CAI tests

described in this section were designed [79] [80]. In this section, the apparatus, instrumentation, procedure, and results of CAI testing of 3PCF-XX and 6PCF-XX sandwich panel

materials will be described. The experimental apparatus and procedure was largely similar

to CAI tests of PXX sandwich panels and so less detail will be used in this section, except

where needed to establish any differences between the test sets.

3.3.1 Apparatus and Instrumentation

Compression after impact tests of 3PCF-XX and 6PCF-XX series materials were mounted in

the same servo-hydraulically actuated MTS load frame used for the CAI tests of PXX series

sandwich coupons, using identical apparatus (described in Chapter 2. Compressive loading

was displacement controlled and applied through hydraulically actuated movement of the

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Chapter 3. Impact Damage and CAI Tests of 3PCF-XX and 6PCF-XX Series

Materials

lower platen at a rate of 0.01 in. per minute. This rate was slower than that used in tests on

PXX series materials, to allow for more measurements and observations to be made during

a test. The load frame with a 3PCF-XX series coupon installed and a close-up picture of a

6PCF-XX coupon installed within the apparatus are shown in Fig. 3.20.

Figure 3.20: Load frame and coupon mounting apparatus used for CAI testing with 3PCF-XX (left)

and 6PCF-XX (right) coupons installed.

The following instrumentation was used for all CAI tests on both 3PCF-XX series and

6PCF-XX series material coupons. The applied displacement and the measured reaction force

were recorded from the load head of the MTS test frame. Far field strain in the direction

of loading was recorded on the front and rear facesheets of each CAI coupon throughout

testing. For the series of tests described in this chapter, in general, four uniaxial strain

gages were placed on the specimen as shown in Fig. 3.21; however, occasionally a strain

gage malfunctioned and this was noted when it occurred. At least three of the strain gages

numbered 1 through 4 in Fig. 3.21 were necessary to assure coupon alignment within the

loading apparatus. For select panels, a biaxial strain gage was used in place of uniaxial

gage #3 in order to facilitate measurement of Poisson’s effects in the coupon. Three direct

current displacement transducers (DCDT) were mounted to monitor the displacement at

several locations between the loading platens, as described in Fig. 2.21, previously. A fourth

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Chapter 3. Impact Damage and CAI Tests of 3PCF-XX and 6PCF-XX Series

Materials

DCDT was used in tests of 3PCF-XX and 6PCF-XX coupons to measure the out-of-plane

displacement of the center of the rear (undamaged) facesheet.

Figure 3.21: Location of strain gages for CAI testing of 3PCF-XX and 6PCF-XX series material

coupons (all dimensions in inches).

Several types of auxiliary instrumentation were used throughout CAI testing. The

high definition video system was not available at the time of these CAI tests; however, an

effort was made to take real time video imagery of selected CAI tests using a handheld digital

camera. Ambient temperature and humidity were again noted for each specimen. In addition,

high speed footage using a Phantom camera system [81] was again used for select panels, as

were digital images using a Vic-3D system [82] for digital image correlation measurements

of full-field, three dimensional displacement and strain. At least one panel damaged at

each impact energy level, for each material system, was considered by the various auxiliary

instrumentations (i.e. coupons damaged at 1 ft-lb. were observed with both high speed

photography, real time photography, and DIC, just not at the same time). Two Phantom

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Chapter 3. Impact Damage and CAI Tests of 3PCF-XX and 6PCF-XX Series

Materials

cameras were used for high speed video photography of CAI failure. One was placed in front

of the test frame as before, while a second camera was placed at an angle to one side in order

to capture the out of plane displacement seen during some CAI failures. The CAI apparatus

with high speed cameras in place is shown in Fig. 3.22. The CAI apparatus with cameras

for digital image correlation measurements was similar to that shown in Fig. 2.22. Digital

image correlation was briefly explained in Chapter 2 and further information can be found

in a resource by Sutton, Orteu, and Schreier [83].

Figure 3.22: Auxiliary apparatus for CAI testing of 3PCF-XX and 6PCF-XX series coupons with

high speed Phantom cameras and necessary lighting systems.

3.3.2 CAI Failure of 3PCF-XX and 6PCF-XX Series Coupons

Based on the results of the impact survey, a series of damage levels was chosen to be studied

in coupons of 3PCF-XX and 6PCF-XX series materials by compression testing after impact.

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Chapter 3. Impact Damage and CAI Tests of 3PCF-XX and 6PCF-XX Series

Materials

Twenty-four coupons were centrally impacted on one facesheet using the drop tower shown

in Fig. 3.8. Impacts at energy levels of 1.0, 3.0, 5.0, and 7.0 ft-lbs. were carried out on

three coupons each of both material types. Damage was inflicted using the 0.5 in. diameter

hemispherical shaped tip. The resulting damage from low velocity impact in the CAI coupons

was inspected non-destructively and the metrics describing the residual dent in each panel

can be found in Appendix A. A displacement controlled compressive load was applied to each

coupon until failure occurred, marked by a sudden drop in the measured reaction force. In

addition, two undamaged coupons (one of each construction type) were tested to failure to

establish the initial compressive strength of the coupons. The compressive strength result for

3PCF-14 was the higher of the two panels tested and is considered more accurate since failure

occurred at the clamped end for 6PCF-8. It is expected that the two types of panels should

have nearly identical undamaged compressive strengths since the facesheet constructions are

the same.

Failure occurred in the current set of CAI testing similarly to tests of PXX series

materials. Global failure of the coupon occurred because of failure in the damaged facesheet

only and still carried some load prior to failure. The failure mode of the 3PCF-XX panels

was identical to the failure mode seen in PXX series panels, which is termed indentation

propagation. However, the 6PCF-XX panels failed by a different failure mode. Instead

of a region of local buckling, a crack appears in the initially damaged facesheet, which

compromises its load carrying capability. The differences between the two failure modes can

clearly be seen in Fig. 3.23.

Stable indentation propagation during CAI testing such as seen in 3PCF-XX tests was

shown for a PXX series test in Fig. 2.26 using video photography for PXX series coupons.

Video photography was also used for select tests of 3PCF-XX and 6PCF-XX materials. Time

lapse photography of a 6PCF-XX series coupons shown in Fig. 3.24 indicates that the initial

dent grows very little prior to the specimen failure. It appears to be nearly the same size at

1000 lbs. of load as it does at 5000 lbs. of load for coupon 6PCF-3. This particular coupon

was impacted at 5 ft-lbs. of energy, but this was typical of all 6PCF-XX series CAI tests. At

91
Chapter 3. Impact Damage and CAI Tests of 3PCF-XX and 6PCF-XX Series

Materials

Figure 3.23: Results of CAI testing of 3PCF-XX and 6PCF-XX series materials: failure modes of

indentation propagation for 3PCF-XX series coupons (left) and crack propagation in 6PCF-XX

coupons (right).

about the 4:00 minute mark, a small crack in the front facesheet appeared, advancing from

the initial damage location transverse to the load direction (vertical). By the 4:30 mark, the

crack had advanced slightly; however, by the 5:00 minute mark the crack was easily visible

and the panel was very near to the residual strength which was found to be 6107 lbs. for

the 6PCF-2 coupon. Between the 5:03 and 5:04 marks in the real time video, the crack

propagated to the edge of the specimen (accompanied by some interlaminar delamination

and facesheet debonding), thus compromising the facesheet. A global failure of the coupon

has thus occurred.

Phantom camera systems [81] were again used to capture failure of both 3PCF-XX

and 6PCF-XX series materials and were quite essential in fully understanding failure, as it

happens extremely quick in real time. A Phantom version 12 video system captured front

views of select panels at 15,001 photos per second and a Phantom version 7 video system

captured side angles at 12,500 photos per second to illustrate any out-of-plane displacement

of the facesheets. Frames taken from footage captured from both view points during CAI

testing of coupons 6PCF-12 and 3PCF-15 show, in Fig. 3.25, the contrasting failure modes

92
Chapter 3. Impact Damage and CAI Tests of 3PCF-XX and 6PCF-XX Series

Materials

Figure 3.24: Results of CAI testing of 6PCF-XX series materials: time lapse images taken throughout test.

93
Chapter 3. Impact Damage and CAI Tests of 3PCF-XX and 6PCF-XX Series

Materials

Figure 3.25: Results of CAI testing of 3PCF-XX and 6PCF-XX series materials: time lapse images

taken from high speed camera during failure for 3PCF-XX (right) and 6PCF-XX (left) materials.

94
Chapter 3. Impact Damage and CAI Tests of 3PCF-XX and 6PCF-XX Series

Materials

occurring during the moment of failure. The sequences taken from the two cameras for

6PCF-12 begin with a small crack already visible growing from the initial impact initiated

indentation. The crack propagates quickly to each side, although it propagates to the right

slightly before the left showing that there may be a difference in stress concentration on either

side of the initial damage due to slight coupon misalignment or other factors. In real time,

however, this was not noticeable for most test cases. Photos, taken at high speed, of coupon

3PCF-15 show indentation propagation failure that is similar to that shown previously in Fig.

2.27. With the aid of the side mounted camera, the high speed camera footage also shows

the out-of-plane deflection in the locally buckled region more clearly than in previous tests

on PXX series materials. Also, in both cases the failed facesheet’s inability to transfer load

causes the entire coupon to buckle globally. Although the global out-of-plane displacement

at the middle point of the coupon is small it can be seen in the side images taken from the

high speed cameras. In the actual video, this feature is easier to see, as the coupon can be

seen to actually move.

Nominal failure stress was calculated from the measured resultant force divided by

the nominal cross sectional facesheet area of each coupon and is shown in Fig. 3.26. Average

measured far-field strain at coupon failure from the four strain gages on each panel was also

reported for each coupon, which is shown in Fig. 3.27. Detailed failure results of nominal

failure stress and failure strain for CAI tests of 3PCF-XX and 6PCF-XX series materials can

be found in Appendix A.

The failure strength of both 3PCF-XX and 6PCF-XX series coupons is shown to drop

dramatically even for lightly impact-damaged specimens. The reduction in coupon strength

of roughly 10 ksi from undamaged specimens to damaged specimens impacted at 1.0 ft-lb.

energy levels was higher than any subsequent drop, even in the most damaged sandwich

panels. The drop of failure strength is shown to decrease in severity with further increasing

levels of damage. Tests of 3PCF-XX series panels with a given damage level were more

repeatable in terms of their failure level than tests at 6PCF-XX series panels. It is also

important to note that failure of 6PCF-XX panels impacted at a given energy level occurred

95
Chapter 3. Impact Damage and CAI Tests of 3PCF-XX and 6PCF-XX Series

Materials

Figure 3.26: Results of CAI testing of 3PCF-XX and 6PCF-XX series materials: failure stress vs.

impact energy.

Figure 3.27: Results of CAI testing of 3PCF-XX and 6PCF-XX series materials: failure strain vs.

impact energy.

at higher stress and strain levels than 3PCF-XX panels. This suggests that the higher density

honeycomb core found in 6PCF-XX panels contributes to the increased CAI strength. It was

shown previously that the residual dent increases dramatically in size for panels with 3 lb.

per cu. ft. density cores (3PCF-XX and PXX series), while the dent does not increase in

96
Chapter 3. Impact Damage and CAI Tests of 3PCF-XX and 6PCF-XX Series

Materials

size noticeably for 6PCF-XX series. This is likely due to the higher strength and stiffness of

the higher density core in response to out-of-plane compressive loads such as the facesheets

pressing inwards at the edges of the initial dent due to the applied compressive load to the

panel. The higher out-of-plane stiffness precludes the indentation propagation failure mode;

instead, the panels fail due to crack propagation due to in-plane stress concentrations in the

facesheet which cause material fiber and matrix failure.

3.3.3 Full Field Displacement Measurements using DIC

A three-dimensional (3D) digital image correlation (DIC) system was again used for full field

displacement and surface mapping of a select group of CAI test coupons for the 3PCF-XX and

6PCF-XX series materials. A brief explanation of the DIC system was provided in Section

2.3.3. The DIC system provided important information about the shape and deformation

of impact damage in each test coupon surveyed. It also helped to validate observations on

the differences between the two observed CAI failure modes, indentation propagation and

crack propagation, which were made through time lapse imagery from video footage. The

DIC system allows observations about damage growth to be quantified. An example of a 3D

DIC representation of the indentation propagation failure mode from a 3PCF-XX CAI test

is shown in Fig. 3.28, while the corresponding two-dimensional (2D) image is shown in Fig.

3.29. An example of the crack propagation failure mode for a 6PCF-XX CAI test coupon

is shown in Fig. 3.30 with a 3D representation and in Fig. 3.31 for the corresponding 2D

representation.

The main benefit of the DIC system to the present research was the ability to quantify

the change in size of the out-of-plane impact damage in the damaged facesheet of the sandwich

panel test coupon during subsequent compressive loading. Four test coupons from both the

3PCF-XX and the 6PCF-XX series materials were selected for instrumentation using the DIC

system. For the 3PCF-XX series tests, coupons 3PCF-05, 3PCF-03, 3PCF-10, and 3PCF-09

were selected to represent the four impact energies used for impacting 3PCF-XX series CAI

test coupons, which were 1.0, 3.0, 5.0, and 7.0 ft-lbs., for the four coupons, respectively. For

97
Chapter 3. Impact Damage and CAI Tests of 3PCF-XX and 6PCF-XX Series

Materials

Figure 3.28: Example 3D representation of the indentation propagation failure mode for a 3PCF-XX

series CAI test coupon.

Figure 3.29: Example 2D representation of the indentation propagation failure mode for a 3PCF-XX

series CAI test coupon.

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Chapter 3. Impact Damage and CAI Tests of 3PCF-XX and 6PCF-XX Series

Materials

Figure 3.30: Example 3D representation of the crack propagation failure mode for a 6PCF-XX series

CAI test coupon.

Figure 3.31: Example 2D representation of the crack propagation failure mode for a 6PCF-XX series

CAI test coupon.

99
Chapter 3. Impact Damage and CAI Tests of 3PCF-XX and 6PCF-XX Series

Materials

the selection of results presented, the dent on each test coupon was measured in the direction

of the coupon width (X-direction), in the coupon load direction (Y-direction), as well as its

depth (out-of-plane or Z-direction). These measurements were made at 0%, 50%, 75%, 90%

and 100% (just prior to failure) of the test coupon’s failure load, and a spline fit curve was

applied to the data points.

The results for the coupon width direction measurements are shown in Fig. 3.32; the

load direction measurements are shown in Fig. 3.33; the dent depth measurements are shown

in Fig. 3.34 for the 3PCF-XX series test coupons. The results for the 3PCF-XX series test

coupons are similar to the results shown previously for PXX series test coupons in Chapter

2. The size of the impact damage in each coupon does not appreciably increase in size prior

to 50% of the eventual test coupon failure load. Subsequently, the size in the coupon width

direction can increase in a stable fashion to as much as one third of the overall coupon width

(5.5 in.). The impact damage size remains constant in the load direction. The depth of the

impact damage also increased during testing for each of the coupons studied with the DIC

system.

Figure 3.32: Results from DIC Measurements: dent growth in coupon width direction for 3PCF-XX

test coupons.

For the 6PCF-XX series material, test coupons 6PCF-10, 6PCF-09, 6PCF-06, and

6PCF-11 were chosen for DIC system observation during compression loading. These panels

were impacted at energy levels of 1.0, 3.0, 5.0, and 7.0 ft-lbs., respectively. The impact

100
Chapter 3. Impact Damage and CAI Tests of 3PCF-XX and 6PCF-XX Series

Materials

Figure 3.33: Results from DIC Measurements: dent growth in coupon load direction for 3PCF-XX

test coupons.

Figure 3.34: Results from DIC measurements: dent depth increase for 3PCF-XX test coupons.

damage growth was again measured for size in the coupon width and load directions, as

well as maximum depth. The results for the width direction measurement are shown in Fig.

3.35; the load direction results are shown in Fig. 3.36, and the dent depth measurements

are shown in Fig. 3.37. The dent growth measured for the 6PCF-XX test coupons was not

nearly as marked as for 3PCF-XX and PXX series coupons. Generally, most of the dent

growth for 6PCF-XX test coupons occurred very near to failure, at greater than 90% of the

eventual failure load. Additionally, the stable growth amount was much smaller then 3PCFXX coupons, when compared in terms of total growth, as well as in terms of percentage of test

101
Chapter 3. Impact Damage and CAI Tests of 3PCF-XX and 6PCF-XX Series

Materials

coupon size. Presumably, the reduced amount of damage growth in 6PCF-XX series coupons

is due to the high strength and stiffness of the higher density core materials these sandwich

panel test coupons contain. Since, any dent growth must be precipitated by crushing of the

honeycomb core underneath the facesheet indentation, a higher stiffness and strength of the

core should lead to less growth, in general.

Figure 3.35: Results from DIC measurements: dent growth in coupon width direction for 6PCF-XX

test coupons.

Figure 3.36: Results for DIC measurements: dent growth in coupon load direction for 6PCF-XX

test coupons.

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Chapter 3. Impact Damage and CAI Tests of 3PCF-XX and 6PCF-XX Series

Materials

Figure 3.37: Results from DIC measurements: dent depth increase for 6PCF-XX test coupons.

3.4 Conclusions from Impact Damage and CAI Tests

of 3PCF-XX and 6PCF-XX Series Materials

A series of tests to determine the impact and CAI response of 3PCF-XX and 6PCF-XX series

materials was presented in the present chapter. The techniques used in these experiments

were similar to those given in Chapter 2, except where changes were made based on lessons

learned, as in the case of material coupon preparation. Based on the damage found during

static indentation and the impact survey of the materials in the present chapter, a large range

of impact energies were considered for CAI testing, extending up to 7 ft-lbs. The increased

damage tolerance, of low velocity impact, of these material systems was attributed to the

increased strength of the S2-glass reinforced facesheets. During CAI testing of 3PCF-XX

and 6PCF-XX materials, failure was also found to occur at higher strengths than PXX series

materials, which were shown in Chapter 2, but similar trends in CAI failure measurements

vs. damage energy were shown.

The key difference in the construction of 3PCF-XX series materials and 6PCF-XX

series materials was the nominal density in the honeycomb core used. The higher density core

contributed to decreased residual dent depth and diameter in those material coupons, which

was found from results of the impact survey. Increased CAI strength was also shown for

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Chapter 3. Impact Damage and CAI Tests of 3PCF-XX and 6PCF-XX Series

Materials

the coupons with the higher density core (6PCF-XX). Most importantly, it was found that

the failure mode for the 6PCF-XX panels was not indentation propagation. Instead, a crack

propagation failure mode was demonstrated for these panels. Results obtained using DIC

systems for full field displacement measurements highlighted the key differences between the

indentation propagation failure and crack propagation failure modes. The differences were

also demonstrated using images taken from video footage, and high speed digital photography. The dependence of the failure mode on the nominal density of the honeycomb core

of these panels is a result which demonstrates the need for a CAI model to be able to predict multiple failure modes. This need was mentioned in Chapter 1 during the literature

review. The current research seeks to develop a model which can predict both failure modes

established in Chapters 2 and 3. Next, in Chapter 4, development of this model will begin

with examination of the relevant theory and a more detailed review of two models similar to

those used in research explained in Chapter 1. Later in Chapter 5, the new CAI model will

be more fully developed, and finally, in Chapter 6, the experimental results of the current

research will be compared with analysis results using the new model.

104
Chapter 4

CAI Analysis Using Existing Models

It has been established that even a low, to moderate damage, from low-velocity impacts, can

cause critical strength reductions in fiber reinforced matrix composite airframe components.

The ability to predict the effect of damage to vehicles and structures made from these materials would represent a valuable design tool. Various attempts have been made to predict

compression after impact (CAI) strength in thin facesheet composite sandwich panels, such

as the material systems considered in Chapters 2 and 3 of the current work. A new finite element model (FEM), described in the next chapter, for analysis of CAI failure in honeycomb

core sandwich panels, builds on current models as described in the literature review given

in Chapter 1. Two of the these models will be discussed in the present chapter. Existing

models have various limitations, such as handling only one type of failure mode, indentation propagation. However, some of the techniques used are incorporated into the proposed

model, so it is pertinent to discuss the theory behind these models, and demonstrate their

use, which will be done presently.

In the next section, the theory behind components of existing models, including laminate theory, plate theory as it relates to ABAQUS [73] finite element analysis (FEA), and

the relations used to homogenize the honeycomb core response, is presented. In subsequent

sections, two existing models are considered: a spring element core finite element model

(FEM) and a solid element core FEM. Both of these models are capable of modeling only

105
Chapter 4. CAI Analysis Using Existing Models

indentation propagation failure and a brief selection of results are compared to experimental

results from the CAI tests on PXX series materials. The description of the new FEM in

Chapter 5 will then continue by building upon this work.

4.1 General Theory for CAI Prediction

Composite sandwich structures consist of two separate composite laminates, called facesheets,

adhesively bonded to a low density, high shear strength core structure such as a foam material

or some other cellular structure. A common core material is a hexagonal cell honeycomb

core structure constructed from aluminum or Nomex, the core material used in the sandwich

panel constructions in this research. The high shear strength and offset from the sandwich

plate’s midplane give the sandwich panel a very desirable high bending stiffness. Both the

facesheets and the core of the sandwich panel need to be modeled accurately. This section

will describe the theory related to the finite elements representing the facesheet and core

components of several recent existing models for predicting the results of CAI testing on

sandwich panels.

4.1.1 Classical Laminate Theory

A discussion of the finite element representation of a composite laminate such as the one

used in FEM of facesheets for sandwich panels is introduced here. Classical laminate theory

is an expansion of classical plate theory based on several assumptions. A layer of a fiber

reinforced polymer laminate can be thought of as a thin plate in a plane of a local Cartesian

coordinate system (1-2-3). Plate theories are used as a simplified substitution for a three

dimensional elasticity solution. A plate theory such as classical plate theory (CPL) or first

order shear deformation theory (FSDT) can be applied in the analysis of such a structure

if the thickness is significantly smaller than each of the other two dimensions. Each layer is

made from a linear, elastic, orthotropic material. The properties of the individual fiber and

matrix materials are smeared or lumped together as layer or ply properties. For a single layer

106
Chapter 4. CAI Analysis Using Existing Models

of fiber reinforced matrix composite, the constitutive relations can be expressed in terms of

the orthotropic compliance matrix with nine independent elastic constants as shown in Eq.

4.1. Here, εi are the extensional strains, γij , are the shear strains, Ei, are the extensional

moduli, Gi are the shear moduli, υ21 are the Poisson’s ratio’s, σi are the extensional stresses,

and τij are the shear stresses. The subscripted symbols i or ij are indices which are given

values 1, 2, or 3 corresponding to the local Cartesian coordinate system.







ε1

ε1

ε3

γ23

γ13

γ12







=





























1

E1

−υ21

E2

−υ31

E3

0 0 0

−υ12

E1

1

E2

−υ32

E3

0 0 0

−υ13

E1

−υ23

E2

1

E3

0 0 0

0 0 0 1

G23

0 0

0 0 0 0 1

G13

0

0 0 0 0 0 1

G12



































σ1

σ2

σ3

τ23

τ13

τ12







(4.1)

If a Cartesian coordinate system is defined so that the 1-direction axis is parallel to

the fibers of the material, a plane of isotropy can be defined for fiber reinforced materials for

rotations about this axis. This requires that E2 = E3, υ12 = υ13, and G12 = G13. Also,

G23 =

E2

2 (1 + υ23)

(4.2)

This results in the conclusion that for the lamina, which is assumed homogenous and

transversely isotropic, there are five independent elastic constants that are needed to define

the lamina. The following classical laminate theory (CLT) also requires that a plane stress

condition is assumed, that is σ3 = τ23 = τ13 = 0. In practice, the stresses that are assumed

to be zero simply must be much smaller than the other three stresses. While these stresses

may be small, they can cause failure since transverse and through the thickness strengths in

composites are usually small. Also, ε3 is notably not assumed to be zero. These assumptions

allow the reduction in size of the compliance matrix and its inverse, the stiffness matrix. The

107
Chapter 4. CAI Analysis Using Existing Models

reduced compliance (4.3) and stiffness matrix (4.4) are:







ε1

ε2

γ12







=











1

E1

−υ21

E2

0

−υ12

E1

1

E2

0

0 0 1

G12

















σ1

σ2

τ12







(4.3)







σ1

σ2

τ12







=











C11 C12 0

C12 C22 0

0 0 C66

















ε1

ε2

γ12







(4.4)

Where,

C11 =

E1

1−υ12υ21

C12 =

υ12E2

1−υ12υ21

=

υ21E1

1−υ12υ21

C22 =

E2

1−υ12υ21

C66 = G12

In order to represent the response of a laminate, a global Cartesian coordinate system

(x − y − z) is defined. A composite laminate consists of one or more layers stacked on top

of one or another where their fiber direction (or local 1-direction) can be oriented in any

direction within the X − Y plane. A plane stress transformation is defined as follows to

transform stresses in each layer from its local coordinate system to the global coordinate

system of the laminate







σx

σy

τxy







=











cos2θ sin2θ −2sinθcosθ

sin2θ cos2θ 2sinθcosθ

sinθcosθ −sinθcosθ cos2θ − sin2θ

















σ1

σ2

τ12







(4.5)

Strain can be transformed as:







εx

εy

1

2

γxy







=











cos2θ sin2θ −2sinθcosθ

sin2θ cos2θ 2sinθcosθ

sinθcosθ −sinθcosθ cos2

θ − sin2

θ

















ε1

ε2

1

2

γ12







(4.6)

108
Chapter 4. CAI Analysis Using Existing Models

The transformed reduced compliance matrix is:







ε1

ε2

γ12







=











S ̄

11 S ̄12 S ̄16

S ̄

12 S ̄22 S ̄26

S ̄

16 S ̄26 S ̄66

















σ1

σ2

τ12







(4.7)

Where if n = cos θ and m = sin θ, then:

S ̄

11 = S11m4 + (2S12 + S66) n

2m2 + S22n4

S ̄

12 = (S11 + S22 − S66) n

2m2 + S12 (n4 + m4

)

S ̄

16 = (2S11 − S12 − S66) nm3 + (2S22 − 2S12 − S66) n

3m

S ̄

22 = S11n

4 + (2S12 + S66) n2m2 + S22m4

S ̄

26 = (2S11 − 2S12 − S66) n

3m − (2S22 − 2S12 − S66) nm3

S ̄

66 = 2 (2S11 + 2S22 − 4S12 − S66) n

2m2 + S66 (n4 + m4

)

The transformed reduced stiffness matrix is:







σ1

σ2

τ12







=











C ̄

11 C ̄12 C ̄16

C ̄

12 C ̄22 C ̄26

C ̄

16 C ̄26 C ̄66

















ε1

ε2

γ12







(4.8)

Where,

C ̄

11 = C11m4 + (2C12 + C66) n

2m2 + C22n4

C ̄

12 = (C11 + C22 − C66) n

2m2 + C12 (n4 + m4

)

C ̄

16 = (2C11 − C12 − C66) nm3 + (2C22 − 2C12 − C66) n

3m

C ̄

22 = C11n

4 + (2C12 + C66) n2m2 + C22m4

C ̄

26 = (2C11 − 2C12 − C66) n

3m − (2C22 − 2C12 − C66) nm3

C ̄

66 = 2 (2C11 + 2C22 − 4C12 − C66) n

2m2 + C66 (n4 + m4

)

In various plate theories, including those used to construct finite elements representing

composite laminates, the response of the material is defined in terms of a reference surface.

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Chapter 4. CAI Analysis Using Existing Models

In classical laminate theory, the composite laminate consisting of the layers of stacked plies

defined above is defined about its midsurface. The response of the material to the deformation is a direct result of Kirchhoff’s hypothesis, which states that a transverse line drawn

through plate straight and perpendicular to the reference surface will remain straight and

perpendicular to the reference surface during deformation and is inextensible. As a result if

the thickness of the laminate is defined as H and the z is defined as the distance from the

midplane, then stress resultants for deformation applied to the laminate can be defined as:

Nx ≡

H/2

Z

−H/2

σxdz

Ny ≡

H/2

Z

−H/2

σydz (4.9)

Nxy ≡

H/2

Z

−H/2

τxydz

Also, moment resultants for the laminate can be defined as:

Mx ≡

H/2

Z

−H/2

σxzdz

My ≡

H/2

Z

−H/2

σyzdz (4.10)

Mxy ≡

H/2

Z

−H/2

τxyzdz

The shear strains of material points within the composite laminate plate are defined

110
Chapter 4. CAI Analysis Using Existing Models

by the extensional and shear strains of the midsurface as:

εx(x, y, z) = ε

o

x

(x, y) + zκo

x

(x, y)

=

∂uo(x, y)

∂x + z



−

∂

2wo

(x, y)

∂x2



εy(x, y, z) = ε

o

y

(x, y) + zκo

y

(x, y)

=

∂vo(x, y)

∂y + z



−

∂

2wo

(x, y)

∂y2



(4.11)

γxy(x, y, z) = γ

o

xy(x, y) + zκo

xy(x, y)

=



∂vo(x, y)

∂x +

∂uo(x, y)

∂y 

+ z



−

∂

2wo

(x, y)

∂x∂y 

The stress and moment resultants are related to the deformation of the composite

plate by the ABD matrix, given in Eq. 4.12, where the Aij , Bij , and Dij terms are defined

in terms of the reduced transformed stiffness matrix components of each layer from Eq. 4.8

and the distance of the top and bottom of each ply to the midsurface of the laminate.







Nx

Ny

Nxy

Mx

My

Mxy







=





























A11 A12 A16 B11 B12 B16

A12 A22 A26 B12 B22 B26

A16 A26 A66 B16 B26 B66

B11 B12 B16 D11 D12 D16

B12 B22 B26 D12 D22 D26

B16 B26 B66 D16 D26 D66



































ε

o

x

ε

o

y

γ

o

xy

κ

o

x

κ

o

y

κ

o

xy







(4.12)

Where

Aij =

Pn

k=1 C ̄

ij

(k)

(zk − zk−1)

Bij =

1

2

Pn

k=1 C ̄

ij

(k)



z

2

k − z

2

k−1



Dij =

1

3

Pn

k=1 C ̄

ij

(k)



z

3

k − z

3

k−1



Hyer [87] presented further details concerning classical plate theory including incorporation of the effects of deformation due to moisture or thermal loads, and some classical

111
Chapter 4. CAI Analysis Using Existing Models

composite laminate failure theories. Kapania, Soliman, Vasudeva, et al. [88] discussed the

important additions of FSDT and higher order shear deformation theory (HSDT) to CPT.

Whereas classical plate theory adheres strictly to the tenants of Kirchhoff’s theory, in FSDT

the normal to the midplanes remain straight during deformation but not necessarily normal leading to additional degrees of freedom considered when evaluating the cross-sectional

response in a laminate. In HSDT, the in-plane displacements are assumed to have a cubic distribution and further additional terms are needed to define laminate strain. Also,

transverse shear in the laminate can be calculated with greater accuracy.

4.1.2 Composite Laminates in Finite Element Analysis

In ABAQUS [73] a user has two options for defining the behavior of a shell section. First, a

general shell section can be used which defines the behavior in terms of the section moments

and forces, such as in Eq. 4.12. However, stresses and strains are not available for output

when the section properties are given. A second method allows the cross-sectional behavior

of the plate to be found by numerical integration through the shell thickness. The ABAQUS

User Manual [89] recommends the latter method when non-linear response is expected during

analyses.

In each finite element analysis (FEA) performed in the present study, the laminates

are defined with composite sections where each layer has individually specified material

properties, thickness, and orientation. The cross-sectional behavior which results in the

generalized stresses Nij and Mij is defined by integration either by Simpson’s rule or Gauss

quadrature. Simpson’s rule with three points per layer is the default in ABAQUS analyses

and is used in the current work except where noted otherwise. In general, Gauss quadrature

is more accurate than the Simpson’s rule for the same number of integration points and

could be used to increase accuracy without a computational time and storage space penalty,

if necessary. Numerical integration can be done at the beginning of the analysis or during

each analysis step. Additional information can be found in the ABAQUS Theory Manual

[90].

112
Chapter 4. CAI Analysis Using Existing Models

Two types of three-dimensional shell elements are available in ABAQUS: conventional

and continuum. Conventional shell elements discretize the reference surface of the plate or

composite laminate (or sandwich panel facesheets in the current research). The thickness

of the element is defined by the section definition, and the nodes have displacement and

rotational degrees of freedom. On the other hand, continuum shell elements discretize the

entire body and the thickness is determined by nodal geometry. Only the displacement

degrees of freedom are considered, as in other solid continuum elements, but the kinematic

and constitutive behaviors are defined as in any of the shell theories.

Both conventional and continuum three-dimensional shell elements in ABAQUS use a

displacement field which measures bending strains approximately equivalent to those in the

Koiter-Sanders thin shell theory [91]. A principal assumption is that the displacement fields

normal to the shell reference surface will not produce bending moments and the bending response of the shell neglects the effects of transverse shear and normal strain. The equilibrium

relationships of this shell theory are derived from the Principle of Virtual Work. The contribution of the stresses to the virtual work done on the shell in terms of the membrane forces,

Nij , and bending moments, Mij , the extensional strain increments along the midplane, δε ̄ij ,

and the membrane curvature increment, δκ ̄ij , can be defined with respect to the planar area

of the shell as:

δΠ = Z

Area



Nijδεo

ij + Mijδκij

dArea (4.13)

113
Chapter 4. CAI Analysis Using Existing Models

The equillibrium equations, as originally proposed by Sanders [91] are:

∂α2N11

∂ξ1

+

∂α1N ̄

12

∂ξ2

+

∂α1

∂ξ2

N ̄

12 −

∂α2

∂ξ1

N22 +

α1α2

R1

V1 . . .

+

α1

2

∂

∂ξ2

 1

R1

−

1

R2



M ̄

12

= 0

∂α2N ̄

12

∂ξ1

+

∂α1N22

∂ξ2

+

∂α2

∂ξ1

N ̄

12 −

∂α1

∂ξ2

N11 +

α1α2

R2

V2 . . .

+

α2

2

∂

∂ξ1

 1

R2

−

1

R1



M ̄

12

= 0 (4.14)

∂α2V1

∂ξ1

+

∂α1V2

∂ξ2

−



N11

R1

−

N22

R2



α1α2 = 0

∂α2M11

∂ξ1

+

∂α1M ̄

12

∂ξ2

+

∂α1

∂ξ2

M ̄

12 −

∂α2

∂ξ1

M22 − α1α2V1 = 0

∂α2M ̄

12

∂ξ1

+

∂α1M22

∂ξ2

+

∂α2

∂ξ1

M ̄

12 −

∂α1

∂ξ2

M11 − α1α2V2 = 0

Here, αi are the coefficients of the displacement of the reference surface as defined by

Sanders [91], ξi are the coordinates along the reference surface, Vi are the transverse stress

resultants, Ri are the principal radii of curvature and the strains are defined as:

11 =

1

α1

∂U1

∂ξ1

+

1

α1α2

∂α1

∂ξ1

U2 +

U3

R1

22 =

1

α2

∂U2

∂ξ2

+

1

α1α2

∂α2

∂ξ1

U1 +

U3

R2

12 =

1

2α1α2



α2

∂U2

∂ξ1

+ α1

∂U1

∂ξ2

−

∂α1

∂ξ2

U1 −

∂α2

∂ξ1

U2



κ11 =

1

α1

∂Uφ1

∂ξ1

+

1

α1α2

∂α1

∂ξ1

φ2 (4.15)

κ22 =

1

α2

∂φ2

∂ξ2

+

1

α1α2

∂α2

∂ξ1

φ1

κ12 =

1

2α1α2

. . .



α2

∂Uφ2

∂ξ1

+ α1

∂φ1

∂ξ2

−

∂α1

∂ξ2

φ1 −

∂α2

∂ξ1

φ2 +

1

2



1

R2

−

1

R1

 ∂a2U2

∂ξ1

−

∂a1U1

∂ξ2



114
Chapter 4. CAI Analysis Using Existing Models

Here, Ui and Φi are the displacements in the i-th direction and rotations about the

i-th Cartesian axes, respectively. The i-th direction or axes refers to the x-, y- or z- global

Cartesian axes, which may also be represented by a 1, 2 or 3, respectively.

The transverse shear stiffness is also considered in the ABAQUS implementation of

shell theory. The transverse shear stress in the ith layer due to a shear force, Vx, where z

is the distance from the reference surface and Bxi is a component of a matrix operator, is

defined as:

τ

i

xz =



B

i

x1

(z − zi) −



1

2



z

2 − z2

i



− zx0 (z − zi)



B

i

x2 + B

i

x0



Vx (4.16)

The subscripted values of z indicate integration points through the shell thickness, or

are defined below, where the values for Bi

x0

are also defined as:

B

i

x0 =

X

i−1

j=1

tj



B

j

x1 −



1

2

(zj+1 + zj ) − zx0



B

j

x2



(4.17)

zx0 =

Pn

i=1 ti



1

2

(zi+1 + zi) Bi

x2 − Bi

x1



Pn

i=1 tiBi

x2

The shear flexibility FS of the composite section is found by equating the shear strain

energy of the section to the result found by integrating the above expression for the shear

stress through the section thickness as follows in Eq. 4.18 where FSiis the shear flexibility

defined for the ith layer.

1

2

j

Vx Vy

k

[FS]







Vx

Vy







=

1

2

Xn

i=1

Z

zi+1

Zi

j

τxz τyz k

[FSi]







τxz

τyz







dz (4.18)

The transverse shear stiffness, τ

i

xz, are calculated based on the constitutive properties

of the material. ABAQUS can determine these automatically based on the shell section

definition. Hourglass stiffness is also required for reduced integration elements whose section

115
Chapter 4. CAI Analysis Using Existing Models

stiffness is not integrated at enough points to keep the element from displacing in in-plane

hourglass modes. The in-plane hourglass modes are defined with respect to the undeformed

coordinates on the reference surface, ξ, the deformed coordinates, Ξ, the hourglass modes,

γ

i

, and the nodal coordinates, Xi

i

, as:

zi =

∂ξ

∂Xi

• ξ

iΓi −

∂Ξ

∂Xi

• Ξ

iΓi

(4.19)

Here, the hourglass modes are defined as:

Γ

1 =

1

Ψ



X

2

1



X

3

2 − X

4

2



+ X

3

1



X

4

2 − X

2

2



+ X

4

1



X

2

2 − X

3

2



Γ

2 =

1

Ψ



X

3

1



X

1

2 − X

4

2



+ X

4

1



X

3

2 − X

1

2



+ X

1

1



X

4

2 − X

3

2



Γ

3 =

1

Ψ



X

4

1



X

1

2 − X

2

2



+ X

1

1



X

2

2 − X

4

2



+ X

2

1



X

4

2 − X

1

2

 (4.20)

Γ

4 =

1

Ψ



X

1

1



X

3

2 − X

2

2



+ X

2

1



X

1

2 − X

3

2



+ X

3

1



X

2

2 − X

1

2



Ψ = 1

2

X

3

1 − X

1

1

 X

4

2 − X

2

2



+



X

1

1 − X

4

1

 X

3

2 − X

1

2



The hourglass stiffness is then chosen as in Eq. 4.21 where G is the shear modulus

and rF is a small numeric coefficient chosen as 0.005 in ABAQUS/Standard [90].

Kh = (rFG)

∂Ni

∂Xj

∂Ni

∂Xj

hA (4.21)

4.1.3 Honeycomb Core as an Orthotropic Continuum

A second type of modeling must be considered for detailed analysis of composite sandwich

panels. Gibson and Ashby [55] define a hexagonal cell honeycomb core as a two dimensional cellular structure with a repeating geometry encapsulating six sided pores. Man-made

honeycombs are readily available and easily found in many composite structures made from

116
Chapter 4. CAI Analysis Using Existing Models

isotropic materials, such as aluminum, and transversely isotropic materials such as Nomex.

Analysis of this type of structure, analytically, usually involves the characterization of inplane properties (width and length directions, in the plane of the cellular structure) separately

from out-of-plane properties (thickness direction, in the direction of the height of the cell

walls). For in-plane loads the cell walls typically bend elastically until a critical load and then

they fail by elastic buckling, plastic yielding, creep, or brittle fracture. The nature of cell

wall collapse is determined by the material the honeycomb is made from. An out-of-plane

loading of the sandwich panel results in elastic extension or compression of the cell walls

before failure, and typically the stiffnesses and strength of the structure are much higher in

this direction. If loading continues beyond the initial failure either during out-of-plane or

in-plane loading, until the cell walls touch, densification of the core begins to occur and the

modulus of the response increases drastically with further loading.

The linear elastic deformation of the honeycomb structure can be described by considering the bending response of the cell walls. Consider the cellular geometry described in

the x1−x2 plane, shown in Fig. 4.1. The following relations were given by Gibson and Ashby

[55] for the in-plane response of the Nomex honeycomb. By assuming the wall material is

isotropic and has modulus, Es, and the thickness of each cell wall, t, is constant, the effective

modulus, E

∗

1

, representing the stiffness of the structure in response to a uniaxial load in the

x1 direction is given by Eq. 4.22. The modulus, E

∗

2

, is given by Eq. 4.23 and the in-plane

poisson’s ratios, υ12 and υ21, are given by Eq. 4.24 and 4.25, respectively. The effective

in-plane shear modulus can be determined using Eq. 4.26.

E

∗

1

ES

=



t

l

3

cos θ

(h/l + sin θ) sin2θ

(4.22)

E

∗

2

ES

=



t

l

3

(h/l + sin θ)

cos3 θ

(4.23)

υ

∗

12 = −

2

1

=

cos2θ

(h/l + sin θ) sin θ

(4.24)

117
Chapter 4. CAI Analysis Using Existing Models

υ

∗

21 = −

1

2

=

(h/l + sinθ) sin θ

cos2 θ

(4.25)

G∗

12

ES

=



t

l

3

(h/l + sin θ)

(h/l)

2

(1 + 2h/l) cos θ

(4.26)

Figure 4.1: Cellular in-plane geometry of hexagonal cell honeycomb core.

A more general method of obtaining effective material properties using energy based

methods was described by Hohe et al. first for triangular cell structures [56], than for quadrilateral and hexagonal cell structures [57], and finally for general cellular structures [58]. The

authors showed that for a volume element of cellular core material and a representative

volume element of a homogenized material to behave identically on a mesoscopic level, the

internal strain energy due to a given volumetric deformation must be equal for both repre118
Chapter 4. CAI Analysis Using Existing Models

sentative elements as:

Z

V ol

(σijdεij ) dV ol =

Z

V ol



σ

∗

ijdε∗

ij

dV ol (4.27)

In general, man-made hexagonal cell honeycomb structures often do not have constant

wall thickness for each cell wall. This can be due to material and construction flaws, but

also is simply typical of the manufacturing process. Also, for honeycombs made of fibrous

materials, such as Nomex, the source material is not isotropic, so a single elastic modulus,

ES, cannot be assumed. A more typical honeycomb core cell type was analyzed by Chen

and Ozaki [59] where the cell walls oriented parallel to the ribbon direction have double the

thickness. They expanded on the results of Eq. 4.23 using this method and validated their

model with a detailed FEM prediction.

Detailed FEM is one possible method for modeling the honeycomb core in studies such

as the present work. In fact, recently Czabaj et al [51] published a CAI prediction model

using ABAQUS shell elements to explicitly model a geometrically correct representation of

the cellular structure of the honeycomb core. However, modeling of the explicit cellular

honeycomb core geometry is time consuming and the subsequent FEA is computationally

expensive. The authors improved the efficiency of their model significantly by only including

the detailed FEM in the location of the sandwich panel model where impact loading and

failure would be modeled. In the rest of their model, they take advantage of the result of Eq.

4.27 to model the honeycomb core as a homogenous orthotropic solid with constitutive response as in Eq. 4.1. Other authors have recognized the efficiency of this modeling technique

and have used homogenized solid core elements in FEM with good results [12] [52].

The finite element representation of the total potential energy of an element for static

119
Chapter 4. CAI Analysis Using Existing Models

analysis of a solid mechanics problem is given by:

Π

(e)

p =

1

2

Z Z Z

V (e)

*

U

(e)

T

[B]

T

[D][B]

*

U

(e)

dV −

Z Z Z

V (e)

*

U

(e)

T

[B]

T

[D]

*

ε 0dV

−

Z Z

S

(e)

1

*

U

(e)

T

[N]

T

*

FdS1 −

Z Z Z

V (e)

*

U

(e)

T

[N]

T

*

FbdV (4.28)

Here,

*

U

(e)

is the displacement vector, *ε 0, is the initial strain vector,

*

F, are the

distributed surface forces or tractions, and

*

Fb is the body force vector, and [D] is the element

stiffness matrix. The matrix [B] is defined as:

[B] =





























∂

∂x 0 0

0

∂

∂y 0

0 0 ∂

∂z

∂

∂y

∂

∂x 0

0

∂

∂z

∂

∂y

∂

∂z 0

∂

∂x





























[N] (4.29)

The matrix of isoparimetric shape functions [N] for an 8-node solid element like the

one used with ABAQUS for the current work, can be written as:

[N(o, p, q)] = 1

8

Θ + 1

4

oΛ1 +

1

4

pΛ2 +

1

4

qΛ3

+

1

2

oqΓ1 +

1

2

pqΓ1 +

1

2

oqΓ2 +

1

2

mpΓ3 +

1

2

opqΓ4 (4.30)

Where o, p, and q, are the local Cartesian coordinates defining the node points, and Θ,

Λi, and Γi are vectors representing deformation modes of the element. The last four vectors,

Γi, represent the hourglass modes which must be accounted for by an hourglass stiffness for

120
Chapter 4. CAI Analysis Using Existing Models

reduced integration elements in the same manner as described for shell elements previously.

4.1.4 Honeycomb Core Non-Linear Out-of-Plane Response

The challenge of accurately representing the honeycomb core response as a homogenous material is including the out-of-plane response, specifically the non-linear compression response.

By consideration of the honeycomb cell geometry shown in Fig. 4.1, Gibson and Ashby [55]

gave the initial linear elastic out-of-plane response for regular hexagons with equal wall thicknesses defined as the out-of-plane Young’s modulus, Poisson’s ratios and the shear modulus

(with respect to the honeycomb material’s shear modulus, GS) to be:

E

∗

3

ES

=



h/l + 2

2(h/l + sin θ) cos θ



t

l

(4.31)

υ

∗

31 = υ

∗

13 = υS (4.32)

G∗

13

GS

=

G∗

23

GS

=

cos θ

h/l + sin θ



t

l



(4.33)

Note that in general the shear moduli, Gij , are not equal. During compressive loading

at the critical load the response of the honeycomb is no longer linear. Gibson [55] noted that

the non-linear response can be due to elastic buckling of the cell walls, plastic collapse of the

cell walls or brittle fracture. Analytically, this has been investigated with limited success;

however, it was shown in Chapter 1 in review of the relevant literature that several researchers

have described the elastic buckling and plastic collapse of cell walls using geometrically correct

FEM representations of the honeycomb core structure [62] [63] [64] [65] with good results.

In these types of FEA, the response of the honeycomb to a flatwise core crushing load is

simulated. The open ends of the cellular structure are fixed as if they were bonded to a

facesheet. The major purpose of the simulations is to predict the core crush strength for a

given honeycomb configuration, and in some cases the post-failure response.

In the present study, the linear elastic out-of-plane modulus and the core crush

strength are defined by experimentally determined constants. The out-of-plane response

121
Chapter 4. CAI Analysis Using Existing Models

of the core is defined as an idealization of a core crush test, as shown in Fig. 4.2. The linear

elastic response and initial post-crushing response are modeled. The densification process is

ignored as the deformation response of the core during CAI modeling is not expected to be

enough to warrant its modeling, as observed from the experimental results. It was explained

in review of the pertinent literature in Chapter 1 that this type of homogenized representation of the honeycomb core in CAI modeling of sandwich panels is well accepted and has

been employed by various authors [42] - [43] [46] [47] [49] [52].

Figure 4.2: Solid element core crush constitutive model.

4.2 FEM with Spring Element Core

Ratcliffe and Jackson [46] as well as Castani ́e et al. [47] considered finite element models using

simple spring elements to represent the honeycomb core in impact damage sandwich panels

undergoing compressive loading. Ratcliffe and Jackson provided helpful insight into the

spring element core model they had developed and encouraged its use in the early stage of the

current research. The following section explains their model and analysis that was conducted

to predict the response of PXX series coupons during CAI tests, as a demonstration.

122
Chapter 4. CAI Analysis Using Existing Models

4.2.1 Explanation of Model Components and Inputs

The finite element model developed by Ratcliffe and Jackson was for use with the commercial

finite element code ABAQUS/Standard [73]. Using symmetry boundary conditions in the

sandwich panel width (x-direction) and loading (y-) direction, only one quarter of a CAI

coupon was modeled. Furthermore, only the front, damaged facesheet was included in the

model. The nodes of the honeycomb core elements which should be attached to a rear

facesheet are instead fixed from moving. It was assumed that the CAI failure of the sandwich

panel does not depend on the response of the rear facesheet. Load is prescribed to the

sandwich panel using a displacement boundary condition. The resulting force at each of the

load end facesheet node points is recorded for determining load vs. displacement response as

well as the failure load for each analysis. Also, a section of potting is included in the model to

simulate an actual CAI coupon closely. In this region, no core elements are included; instead

the facesheet node points are fixed in the out-of-plane z-direction. The spring element core

model is shown in Fig. 4.3.

Figure 4.3: Spring element core sandwich panel CAI FEM with boundary conditions.

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Chapter 4. CAI Analysis Using Existing Models

The facesheet is represented by a mesh of S4 conventional shell elements with four

nodes on each element. The mesh is generated in a rectangular grid fashion in a size of

80x80 elements for the 3 in. by 3 in. region which is one quarter of a PXX series sandwich

panel. A mesh convergence study is not presented with the present work since this model was

developed by Ratcliffe and Jackson [46]. The shell section is defined as a composite laminate

of PXX series type construction, which was presented in Chapter 2 of the current work. The

facesheet material’s orthotropic engineering constants which define the constitutive response

of each layer of the laminate were defined as in Table 4.1.

Table 4.1: Spring core element FEM analysis: engineering constants used for layers of PXX series

sandwich panel facesheets.

The core is represented by a computationally efficient mesh of ABAQUS SP RINGA

spring elements. The springs define the interaction between one node of the facesheet and

one node fixed where the rear facesheet would be at a distance equal to the thickness of the

honeycomb core, in this case, 1 in. The spring definition used is an idealized representation

of the response of a Nomex honeycomb core during a flatwise compression test. SP RINGA

elements can be defined with a non-linear response using force and displacement data. The

force in each spring element per unit planar area (in the x-y plane) is equivalent to the

z-direction average stress in the equivalent area of Nomex honeycomb core. For example,

for the geometry and mesh described, each spring element represents 0.00141 in.2 of the

honeycomb core. The initial linear elastic modulus of the 3 lb. per cu. ft. density core used

in the PXX panels is 20 ksi and the crush strength is 270 psi. The end of the linear elastic

region of the spring response (corresponding to core crush failure) would then be stress times

area equals 0.380 lbs. at 0.0135 in. of compression inducing displacement. The idealized

core crush response used to define the spring elements is shown in Fig. 4.4.

Initial impact damage to the sandwich panel is included in the model only as a dimple

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Chapter 4. CAI Analysis Using Existing Models

Figure 4.4: Spring element core crush constitutive model.

in the facesheet of the approximate shape of the residual dent corresponding to the PXX

series coupon that is being modeled. The indentation is defined by the maximum dent depth

and diameter of the appropriate panel, as reported in the experimental results of Chapter

2 of the current work. Panels P11, P04, P06, and P08 were chosen to demonstrate the

capabilities of the spring element core model, which covers each of the energy levels that

PXX series CAI coupons were impacted at (0.5, 1.0, 1.5, and 2.0 ft-lbs., respectively). Initial

core damage from low-velocity impact can be included in the model by modification of the

non-linear spring element response in a defined region of the model. The response of damaged

core spring elements is shown in Fig. 4.4. In their model analysis, Ratcliffe and Jackson [46]

found that inclusion of core damage resulted in a reduction in the predicted failure strength

of the model. McQuigg et al [48] later found that inclusion of core damage resulted in a more

gradual “rounded” failure which appeared in the force vs. displacement results for a given

analysis. Since, the typical force vs. displacement results of the model (shown in Fig. 4.5)

were more representative of experimental results, (shown in Chapter 2), core damage was

not included in the analysis used to demonstrate the spring element core model. The effect

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Chapter 4. CAI Analysis Using Existing Models

of including core damage to approximate the region of impact damaged core beneath the

residual dent is shown in Fig. 4.5. Additionally, Ratcliffe and Jackson [46] used an tensile

core spring element stiffness an order of magnitude greater than the compressive stiffness in

order to control unrealistic out-of-plane deformation.

Figure 4.5: Spring element core FEM results: Typical reaction force vs. applied displacement with

and without effect of including initial core damage.

4.2.2 CAI Analysis Results for Spring Element Core Model

Four test cases were used to demonstrate the capability of the spring core model. Analysis

were performed on the CAI response of sandwich panels with geometry and materials corresponding to PXX series materials with damage corresponding to 0.5, 1.0, 1.5, and 2.0 ft-lb.

impact energy as determined in measurements and observations made on the P11, P04, P06,

and P08 coupons, respectively. Brief analysis results are presented here. The model correctly predicts indentation propagation failure growth in PXX series sandwich panels. Since

no facesheet failure theory is included in the model, this is the only type of failure mode

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Chapter 4. CAI Analysis Using Existing Models

the model is capable of predicting. The model results typically appear as shown in Fig. 4.6

after failure has occurred. The colored contours in Fig. 4.6 represent out-of-plane displacement. Maximum displacement is slightly more than a tenth of an inch, which is typical of

experimental results.

Figure 4.6: Sample spring element core FEM results: indentation propagation failure mode with

out-of-plane displacement indicated by colored contours (blue indicates maximum negative displacement).

The force vs. displacement results for each test case are shown in Fig. 4.7. Failure is

indicated by a sudden drop in reaction force, the same as in the experimental results. The

rounded top of the force vs. displacement results which depicts a more gradual failure than

what is expected from experimental results presents itself again for the test cases with the

larger initial dents (P06 and P08). This trend suggests the model may provide decreasing

accuracy in analysis of CAI coupons with increasing residual dent size.

Analysis results using the spring element core model for failure load, far field failure

stress, and far field failure strain are shown in Table 4.2. Select experimental results are

repeated from Chapter 2 of the present work for comparison. The analysis results collected

using the spring element core model compare favorably to the experimental results. The

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Chapter 4. CAI Analysis Using Existing Models

Figure 4.7: Sample spring element core FEM results: reaction force vs applied displacement for

sample analyses on PXX series panels.

results compare best for the middle of the damage range considered and the analysis results

are less accurate for the least damaged case (P11) and the most damaged case (P08). Damage

not included in this model, such as initial core damage, initial facesheet damage, and facesheet

failure during CAI response would likely reduce the failure load, stress, and strain predicted

by this model. In all cases, this would reduce the accuracy of the predicted results when

compared to the experimental findings. Also, for higher impact energy levels the resulting

impact damage that is neglected would be more significant. This again suggests that this

model would be less accurate for more highly damaged cases.

Table 4.2: Spring core element FEM results: failure metrics.

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Chapter 4. CAI Analysis Using Existing Models

Through the experience of using the spring element core model for analysis of CAI

of honeycomb core sandwich panels, the attractiveness of the model as a design tool was

highlighted. The main benefits of the model are its simplicity, its ease of implementation

and the computational efficiency of the model. A design engineer could very quickly use this

type of model to assess a baseline reduced strength for a lightly damaged sandwich panel,

with confidence, as long as the expected damage was minimal. The computational efficiency

of the model is much better than an FEM with a continuum representation of the core using

solid elements since the degrees of freedom in the spring element core model are much less.

4.3 FEM with Solid Orthotropic Element Core

The homogenization of the cellular honeycomb core structures into an equivalent solid continuum greatly simplifies the process of modeling composite sandwich panels while still giving

the engineer an ability to model core response with high fidelity. Authors that have used

this method for modeling of CAI response of the honeycomb core include Shyprykevich et

al [12], Hwang and Lacy [49] [50], Czabaj et al [51], Xie and Vizzini [52] [53], and Schubel

[54]. In the present study a FEM was developed using a solid element core. A simple version

of this model was used to demonstrate the capability of previous models to capture benefits

and challenges of using this type of model. A brief explanation of this model and a limited

selection of results are discussed in the present section. A full discussion of this model with

the implementation of new techniques for CAI modeling is presented in Chapter 5.

4.3.1 Explanation of Model Components and Inputs

A simple solid element core model was developed here for analysis of CAI sandwich panel

coupons. The commercial FEA code ABAQUS/Standard [73] was used in this analysis.

Symmetry was employed to reduce the degrees of freedom of the model. From symmetry

in both the sandwich panel width (x-direction) and loading (y-direction) directions, only

one quarter of a CAI coupon was necessary. Both facesheets were included in the model

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Chapter 4. CAI Analysis Using Existing Models

and were free to displace as they would with the boundary conditions imposed on them in

experimental CAI tests. This is possible because of the shear stiffness given to the sandwich

panel by the honeycomb core which is included in the solid element core definition (i.e. it

is not necessary to fix the rear facesheet). Although failure is expected in only the failed

facesheet, the inclusion of both facesheets in the model allows for the comparison of the

loading of both facesheets throughout the analysis. Also, the shear stiffness of the core

may play a role in the indentation propagation failure mode. In either case, the fidelity

of the model is improved. Load is prescribed to the model through the use of an applied

displacement boundary condition and the resulting force is recorded at each node point at

the appropriate side of the model. A section of potting is not included in this model, but

the end nodes are fixed in the z-direction (out-of-plane direction) to simulate the effect of

the applied potting and end clamping. Other effects of potting to the panel response are

assumed negligible. The solid element core model is shown for reference in Fig. 4.8.

Figure 4.8: Solid element core sandwich panel CAI FEM with boundary conditions.

The continuum shell element, SC8R, was chosen to mesh the facesheets of the sand130
Chapter 4. CAI Analysis Using Existing Models

wich panel. This element is an 8-node quadrilateral general-purpose continuum shell, with

reduced integration and finite membrane strain formulation. Hourglass control is provided

though the appropriate stiffness is required. An 80x80x1 element grid style mesh was used

for each facesheet for the results obtained in the current chapter. The honeycomb core was

modeled using the solid three dimensional element, C3D8R. This element is an 8-node linear

brick featuring a reduced integration formulation. Hourglass control is used. The core region

was modeled using an 80x80x8 element grid mesh. The model used for the analysis discussed

in the present chapter is similar to the new model which will be further developed in Chapter

5. More detail will be provided concerning the mesh pattern and a full mesh convergence

study will be presented.

The attributes of the facesheets and core of the sandwich panel model are defined as

follows. The facesheets are defined as a composite laminate with two layers of GFRP woven

fiber material to simulate the material system used in the PXX series coupons presented

in Chapter 2. The engineering constants which define each transversely isotropic layer of

the facesheet laminate are in Table 4.2. The orthotropic material response of the continuum

represented 3 lb. per cu. ft. Nomex honeycomb core was defined using the material constants

in Table 4.3. The non-linear crush response in the z-direction was approximated by the

idealized core crush response shown in Fig. 4.2. The linear elastic orthotropic response as

well as the crushing failure of the core was implemented using the ABAQUS user subroutine,

UMAT as follows. In the z-direction, the compression response of the core elements is linear

elastic with a Young’s modulus of 20 ksi until the compressive strength which is 270 psi for this

material. Failure is determined to have occurred when the corresponding compressive strain,

0.0135 in/in has been reached. At this point the resultant stress from further deformation on

the element is reduced to 60% of the stress at failure in all six components of the stress tensor

for the material point. This value is chosen to reflect the volume averaged stress resultant

from a damaged region of core as determined by experimental core crush response found in

literature [46]. Also, the three extensional moduli and the three shear moduli are reduced to

zero.

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Chapter 4. CAI Analysis Using Existing Models

Table 4.3: Sample solid core element FEM analysis: engineering constants used for orthotropic

continuum representation of Nomex honeycomb core.

Several types of impact damage can be included in the solid element core model. An

initial indentation is included which is defined by the maximum dent depth, hmax, and dent

diameter, d, found in experimental results on the corresponding coupon to be modeled. The

contour of the dent is defined using Eq. (4.34) where xn and yn are the Cartesian coordinates

of the node location in the damaged area on the surface of the dent. The impact damage

dent is assumed perfectly circular in area.

zdent =

−hmax

2

 

1 + cos 

2π

p

xn

2 + yn2

d

!! (4.34)

Other types of damage which can be included in the solid element core model include

degradation of extensional and shear moduli which define the facesheet and core materials

included in the model. The purpose of this reduction is to simulate the effects of various

types of impact damage, as discussed in Chapter 1, and shown in Chapters 2 and 3. Types

of impact damage to the core include buckling and tearing of the honeycomb cell walls.

Facesheet damage resulting from low velocity impact can include interlaminar delaminations,

intralaminar matrix cracks, and fiber cracks. The reduction of stiffness in the areas of damage

is estimated from the severity of damage found by experimental observation. This will be

discussed further in Chapter 5. Inclusion of this type of initial impact damage in the model

is defined by damaged core area diameter, damaged core area maximum depth, damaged

core area stiffness reduction, damaged facesheet area diameter and damaged facesheet area

stiffness reduction. The solid core model performs well with inclusion of each of these types

of damage. An example of the resulting force vs. applied displacement curve for a typical

PXX series coupon where failure is determined by a sudden drop in resulting force is shown

in Fig. 4.9.

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Chapter 4. CAI Analysis Using Existing Models

Figure 4.9: Sample solid element core FEM results: typical reaction force vs. applied displacement.

The elements where stiffness reduction of the damaged facesheets and damaged core

was included are shown in Fig. 4.10 where the damaged elements are highlighted. For this

particular case, the maximum damaged core depth was 0.25 in.; the damaged core area

diameter was equal to the dent diameter, the damaged core stiffness reduction was 40%; the

damaged facesheet area was 30% of the dent diameter and the stiffness reduction was 40%.

Figure 4.10: Damaged core elements (left) and damaged facesheet elements (right) in the solid

element core model example.

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Chapter 4. CAI Analysis Using Existing Models

4.3.2 CAI Analysis Results for Solid Element Core Model

PXX series coupons P11, P04, P06, and P08 were also used for a brief analysis to demonstrate

the results of a solid element core CAI model. These coupons had damage corresponding to

impacts at 0.5, 1.0, 1.5, and 1.5 ft-lbs., respectively, and appropriate inputs were made to

the model based on the experimental results obtained in observation of these panels which

was presented in Chapter 2. The inputs used in this analysis are shown in Table 4.4. Core

damage was included in the FEM. The core damage input for damage area diameter is given

as a percentage of the geometric dent diameter. The damaged core region depth and stiffness

reduction (as a percentage of the pristine properties) was assumed constant for all panels.

The analysis was done with and without facesheet damage. The topic of including facesheet

damage in the model has not been well covered in the literature, although the technique of

reducing constitutive properties of the facesheet materials in the simulated damage region

has been used. A selection of facesheet damage was included for each panel to compare to

the results found without using facesheet damage. A full study of the inclusion of facesheet

damage in the new CAI model presented in the present work is found in Chapter 5, although

the fidelity of the new model has been greatly increased from the continuum core model

discussed in the present chapter.

Table 4.4: Sample solid core element FEM analyses: inputs used for demonstration.

The reaction force vs. applied displacement results for the first four analyses done

without facesheet damage is shown in Fig. 4.11. The response of each CAI coupon is

linear until failure, which is expected from experimental results. The full analysis results

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Chapter 4. CAI Analysis Using Existing Models

are shown in Table 4.5, including failure load, failure stress, and failure strain as well as the

expected experimental values. The results for analyses done without facesheet damage are

given the designation, PXX, and the results with facesheet damage are given the designation

PXXa. The analysis results presented here are only meant to be preliminary results used as

a demonstration of previously used modeling techniques for this type of analyses.

Figure 4.11: Sample solid element core FEM results: reaction force vs applied displacement, model

did not include simulated impact damage in the facesheets.

Table 4.5: Sample solid element core FEM results: failure metrics.

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Chapter 4. CAI Analysis Using Existing Models

A comparison of the modeling results with and without impact damage modeled in

the facesheets is shown in Fig. 4.12. Facesheet damage mostly had only a small effect on

the prediction made by the model, except for coupon P08, the panel with the most severe

reductions of facesheet properties in the damaged region. The predicted failure stress of the

panel actually increased for this case. This suggests that the lack of stiffness in the damaged

facesheet area actually delays the onset of indentation propagation, which is an interesting

result. It does make physical sense though, as during the initial compressive loading of the

panel, the initially indented area would displace compressively in-plane rather out-of-plane

into the core because the severe extensional stiffness reduction of the facesheet puts the

facesheet stiffness on the same order of magnitude as the core damage stiffness. The predicted

failure points for each of the panels is not as accurate when compared to experimental results

as the spring element core model presented earlier. However, the fidelity of the model has

been increased. It is expected that if the model were studied fully, the results would improve.

This work is done for the complete new model introduced in Chapter 5 which takes advantage

of new FEM techniques for this type of analysis.

Figure 4.12: Sample solid element core FEM results: failure stress vs. impact energy with (WFD)

and without simulated facesheet impact damage (NFD).

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Chapter 4. CAI Analysis Using Existing Models

4.4 Conclusions from CAI Analysis Using Existing

Models

In the present chapter, development of the proposed model began with a more in depth

consideration of the existing CAI models than was given in the literature review presented in

Chapter 1. First, the theory was presented which is relevant to the finite element modeling

techniques used to simulate the facesheets and core of the sandwich panels which are the

subject of the current research. This theory included an explanation of classical laminate

theory, as well as the development of the specific shell theory, Koiter-Sanders, implemented

in ABAQUS shell elements, which are used to simulate the facesheets in the proposed model.

The theory presented also included simple techniques for homogenization of the core based on

the structural geometry. In the present research, orthotropic material properties will be used

to represent a continuum response for the core using solid three-dimensional finite elements.

The formulation of these elements by total potential energy was shown. An explanation of

the idealization used to represent the core crush response of these elements was also given.

In the latter part of the present chapter, two examples of the existing FEM for analysis

of the CAI response of thin facesheet honeycomb core sandwich panels were shown. The

examples included a spring element core model, as first presented by Ratcliffe and Jackson

[46], and a solid element core model, which is similar to examples given in the literature

review in Chapter 1 [12] [52], but is able to effectively capture the full indentation propagation

failure. The types of elements used, the initial impact damage modeled, and the analysis

cases performed were explained for each of these models. The results of several analyses

performed were compared to experimental results from CAI tests of PXX series materials,

first reported in Chapter 2. The failure measures, such as stress and strain, compared well

for each model. However, it was shown how the spring element model seemed to misrepresent

the failure mode for the higher levels of damage and it is presumed that the model would be

ineffective for even higher levels of damage, such as those seen in 3PCF-XX and 6PCF-XX

series material tests, shown in Chapter 3. A full development of a solid element core model

137
Chapter 4. CAI Analysis Using Existing Models

with a progressive failure analysis for facesheet damage and increased impact damage fidelity

will be given treatment in Chapter 5, next.

138
Chapter 5

Development of a New Model for CAI

Analysis

In the previous chapter, development of a new finite element model (FEM) for analysis of

CAI failure in honeycomb core sandwich panels began with an overview of the related theory.

Later in that chapter, a solid element core FEM was briefly demonstrated as representation

of the current models. A new FEM for CAI analysis with a solid element, continuum representation of a honeycomb core using homogenized properties will be fully developed in

the present chapter. The new model will contain an implementation of a progressive failure

analysis (PFA) for composite laminates in the facesheet region of the sandwich panel model.

This inclusion represents an important contribution to the development of analysis of the

CAI response of thin facesheet honeycomb core sandwich panels. The need for this type of

analysis was recognized by several authors, including Shyprykevich et al. [12], Czabaj et al.

[51], and Schubel et al. [54]. This capability allows the model to predict CAI failure by

multiple modes and gives the engineer the ability to understand the contribution of nominal

core density to failure mode. The need for this capability was shown in the current research

in Chapter 3.

In addition to the inclusion of composite laminate PFA for crack or damage propagation in the facesheet of the sandwich panel, a second major contribution to CAI analysis

139
Chapter 5. Development of a New Model for CAI Analysis

will be discussed. Impact damage will be defined in the present model as a high fidelity

representation based on measurements and observations taken from a detailed first-hand experimental test survey, as described in Chapters 2 and 3 of the current research. The level of

detail for the depiction of impact damage in the new CAI model is higher than the current

models. It will be demonstrated in the present chapter that this level of damage depiction

can be used to develop a much improved level of understanding about what impact damage

traits contribute significantly to CAI failure. First, however, development of the pertinent

theory will continue with the discussion of Multicontinuum Theory (MCT) and MCT failure theory. Once the discussion of theory is complete and the new model has been fully

described, the chapter will conclude with a mesh convergence study, as well as a sensitivity

study on key FEM parameters.

5.1 Progressive Failure Analysis Theory

ABAQUS includes an implementation of PFA developed by Lapcyk and Hurtado [72] which

includes the Hashin failure criterion [71] for crack initiation and then evaluates damage

propagation by considering energy release rates associated with compressive and tensile fiber

and matrix fracture. The challenge with using the ABAQUS built-in PFA is establishing the

appropriate energy release rates for a given facesheet material. In addition, in the current

implementation significant convergence problems exist unless damage stabilization is used to

slow damage propagation [89].

An alternative is available for use with ABAQUS in the form of commercially available

software, Helius:MCT [92], developed by Firehole Composites, Inc. Helius:MCT is unique in

that it makes use of multi-continuum theory, which will be discussed in the present chapter as

developed by Mayes and Hansen [75]. The failure theory used considers the three-dimensional

state of stress of the element in question and only requires material strength values for

the facesheet constituent materials, which makes it considerably easier to implement then

ABAQUS’ own PFA. Practical use of the commercial version Helius:MCT is easily learned

140
Chapter 5. Development of a New Model for CAI Analysis

through documentation consisting of a user’s manual, examples, and tutorials.

5.1.1 Multicontinuum Theory

In general, many laminate theories, including the theory implemented in ABAQUS, used

to model the linear elastic response of sandwich panel facesheets are considered macromechanical. They homogenize the material properties of the laminate instead of considering

the material properties of the constituent materials (i.e. the fibers and the matrix). In

the present work, the failure initiation and damage propagation in the composite laminates

facesheet will be predicted using a more detailed approach, which will require the fiber and

matrix average stress states. In order to facilitate this, a multi-continuum theory (MCT) is

used to describe the stress state of the constituent materials in terms of the stress state of

the laminate.

The present MCT theory, as summarized by Mayes and Hansen [75], includes the

following assumptions. The behavior of the fibers is linear elastic, while the matrix behavior

is non-linear elastic. A perfect bonding exists between the fibers and matrix. Stress concentrations which occur at fiber boundaries are only included as a contribution to the volume

averaged stress state. Fiber distribution is idealized as uniform and hexagonal and the effect

of this distribution on composite strength and stiffness was accounted for by analysis using a

finite element model of the microscopic geometry. Finally, a piecewise stress-strain will result

from implementation of MCT failure theory because one constituent can fail while leaving

the other intact.

A volume average of a representative region of a continuum material is taken to

characterize the stress tensor for a given material point as given by:

σ =

1

V ol Z

σ(x)dV ol (5.1)

The concept of multicontinuum extends this idea to the constituent level. That is,

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Chapter 5. Development of a New Model for CAI Analysis

within a continuum region there are coexisting materials (i.e. fiber and matrix) whose individual average stress state can also be found by the following volume integrals:

σf =

1

Volf

Z

σ(x)dVolf (5.2)

σm =

1

Volm

Z

σ(x)dVolm (5.3)

This leads to the following relationship:

σ = φfσf + φmσm (5.4)

Where φf and φm are the fiber and matrix volume fractions, respectively. Likewise,

the relationship between composite and constituent volume averaged strain state is:

 = φf f + φmm (5.5)

For the case of woven fiber composite laminates, the volume averaged stress states are

sequentially decomposed into the constituent average stress state of the warp and fill fiber

tows and matrix. First, the composite average stress and strain states are mapped into warp

tow stress and strain states, and stress and strain states for a super constituent consisting of

the fill tow material and the matrix pockets in the woven material as:

σ = φf ill/matσf ill/mat + φwarpσwarp (5.6)

 = φf ill/matf ill/mat + φwarpwarp (5.7)

The fill tow / matrix super constituent volume averaged stress and strain state is then

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Chapter 5. Development of a New Model for CAI Analysis

reduced to fill tow and matrix pocket volume averaged stress and strain states as:

σf ill/mat = φf illσf ill + φmatσmat (5.8)

f ill/mat = φf illf ill + φmatmat (5.9)

The fiber and matrix volume average stress and strain states for the warp and fill

tows can then be calculated using Eqs. 5.4 and 5.5, respectively.

The constitutive relations between volume average stress and strain states for the

composite, and then fiber and matrix constituents are given as:

{σ} = [C]{}

{σf } = [Cf ] {f } (5.10)

{σm} = [Cm] {m}

Where [C] is the 6x6 constitutive matrix. Since MCT failure theory is piecewise

continuous, the constitutive equation used must be assumed to be linearized about the current

stress state for when some form of failure has occurred. Substitution of Eqs. 5.10 into Eq.

5.4 results in:

[C]{} = φf [Cf ] {f } + φm [Cm] {m} (5.11)

Further substitution results in:

[C] (φf {f } + φm {m}) = φf [Cf ] {f } + φm [Cm] {m} (5.12)

Which is then solved for {f } as:

{f } =

φm

φf

([C] − [Cf ]) −1([Cm] − [C]) {m} (5.13)

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Chapter 5. Development of a New Model for CAI Analysis

Substitution of Eq. 5.13 into Eq. 5.5 yields a matrix average strain state in terms of

the composite average strain state as:

{m} =

1

φm

([Cm] − [Cf ]) −1([C] − [Cf ]) {} (5.14)

The fiber average strain state can then be computed as:

{f } =

1

φf

({} − φm {m}) (5.15)

The matrix and fiber average stress states can then be found through the appropriate

linearized constitutive relations.

For woven materials, the first decomposition of the composite average strain state

into the fill tow / matrix pocket super constituent strain state and the warp tow constituent

strain state can be written as:

{warp} =

1

φwarp



[Cwarp] −



Cf ill/mat −1



[C] −



Cfill/mat {} (5.16)



fill/mat	=

1

φf ill/mat

({} − φwarp {warp}) (5.17)

The second decomposition can then be written as:

{mat} =

1

φmat

([Cmat] − [Cf ill]) −1

Cf ill/mat

− [Cf ill]

 f ill/mat	

(5.18)

{f ill} =

1

φf ill

f ill/mat	

− φmat {mat}



(5.19)

Here, φf ill and φmat are the volume fractions of the fill tow and matrix pockets with

respect to the fill tow / matrix pockets super constituent, rather than the composite. The

volume average strain state in the warp and fill tows of their respective fiber and matrix

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Chapter 5. Development of a New Model for CAI Analysis

constituents can then be calculated using a third decomposition, as:

{m}

f ill =

1

φm

([Cm] − [Cf ]) −1([Cf ill] − [Cf ]) {f ill} (5.20)

{f }

f ill =

1

φf

({f ill} − φm {m}) (5.21)

{m}

warp =

1

φm

([Cm] − [Cf ]) −1([Cwarp] − [Cf ]) {warp} (5.22)

{f }

warp =

1

φf

({warp} − φm {m}) (5.23)

The corresponding volume averaged stress state can then be calculated using the

appropriate linearized constitutive relations.

{σf }

f ill = [Cf ]f ill {f }f ill (5.24)

{σm}

f ill = [Cm]f ill {m}f ill (5.25)

{σf }

warp = [Cf ]warp {f }warp (5.26)

{σm}

warp = [Cm]warp {m}warp (5.27)

5.1.2 MCT Failure Theory

The failure theory used in Helius:MCT is a form of the multicontiuum failure theory first

developed by Garnich and Hansen [74] and later revisited by Mayes and Hansen [75]. The

MCT failure criterion retains the quadratic form of the Hashin failure criterion [71]. The

stress based criterion makes use of four of the five transversely isotropic stress invariants

145
Chapter 5. Development of a New Model for CAI Analysis

given as:

I1 = σ11

I2 = σ22 + σ33

I3 = σ

2

22 + σ

2

33 + 2σ

2

23 (5.28)

I4 = σ

2

12 + σ

2

13

I5 = σ22σ

2

12 + σ33σ

2

13 + 2σ12σ13σ23

The five transversely isotropic stress invariants are a variant of the usual isotropic

invariants of the stress tensor. The usual stress invariants are well-known as the coefficients

of the cubic equation found from expansion of Eq. 5.29, which is used when determining the

principle stresses and planes for a given stress tensor. It can be noted that the usual stress

invariants are valid for all rotations of a given coordinate system. For a transversely isotropic

system, only rotations about the 1 -axis are considered. It was noted by Hashin [71] that

from this premise, it is relatively easy to see that I1 and I4 are invariant for rotations about

the 1 -axis. I2, I3 and I5 can then be shown to be invariant from comparisons of I1 and I4 to

the three usual isotropic stress invariants.



















σ11 − λ σ12 σ13

σ12 σ22 − λ σ23

σ13 σ23 σ33 − λ



















= 0 (5.29)

The general form of the MCT failure criterion is a simplification of Hashin’s criterion

based on the following assumptions. Stress interaction terms are not used since experimentally determining their coefficients is very difficult and ignoring them results in only small

errors. Linear terms are also not used since they arise due to internal self-equilibrating

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Chapter 5. Development of a New Model for CAI Analysis

stresses. The resulting general form is:

a1I

2

1 + a2I

2

2 + a3I3 + a4I4 = 1 (5.30)

The fifth transversely isotropic invariant is simply not used because it is cubic in

stress, and the failure criterion is meant to have a quadratic form.

The principal attractiveness of MCT is that it determines fiber and matrix failure by

using the fiber and matrix average stress states as opposed to the composite average stress

states. Therefore, the general form of the MCT failure criterion is further revised into a

matrix failure criterion and a fiber failure criterion for unidirectional composites. For woven

composites the fiber failure criteria remains the same, but is used independently for the warp

and fill tows, while a revised criterion is used for matrix failure . As set forth by Schumacher

and Key [76], the fiber failure criterion is:

± a

f

1



I

f

1



2 + a

f

4

I

f

4 = 1 (5.31)

Where the coefficients of the criterion are given with respect to the fiber tensile,

compressive, and shear strengths as:

± a

f

1 =

1



±σ

f

T /C

2

(5.32)

a

f

4 =

1



σ

f

S12

2

(5.33)

The matrix criterion for the matrix constituent in both unidirectional and woven

composites is given as:

± a

m

2

(I

m

1

)

2 + am

3

I

m

3 + a

m

4

I

m

4 = 1 (5.34)

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Chapter 5. Development of a New Model for CAI Analysis

Where the coefficients for the unidirectional composite case are given as:

+ a

m

2 =

1

((+σ

m

T

) + (+σ

m

T2

)) 2



1 −

(+σ

m

T

)

2 + (+σm

T2

)

2

2 (σ

m

S23)

2



(5.35)

−a

m

2 =

1

((−σ

m

C

) + (−σ

m

C2

)) 2



1 −

(−σ

m

C

)

2 + (−σm

C2

)

2

2 (σ

m

S23)

2



(5.36)

a

m

3 =

1

2 (σ

m

S23)

2

(5.37)

a

m

4 =

1

(σ

m

S12)

2

(5.38)

The coefficients for the woven composite case are given as:

± a

m

2 =

1

(+σ

m

T

)



1 −



±σ

m

T /C

2

2 (σ

m

S23)

2



 (5.39)

a

m

3 =

1

2 (σ

m

S23)

2

(5.40)

a

m

4 =

1

(σ

m

S11)

2

(5.41)

In these equations, the subscripts indicated which material strength is represented

by σ: T indicates tensile, C indicates a compressive strength, S12 indicates in-plane shear,

S23 indicates transverse shear, and T2 and C2 indicate the normal stress corresponding to

transverse matrix failure once the matrix has already failed, previously by in-plane failure,

for tensile and compressive forces, respectively.

5.1.3 Material States for Woven Composite Laminates During PFA

As a result of MCT failure theory, a composite lamina can be simulated in multiple states

of failure since individual lamina constituents are predicted to fail separately. Based on the

three level MCT decomposition of the average stress state of a woven fiber lamina into the

average stress state of its constituent materials, there are five total constituents to consider.

These constituents are the fill tow fibers, the fill tow matrix, the warp tow fibers, the warp

148
Chapter 5. Development of a New Model for CAI Analysis

tow matrix, and the matrix pockets in between the woven tows. Each of these constituents

can be modeled independently with failed or intact status for a given representative volume

element (RVE), although no explicit failure criteria exists for matrix pockets between tows.

The matrix pockets are assumed failed if another matrix constituent (in the warp or fill tows)

is determined to have failed. The Helius Theory Manual [93] defines nine unique damaged

average stress states that take into account combinations of the state of these constituents

that are used to describe a (RVE) within a layer for a given sandwich panel facesheet. These

states are as follows (matrix pockets between tows are assumed to have failed for states 4-9):

1. All constituents intact

2. Failed fill tow matrix constituent

3. Failed warp tow matrix constituent

4. Failed fill and warp tow matrix constituents

5. Failed fill tow fiber and matrix constituents

6. Failed warp tow fiber and matrix constituents

7. Failed fill tow fiber and matrix constituents, and failed warp tow matrix constituent

8. Failed warp tow fiber and matrix constituents, and failed fill tow matrix constituent

9. Failed warp and fill tow fiber and matrix constituents.

5.2 Introduction to Proposed FEM for CAI Analysis

A new finite element model (FEM) for the prediction of CAI failure in honeycomb core

sandwich panel coupons has been developed in the current research. The current model uses

some aspects of the solid element core FEM developed by several other authors including

Shyprykevich et al. [12], Hwang and Lacy [49] [50] , Czabaj et al. [51], Xie and Vizzini

149
Chapter 5. Development of a New Model for CAI Analysis

[52] [53], and Schubel [54]. A simple version of this model which included only previously

developed aspects was discussed briefly in Chapter 4. The major contributions of the current

research to the state-of-the-art of models for CAI analysis of honeycomb core sandwich panels

are covered in the present chapter. This discussion began with an overview of Multicontinuum

Theory (MCT) and the associated MCT failure theory for composite laminate failure analysis.

MCT failure theory is used in the current research in an implementation of progressive

failure theory (PFA) in the facesheets of the FEM. Firehole Composites implemented MCT

failure theory in their commercially available software, Helius:MCT [92]. A custom version

of this software was obtained for the present research which would allow for its use in a FEM

for CAI analysis. This custom version was compatible with the ABAQUS user subroutine,

UMAT, used to implement the core model. The result of the inclusion of Helius:MCT in

the current model is the ability to predict the onset of multiple failure modes, including the

previously modeled dimple propagation failure mode (also seen in test coupons discussed

in Chapters 2 and 3), and also the facesheet crack propagation failure mode (discussed in

Chapter 3). The inclusion of a PFA for implementation of multiple competing failure modes

in a single model for CAI analysis is the first major contribution for the analysis part of the

current research.

A second major development of the current research is the inclusion of increased

impact damage detail. In Chapters 2 and 3, a significant level of data was presented from

evaluation of damage formation and CAI failure in three honeycomb core sandwich panel

material systems. A total of 32 test coupons were compressively loaded to failure with

impact damage present. Both destructive and non-destructive evaluation (NDE) techniques

were used to describe the impact damage in these test coupons. The availability of this

data led to its inclusion in the new model, which is another major unique contribution of

the current research. A description of how the impact damage data was included will be

discussed in this section. First, the geometry and boundary conditions of the new model will

be introduced. Following this introduction, the implementation of the non-linear core model

through the ABAQUS user subroutine, UMAT, will also be briefly discussed.

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Chapter 5. Development of a New Model for CAI Analysis

5.2.1 Geometry, Boundary Conditions and Finite Elements

A FEM was developed for analysis of the CAI response of honeycomb core sandwich panel

coupons using the commercial FEA code ABAQUS/Standard. The FEM includes representations of both front (damaged) and rear facesheets, as well as a continuum solid representation

of the homogenzied, honeycomb core. It is only necessary to model one quarter of the sandwich panel coupon during an analysis due to symmetry of the coupon, the impact damage

present in the front facesheet, and the expected failure modes. A global coordinate system

will be established in the following manner. If the major two dimensions (i.e. length and

width) of the sandwich panel plate are located in the x − y plane of a Cartesian coordinate

system, where the loading direction is parallel to the y-axis, only the top right quarter of

the sandwich panel coupon is modeled. This is the region located in the Cartesian quadrant

where points are defined by positive x and positive y coordinates. The length of the model in

the y-direction is then l/2 where l is the length of the coupon modeled. Likewise, the width

in the x-direction modeled is w/2, and the thickness is (tc + 2tf ) where w is the coupon

width, tc is the thickness of the core, and tf is the facesheet thickness. The area of the model

used to simulate impact damage will thus be located on the front facesheet on the z-axis of

the global coordinate system, as highlighted in Fig. 5.1.

The following boundary conditions were used in the current model. It is required

that the element node points located along the line x = 0 be fixed in the x-direction for

symmetry in this direction. For y-direction symmetry, nodes along the line y = 0 are fixed

from displacement in the y-direction. Rotational boundary conditions are not necessary

for any node points since the elements used are defined using only displacement degrees of

freedom. A third initial boundary condition was applied at the facesheet nodes located at

(x, y = l/2, z), to simulate the effects of the coupon clamp and potting used in experimental

conditions. At the facesheet nodes only at these locations, the nodes were restricted from

displacement in the out-of-plane, z-direction. During the analysis step, loading was applied to

the nodes located at the coordinates (x, y = l/2, z) using an applied displacement boundary

condition to simulate the displacement controlled loading used in CAI testing described in

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Chapter 5. Development of a New Model for CAI Analysis

Figure 5.1: New CAI model: FEM Geometry.

Chapters 2 and 3. The boundary conditions of the new CAI model are shown in Fig. 5.2.

Figure 5.2: New CAI model: FEM node points (highlighted in red) for boundary conditions of

symmetry (left), simulated potting (center), and applied displacement (right).

Shell elements and solid brick elements were used to model the facesheets and the core

of the sandwich panel, respectively. The ABAQUS continuum shell element, SC8R, was used

in the finite element representation of the sandwich panel facesheets. The main benefit of

continuum shell elements relative to conventional shell elements is the explicit consideration

152
Chapter 5. Development of a New Model for CAI Analysis

of the shell thickness. In the continuum shell formulation, only displacement degrees of

freedom are considered, as opposed to displacement and rotation degrees of freedom, as used

in conventional shell elements. The SC8R elements are a reduced element formulation that

increases the computational efficiency, while making marginal accuracy sacrifices, if any, due

to the location of the Gauss integration points. The constitutive response of the element

shell section is defined as in classical laminate theory (CLT), which was discussed in Chapter

4. Each ply layer of the composite shell section was defined using orthotropic engineering

constants found from various experimentally derived material data available in the literature.

The exact material constants used in each analysis are discussed in Chapter 6.

Special consideration is given to the front, impact damaged facesheet in the form of the

progressive failure analysis, accomplished through the Helius:MCT software discussed previously. The use of Helius:MCT does not change the element formulation or the constitutive

model. It simply requires the explicit specification of various material and element properties, some of which are normally automatically calculated by the ABAQUS/Standard solver.

The use of Helius:MCT requires a special material file written using the Firehole Composites

auxiliary software, “Helius Material Manager.” The Material Manager determines the in

situ properties of the lamina’s fiber and matrix constituents based on the material constants

provided, usually from experimentally determined sources for a given material. Through

the course of the analysis, Helius:MCT uses these in situ constituent material properties to

determine the fiber average stress state and matrix average stress state for a given material

point based on the average stress state of the lamina determined by the ABAQUS/Standard

finite element solver. The constituent material properties will thus also be given in Chapter

6. Normally, in the course of pre-processing for a FEA using Helius:MCT, the auxiliary Firehole Composites software, “x-STIFF”, is used to calculate extraneous stiffness parameters,

such as the thickness modulus and the hourglass stiffness necessary for the reduced integration specific element formulation. These properties can also be estimated using various

relationships given in the ABAQUS Theory Manual [90].

The 8-node, solid brick, ABAQUS finite element, C3D8R, was used to represent the

153
Chapter 5. Development of a New Model for CAI Analysis

honeycomb core of each sandwich panel CAI test coupon modeled as a homogenized, continuum region. The elastic response of this element was implemented using nine orthotropic

engineering properties to represent the constitutive model. The out-of-plane modulus, the

L-direction shear modulus, and W-direction shear modulus for the corresponding honeycomb

core were given in the literature [86] as experimentally determined constants found using the

appropriate test standards (e.g. ASTM). The in-plane extensional moduli and shear modulus

for the continuum representation were determined using the equations given in the theory

section of Chapter 4. All of the appropriate constants used to define each analysis will be

given in Chapter 6. Since, a non-linear model was necessary for the out-of-plane response of

the homogenized core, an ABAQUS subroutine, UMAT, was written in FORTRAN to implement both the linear elastic response and the idealization of the non-linear flatwise core

crush curve described previously, in Chapter 4. The implementation of the core response by

UMAT will be described in the next section.

5.2.2 Honeycomb Core Implementation using UMAT

The linear elastic orthotropic response as well as the non-linear crushing failure of the core was

implemented using the ABAQUS user subroutine, UMAT, which is written in the FORTRAN

programming language. As written, the UMAT requires the following inputs to be read

from the ABAQUS/Standard input file under a “user material” ABAQUS keyword for the

appropriate material. First, the nine orthotropic engineer constants are given which define

the linear elastic response of the material as defined by Eq. 4.1. The 10th value is a constant

which acts as a marker for the material point which defines it as either a “damaged” or

“undamaged” material point. This is only with respect to the initial material model, and

has no bearing on the results of any subsequent failure analysis. The flatwise core crush

strength of the material, given as the associated failure strain value is the 11th material

constant. Finally, the 12th material property sets the stress reduction in the element which

results when an element is determined to have failed from out-of-plane compressive loading

during an analysis step. This stress reduction is also defined by experimental data (i.e. a

154
Chapter 5. Development of a New Model for CAI Analysis

flatwise core crush test result for the stress-strain response). The specific inputs used in

individual analyses of experimental test coupons under CAI load are given in Chapter 6.

The damaged region is determined by user inputs which are discussed in the last

section of the present chapter. The reduction in stress is an idealization of the resulting

stress after failure for a flatwise compression test. Experimental core crush results for Nomex

material generally show a brittle wall collapse and folding which results in a succession

of rising and falling stress resultant for a displacement controlled test [62] [63] [64]. This

behavior is averaged to a single stress value, which was selected based on the idealization

of core crush experimental results. Ideally, a flatwise compression test would have been

completed on the materials used in this research in order to gain material specific information;

however, this was not completed so the estimate was used. Once the initial crush strength has

been reached, successive cell wall collapse occurs at a much lower level of applied load since

the cell wall stability has been compromised. Cell wall densification, and the corresponding

eventual increase in crush stiffness, are not modeled in the present analysis, since this core

behavior is not typically found due to indentation propagation failure during CAI testing. For

all current analyses, after failure, the stress tensor components are reduced to 60% of their

initial values. All extensional and shear moduli are set to zero so the stress remains constant

after failure, resulting in perfectly plastic response for any remaining deformation. The nonlinear crush response in the z-direction for a 3PCF Nomex honeycomb was approximated by

the idealized core crush response shown in Fig. 5.3. The 6PCF core response used is similar,

except the appropriate constants are used for linear elastic modulus and core crush strength

to define the idealization. The red and blue curves in Fig. 5.3 represent the response of

impact damaged and initially undamaged core elements, respectively. The marker, which

was mentioned as the 10th subroutine input, previously, determines which curve is used for

a given material point.

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Chapter 5. Development of a New Model for CAI Analysis

Figure 5.3: Idealized core crush response use to define non-linear constitutive core behavior of 3PCF

Nomex core.

5.2.3 Impact Damage Modeling

Impact damage present in a test coupon during CAI testing of honeycomb core sandwich

panels plays an important role in determining the failure strength for a given coupon. The

subject of damage formation in composites, including honeycomb core sandwich panels, has

been studied extensively. The literature review of Chapter 1, detailed selections from this

body of work. The inclusion of impact damage in the various analysis methods used currently

for CAI failure of sandwich panels, also presented in Chapter 1, has been treated to a much

lesser extent. The large amount of data available from the current research, discussed in

Chapters 2 and 3, makes possible the incorporation of impact damage to a much fuller

extent in the new analysis model. The treatment of initial impact damage in models of CAI

sandwich panel test coupons is the subject of the present section. The sensitivity of the FEM

to each of the measurements used to define the impact damage model will be discussed in a

later section of this chapter. This information represents one of the major contributions of

the present work.

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Chapter 5. Development of a New Model for CAI Analysis

The most commonly included type of impact damage in models for analysis of sandwich panel CAI failure is a dimple in the geometry of one facesheet. This is used to represent

the residual dent that results from a low velocity impact on such a structure. In the new

FEM, a residual dent is included in the coupon geometry using measurements from the corresponding experimental test coupon for the dent’s maximum depth and maximum diameter.

From symmetry, only one quarter of the residual dent is modeled, and the dent is assumed

to be circular. This assumption is used since the test coupons modeled were impacted with

a hemispherical shaped blunt impact tip. The indentation modeled affects the facesheet geometry, as well as the core geometry, and their resulting finite element meshes. The contour

of the dent at the front facesheet to core interface is defined using Eq. 5.42 where the maximum dent depth, hmax, and dent diameter, d, are necessary to inputs into the model, and

xn and yn are the nodal Cartesion coordinates. The lower surface of the facesheet follows

the surface defined by this curve. The upper surface follows the same curve but is offset by

the defined thickness of the facesheet which is 0.02 in. in all analyses. This dimension is

the nominal facesheet thickness of the sandwich panel test coupons described in Chapters 2

and 3. No thickness change is modeled in the impact damage region of the facesheets. The

top surface of the continuum core also follows the curve defined by Eq. 5.42. The through

the thickness nodal locations are adjusted so equal spacing is maintained for element node

locations between the indented top surface and the lower surface of the continuum core. A

close up view of the geometry of the initial indentation included in the facesheet is shown in

Fig. 5.4.

zdent =

−hmax

2

 

1 + cos 

2π

p

xn

2 + yn2

d

!! (5.42)

In addition to the geometric indentation, other types of damage can be incorporated

into the FEM, many of which have not been used or adequately discussed in the prior literature reviewed. The impact damage model described here attempts to simulate the presence

of the various types of damage seen in the tested materials, discussed in Chapters 2 and 3.

This damage was observed and quantified through destructive and non-destructive evaluation

157
Chapter 5. Development of a New Model for CAI Analysis

Figure 5.4: New CAI analysis model: close-up view of indented region of FEM.

(NDE) techniques after static indentation, and low velocity impact tests, to specifically study

impact damage formation in these materials. In addition, some measurements were collected

in observation of damage present on the CAI test coupons, so additional information is available pertaining to particular test coupons which will be used in analysis. Types of damage

observed in the facesheets of the PXX, 3PCF-XX, and 6PCF-XX series materials include

delaminations, longitudinal matrix cracks, transverse fiber cracks and facesheet penetration.

Types of damage observed in the core of the sandwich panels include brittle fracture of the

cell walls, buckling of the cell walls, and voids in the cellular material where the cellular

structure had been completely crushed. The effect of each of these damage types can be

included in the model on a macroscopic level by degradation of the constitutive material

properties of the corresponding damaged region (e.g. damaged facesheet region, or damaged

core region). These regions must be defined by both their dimensions and the proper material

property degradation amount. Both of these will now be described, first with respect to the

damaged core region, and second, with respect to the damaged facesheet region.

Typical core damage in a thin facesheet honeycomb core sandwich panel from low

158
Chapter 5. Development of a New Model for CAI Analysis

velocity impact damage is shown in Fig. 5.5. The damaged core region is assumed to be

circular in shape and concentrically located with respect to the residual dent previously

discussed. It can therefore be described geometrically using a maximum radius and depth,

measured from the front, damaged facesheet. The measurements used for this definition are

taken from the low velocity impact damage survey corresponding to the specific material

modeled. The impact damaged core region is assumed to be uniform in depth, to simplify

the FEM input file definition. This assumption represents a conservative estimate of the size

of the damaged core region.

Figure 5.5: Examples of core damage from destructive microscopy of 3PCF-XX (left) and 6PCF-XX

(right) series materials.

An example of the damaged core region included in the new FEM model is shown in

Fig. 5.6. In addition to the geometric definition of this region, the damage also requires a

set value for the material property degradation (i.e. an element stiffness reduction). In the

present research, it is assumed that the stiffness of the damaged core region is 60% of the

initial properties. This was based on the idealization of stress-strain curves found by flatwise

core crush test by similar materials by other researchers [46]. The effect of the uncertainty of

this value, as well as the geometric dimensions of the damaged core region will be discussed

in a subsequent section of this chapter.

Images from microscopy of impact damaged test coupons in Fig. 5.7 show the variation in facesheet damage between lightly damaged (lefT) and more heavily damaged test

159
Chapter 5. Development of a New Model for CAI Analysis

Figure 5.6: New CAI analysis model: damaged core region example.

coupons (right). In the more heavily damaged coupons, a region of facesheet fracture

(failed fibers and matrix) is readily apparent. To incorporate these differences, the damaged facesheet region of the new model is actually two separately defined element groups.

First, a region of moderate facesheet damage is included in all CAI test coupon models based

on the location of inter-fiber fracture (IFF) or matrix cracking found from observations and

measurement by optical microscopy. An example of a microscopically observed matrix crack

is shown in Fig. 5.8. The area of matrix-damaged facesheet incorporated in the new FEM for

CAI analysis is assumed circular and concentrically located with respect to the facesheet dimple. Geometrically, it is only necessary to define this region by an experimentally determined

diameter. It is also defined by a reduction in the element stiffness from the stiffness based

on pristine material properties, which will be discussed later. The second region of facesheet

damage is only modeled for heavily damaged sandwich panels, where facesheet fiber fracture

was observed. An example is shown in Fig. 5.7. This region is assumed to be one element

wide in the coupon load (y-)direction, and is defined in the coupon width (x-)direction by

the corresponding length measured during testing for damage formation. It is also defined by

a reduction in stiffness from pristine material properties. The geometric representations of

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Chapter 5. Development of a New Model for CAI Analysis

the two damaged facesheet regions used in the new FEM model to represent impact damage

prior to any compressive loading is shown in Fig. 5.9. The stiffness reductions used for the

two damaged facesheet regions will now be discussed.

Figure 5.7: Examples of facesheet damage from microscopy of PXX (left) and 3PCF-XX (right)

series materials.

Figure 5.8: Example of matrix cracking as a result of impact damage observed by optical microscopy.

The two regions of facesheet damage require individual reductions in stiffness. The

IFF region requires a reduction in stiffness consistent with matrix damage to that area of

the woven fiberglass facesheets. The region of fiber fracture requires a reduction in stiffness

161
Chapter 5. Development of a New Model for CAI Analysis

Figure 5.9: New CAI analysis model:facesheet element regions representing areas of observed IFF

(left) and fiber fracture (right), prior to any compressive load analysis steps.

consistent with both matrix failure and fiber failure. In keeping with model consistency,

the stiffness reductions used by Helius:MCT for the progressive failure analysis will also be

used to define the impact damage of the initial model. The stiffness reduction recommended

by Firehole Composites for use with their Helius:MCT software for matrix failed elements

is 90% for the matrix constituent material properties. This stiffness reduction is used for

the region representing impact induced IFF. The reduction for fiber failed elements (matrix

failure assumed to have occurred prior to fiber failure) is 90% for matrix constituent material

properties and 99% for fiber constituent material properties. These reductions are used for

the region representing impact induced fiber failure. The constituent material properties

which are used for both fiber and matrix materials are the in situ properties determined

by the Helius Material Manager based on the ply properties of the material found in the

appropriate literature. Once the appropriate stiffness reduction has been applied to the fiber

and matrix constituent material properties associated with each region, the laminate level

material properties are calculated from the appropriate relationships.

The calculation of damaged lamina level properties from damaged constituent level

properties involves the calculation of effective moduli of woven composites. This is an area

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Chapter 5. Development of a New Model for CAI Analysis

of micromechanics analysis which has received some research attention; however, unlike the

calculation of unidirectional fiber-reinforced composite laminas, there are no widely accepted

micromechanics relationships. The principal focus of establishing the appropriate relationships has centered on strategies to estimate the effects of waviness on woven lamina engineering properties. Whitcomb and Tang [94] reviewed previous attempts and noted they varied

from simple models based on modified classical laminate theory, to full three-dimensional

finite element models. The authors began the development of their own work with the study

of the characteristics of a weave which dominate its response. For instance, they noted that

the 8-harness weave exhibits very slight coupling between in-plane extension and shear. They

found that weave-specific behavior depends on properties such as tow stacking order, weave

type, and of course, waviness. The authors continued with the development of a building

block approach to simple formulations for engineering properties based on waviness and other

weave properties, before comparison to a detailed FEM model.

The types of weave used in the facesheets of the sandwich panels studied in the present

research are style 7781 E-glass weaves for PXX series materials (discussed in Chapter 2) and

style 6781 S2-glass weaves for 3PCF-XX and 6PCF-XX series materials (discussed in Chapter

3). Both of these weaves are identical 8-harness satin weaves, with the only difference being

the quality of the fibers (S2 glass is considered higher quality with superior stiffness and

strength). The micro- and meso-mechanics of these types of weaves were studied by Searles et

al. [95]. The authors noted that 8-harness (8H) satin weaves reduce the number of exchanges

of the fill and warp tows, thereby improving the composite stiffness and strength of the woven

ply. In addition, these materials are especially important in aerospace structures since they

can be molded into highly complex structures and shapes. The authors chose cubic splines

to approximate the two-dimensional cross section of 8H weaves. Using these approximations

to incorporate any inherent irregularities in the weave architecture, the authors then used

composite cylinder assemblage to approximate effective micromechanics properties of the

local weave and classical laminate theory (CLT) to approximate the 8H weave as a two layer

laminate.

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Chapter 5. Development of a New Model for CAI Analysis

Another example of work considered in the present research includes a method by Gao

et al. [96] to consider calculation of damaged weave material properties through analysis of

specific damage geometry using Castigliano’s second theorem. Also, Angioni et al. [97]

classified various methods as either micromechanics of materials, finite element analysis,

and asymptotic expansion homogenization methods (AEHM). The authors then compared

AEHM to other analysis methods in order to draw conclusions on its relative effectiveness at

predicting the engineering properties for various weave architectures. AEHM proved equal

to the best analytic method and the authors mentioned it has the added benefit of providing

the ability to determine local stresses and strains.

Each analysis method discussed in the four examples, seeks to consider the effective

moduli of woven composites. The various methods differ in the amount of weave definition

considered, as well as the complexity of implementation. Typically, tow waviness is the

principal consideration on the resulting material property definition, even though it is not the

only consideration in a more detailed approach. In the present research, a very simple method

for estimating damaged weave properties will be used, since analysis of weave properties is not

the primary concern of the current research. The following describes the method, original to

the current research, to approximate the effect of waviness on damaged material properties.

A ply layer of epoxy matrix pre-impregnated woven fiberglass is considered as a four

layer composite laminate. Four plies are considered instead of two so that the laminate can

be considered balanced and symmetric. This allows for appropriate engineering constants to

be easily calculated from CLT. The appropriate relations used in CLT were given as Eqs.

4.3 through 4.12. The stacking sequence of unidirectional layers used to represent a single

woven layer is [0/90]S. In order to use this method, the engineering properties associated

with the individual layers were calculated using formulas from the mechanics of materials.

These formulas were taken from the book by Hyer [87]. The rule of mixtures result is used to

calculate the fiber direction Young’s modulus, E

C

1

, and the in-plane Poisson’s ratio, υ

C

12. The

rule of mixtures uses the fiber and matrix volume fractions, φ

f and φm, and the appropriate

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Chapter 5. Development of a New Model for CAI Analysis

constituent material properties.

E

c

1 = φfE

f

1 + φmE

m (5.43)

υ

c

12 = φfυ

f

12 + φmυ

m (5.44)

The modified rule of mixtures [87] is generally used in Mechanics of Materials for

unidirectional results for increased level of accuracy in estimation of the transverse extensional modulus. The inverse of the transverse layer modulus is given with respect to the fiber

volume fraction, the transverse fiber modulus, and the matrix modulus as in Eq. 5.45.

1

Ec

2

=

1 −

p

φf

Em

+

p

φf

p

φfE

f

2 +



1 −

p

φf



Em

(5.45)

Finally, the expression for in-plane shear modulus of a unidirectional layer used for

Mechanics of Materials is taken from the concentric cylinders result [87]. The composite

shear modulus, GC

12, is given with respect to the matrix shear modulus, Gm, the fiber volume

fraction and the fiber shear modulus, G

f

12.

G

c

12 = Gm







Gm + G

f

12

− φf



Gm − G

f

12



Gm + G

f

12

+ φf



Gm − G

f

12



 (5.46)

The Mechanics of Materials relations are used with the in situ pristine fiber and matrix

constituent properties found by the Helius Material Manager to calculate unidirectional ply

properties. CLT is then used to calculate idealized properties of a single woven layer using

the stacking sequence that was mentioned above. These idealized properties are generally

much higher than the expected properties of the corresponding woven ply. Since, the actual

pristine properties of a woven ply are known, a “waviness factor”, W, for each engineering

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Chapter 5. Development of a New Model for CAI Analysis

property can be calculated as follows (for E1 in this example) in Eq. 5.47.

WE1 =

E

actual

1

ECLT

1

(5.47)

Here, E

actual

1

, is the lamina extensional modulus determined by the appropriate ASTM

test standard and available in published literature, and E

CLT

1

, is the idealized lamina extensional modulus calculated using the method outlined. Now, that this “waviness factor” has

been determined, idealized versions of the damaged material properties for the matrix damaged element regions of the FEM, as well as the fiber damaged element regions of the FEM

are next calculated using the CLT method, but this time using fiber and matrix constituent

properties with the appropriate stiffness degradations (e.g. 90% reduction in matrix stiffness

and 99% reduction in fiber stiffness for the region associated with fiber cracking in the FEM).

The “waviness factor” is then used to calculate more appropriate degraded properties as follows in Eq. 5.48 for the damaged Young’s modulus in the fill tow direction. Here, E

idealdam

1

is the idealized damaged Young’s modulus calculated from CLT.

E

dam

1 = WE1E

idealdam

1

(5.48)

The damaged warp modulus, E

dam

2

, and the damaged in-plane shear modulus, Gdam

12 ,

are calculated in the same fashion. The Poisson’s ratios are not degraded from the values

used from literature. The out-of-plane Young’s modulus, E

dam

3

, is assumed to degrade from

the values used from literature by the same amount calculated for the fill modulus. Additionally, the calculated degradation of the in-plane shear modulus is applied to the other

two shear moduli required for the fully orthotropic engineering property definition of the

damaged facesheet plies. Obviously, there are quite a few assumptions associated with the

method outlined in this section for calculating the degraded properties of impact damaged

regions of the model. Although, the methods used may not be accurate in the strictest sense

necessary for research in the specific area of calculation of woven engineering properties, they

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Chapter 5. Development of a New Model for CAI Analysis

do give approximations which are accurate enough to be useful for the present research. The

sensitivity of the new FEM model to uncertainty in the degraded material properties will be

further discussed later in the current chapter.

5.3 Mesh Pattern and Convergence

A three-dimensional grid pattern was used to mesh the model geometry for both the core

and the facesheets. This allows for efficient model creation without the need for a preprocessor such as ABAQUS/CAE [73]. Instead, the ABAQUS input file, for each completed

analysis, was written by a custom MATLAB [84] function. The mesh density, panel geometry, and damage definition could be efficiently adjusted for various analyses while retaining

mesh connectivity, and the connectivity between the facesheets and the core of the panel.

The ABAQUS continuum shell element, SC8R, was used to simulate the facesheets of the

sandwich panel, while the ABAQUS linear solid brick element, C3D8R, was used to model

the continuum-represented, homogenized, honeycomb core. The grid mesh was defined by

the number of elements in the coupon width direction (eX), the number of elements in the

coupon load direction (eY ), and the number of elements in the out-of-plane direction (in the

core region only, eZc). Only one conitnuum shell element was used through the thickness

of each facesheet. The total number of elements for a given analysis is then given by the

following expression: eT OT AL = eX ∗ eY ∗ (eXc + 2). Mesh convergence was studied individually in the coupon width, load, and through the thickness direction, while keeping the

mesh density in the directions not being studied at a nominal value. The mesh pattern and

convergence study is presented in the following sections.

5.3.1 Mesh Convergence: Coupon Width Direction (eX)

For the mesh convergence study in the coupon width direction, four test cases were chosen

from the 32 coupons tested to CAI failure. Of the four coupons chosen, two were chosen

from the 3PCF-XX series materials, and two were chosen from the 6PCF-XX series materials.

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Chapter 5. Development of a New Model for CAI Analysis

Information about both sandwich panel material systems was given in Chapter 3. The reason

for this selection was that mesh convergence for the new model in the coupon width direction

would be studied for both CAI failure modes found in experimental testing (indentation

propagation and crack propagation). The specific coupons, chosen from each material system,

included one lightly damaged test case (i.e. damaged by a 1 ft-lb. energy level impact), and

one heavily damaged test case (i.e. damaged by a 7 ft-lb. energy level impact). The lightly

damaged panels selected were 3PCF-02 and 6PCF-07, and the heavily damaged test cases

were 3PCF-16 and 6PCF-14. More information about these specific test coupons can be

found in Chapter 3. Specific inputs used to define the ABAQUS input file can be found in

Chapter 6 (other than the mesh used, which will be described in this section). The PXX

series materials were not used for this portion of the mesh study, since the results would be

expected to be similar to the results for the 3PCF-XX series test cases.

Each of the test cases would be considered with the following number of elements in

the coupon width direction: 40, 60, 80, 120, and 160. 80 elements was considered to be a

moderate mesh density, so the number of elements in the coupon load direction was set to

80. The number of elements in the thickness direction was 10 (2 facesheet elements and 8

core elements) for 3PCF-XX test cases, and 6 (2 facesheet elements and 4 core elements) for

6PCF-XX test cases. The reason for the reduction in elements in the thickness direction for

6PCF-XX test cases was this. Experience gained during model development had shown that

the crack propagation failure mode did not depend on the through the thickness number of

elements, since that part of the mesh largely effected the out-of-plane deformation of the

model (although this was not explicitly studied). The reduction in model degrees of freedom

for the 6PCF-XX test cases improved computational efficienecy. (Analysis of 6PCF-XX

test case took more computation time, since it largely depended on the progressive failure

analysis.)

The mesh dependency of the new FEM for CAI analysis was evaluated based on the

result of global coupon CAI failure load. Other results for CAI failure strength (stress) or

strain could also have been measured, but the results would have been similar. Each test

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Chapter 5. Development of a New Model for CAI Analysis

case was subjected to the boundary conditions described previously in this chapter and a

displacement prescribed load, in order to simulate an experimental CAI test. The CAI failure

load was determined when a sudden drop in reaction force was observed, just as it was in

experimental testing described in Chapters 2 and 3. The results for each test case used in

this portion of the mesh convergence study are shown in Fig. 5.10.

Figure 5.10: Mesh convergence study results: CAI failure load vs. number of elements (eX).

The results of the study of the dependence of the FEM result for CAI failure load of

the test coupons on the number of elements in the coupon width direction are as follows.

The results for the 3PCF-XX test coupons had little dependency on the eX mesh density, for

neither the lightly damaged test case, nor the heavily damaged test case. On the other hand,

6PCF-XX cases do appear to be dependent, though the results are very similar for both the

lightly and heavily damaged test cases. Another manner of checking solution convergence

is to look at the change with increasing number of elements. The solution change from the

next lower density (as a percentage) vs. number of elements is shown in Fig. 5.11. This

result shows that the overall change in model result for each additional amount of elements

was very small (about 3% or less for every data point).

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Chapter 5. Development of a New Model for CAI Analysis

Figure 5.11: Mesh convergence results: % change in CAI failure load vs. number of elements (eX).

5.3.2 Mesh Convergence: Coupon Load Direction (eY )

The same four test cases were chosen for the coupon load direction convergence study, as

in the study described in the previous section. Each of these cases was again studied for

mesh dependence (though this time in the coupon load direction) with the following number

of (eY ) elements: 40, 60, 80, 120, and 160. The number of elements in the coupon width

direction was set to the nominal value of 80, and the number of elements in the thickness

direction was 10 (2 facesheet elements and 8 core elements) for 3PCF-XX test cases, and 6 (2

facesheet elements and 4 core elements) for 6PCF-XX test cases. The mesh dependency of

the new FEM for CAI analysis was again evaluated based on the solution for the CAI failure

load. Each test case was subjected to the boundary conditions described previously in this

chapter, and a displacement prescribed load, in order to simulate an experimental CAI test.

The results for each test case used in this portion of the mesh convergence study are shown

in Fig. 5.12.

The results for the mesh dependence on element density in the coupon load direction

were slightly skewed. The largest dependence was again found for a 6PCF-XX series test

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Chapter 5. Development of a New Model for CAI Analysis

Figure 5.12: Mesh convergence results: CAI failure load vs. number of elements (eY).

case (the lightly damaged 6PCF-07); however, little dependence on the number of elements

was shown for the other, highly damaged 6PCF-XX series test case. On the other hand, little

mesh dependence was shown for the lightly damaged 3PCF-XX series test case, while some

mesh dependence was shown for the highly damaged 3PCF-XX series case. The mesh density

in the coupon load direction for the 3PCF-16 test case showed convergence when the number

of elements was increased to 80 based on the limited change in CAI failure load achieved

when increasing the mesh density further. These trends are also apparent by looking at the

% change in CAI failure load versus number of elements, shown in Fig. 5.13.

In Fig. 5.13, the convergence of three of the four test cases can be seen clearly.

The highly damaged 6PCF-14 test case does not appear to converge as well with the data

displayed in this form; however, it was shown in Fig. 5.12, previously, that the CAI failure

load predicted for this test case is roughly the same for both 40 elements and 160 elements.

The failure load is slightly increased for the intermediate mesh densities, but the overall mesh

dependence is low.

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Chapter 5. Development of a New Model for CAI Analysis

Figure 5.13: Mesh convergence results: % change in CAI failure load vs. number of elements (eY).

5.3.3 Mesh Convergence: Coupon Thickness Direction (eZc)

Four test cases were again used for the third, and last, section of the mesh convergence

study. This section covers mesh dependence in the throug the thickness direction of the core

region. Only coupons expected to fail by the indentation propagation failure mode were

considered for this portion of the study. As was discussed earlier, the through the thickness

mesh density primarily effects only the out-of-plane deformation of the model. Since, the

out-of-plane deformation was shown in experimental tests to contribute very little to the

crack propagation failure mode, the same results can be expected from the physics-based

FEM. Two test cases were chosen from the PXX series materials, and two were chosen from

the 3PCF-XX series materials. Information about both sandwich panel material systems was

given in Chapters 2 and 3, respectively.

The specific coupons used included one lightly damaged, and one heavily damaged

coupon from each of the material systems. The lightly damaged panels selected were P11

and 3PCF-02, and the heavily damaged test cases were P09 and 3PCF-16. More information

172
Chapter 5. Development of a New Model for CAI Analysis

about these specific test coupons can be found in Chapters 2 and 3. Specific inputs used to

define the ABAQUS input file can be found in Chapter 6, while the mesh used in each of

these analyses will be described in the present section. The through-the-thickness number

of elements in the core region of the model was varied from four to eleven elements. Four

elements is the lowest number of elements which can be used while reasonable FEM results

can be expected. For all test cases, convergence was found by the time the number of elements

was increased to eleven. The number of elements in the coupon load and width directions

were both set to the nominal values of 80. The mesh dependency of the new FEM for CAI

analysis was evaluated based on the result of global coupon CAI failure load, as it was for

the two previous parts of the mesh studies. The results for each test case used in this portion

of the mesh convergence study are shown in Fig. 5.14.

Figure 5.14: Mesh convergence results: CAI failure load vs. number of elements (eZc).

The results for this mesh dependence study are also somewhat varied. For lightly

damaged coupons, mesh convergence is shown, although for the 3PCF-02 case, it actually

appears that the case is hardly mesh dependent at all on the through the thickness number

of elements. Mesh convergence is also less apparent for the highly damaged coupons. The

173
Chapter 5. Development of a New Model for CAI Analysis

percent change with increasing number of elements in Fig. 5.15 is more encouraging, however.

The change for almost all test cases is 3% or less, with the lone outstanding value being from

an analysis with low mesh density. Still, while it does not appear that the mesh of the highly

damaged test cases has converged, it can be said that a reasonable mesh density can be

selected as eight elements. Only an insignificant change in analysis result would be expected

for higher mesh densities.

Figure 5.15: Mesh convergence results: % change in CAI failure load vs. number of elements (eZc).

5.3.4 Additional Notes from the Mesh Convergence Study

The new FEM model’s dependence on mesh density in the test coupon width, load, and

through the thickness directions was studied. The dependence of the CAI failure load was

more dependent on mesh density in the coupon width (eX) and load (eY ) direction for

test cases which failed by crack propagation (6PCF-XX series materials) than for test cases

which failed by indentation propagation (3PCF-XX series materials). This was anticipated

since the failure theory used by Helius:MCT progressive failure analysis software can be

expected to be mesh dependent. As element size decreases near an area of stress concentration

174
Chapter 5. Development of a New Model for CAI Analysis

in the model, element stress will increase, especially at the material points closest to the

stress concentration. This means that as the mesh density increases, failure will begin and

propagate more quickly. This requires that the mesh size in the coupon load and width

direction be fixed at a value which is known to produce reasonable results. For this reason,

a mesh of 80 x 80 (eX x eY ) was chosen for subsequent analyses expected to exhibit the

indentation propagation failure mode, while a mesh of 120 x 120 was chosen for the analyses

expected to exhibit the crack propagation failure mode. Less mesh dependence was shown

in results for through the thickness number of core elements (eZc) for PXX and 3PCF-XX

series materials. A nominal value of eight eZc elements was chosen based on this convergence.

Four elements through the core region thickness will continue to be used for 6PCF-XX series

materials. Although no specific tolerance was selected to define mesh convergence, these

meshes were found to produce reasonable results for the test cases considered. It was shown

that only small changes in results could be expected by increasing the mesh density further

for all cases.

5.4 FEM Sensitivity Studies

The FEM representation of low velocity impact damage in CAI test coupons was previously

discussed in Section 5.2.3. The large amount of CAI test data generated in the experimental

portion of the current research, which was discussed in Chapters 2 and 3, meant that important details could be included in the FEM prior to analysis. The following section will

describe how each detail affects the overall model results for CAI analysis. The purpose of

this study is to identify the confidence level associated with various aspects of the model.

In addition, some aspects of the model are identified as areas of necessary improvement for

future CAI model development, or use of the current model in an engineering design problem.

The damage included in the FEM prior to analysis using the ABAQUS/Standard

solver is defined using a series of inputs to an original, custom “function” written in the

MATLAB programming language. The majority of the function inputs are the result of

175
Chapter 5. Development of a New Model for CAI Analysis

explicit measurements taken using destructive evaluation and NDE techniques, and have

low levels of uncertainty associated with them. The following section will describe most of

these inputs, including the measurements of the residual dent’s diameter, the residual dent’s

maximum depth, the core damage region’s diameter, the facesheet’s IFF region’s diameter,

and the facesheet’s fiber fracture region’s length (only used in models of highly damaged

test coupons). Each of these measurements is applied to the corresponding individual model

with a high precision, due to mesh density or other factors.

One additional MATLAB function input, taken from explicit measurement of a given

test coupon, is the depth of the impact damaged core region of the model. Unfortunately,

due to the mesh pattern and density used, the application of this measurement to the FEM

is done with reduced precision. The possible effect of this uncertainty on the CAI analysis

results is discussed in its own section. Finally, the last three model inputs discussed are the

stiffness reductions given to the material properties associated with damage in the model’s

core and facesheet regions. These three inputs were taken from various sources, and are

not experimental test measurements. The unique uncertainty they add to the model will be

discussed in the third sensitivity study subsection which follows.

5.4.1 Sensitivity to Impact Damage Definition

This section will describe the sensitivity of the new CAI model to the following MATLAB

function inputs: the residual dent’s diameter, the residual dent’s maximum depth, the core

damage region’s diameter, the facesheet’s IFF region’s diameter, and the facesheet’s fiber

fracture region’s length. Four test coupon models were used in these sensitivity studies:

3PCF-02, 3PCF-16, 6PCF-07, and 6PCF-14. These models were specifically chosen for the

following reasons. Two panels were chosen from material systems expected to fail at each

of the two CAI failure modes discussed in the current research: indentation propagation

(3PCF-XX), and crack propagation (6PCF-XX). This will allow the sensitivity of the model

for these inputs to be tested for each specific failure mode. For each of these two material

systems, a lightly damaged test coupon was studied (3PCF-02 and 6PCF-07), as well as a

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Chapter 5. Development of a New Model for CAI Analysis

highly damaged test coupon (3PCF-16 and 6PCF-14). This will allow the sensitivity of the

model to various initial levels of damage to be determined.

Each sensitivity study was conducted for one specific input, while the remaining inputs

were kept constant. Both a conservative change and a non-conservative change were studied,

so that the total number of sensitivity analyses conducted was twice the number of inputs.

The nominal inputs for each of the four test cases used in the sensitivity studies are given in

Table 5.1 below. The effect of an uncertainty of +/-15% with respect to each of the model

inputs was considered. This level of uncertainty is very large with relation to the actual

precision associated with the measurements of the inputs studied; however, some inputs will

have larger effect on the model then others. This large level was chosen so that at least some

change could be seen in each of the analyses completed. Since the change in each inputs was

the same, each of the inputs discussed in the current section could be directly compared and

ranked.

Table 5.1: Nominal input values for MATLAB function for Abaqus input file creation used during

the sensitivity studies.

A specific example can be used to explain the process used to study model sensitivity

to each input. The sensitivity of the FEM to the measurement of the residual dent depth

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Chapter 5. Development of a New Model for CAI Analysis

and subsequent ABAQUS input file definition of the 3PCF-02 test coupon will be used. The

measured dent depth of this particular test coupon was 0.005 in. using a dial caliper, which

had a measurement tolerance of 0.001 in. As was mentioned previously, an uncertainty of

+/-15% was studied. This meant that two analyses were completed. With all other model

definition inputs left at their nominal values, an analysis was completed of the 3PCF-02

coupon with a conservative dent depth value of 0.00575 in. and a non-conservative value of

0.00425 in. Each of the two cases was considered for their effect on coupon CAI failure. The

global failure of the the test coupon can be discussed with respect to failure load, failure

stress, and failure strain. For this example, all three will be discussed, although it will be

shown that the results are very similar. Thus, for the results thereafter, only coupon failure

load will be used.

The sensitivity study results for the example problem (change in 3PCF-02 model

failure load due to potential uncertainty of the residual dent depth input) are shown in Table

5.2. The failure load, failure stress, and failure strain for both the non-conservative and

conservative analyses are shown. The average of the two results is also given. Finally, the

percent change from this average for either a 15% conservative or non-conservative estimate

is given. This information was gathered for each of the inputs considered in the current

section. For each test case, the sensitivity of the model to each input could then be ranked

from most sensitive to least sensitive. Thus, the importance of each input to the overall CAI

analysis result can be shown.

The overall results of the study of the sensitivity of the CAI model to the MATLAB

function inputs of the residual dent’s diameter, the residual dent’s maximum depth, the core

damage region’s diameter, the facesheet’s IFF region’s diameter, and the facesheet’s fiber

fracture region’s length are shown in Table 5.3. For the lightly damaged coupons, which

do not include the fiber fracture region, the sensitivity is ranked from 1 (most) to 4 (least

sensitive). For the highly damaged coupons, which include a fiber fracture region, the ranking

is from 1 to 5.

The sensitivity of the model to a relatively large uncertainty (+/-15%) was surpris178
Chapter 5. Development of a New Model for CAI Analysis

Table 5.2: Detailed sensitivity results of 3PCF-02 test coupon model to residual dent maximum

depth definition.

Table 5.3: Sensitivity study results for various MATLAB function inputs.

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Chapter 5. Development of a New Model for CAI Analysis

ingly small for most test cases. Except for two studies, the model sensitivity was 5% or less.

For most of the inputs used for each of the four test cases, the sensitivity was less than 2%.

The exceptions were the 3PCF-16 model’s sensitivity to dent diameter and core damage diameter inputs. Fortunately, for both of these inputs, the actual uncertainty associated with

the measurements is much smaller than the uncertainty studied. The experimental measurements for these two inputs, shown in Table 5.1, were about 1 in. Thus, the uncertainty

studied (15%) meant that the conservative and non-conservative estimates varied from the

nominal value by about 0.15 in. The experimental uncertainty associated with these measurements can be estimated as 1/60th of an inch for the dent diameter, and is less than 0.001

in. for the core damage region diameter. Therefore, since the actual uncertainty associated

with these two measurements is much smaller, the change in model results is expected to be

much smaller.

A few other interesting trends can be seen in the results. First, the measurement of

the dent diameter has a significant effect on all cases considered. Thus, it is important that

this input is accurate. Additionally, the test cases which can be expected to fail by crack

propagation (6PCF-XX) had very little sensitivity to changes in the core damage region’s

size. This can be expected since core damage primarily impacted out-of-plane deformation

of the test coupons, which is already very small during the crack propagation failure mode.

Finally, each input considered in the current section was shown to have some effect on the

model results. So, it can be concluded that each of these inputs should not be neglected in

the CAI model.

5.4.2 Sensitivity to Core Damage Depth Definition

Special attention was given to the sizing of the core damage region’s depth. This measurement, taken using the destructive evaluation of test coupons by optical microscopy, has a

low uncertainty level associated with the experimental result. However, due to the low mesh

density used, it cannot be implemented with the same precision. The sensitivity of the FEM

analysis results was studied using the test cases described previously: 3PCF-02, 3PCF-16,

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Chapter 5. Development of a New Model for CAI Analysis

6PCF-07, and 6PCF-14. The measurements used as input for the depth of the core damage

for each of these cases can be found in Table 5.1. The MATLAB function for ABAQUS input

file creation was programmed in such a way as to define the core damage region’s depth to

the nearest element. The mesh was defined with eight elements through the core thickness.

The sensitivity was studied with respect to a change in core damage region depth of +/- one

element, since this is the possible error. The results of this portion of the sensitivity studies

are shown in Table 5.4. The global coupon CAI failure load was again used as the primary

indication of sensitivity.

Table 5.4: Sensitivity study results, core damage region depth input.

Remarkably, the change in CAI failure load associated with the core damage region’s

depth was small for three of the four test cases. For both crack propagation cases (6PCF-07

and 6PCF-14), the percent change for each case was just less than 1%. Of course, it should

be expected that this input will have less effect on the crack propagation failure mode, than

for the indentation propagation failure mode. This is due to the fact that the core damage

primary impact out-of-plane deformation, as has been mentioned previously. However, for

the highly damaged low density core test case (3PCF-16), the percent change was even

smaller. For the lightly damaged case, 3PCF-02, the percent change was the largest, but this

was mostly due to the lack of core damage in the non-conservative case (minus one element

meant no damaged core elements were used). This result suggests that the depth of core

damage is less important; however, it is important that at least some finite core damage

depth is used.

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Chapter 5. Development of a New Model for CAI Analysis

5.4.3 Sensitivity to Element Stiffness Degradation

The final portion of the sensitivity study was done with respect to the degradation in stiffness

from pristine material properties which are incorporated in the elements within the “damaged” regions of the FEM. The three damaged regions in the models have been previously

described within the present chapter, and include a damaged core region, and two damaged

facesheet regions. The principal damaged facesheet region represents a region of inter-fiber

fracture (IFF), while for the highest damage test cases, a secondary damaged facesheet region

is modeled which represents failure to both matrix and fiber constituents. The manner in

which these regions are defined, and the stiffness degradations are incorporated was previously discussed in Section 5.2.3.

Three seperate material property degradation values are required, one for each region.

The elements which are incorporated into the core damage region are reduced to 60% of their

initial stiffness. From Fig. 4.3, it can be seen that at the point an initially undamaged element

reaches compressive failure, the stress is reduced to the stress level at which a damaged

element would have obtained. Therefore, the stiffness reduction controls this level, in addition

to the damaged element stiffness. The damaged facesheet elements have material properties

which were calculated from constituent material properties and a “waviness” factor. The

constituent material properties are degraded as follows. For an element representing the IFF

region, matrix properties are degraded by 90% from their initial stiffness. For an element

representing a fiber failed region, matrix properties are still degraded by 90%, but fiber

properties are also degraded by 99% which means that overall a large “soft” discontinuity

will exist in the mesh.

The conservative and non-conservative changes to these material property degradation amounts were as follows. An uncertainty of +/-15% was again used for the damaged

core element material property degradation. This means that a non-conservative degradation of 25% and a conservative degradation of 55% were studied. This range considers the

values which can be considered reasonable from the literature [62] [63] [64].The values used

for matrix and fiber degradation were recommendations from Firehole Composites for use

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Chapter 5. Development of a New Model for CAI Analysis

with their software, Helius:MCT. However, in general, these values are based on fitment to

and understanding of experimental results specific to the materials being studied. This is especially true for the matrix degradation value. Fiber degradation is generally less important,

as long as it is sufficiently large. Therefore, since a large amount of uncertainty is associated

with these values, the values used to study model sensitivity were set as follows. For matrix

property degradation, a conservative value of half the damaged stiffness (5%), and a nonconservative value of twice the damaged stiffness (20%) was chosen. (90% degradation for

matrix constituent material properties means that these properties are 10% of their initial

values.) For the damaged fiber properties, which are 1% of the pristine stiffness, the conservative value of 0.5%, and the non-conservative value of 2% was used. It should be noted

that in addition to the degradation of model regions which are modeled as damaged, these

stiffness reductions are also used by the Helius:MCT software during the CAI analysis for

progressive damage. The sensitivity study takes this into account by adjusting these values

as well.

The results of the third and final portion of the sensitivity studies are shown in Table

5.5. The sensitivity is again shown as a percent change in the CAI failure load. First, the

core stiffness reduction value is shown to influence the coupons which fail by indentation

propagation more than those which fail by crack propagation, as expected. In fact, for

the lightly damaged 6PCF-07 test case, the change in core stiffness reduction has almost no

effect. For the more highly damaged case, 6PCF-14, there is another interesting effect. There

is increased out-of-plane deformation present in this test case due to the dent’s geometry.

Despite the high density core, the large dent depth causes increased though the thickness load

transfer from front facesheet to core, causeing higher deformation. Fiber stiffness reduction

has a very small effect on the overall model result for most test cases, although it is slightly

increased for the 6PCF-14 test case. It is recommended that a conservative estimate of

stiffness degradation normally be used if there is some question of the nominal value. If fact,

in a newer version of the Helius:MCT software package, not used in this research, Firehole

Composites reduced the recommended residual stiffness of the fiber constituent from 1% to

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Chapter 5. Development of a New Model for CAI Analysis

0.0001%.

Table 5.5: Sensitivity study results for element stiffness degradation inputs.

Finally, the change in matrix stiffness degradation has a varied effect on the resulting

CAI failure load. In the literature, this value is discussed in regards to the type of progressive

failure, the type of matrix cracks present, and their orientation [69] [70]. From observations

made during the present research, a specific recommendation would be to implement a gradual degradation approach to matrix failure, as opposed to the single stiffness degradation

which is done in the Helius:MCT software for woven composites. This observation is made

with regards to the progressive failure analysis, rather then the initial stiffness reduction

that is given to the impact damaged regions of the facesheet. In the present research, matrix

failure in analysis results is similar to experimental test results. It does not display the large

amounts of matrix failure which can be characteristic of a continuum damage model, due to

the large stress concentrations considered in CAI analysis.

5.4.4 Final Notes on the FEM’s Sensitivities

A study of sensitivity to the inputs associated with the new CAI analysis model has been

completed. The results are very positive from this study, since most of the changes in failure

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load observed were very small, given the large changes in the nominal input values which were

considered. For some results which did show large changes in CAI failure load for a given

input, it was stated that model confidence for these inputs was still high if the uncertainty

associated with the actual measurement is very low. The following conclusions can be made

which separate model confidence in the inputs studied into the three categories: excellent,

good, and reduced.

For the model inputs for the residual dent depth, the dent diameter, the damaged

core region diameter, and the crack length (i.e. length of the fiber fracture region present

in the more highly damaged test coupon cases), the model confidence is evaluated to be

“excellent.” This is based on low sensitivity of the model to these inputs, combined with

very high precision with which these measurements were taken. The model confidence in

the input which defines the diameter of the facesheet IFF region is only slightly less and

is the sole input with confidence defined as “good.” The reason for this is slightly reduced

precision at which this measurement was taken, but still very low sensitivity of the model

to this input. Finally, the confidence associated with the remaining model inputs can be

defined as “reduced.”

The “reduced” confidence inputs are considered the most reasonable source of any

error that may be found in the analysis results when they are compared to the experiments.

While all of the inputs are significant to the analysis results, these inputs are the in need of the

most future attention if the accuracy in the prediction of CAI failure is to be improved. The

confidence in the following inputs is considered to be “reduced”: the depth of the damaged

core region, and the stiffness reduction associated with “damaged” elements in the core, the

facesheet IFF region, and the facesheet fiber fracture region. The uncertainty in the core

damage depth could be easily improved by refining the model’s mesh. However, it was shown

that the depth of the core damage has limited impact on the analysis results, as long as some

damage is present. The stiffness reduction inputs are the areas of highest uncertainty. The

core reduction input should be found in future research through a simple flatwise core crush

test. The matrix and fiber degradation values come from cutting edge areas of composite

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Chapter 5. Development of a New Model for CAI Analysis

damage research. With future research, the confidence in these values will increase.

5.5 Conclusions from the Development of the New FEM

for CAI Analysis

The development of a new model for CAI analysis of thin facesheet honeycomb core sandwich

panels was described in the present chapter. Two significant contributions of this research

to the understanding of CAI analysis were given as follows. One is the implementation

of PFA for facesheet failure using a commercial implementation of multicontinuum failure

theory, Helius:MCT, by Firehole Composites. An explanation of the relevant theory to the

current research then continued with the development of multicontinuum theory (MCT), as

developed by Garnich and Hansen [74], and MCT failure theory, as developed by Mayes and

Hansen [75]. The second signicant contribution made in the current chapter is the inclusion

of significant low velocity impact damage detail in the the new CAI model. A small amount

of micromechanics theory was used in the description of how this impact damage is included

in the model.

The chapter continued with an in-depth introduction to the new CAI model. This

section included details on model geometry, boundary conditions, and type of elements used.

Two final sections of the current chapter discussed the mesh pattern and convergence, as well

as the model sensitivity to uncertainties associated with the important inputs to the custom

MATLAB function for creation of the ABAQUS input files. The mesh convergence section

showed that a relatively simple mesh can be used to obtain good results. Additionally, it was

shown that only small changes should be expected to analysis results as a result of increasing

mesh density. It was later shown that through the thickness mesh density is important to test

cases which fail by indentation propagation, while coupon load and width direction density

is more important to test cases which fail by crack propagation. The latter result is expected

since mesh has a significant influence on continuum damage models.

The sensitivity study was used to show the importance of each input to the overall

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Chapter 5. Development of a New Model for CAI Analysis

model results. Each input was discussed with relation to overall model confidence. The most

uncertainty in the model was found to come from the values which determine the amount

that the stiffness associated with “damaged” elements are degraded from pristine material

property values. The uncertainty in each input has some finite effect on the CAI model

result, but confidence is achieved through careful and accurate measurement of the inputs

during experimental testing. This concluded the development of the new CAI model in the

present chapter. Chapter 6, which follows, will discuss the finite element analysis of each of

the 32 experimental test coupons. The analysis results will be compared to experimental test

results found in Chapter 2 and 3, and these results will ultimately be used to validate the use

of the new model. In addition, specific attention will be given to the effect of core density

(and resulting continuum core properties) on the failure strength and CAI failure mode of

the test coupons. This will be done through a parametric study of varying core density.

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Chapter 6

Analysis of Test Coupons and Other

CAI Analysis Results

A new finite element model (FEM) for the compression after impact (CAI) analysis of thinfacesheet honeycomb core sandwich panels with low velocity impact damage has been developed. In Chapter 4, theory about the basics of classical laminate theory (CLT), ABAQUS

finite element formulations, and continuum representation of homogenized honeycomb core

material properties was discussed as pertinent to the new FEM. Also, in the chapter, the

use of two models which represent the current state of development of finite element analysis

(FEA) of CAI failure in honeycomb core test coupons was presented. The use of these models

has shown that a limited representation of the indentation propagation failure mode existed

prior to the current research.

Subsequently, in Chapter 5, the new developments of the current research for CAI

analysis was presented. The two major advantages of the new model include the incorporation

of a progressive failure analysis for damage propagation in the facesheets, and a detailed

representation of the impact damage included in the model prior to the CAI analysis. The

former’s importance is two-fold. First, a more accurate representation of the indentation

propagation failure mode can be achieved. Second, the new FEM has the ability to represent

multiple failure modes, to include the crack propagation failure mode of the high density

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Chapter 6. Analysis of Test Coupons and Other CAI Analysis Results

honeycomb core materials found during the current research. The detailed impact damage

representation has benefits as well. In addition to providing a more accurate representation

of the CAI test coupons, each part of the damage was studied for its specific contribution to

the CAI result.

The purpose of the present chapter is to validate the new FEM by comparing analysis

results with experimental test results. In Chapters 2 and 3, tests were completed on several

honeycomb core sandwich panel material systems. A total of 32 test coupons were damaged

with a low velocity impact and tested to CAI failure. The impact damage in each of these

test coupons was considered using non-destructive evaluation (NDE) techniques. This data,

combined with some data taken using dissection of impact survey coupons, was used to define

32 total analyses. In the present chapter, the results of these analyses are compared with

experimental test results. Comparisons are done primarily with respect to global coupon failure results (e.g. CAI failure load). In addition, results from alternate observation techniques

are used, including time lapse images from high speed video photography, and measurements

that were taken by digital image correlation (DIC).

6.1 Analysis of CAI Response of PXX Series

Panels

The following section will be used to compare the analysis results obtained using the new

FEM with experimental test results for PXX series CAI test coupons, which were discussed

in Chapter 2. During these CAI tests, a total of eight coupons were tested to failure under

end-loaded compressive conditions. Low velocity impact damage was inflicted on each of

these test coupons, prior to compressive loading in the energy level range from 0.5 to 2.0

ft-lbs. Two coupons were impacted at each of the following energy levels: 0.5, 1.0, 1.5 and 2.0

ft-lbs. A unique FEM was created to represent each of the tested coupons, and an analysis

was completed to assess the coupons’ CAI response. The results of these analyses will be

presented and compared to the experimental results, but first, each model will be described.

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Chapter 6. Analysis of Test Coupons and Other CAI Analysis Results

6.1.1 PXX Analysis Inputs

Each FEM used for analysis of PXX series CAI tests was defined with appropriate geomtry.

Since, the models take advantage of symmetry, a 3 in. by 3 in. quadrant of the 6 in. by 6

in. PXX test coupons was modeled with appropriate boundary conditions. The materials,

discussed in more detail in Chapter 2, consisted of E-glass/Epoxy woven fabric facesheets

with two 0.01 in. plies in each facesheet for a total thickness of 0.02 in. and 1 in. thick,

3 lb/ft3. Nomex honeycomb core. These dimensions were used to define the facesheets and

core, respectively, in the FEM.

The material properties associated with the plies of the composite laminate facesheets

are defined in Table 6.1. The lamina material properties are similar to the properties given

by AAR composites [78], while the fiber and matrix constituent properties are the in situ

properties calculated using the Helius Material Manager. Deviations in the lamina material

properties from the AAR Composites provided properties were done when it was found during

experimental testing that the Young’s modulus was not accurate. The Young’s modulus of

all PXX series experimental test coupons was about 3.5 Msi. Additional material properties

were consulted, and since the exact epoxy material was unknown, the Advanced General

Aviation Transport Exerpiments (AGATE) properties for 3M E-Glass Fabric were chosen

since they most closely resembled the experimentally determined stiffnesses. The strengths

corresponding to E-glass/epoxy materials are given in Table 6.2 [98]. The strengths include

the weave knee strengths, which are used by the commercial software, Helius:MCT, to predict

matrix failure. The weave knee strengths were set at 85% of the lamina strengths.

In Table 6.3, the homogenized orthotropic properties for the continuum representation

of the Nomex honeycomb core are given. These material properties were either given by the

Hexcel Corp. data sheet [86], or were calculated by the appropriate equations found in Gibson

and Ashby [55]. The flatwise compressive strength of the Nomex honeycomb was 270 psi.

[86]; the corresponding compressive failure strain used in the ABAQUS user subroutine was

0.0135 in/in. Each analysis was displacement controlled. A sufficiently large displacement

(usually 0.035 in.) was given in the input file; however, the analysis was usually not carried

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Chapter 6. Analysis of Test Coupons and Other CAI Analysis Results

Table 6.1: E-glass/Epoxy woven fabric lamina material properties used in the CAI analysis of PXX

series test coupons.

Table 6.2: E-glass/Epoxy woven fabric lamina strengths used in the CAI analysis of PXX series

test coupons.

out until the maximum applied displacement due to convergence problems which appear

post-failure in the analysis. This does not affect the CAI response and failure that the

analysis predicts, but limit the usefulness of the model for post-failure response analysis.

(Post-failure response was not a goal of these analyses.)

Table 6.3: 3PCF Nomex honeycomb core orthotropic engineering constants used in the CAI analysis

of PXX and 3PCF-XX series test coupons.

Damage incorporated into the model to simulate the low velocity impact damage

was detailed in Chapter 5. The components of this damage first included a geometric dent,

defined by a maximum diameter and depth. Also, a specific set of core elements was defined as

“damaged” based on experimental observations. This region requires a depth and diameter,

as well as a stiffness degradation to be specified. Next, a set of facesheet elements was defined

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Chapter 6. Analysis of Test Coupons and Other CAI Analysis Results

as damaged based on the presence of inter-fiber fracture (IFF). This set was defined by a

measured diameter, and a stiffness degradation of the matrix constituent material properties.

Finally, for highly damaged test coupons, a second set of elements was included, along the

x-axis (width direction) of the FEM, defined using a length, measured from the model’s

coordinate system origin, to represent fiber fracture. A fiber constituent material property

degradation was also included in this region, in addition to the matrix property degradation.

The dent depth and diameter definition was taken from the actual experimental measurements of individual PXX series CAI test coupon, prior to compressive loading. The

inputs of damaged core region depth and diameter, as well as the damaged facesheet region

diameter (and length for the fiber damaged region in highly damaged coupons), was taken

from results of the drop tower impact survey of damage formation. Thus, models of test

coupons impacted at the same impact energy (e.g. P11 and P12, or P04 and P05) have identical inputs for these damage components. The numeric values which concern the geometry

of the impact damage dent and the damaged material regions can be found in Table 6.4.

Table 6.4: MATLAB program inputs for creation of ABAQUS input files to run analyses of PXX

series test coupons.

The three values which define the material property degradation in all analysis models

are as follows.

1. The stiffness of “damaged” core element was reduced to 60% of the pristine properties.

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Chapter 6. Analysis of Test Coupons and Other CAI Analysis Results

2. The stiffness of the matrix constituent properties of “damaged” elements in the IFF

region of the facesheet model was reduced to 10% of the pristine properties.

3. For the fiber fracture region in some analysis models, fiber properties are reduced to

1% of their pristine value in addition to the 90% reduction in matrix properties.

6.1.2 PXX Analysis Results

A set of analyses on the CAI response and failure of each of the eight PXX series test coupons

was performed. First, to demonstrate the appropriate response of the coupon at failure, the

reaction force vs. applied displacement is considered. From experimental testing, in Chapter

2, it is expected that at failure, a sudden, instantaneous drop in reaction force will occur.

This response is demonstrated in the reaction force vs. the applied displacement results

obtained for each of the eight analyses, which are shown in Fig. 6.1. The reaction force is

obtained in the analysis by summing the force resultant at each node where displacement is

applied, and then multiplying by two (since symmetry is used).

For the PXX series tests, the failure mode expected is indentation propagation. In

order to correctly predict this failure mode, the present model needs to be able to predict

local buckling of the facesheet as well as the facesheet crack which propagates with the region

of local buckling. The present model is highly successful at capturing this failure mode, as

shown in Fig. 6.2, through the use of a non-linear core model, as well as simulated facesheet

failure using the implementation of progressive failure analysis. In Fig. 6.2, the indentation

propagation failure of an example test coupon, as predicted by analysis, is compared to a

sequence of photos from high speed photography, which was first shown in Chapter 2. Model

results for out-of-plane displacement shows where local buckling as occurred. Model results

for element damage show how damage propagates in both the core (by crushing), and the

facesheets (simulating crack propagation).

The typical results used to establish the condition of the simulated sandwich panel

coupon at CAI failure are failure load, failure stress, and failure strain. The results obtained

for the analysis of PXX series coupons are shown in Table 6.5. The results for failure stress

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Chapter 6. Analysis of Test Coupons and Other CAI Analysis Results

Figure 6.1: PXX analysis results: reaction force vs. applied displacement for analysis of PXX series

test coupons.

were used for validation of the model by comparison to experimental test results, although

if failure load or strain had been used, the results would have been similar. The results

comparison is shown in Fig. 6.3.

The correct failure mode, indentation propagation, was established for all eight of the

analyses completed. The analysis results for CAI strength of the eight PXX test coupons

show good agreement with experimental test results. The error range was from about 20%, to

less than a percent; the largest error pertains to the two lightly damaged test cases, P11 and

P12. Although the largest errors are significant, the analysis results are conservative. More

importantly, however, the analysis results and experimental test results appear to approach

similar minimum levels of coupon strength with increasing impact energy. This phenomenon,

where a minimum failure stress is approached, is the basis for the CAI failure strength which

typically appears in literature. The ability of the FEM to predict this behavior is a strong

indication that a significant level of fidelity has been achieved.

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Chapter 6. Analysis of Test Coupons and Other CAI Analysis Results

Figure 6.2: Demonstration of correct failure mode prediction for example analysis of PXX series

material coupons using the new FEM for CAI analysis.

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Chapter 6. Analysis of Test Coupons and Other CAI Analysis Results

Table 6.5: PXX analysis results: failure load, strength and strain for analysis of PXX series test

coupons.

Figure 6.3: PXX analysis results: comparison of PXX test coupon analysis failure strength to

experimental test results.

One final comparison which can be made between the PXX series analysis results

and experimental test results is of indentation growth predicted during analysis to measure196
Chapter 6. Analysis of Test Coupons and Other CAI Analysis Results

ments taken using the digital image correlation (DIC) system during experimental testing.

A DIC system is used to take full-field displacement measurements and is capable of fullfield, three-dimensional surface mapping. For comparisons, similar data from analysis was

collected using the ABAQUS post-processor, ABAQUS/Viewer. In Chapter 2, DIC measurements were shown for the size of the indentation in the front damaged facesheet of select

panels throughout the linear elastic portion of the CAI test, to show the magnitude of the

stable indentation propagation. The measurements that were taken included the maximum

length of the elliptical indentation along its semi-major axis (taken in the coupon width

or X-direction), the maximum width of the elliptical indentation along its semi-minor axis

(taken in the coupon load or Y-direction), and the maximum depth of the indentation. For

comparison purposes, the corresponding length, width, and depth of the CAI analysis predicted indentation propagation (found using ABAQUS/Viewer) is shown in Figs. 6.4, 6.5,

and 6.6, respectively.

Figure 6.4: PXX analysis results: dent growth in the coupon width direction (x-direction) predicted

from FEA of PXX test coupons.

The indentation growth in Figs. 6.4, 6.5, and 6.6 is very similar to the DIC experimental test results shown in Figs. 2.34, 2.35, and 2.36, respectively. It should be noted

that the four test cases used in each figure are the same for both analysis and experimental

test results. The analysis successfully demonstrates stable dent growth in the coupon width

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Chapter 6. Analysis of Test Coupons and Other CAI Analysis Results

Figure 6.5: PXX analysis results: dent growth in the coupon load direction (y-direction) predicted

from FEA of PXX test coupons.

Figure 6.6: PXX analysis results: maximum dent depth growth predicted from FEA of PXX test

coupons.

direction (also the analysis x-direction), while the size of the dent remains nearly constant

in the load direction. The size of the FEM dent stays approximately unchanged until 50% of

the coupon’s eventual failure load, which is expected from experimental testing. The magnitude of the dent growth in analysis does not reach the same amount of dent growth as found

experimentally. The final dent size just before failure is smaller during FEA. This is readily

apparent in the results for the maximum depth. The maximum dent depth at failure, in

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Chapter 6. Analysis of Test Coupons and Other CAI Analysis Results

each of the four cases considered, is a whole order of magnitude less than the maximum dent

depth at failure found from the DIC result. This can be seen by comparing Fig. 6.6 with

Fig. 2.36.

6.2 Analysis of CAI Response of 3PCF-XX Series

Panels

CAI tests were conducted on two addional, nearly identical, sandwich panels, with the only

difference in construction being the density of the honeycomb core. The experimental testing

on these materials was described in Chapter 3. The first of these materials, given the designation 3PCF-XX, contained the lower of the two core densities. It was expected, and in fact

found, that the CAI failure mode (indentation propagation) of the 3PCF-XX test coupons

would be identical to that of the PXX series panels. In the following section, the CAI analysis

results for 3PCF-XX series test specimens will be compared with experimental test results

for these panels. For the 3PCF-XX series CAI tests, a total of twelve coupons were tested

to failure. Low velocity impact damage was inflicted on each of these test coupons, prior

to compressive loading. Three coupons were impacted at each of the following four energy

levels: 1.0, 3.0, 5.0 and 7.0 ft-lbs. An analysis of each coupon has been completed using a

unique FEM using inputs from observations made on experimental test coupon. The following section will described the inputs used to created the FEM, the analysis results, and the

experimental test comparison.

6.2.1 3PCF-XX Analysis Inputs

Each FEM, which takes advantage of symmetry as described in Chapter 5, represents a 2.75

in. by 2.75 in. quadrant of a 3PCF-XX series coupon. The 0.02 in. thick facesheets consisted of woven S2-glass plies, and the core was a 0.75 in. thick 3 lb/ft3

. Nomex honeycomb.

Additional material details can be found in Chapter 3. The elastic facesheet material properties used in the analyses are summarized in Table 6.6. The lamina material properties

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Chapter 6. Analysis of Test Coupons and Other CAI Analysis Results

are similar to the those published for the material by the National Institute of Aerospace

Research (NIAR) [85], though they differ slightly due to processing by the Helius Material

Manager. The matrix and fiber constituent properties are the in situ properties calculated

by the Material Manager. The material strengths used can be found in Table 6.7 for the

S2-glass/epoxy facesheets, which includes the knee strengths for matrix failure prediction,

which are set at 85% of the lamina strengths. The material strengths are based on the NIAR

data [85], except the in-plane shear strength which was artificially increased to prohibit unrealistic matrix failure during analysis in the 45 degree plies. (It can also be noted that the

experimental test results for in-plane shear, which can be obtained by contacting the NIAR

test engineers, do not exhibit a true failure point. The engineers stop the test prior to failure

once 5% strain was reached.)

The material properties used in the continuum representation of the Nomex honeycomb are shown in Table 6.3, previously. These material properties were either given by in

the literature by Hexcel Corp. [86], or were calculated using the equations found in Gibson

and Asby [55]. The out-of-plane compressive failure strength was again 270 psi [86]and the

corresponding compressive failure strain for the Nomex honeycomb was 0.0135 in/in. Each

analysis was displacement controlled, similar to the description given in the previous section

for the PXX series analyses.

Table 6.6: S2-glass/Epoxy woven fabric lamina material properties used in the CAI analysis of

3PCF-XX and 6PCF-XX series test coupons.

The components of impact damage used to define the geometry of “damaged” regions

of the model and the appropriate material properties are as described in the previous section

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Chapter 6. Analysis of Test Coupons and Other CAI Analysis Results

Table 6.7: S2-glass/Epoxy woven fabric laminate strengths used in the CAI analysis of 3PCF-XX

and 6PCF-XX series test coupons.

for the PXX series coupons. Further detail was described in Chapter 5. The numeric values

which govern the geometry of the impact damage dent and the damaged material regions in

the 3PCF-XX analysis models can be found in Table 6.8.

Table 6.8: MATLAB program inputs for creation of ABAQUS input files to run analyses of 3PCFXX series test coupons.

The three values which define the material property degradation in all analysis models

are as follows, and they are identical to those used for PXX series analyses:

1. The stiffness of “damaged” core element is reduced to 60% of the pristine properties.

2. The stiffness of the matrix constituent properties of “damaged” elements in the IFF

region of the facesheet model is reduced to 10% of the pristine properties.

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Chapter 6. Analysis of Test Coupons and Other CAI Analysis Results

3. For the fiber fracture region in some analysis models, fiber properties are reduced to

1% of their pristine value in addition to the reduction in matrix properties.

6.2.2 3PCF-XX Analysis Results

The indentation propagation failure mode was demonstrated for each of the 3PCF-XX analyses completed, as expected from experimental testing discussed in Chapter 3. The FEM

representation of this failure mode was shown previously for a PXX series example in Fig.

6.2. The appropriate reaction force vs. applied displacement was also predicted in each analysis, where a sudden drop in reaction force is found at failure. This response is demonstrated

for the 3PCF-XX series analysis in Fig. 6.7.

Figure 6.7: 3PCF-XX analysis results: reaction force vs. applied displacement for analysis of 3PCFXX series test coupons.

The main comparisons between analysis results and experimental test results will

again be made using results for coupon failure strength. Results can also be obtained from

FEA for failure load and failure strain. The results obtained for the analysis of 3PCF-XX

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Chapter 6. Analysis of Test Coupons and Other CAI Analysis Results

series coupons are shown in Table 6.9, for each predicted CAI failure analysis result, with

comparisons to experimental test results and the associated errors. The results comparison

is shown graphically, in Fig. 6.8, for CAI failure strength of the 3PCF-XX series specimens,

though this comparison would be similar if shown for failure load or failure strain.

Table 6.9: 3PCF-XX analysis results: failure load, strength and strain for analysis of 3PCF-XX

series test coupons.

Many of the 3PCF-XX analysis results show good agreement with experimental test

results. The error ranged in magnitude from about 20% to less than a percent, for failure

load, strength, and strain. Although the largest errors are significant, the analysis results

are generally conservative, except for the test coupons with the lowest amounts of damage.

From this result, it can be concluded that the damage included in the analysis of 3PCF-XX

test coupons to represent a low velocity impact at 1.0 ft-lbs. was non-conservative. The

analysis results for failure strength approach a minimum, which is shown by comparison of

the analysis results for the models with damage representing both 5.0 and 7.0 ft-lbs. energy

level impacts. The failure stress result for each of these six analysis data points are similar.

The behavior of the CAI models with large amounts of damage suggests that the model

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Chapter 6. Analysis of Test Coupons and Other CAI Analysis Results

Figure 6.8: 3PCF-XX analysis results: comparison of 3PCF-XX test coupon analysis failure strength

to experimental test results.

would be useful in estimating the CAI strength of coupons which fail by the indentation

propagation failure mode.

A comparison can again be made between the stable dent growth predicted in the

FEA and the stable dent growth measured using the DIC system. The DIC system was

used for a select set of four 3PCF-XX series test coupons, and was discussed previously in

Chapter 3. Results for the predicted indentation growth found during analysis were also

produced using the ABAQUS/Viewer for these four test cases. One test case was considered

at each of the four damage levels (1.0, 3.0, 5.0 and 7.0 ft-lbs.) The analysis results for the

dent length measurements in the coupon width (x-) direction, coupon load (y-) direction,

and the dent depth measurement in the through the thickness (z-) direction are shown in

Figs. 6.9, 6.10, and 6.11, respectively. These analysis results can be compared to the DIC

experimental results shown in Figs. 3.32, 3.33, and 3.34, respectively.

The results for dent growth during FEA of 3PCF-XX series tests, and the comparison

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Chapter 6. Analysis of Test Coupons and Other CAI Analysis Results

Figure 6.9: 3PCF-XX analysis results: dent growth in the coupon width direction (x-direction)

predicted from FEA of 3PCF-XX test coupons.

Figure 6.10: 3PCF-XX analysis results: dent growth in the coupon load direction (y-direction)

predicted from FEA of 3PCF-XX test coupons.

to experimental test results, was very similar to the results previously shown for PXX series

tests. As expected from experimental testing, more growth is seen in the coupon width

direction, than in the coupon load direction. The stable dent growth measurement in the

width direction is only slightly smaller than the measurements taken with the DIC system.

However, as seen in PXX series results, the dent depth does not obtain the same amount

of growth seen in DIC measurements of 3PCF-XX series experimental tests. This can be

shown by comparison of Fig. 6.11 to Fig. 3.34. The dent depths found in analysis are about

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Chapter 6. Analysis of Test Coupons and Other CAI Analysis Results

Figure 6.11: 3PCF-XX analysis results: maximum dent depth growth predicted from FEA of 3PCFXX test coupons.

half the size at failure as the corresponding measurements taken in experimental tests. From

this result, it appears that the model is less stable and more prone to local buckling due to

out-of-plane deformation than an experimental test panel.

6.3 Analysis of CAI Response of 6PCF-XX Series

Panels

Analysis of the second of two nearly identical honeycomb core sandwich panels, described in

Chapter 3, will be discussed in the following section. The only difference in the construction

of these two materials was the density of the honeycomb core. The subject of the current

section, dubbed 6PCF-XX, contained the higher density core. A different failure mode, called

crack propagation in the current research, was found to result from the presence of the high

density honeycomb core. CAI analysis results obtained for the 6PCF-XX series test coupons

will be compared with experimental test results in this section. Like the 3PCF-XX series

CAI tests, a total of twelve 6PCF-XX coupons were tested to failure. Low velocity impact

damage was inflicted on these test coupons at each of the following four energy levels: 1.0,

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Chapter 6. Analysis of Test Coupons and Other CAI Analysis Results

3.0, 5.0 and 7.0 ft-lbs. The following section describes each CAI analysis completed, the

analysis results, and then the comparison to the experimental test results.

6.3.1 6PCF-XX Analysis Inputs

The geometry of the 6PCX-XX test coupon models was identical to those described previously

for the 3PCF-XX set. Complete details on the construction of these materials were given

in Chapter 3. The elastic material properties used in the analyses were summarized in

Table 6.6 for the S2-fiberglass/Epoxy facesheets, and the corresponding lamina strengths

and knee strengths were given in Table 6.7. These values are similar to those available in

the literature [85], but some differences were discussed in the previous section. The elastic

material properties for the higher density 6 lb/ft3. (6PCF) honeycomb core are given in Table

6.10. These properties are either given in by Hexcel Corp. [86], or were calculated using the

relations found in Gibson and Ashby [55]. The out-of-plain compressive failure stress for

the higher density, 6PCF, Nomex core was 925 psi [86], and the corresponding compressive

strain value used to mark the onset of flatwise compressive failure in the ABAQUS UMAT

was 0.0154 in/in. Each analysis was again displacement controlled as described in Section

6.1.1.

Table 6.10: 6PCF Nomex honeycomb core orthotropic engineering constants used in the CAI analysis of 6PCF-XX series test coupons.

The components of impact damage used to define the geometry of “damaged” regions

of the model and the appropriate material properties are as described previously in the

current chapter, and in further detail in Chapter 5. The numeric values which govern the

geometry of the impact damage dent and the damaged material regions in the 6PCF-XX

analysis models can be found in Table 6.11. As was mentioned in previous sections, the dent

depth and diameter were measured using the individual experimental test coupons prior to

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compressive loading. Other inputs were taken from coupons used in the damage formation

tests when destructive evaluation techniques were necessary. Thus, they are common to a

particular impact energy level (e.g. the damaged core region geometry will be the same for

all analysis models representing coupons damaged at 3.0 ft-lbs. impact energies). The three

values which define the material property degradation in all analysis models are as follows,

and are identical to those used in PXX and 3PCF-XX series analyses:

1. The stiffness of “damaged” core element is reduced to 60% of the pristine properties.

2. The stiffness of the matrix constituent properties of “damaged” elements in the IFF

region of the facesheet model is reduced to 10% of the pristine properties.

3. For the fiber fracture region in some analysis models, fiber properties are reduced to

1% of their pristine value in addition to the reduction in matrix properties.

Table 6.11: MATLAB program inputs for creation of Abaqus input files to run analyses of 6PCF-XX

series test coupons.

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Chapter 6. Analysis of Test Coupons and Other CAI Analysis Results

6.3.2 6PCF-XX Analysis Results

The newly developed FEM for analysis of CAI test coupons was used to study the 6PCF-XX

series test coupons. This set of materials was of particular interest during analysis, because

one of the principal contributions of the current research is the implementation of progressive

failure analysis (PFA) of the FEM facesheets. This inclusion gives the model the ability to

predict a new failure mode, crack propagation, not previously shown in sandwich panel CAI

analysis. The following results will show that the new model is successful in predicting

crack propagation failure in each of the twelve 6PCF-XX CAI test coupons with the higher

density 6 lb/ft3. Nomex honeycomb core. First, to demonstrate the appropriate response

of the coupon at failure, the reaction force vs. applied displacement is considered. From

the results of experimental testing, discussed in Chapter 3, it is expected that at failure an

instantaneous drop in reaction force will occur. This is demonstrated in the FEA analysis

results for reaction force vs. applied displacement, which are shown in Fig. 6.12.

Figure 6.12: 6PCF-XX analysis results: reaction force vs. applied displacement for analysis of

6PCF-XX series test coupons.

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Chapter 6. Analysis of Test Coupons and Other CAI Analysis Results

For most of the results shown in Fig. 6.12, there was a very clear reduction in reaction

force, although it is not as large as seen in previous analysis results for PXX and 3PCF-XX

series materials, shown in Figs. 6.1 and 6.7, respectively. Once the drop in reaction force

begins in the 6PCF-XX analysis results, the ABAQUS/Standard solver begins to demonstrate

poor solution convergence in each subsequent iteration, more so than it did for the indentation

propagation failure. The result is that either the ABAQUS/Standard solver exits, or a user

input halts the analysis to keep the size of the resulting ABAQUS output database file (.ODB

file) reasonable. One analysis, for the 6PCF-06 coupon, continues to increase in reaction force

once initial reduction has been reached. Although the soft discontinuity, or “crack” in the

FEM has propagated across the front facesheet, the coupon still continues to hold substantial

load. This is due to softening of elements after matrix failure, generally when excess matrix

failure occurs, prohibiting appropriate fiber failure later. The possibility of this occurring is

one drawback of using a continuum damage model for PFA in the current research. It was

noted during the course of the research, that for a less dense mesh this was less likely to

occur. Adjusting the mesh is thus one solution which can be used to obtain a better result.

For the 6PCF-XX series material coupons, the failure mode expected from the experimental test results is crack propagation. It is expected that, in the linear elastic portion of

a 6PCF-XX test coupon’s CAI response, there will be minimal growth of the impact damage

dent. There may be some modest, stable growth of a facesheet crack which begins at the

location of the impact damage. The new model is successful, using Helius:MCT, at capturing

the crack propagation failure mode, as shown in Fig. 6.13. The unstable crack propagation

for an example test coupon in the FEA analysis is compared to a sequence of photos from

high speed photography of an experimental test, which was first shown in Chapter 3. Model

results for out-of-plane displacement shows that no local buckling is predicted, and there

is very little dent growth during the analysis. FEA results for element damage predict the

facesheet crack which appears in experimental results.

The point of sudden drop in coupon reaction force in the FEA results for force vs.

displacement indicates the point of global coupon failure. (For the 6PCF-06 case, the failure

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Chapter 6. Analysis of Test Coupons and Other CAI Analysis Results

Figure 6.13: Demonstration of crack propagation failure mode for example analysis of 6PCF-XX

series material coupons using the new FEM for CAI analysis.

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Chapter 6. Analysis of Test Coupons and Other CAI Analysis Results

point chosen was the first sudden drop in reaction force. Where the reaction force increased

again after failure, this behavior is thought to be a flaw of the composite damage analysis

method chosen, due to excess matrix failure predicted in the model.) The main focus of this

discussion on the the differences between the analysis results and the experimental test results

will again be CAI strength. However, results can also be obtained from FEA for failure load,

and failure strain, and these analysis results compare to experimental test results in a similar

manner. The results for the analysis of 6PCF-XX series coupons are shown in Table 6.12,

for CAI failure load, strength, and strain, with numerical comparison to experimental test

results. The results comparison is shown graphically, in Fig. 6.14, for failure stress.

Table 6.12: 6PCF-XX analysis results: failure load, strength and strain for analysis of 6PCF-XX

series test coupons.

The FEA results of the 6PCF-XX series test coupons tended to be non-conservative.

This is shown in Fig. 6.14. Numerically, the errors for predicted failure load, stress and

strain varied from about 20% to less than a percent, as in the analyses for the two other

material systems. Only a few of the results were in error by 20%; however, most were under

15%. There does not appear to be any correlation between the accuracy of the model for a

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Chapter 6. Analysis of Test Coupons and Other CAI Analysis Results

Figure 6.14: 6PCF-XX analysis results: comparison of 6PCF-XX test coupon analysis failure

strength to experimental test results.

specific analysis result and the damage level of the test coupon. It is interesting to note that

in the analysis predictions, there is very little spread in the CAI failure results for a given

impact damage level, though the impact damage inputs do very. This is contrast to the large

amount of variation in the experimental CAI test results found at a certain impact energy

level. It was shown in the sensitivity studies in Chapter 5 (specifically in Table 5.3), that the

model sensitivity to damage definition inputs was small for the 6PCF-XX series analyses.

Since, only the dent depth and diameter varied with each analysis and the remaining inputs

were kept constant (since they came from the 6PCF-XX impact survey specimen and not the

actual CAI test specimen), one can expect little variation in the analysis prediction results.

A comparison was again made between analysis predictions for indentation growth

and experimental test measurements of select 6PCF-XX series test coupons using the DIC

system. Analysis prediction results for dent size in the coupon width and load directions, and

the maximum dent depth can be seen in Fig. 6.15, 6.16 and 6.17, respectively. Comparisons

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Chapter 6. Analysis of Test Coupons and Other CAI Analysis Results

were made with respect to the DIC experimental test results which were shown previously

in Fig. 3.35, 3.36 and 3.37, respectively.

Figure 6.15: 6PCF-XX analysis results: dent growth in the coupon width direction (x-direction)

predicted from FEA of 6PCF-XX test coupons.

Figure 6.16: 6PCF-XX analysis results: dent growth in the coupon load direction (y-direction)

predicted from FEA of 6PCF-XX test coupons.

There was little to no predicted growth of the residual dent during the FEA of 6PCFXX series test coupons. This was expected from the experimental test results. Some growth

appears at the very last stage of the coupon response in the coupon width direction, shown

in Fig. 6.15. These results compare well to the experimental test results shown in Chapter

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Chapter 6. Analysis of Test Coupons and Other CAI Analysis Results

Figure 6.17: 6PCF-XX analysis results: maximum dent depth growth predicted from FEA of 6PCFXX test coupons.

3 The correlation between the experimental test results and the FEA predictions is stronger

for the 6PCF-XX series materials, than it was for the PXX or the 3PCF-XX series materials.

6.4 Parametric Study of CAI Response with Various

Core Densities

One of the major conclusions of the present research is that there is a large dependence of

the CAI failure mode in the sandwich panels studied on the density of the honeycomb core

material included in their construction. In the present study, the traditional sandwich panel

CAI failure mode, indentation propagation, is found for panels with the lower density 3 lb/ft3.

honeycomb core. The higher density, 6 lb/ft3., core clearly produced a different failure mode,

crack propagation, and higher failure strengths. As a result, a parametric study has been

completed to determine the critical density of the honeycomb core at which the failure mode

transitions from indentation propagation to crack propagation failure mode. In addition,

one of the purposes of this study was to determine the increase in failure strength possible

by increasing the core density, without changing any of the other parameters. The strength

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Chapter 6. Analysis of Test Coupons and Other CAI Analysis Results

increase was studied with respect to the mass penalty caused by increasing the honeycomb

core density. The material properties which define the crush response of the various density

Nomex honeycomb cores will be discussed in the following section. Following that, the results

of the parametric study analyses will be presented.

6.4.1 Discussion of Core Crush Property Variance with

Core Density

A single CAI model was chosen to determine the effect of the core density on the CAI

response. For the parametric study, the geometry modeled corresponds to the 3PCF-XX

and 6PCF-XX test coupons, so that a single 2.75 in. by 2.75 in. quadrant of a test coupon

is modeled with 0.02 in. thick facesheets and a 0.75 in. thick core. Damage in each model

used with the parametric study was modeled using the inputs for the 3PCF-13 test coupon,

which were given previously in Table 6.8. The stiffness reductions for the damaged core, IFF

damaged facesheet, and fiber fracture damaged facesheet regions’ stiffness reductions are as

follows, (and used in all other analyses discussed withing the present chapter:

1. “Damaged” core elements was reduced to 60% of their original stiffness.

2. The matrix constituent stiffness reduction was 90% in the IFF regions of the facesheet

model.

3. The fiber constituent reduction was 99% and the matrix constituent stiffness reduction

was 90% when fiber fracture is predicted in the PFA.

It was noted in the experimental test results discussed in Chapter 3, that the core

density will have a small, but noticeable effect on damage formation in the sandwich panel.

However, the damage was kept constant for the parametric study so that the honeycomb

core properties are the only variable which can change the analysis results. The results of

this study can be thought of as conservative, since impact damage formation was shown to

decrease in size with increased core density.

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Chapter 6. Analysis of Test Coupons and Other CAI Analysis Results

The honeycomb core considered throughout the present research, in each of the three

material systems considered, is a hexagonal cell Nomex honeycomb with 0.125 in. cell size.

Commercially available Hexcel material property data lists core crush and plate shear data

for this type of honeycomb at a variety of nominal densities, including the 3 and 6 lb/ft3.

densities, which were primarily studied in the present research. The values for the core crush

strength and modulus, for each density Nomex honeycomb core listed in the available data

[86], is shown in Figs. 6.18 and 6.19, respectively.

Figure 6.18: Core crush strength of Nomex honeycomb shown varying with nominal core density,

and the data fit calculated for use with the parametric study analyses.

A linear relationship was found based on a regression fit of this data, which could

then be implemented in the MATLAB function for ABAQUS input file creation. The linear relationships calculated in the present research for the core crush strength and linear

elastic modulus are given in Figs. 6.18 and 6.19, respectively. The in-plane shear properties necessary for the FEM were also found, similarly. Other properties necessary, including

the in-plane extensional moduli, were calculated using the relationships given in Gibson and

Ashby [55]. The parametric study was completed with continuum core models representative

of honeycomb core densities ranging from 3 to 6 lb/ft3., with a step size of 0.5 lb/ft3. The

bounds on the honeycomb core density were chosen so that both indentation propagation

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Chapter 6. Analysis of Test Coupons and Other CAI Analysis Results

Figure 6.19: Core crush modulus of Nomex honeycomb shown varying with nominal core density,

and the data fit calculated for use with the parametric study analyses.

and crack propagation failure modes would be represented in the parametric study results.

6.4.2 Results of the Parametric Study

The results of the parametric study clearly show the usefulness of a CAI model which can

handle multiple failure modes. After each of the seven analyses was completed, both failure

modes were represented in the parametric study. The failure strength was predicted for each

honeycomb core density uesd in the analyses completed. The predicted failure strength vs.

core density is shown in Fig. 6.20. The type of failure mode is indicated by the symbol and

the color used for a particular data point.

From the results in Fig. 6.20, the following two conclusions can be made. First, the

failure strength of the sandwich panel test coupon increases with honeycomb core density.

Second, at a given honeycomb core density, the failure mode will transition from indentation

propagation to crack propagation. This is clearly seen to occur near the 4 lb/ft3. core density

level. It can also be seen that the failure strength has reached a maximum once the failure

mode changes to crack propagation. This clearly suggests that a trivial mass penalty could

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Chapter 6. Analysis of Test Coupons and Other CAI Analysis Results

Figure 6.20: Parametric study results: failure strength vs. nominal core density associated with

continuum core properties.

be added to the sandwich panel to obtain a significant strength increase. The predicted

strength increase vs. the calculated mass penalty is considered in Fig. 6.21.

Figure 6.21: Parametric study results: percentage strength increase vs. normalized mass increase.

The increase in failure strength in Fig. 6.21 is calculated as a percentage of the three

lb/ft3

. failure strength. The mass of the test coupon model is normalized with respect to the

complete sandwich panel structure, which includes both the facesheets and the core. The

increase in mass is due only to the increase in core density, but is shown as a percentage of

the complete panel mass. The strength increase is a maximum once the failure mode has

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Chapter 6. Analysis of Test Coupons and Other CAI Analysis Results

transitioned from indentation propagation to crack propagation. With respect to the data

point representing the 4 lb/ft3. case, a strength increase of just over 40% was achieved for

only a 10% weight penalty. Since the CAI strength of a composite material is typically one of

the most conservative strength estimates, this predicted strength increase is very significant!

6.5 Conclusions from the Results of Using the New

FEM for CAI Analysis

In the current chapter, results were presented for FEA completed using the new CAI anlayis

model for three sandwich panel material systems. The material systems, damage formation

for these systems, and their CAI response had been rigorously described, in Chapters 2 and 3.

The model successfully performed high fidelity representation of both the indentation propagation, and the crack propagation failure modes for the appropriate material systems. These

representations included both large-scale out-of-plane deformation controlled by a classic core

crush model, and fiber reinforced composites failure, as depicted by the commercial software,

Helius:MCT. An analysis was completed which corresponded to each of the 32 experimental

test coupons, and analysis results were then compared with experimental test results. In

addition, the dependence of the CAI failure mode on honeycomb core density was examined

using a parametric study.

Good correlation with experimental test results was demonstrated for many of the

CAI analysis results. Some of the analyses resulted in larger error levels (∼20%), which is

similar to other CAI analysis models. Many of the new CAI analysis predictions had a much

smaller error. Some of the analyses obtained with the new CAI model demonstrated less

than a 1% error between analysis predictions and experimental test results. These results

were obtained despite some uncertainty in the model inputs. Many of the details included

in the present model were not previously available in CAI models, so the current study

will have increased our understanding of CAI analysis. It is especially unique, that the

current model is validated based on a large amount of experimental data, rather than just a

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Chapter 6. Analysis of Test Coupons and Other CAI Analysis Results

single data point. In addition, the usefulness of the model’s ability to predict multiple CAI

failure modes, through competing core and facesheet failure models, was demonstrated in a

parametric study. The results showed that significant improvements in CAI failure strength

can be obtained by small increases in core density for thin facesheet honeycomb core sandwich

panels.

Chapter 6 completed the results of the current research. In Chapter 7, the conclusions

of the current research will be discussed, and some suggestions with regards to future work

in this research area are introduced.

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Chapter 7

Conclusions and Future Work

Composite structures are increasingly being considered as lightweight alternatives in the

design of tomorrow’s aerospace vehicles, from small private propeller driven planes, to the

newest commercial jetliners, and the next generation of heavy lift vehicles for future space

exploration. They are already used extensively in modern commercial satellites. Currently,

the major design challenges in composites pertain to damage repair, and ultimately, the

understanding of damage formation and response of a composite structure with damage

present. One aspect of the latter challenge is the understanding of composite sandwich

structure response to compression after low velocity impact. This has been the subject of

the present research, which has included both experimental testing and finite element analysis

(FEA).

The current state of compression after impact (CAI) research was described in Chapter

1, with respect to both experimental testing and analysis. In the area of experimental testing,

results are available in the literature for damage formation in composite laminate plates, as

well as sandwich constructions with cellular, hexagonal honeycomb cores. CAI testing has

been completed by various authors, and unique failure characteristics were demonstrated

for sandwich constructions. The formation of damage can be evaluated using destructive

techniques, as well as newer non-destructive evaluation (NDE). Many of these methods were

used in the experimental testing portion of the present research. Chapter 1 continued with

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Chapter 7. Conclusions and Future Work

an introduction to the current CAI analysis methods, and identified important areas of

improvement which are needed for FEA. One of the tools identified was a progressive failure

analysis (PFA) for damage propagation in the facesheets. Also, although both experimental

testing and analysis work has been completed, the models available in the literature have

received very little validation through comparison to experimental test results. One of the

reasons for this is the lack of complete experimental detail available for any one specific

material system in the literature, which is necessary for CAI modeling.

The current research contained a detailed experimental study, which produced new

interesting results. In addition, it would later be used to aid and direct model development.

In Chapter 2, the experimental testing techniques were introduced and the testing results

were summarized for a single Nomex honeycomb core sandwich panel with thin woven fiberglass reinforced facesheets. Damage formation was studied, as well as the CAI response.

In addition, novel instrumentation and observation techniques were used to gain a detailed

understanding of these tests, which has not been previously available. The experimental test

portion of the current work continued in Chapter 3, with two additional material systems.

Although these materials varied slightly from the original set discussed previously, they were

identical to each except for one important difference. The density of the honeycomb core, 3

lb/ft3. in one material, and 6 lb/ft3. in the other, was used to assess the core density’s effect

on damage formation and CAI response. Two CAI failure modes were seen in test results,

highlighting the need for new analysis model development.

The current state of FEA for the CAI response of thin facesheet honeycomb core

sandwich panels was considered in Chapter 4. The subject of relevant theory, with respect to

composite laminates, ABAQUS finite elements, and honeycomb core modeling, was discussed.

Two finite element models (FEM) were used to obtain results for a small selection of the tested

sandwich materials. First, a spring element core model, which was developed by Ratcliffe

and Jackson [46], was used. Second, a solid element core model was discussed, which would

provide the foundation for a new model to be developed in Chapter 5. In this chapter,

a type of continuum damage model for PFA in composite laminates was discussed. This

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Chapter 7. Conclusions and Future Work

failure model, which uses multicontiuum theory (MCT), is implemented in the commercially

available software, Helius:MCT, by Firehole Composites. A custom version of this software

was provided by Firehole for the present research, to allow its use with the FEM. The custom

version allowed for software compatibility with the custom ABAQUS user subroutine, UMAT,

used for out-of-plane compressive failure of the core with the present research. This software

provided the ability to consider damage propagation in the facesheets, which was needed as

previously discussed by this and other authors. The development of the new model continued

in Chapter 5 with a detailed discussion of impact damage inclusion. Since a large amount

of data was available from the experimental test results, a large amount of detail could be

included. A mesh convergence study and a sensitivity study were completed using the new

model and the results were presented.

Finally, in Chapter 6, results were presented for the FEA of each of the 32 CAI

test coupons using unique models developed from experimental test data. These results

were compared to experimental test results. Also, a parametric study was completed using

the new FEM to obtain additional results for the CAI response of thin facesheet sandwich

constructions with varying honeycomb core density. This completed the development and

results of the present research. The present chapter will be used to highlight the important

conclusions of this work, first for the experimental test results, and then for the analysis

results and comparison to experiment. Finally, anticipated and suggested future work in the

area of CAI response of thin-facesheet honeycomb core sandwich panels will be discussed.

7.1 Conclusions

Results for an experimental study and finite element analysis of thin facesheet honeycomb

core sandwich panels in response to compression after impact (CAI) loading have been described. The experimental work consisted of tests to describe the damage resistance and

damage tolerance of the sandwich panels in question. This work has been completed in an

ideal setting for determining the response of these materials both to impact, as well as CAI

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Chapter 7. Conclusions and Future Work

loading, at NASA Langley Research Center, in Hampton, VA. Using various instrumentations, a large amount of data has been presented. Some was then used for validation of the

FEA. A new and interesting conclusion is made with regards to failure mode dependency

on core density. This is supported by detailed instrumentation. The present analysis of

sandwich panel test coupons focused primarily on the development and utilization of a FEM

for prediction of the CAI response and failure. Elements of previous modeling attempts are

used and combined with new techniques in the proposed model. The major analysis conclusions will focus on the new use of PFA in the facesheets and high fidelity impact damage

representation. Results were produced for models developed from experimental test data,

and compared to the experimental results. The conclusions made from research results are

discussed in the following sections, first for experiments, and then analysis.

7.1.1 Experimental Testing Conclusions

A series of experiments was completed on three material systems consisting of honeycomb

core sandwich panels with woven fiberglass fabric facesheets. The purpose of these tests

was to understand damage formation in response to a low velocity impact, and then the

failure response to CAI loading. The PXX series material coupons consisted of 1 in. thick,

3 lb/ft3. Nomex honeycomb core, and 0.02 in. thick woven E-glass facesheets. 3PCF-XX

series materials consisted of 0.75 in. thick, 3 lb/ft3. Nomex honeycomb core and 0.02 in.

thick woven S2-glass facesheets. The 6PCF-XX series panels were identical in construction

to the 3PCF-XX series panels except that the Nomex honeycomb core had a nominal density

of 6 lb/ft3.

Static indentation tests and low velocity impact tests were used to assess damage formation, as well as to select the impact energies of interest for CAI testing. Static indentation

resulted in similar damage to drop impact, although the results were found to be conservative

since lower energy was required in static indentation to produce the damage response typical

of higher energy impacts. Force and displacement data was collected for static indentation.

The area under the force vs. displacement curve was determined by numerical integration to

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Chapter 7. Conclusions and Future Work

estimate the energy absorbed by the material during indentation. Typical damage included

a residual dent in the facesheet, which was described by maximum dent depth and diameter. Another type of damage observed during static indentation was discoloration of the

facesheets, which indicated areas of facesheet material fracture. Various levels of crushed

core were found in the impacted region of the sandwich panel using destructive evaluation

techniques. For each material system an energy level was determined at which complete

facesheet fracture occurred. This energy level was determined to be constant for a particular

material system.

Low velocity impact testing using a drop tower completed the study of damage formation in each the materials. Impact force vs. time data was collected for each impact

recorded. Force was found to increase with impact energy until facesheet fracture occured.

The maximum force recorded for higher energy impacts did not increase, although the length

of the impact did increase. Typically, for both static indentation and drop impact, the 3PCFXX and 6PCF-XX series panels absorbed more energy and a higher impact force could be

obtained before facesheet fracture, than PXX series panels. This was expected since the

strength and stiffness of the woven S2-glass facesheet used in the 3PCF-XX and 6PCF-XX

series coupons was higher than the E-glass materials used in the PXX series specimens. The

types of damage found for drop impact was similar to static indentation. The depth and

diameter of the impact damage dent was found to increase to a maximum before leveling

with increasing impact energy. On the other hand, the amount of matrix and fiber cracks

did continue to increase with impact energy. Typically, higher levels of impact damage were

found in PXX series panels than in the other two material systems for a given energy level.

From this result, the energy levels of interest for CAI testing included higher energy levels

for 3PCF-XX and 6PCF-XX series panels, than for PXX specimens.

CAI tests were completed on PXX series coupons with damage from impacts of energies up to 2 ft-lbs. and on 3PCF-XX and 6PCF-XX series coupons with damage from

impacts of energies up to 7 ft-lbs using a 0.5 in. hemispherically shaped impact tip. Coupons

were nominally sized at 6 in. by 6 in. and the load application ends were potted to prevent

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Chapter 7. Conclusions and Future Work

erroneous failure of the coupons ends clamped in the test fixture. Various types of instrumentation and recording equipment were used. Instrumentation recorded force, displacement,

and strain information for each material coupon. Recording equipment, including high definition cameras, high speed photography, and digital image correlation (DIC) was used to

ascertain the resulting failure mode.

Failure in the front, damaged facesheet of each material coupon was found to be the

principal factor in global panel failure due to compressive loading. Panel failure was found

to be indicated by a sudden, instantaneous drop in the force vs. displacement curve for each

coupon. Failure strength for CAI specimen was compared to the compressive strength of an

undamaged specimen. The reduction in residual strength of a material coupon was found to

be most severe for lightly damaged coupons. Increasing levels of damage resulted in further

reduction in residual strength, but the reduction between adjacent data points decreased

in magnitude. New insight was gained into the CAI response and ultimate failure of test

coupons using novel instrumentation techniques. High speed video photography captured

images of failure. These images were not previously available in the literature. In addition,

the DIC system was used to make full-field surface maps, and deformation measurements of

the front, damaged facesheet of each of the experimental test specimens. The results shown

in the current work quantified the stable growth of the impact damage dent at various times

in the linear elastic portion of the CAI test response. These results confirmed the growth

observed in test video, and provided clarity to coupon response, which had previously been

observed only using large systems of strain gages.

Two CAI failure modes were found during the experimental investigation. In material

systems with 3 lb/ft3. density honeycomb cores, an indentation propagation failure mode

resulted which is essentially a local buckling of the facesheet due to the collapse of the

honeycomb core beneath. A crack is present in the facesheet, but the propagation of the

residual indentation transversely across the facesheet precedes the crack. In testing of the

higher density, 6 lb/ft3. core materials, a second failure mode was found, which was termed

crack propagation. A transverse fiber crack propagates across the facesheet, without any

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Chapter 7. Conclusions and Future Work

local facesheet buckling or core crush. Since the 3PCF-XX and 6PCF-XX series panels are

identical except for the their honeycomb density, the failure mode was found to be dependent

on this material property alone. Full field measurements using the DIC system and VIC-3D

software also demonstrated the difference in these two material modes, prior to failure. It

was concluded that the higher density core also resulted in very little dent growth, prior to

failure. The effect of core density on damage formation and CAI response in honeycomb core

sandwich panels highlighted the need for new analysis techniques.

7.1.2 Analysis Conclusions

A FEM with new analysis techniques implemeneted has been developed for the prediction

of the CAI response of honeycomb core sandwich panels using the commercial finite element

code, ABAQUS/Standard. A literature review was presented which outlined past work in

this area and defined the state of the art in this area. The new FEM uses some techniques

currently available, which worked well in previous models. The facesheets and the core of the

new FEM were modeled separately using the following techniques. The non-linear core model

consists of an idealization of the stabilized crush response found by experiment for a Nomex

honeycomb core. This response can be defined by an initial linear elastic modulus, the core

crush strength, and a stress reduction at failure. A spring element core model was studied

which introduces this concept, since with spring elements this is the only core response that

can be modeled. The force vs. displacement result of this model near failure was found to

significantly differ from experimental observations, except in select cases. The reduction in

reaction force at failure was shown to be “rounded,” instead of the instantaneous reduction

seen in experimental tests. A solid, orthotropic continuum representation of the linear elastic

response of the honeycomb core was included, in addition to the non-linear crush response.

The core, modeled using solid brick elements was defined by a user subroutine. A solid

element core model was presented in order to show the benefits of these modeling techniques.

The solid element continuum representation of the honeycomb core was implemented using an

ABAQUS user subroutine, UMAT. This subroutine, written in the FORTRAN programming

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Chapter 7. Conclusions and Future Work

language, provides for both the linear elastic response of the core, as well as the non-linear

through the thickness crushing response.

One of the major focuses of the current research was implementation of progressive

failure analysis of the facesheets of honeycomb core sandwich panels for use in CAI analysis.

The commercial software, Helius:MCT, was used for this. This software uses multicontinuum

theory (MCT) failure theory for a continuum damage representation failure analysis of the

facesheets during the analysis. The primary purpose of MCT is for higher accuracy in

laminate failure prediction, by defining constituent level failure based on constituent level

average stress states. The constituent level average stress states are found by decomposition

from laminate average stress states using MCT. A successful implementation of PFA is absent

from previous CAI models, so CAI analysis with this capability is concluded to be the first

of its kind. The new FEM model has the ability to successfully model and predict multiple

failure modes, including the two modes found in the experimental work presented in the

present study: indentation propagation and crack propagation. The new model’s results

demonstrated high-fidelity physics based representations of both failure modes.

A mesh convergence study was completed to determine the new model’s mesh dependency. The study showed that mesh dependence varied somewhat based on the failure mode

exhibited by the sandwich panel structure. While the through the thickness mesh density was

more important for the indentation propagation failure mode, the in-plane mesh density was

shown to affect the crack propagation mode. The latter result confirms that the continuum

damage propagation methods used by the Helius:MCT software is mesh dependent.

In addition, several other interesting developments in CAI analysis resulted from the

present work. A highly detailed FEM representation of the impact damage in the CAI

analysis model was used. The “damaged” regions of elements in both the core and facesheet

were defined using measurements taken from the experimental work, and material property

stiffness reductions. Since the implementation of the inputs used to define these components

of the model (through a custom MATLAB language program which writes an ABAQUS

input file) was quite intensive, a sensitivity study was used to assess the effect of the damage

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Chapter 7. Conclusions and Future Work

properties on the model. They were also used to assess overall confidence in the model based

on specific inputs.

Some inputs, such as dent diameter, and maximum dent depth, were evaluated as

having an “excellent” level of confidence. This rating was given for inputs with low measurement uncertainty, which might also result in only small changes to model results if excessive

errors were present. A “good” confidence rating was given to the diameter of the facesheet

region associated with inter-fiber fracture. The reason for this was that a higher level of

uncertainty exists for this measurement; however, it was demonstrated that the uncertainty

would only result in a small net change in model results. Finally, the confidence in some

model definitions was evaluated as “reduced.” First, the mesh density used was not the

best for an accurate depiction of the depth of the damaged core. This issued could have be

resolved with a change in the mesh pattern used. Still, it was shown that the depth of the

core damage in the model was largely inconsequential, so long as at least some damage was

present.

Finally, the “reduced” confidence label was also given to the stiffness reduction values.

First, the core stiffness reduction uncertainty could have been improved by conducting a

flatwise core compression test on the honeycomb core materials of interest. The matrix

constituent stiffness reduction and the fiber constituent stiffness reduction are the two final

areas of reduced confidence. These two properties are used in both the definition of initially

damaged element material properties, as well as the progressive failure analysis completed

by Helius:MCT. It was concluded that with the current continuum damage method, these

values need to be improved using experimental testing of the woven fiberglass reinforced

facesheets. Also, a more gradual stiffness reduction would be more appropriate to some of

the material properties, namely, in-plane shear stiffness.

The new CAI model was used to analyze the CAI response of each of the 32 coupons

tested to failure during experimental work. Results were given for failure load, failure stress,

and failure strain. Specific consideration was given to analysis results for coupon failure

strength for comparison to experimental test results, but any of the global failure measure230
Chapter 7. Conclusions and Future Work

ments could have been used. The new model showed similar error to other currently available

CAI models for some of the analyses when compared to experiments. However, for many of

the results, the resulting error was lower, and for some results, the error was significantly low.

It was shown that each of the damage definition inputs have a small, but significant effect

on the overall model results. Thus it is important to have a low uncertainty associated with

the experimental test measurements used in the analysis model inputs. Acceptable analysis

results were obtained for the current research, but improvements in the accuracy of the CAI

model predictions could be made by improving the experimental test observations used.

The final result discussed in the present work was a parametric study on the effect of

core density on sandwich panel CAI response. This result clearly showed that increasing the

specien’s core density will change the failure mode from indentation propagation to crack

propagation. In addition, CAI failure strength was increased with the core density increase,

until the failure mode changed to crack propagation. The parametric study results showed

that a substantially large CAI strength increase could be obtained for only a small increase

in mass. This result demonstrates the new abilities of the new model for CAI analysis, as

well as its benefit to engineering design.

7.2 Future Work

During the course of this research, several areas of future work were identified. First, some

suggestions for future experimental testing will be discussed, then for future analysis work.

There exists a great deal of results in the literature for CAI test results on coupon, but

not enough work has been done on CAI testing at the component or full scale structural

levels. With the advancements that have been made recently in development of digital image

correlation measurements, there exists the possibility for an understanding not previously

achieved for structural level CAI response.

Additionally, another area of future importance in CAI testing is materials that have

been repaired. Frequently, in the commercial sector of the aerospace industry, damaged

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Chapter 7. Conclusions and Future Work

composite components are replaced when they are inspected and found to contain damage.

However, the repair of composite damage is an emerging research area. In the future, it

is possible that the development and use of repair methods on composite structures will

be seen in the operational use of aerospace structures, and perhaps other structures which

contain composites as well (e.g. boat hulls). More work will need to be done in the area

of compression testing of these damaged, then repaired, composite structures for evaluating

various repair methods to be used in a commercial setting.

Future tasks were also identified in the area of analysis. More work will need to be done

to improve the accuracy and reliability of existing models before they can be used outside of

the academic research setting. There simply isn’t enough confidence in the existing models.

Also, in many cases the commercial alternative is to just replace, or in very few cases, repair

damage. There is not enough emphasis on the possibility of damage that may be undetected.

This research, as well as previous work, has shown the drastic strength reductions that can

occur due to even light damage. CAI models can predict strength reductions due to light,

undetectable damage, as well as larger mounts of damage, so future work should continue to

improve these models.

One of the main tasks of the current research was the implementation of a composite laminate progressive failure analysis in the CAI model. This implementation was done

through the use of special version of the commercial software, Helius:MCT. The changes

that were implemented for this research are apparently planned for future, validated releases

of the software, so it will be more widely available. This software has excellent value in

composite laminate failure analysis, but improvements can be made. Key parameters used

to calculate the post-failure stiffness of “damaged” elements still have large amounts of uncertainty associated with them. With more work and experience, more confidence in these

failure criteria can be found. It was mentioned previously, that a more gradual reduction

in material stiffness, especially where matrix plasticity and failure is concerned, would be

highly beneficial and more indicative of the physical reality. This is already implemented in

Helius:MCT for unidirectional composites, and possibly, Firehole is already developing this

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Chapter 7. Conclusions and Future Work

for woven composites like the ones used in this research.

Continuum damage models for composites, such as Helius:MCT, are not the only

emerging technology in composite failure theory. In fact, it can be argued that while they

are the most developed, they are easy to understand and use, and they are a great resource,

they are no longer on the cutting edge in terms of composite failure analysis. Other methods

exist, some of which were discussed in Chapter 1. A great deal of emphasis in future work

will need to be placed on the importance of matrix deformation and failure, particularly on

the size, orientation, and placement of matrix cracks. Some of the models being developed

currently are accounting for this. It will be interesting to see their implementation for low

velocity impact damage formation in composites, as well as CAI.

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[95] Searles, K., Odegard, G., and Kumosa, M., “Micro- and mesomechanics of 8-harness

satin woven fabric composites: I - evaluation of elastic behavior,” Composites: Part A,

Vol. 32, 2001, pp. 1627 – 1655.

[96] Gao, X.-L., Li, K., and Mall, S., “A mechanics-of-materials model for predicting Young’s

modulus of damaged woven fabric composites involving three damage modes,” International Journal of Solids and Structures, Vol. 40, 2003, pp. 981 – 999.

[97] Angioni, S., Meo, M., and Foreman, A., “A comparison of homogenization methods for

2-D woven composites,” Composites: Part B, Vol. 42, 2011, pp. 181 – 189.

244
REFERENCES

[98] “B-basis design allowables for epoxy-based prepreg: 3M E-glass fabric 7781 / SP381,”

Advanced General Aviation Transport Experiments, available on the NIAR AGATE

website http://www.niar.twsu.edu/agate/Documents/default.htm, Last accessed June

9, 2011, September 2001.

245
Appendix A

Additional Results of CAI

Experiments

Table A.1: Additional results of impact survey of PXX series materials: panel 1 damage metrics.

Table A.2: Additional results of impact survey of PXX series materials: panel 2 damage metrics.

246
Chapter A. Additional Results of CAI Experiments

Figure A.1: Additional results of CAI testing of PXX series materials: residual dent depth vs.

impact energy.

Figure A.2: Additional results of CAI testing of PXX series materials: residual dent diameter vs.

impact energy.

247
Chapter A. Additional Results of CAI Experiments

Table A.3: Additional results of impact survey of PXX series materials: panel 3 damage metrics.

248
Chapter A. Additional Results of CAI Experiments

Table A.4: Additional results of CAI testing of PXX series materials: impact damage metrics.

Figure A.3: Additional results of CAI testing of 3PCF-XX and 6PCF-XX series materials: residual

dent depth for impacts on coupons used for CAI testing of 3PCF-XX and 6PCF-XX series materials.

249
Chapter A. Additional Results of CAI Experiments

Table A.5: Additional results of CAI testing of PXX series materials: CAI failure metrics.

250
Chapter A. Additional Results of CAI Experiments

Table A.6: Additional results of CAI testing of 3PCF-XX and 6PCF-XX series materials: 3PCF-XX

static indentation results.

Table A.7: Additional results of CAI testing of 3PCF-XX and 6PCF-XX series materials: 6PCF-XX

static indentation results.

Figure A.4: Additional results of CAI testing of 3PCF-XX and 6PCF-XX series materials: residual

dent diameter for impacts on coupons used for CAI testing of 3PCF-XX and 6PCF-XX series

materials.

251
Chapter A. Additional Results of CAI Experiments

Table A.8: Additional results of CAI testing of 3PCF-XX and 6PCF-XX series materials: impact survey results describing the

residual damage for 3PCF-XX materials.

252
Chapter A. Additional Results of CAI Experiments

Table A.9: Additional results of CAI testing of 3PCF-XX and 6PCF-XX series materials: impact

survey results describing the force and length of impact for 3PCF-XX materials.

253
Chapter A. Additional Results of CAI Experiments

Table A.10: Additional results of CAI testing of 3PCF-XX and 6PCF-XX series materials: impact survey results describing the

residual damage for 6PCF-XX materials.

254
Chapter A. Additional Results of CAI Experiments

Table A.11: Additional results of CAI testing of 3PCF-XX and 6PCF-XX series materials: impact

survey results describing the force and length of impact for 6PCF-XX materials.

Table A.12: Additional results of CAI testing of 3PCF-XX and 6PCF-XX series materials: results

for impacts on 3PCF-XX coupons used for CAI testing.

255
Chapter A. Additional Results of CAI Experiments

Table A.13: Additional results of CAI testing of 3PCF-XX and 6PCF-XX series materials: results

for impacts on 6PCF-XX coupons used for CAI testing.

256
Chapter A. Additional Results of CAI Experiments

Table A.14: Additional results of CAI testing of 3PCF-XX and 6PCF-XX series materials: results for failure of 3PCF-XX series

panels during CAI testing.

257
Chapter A. Additional Results of CAI Experiments

Table A.15: Additional results of CAI testing of 3PCF-XX and 6PCF-XX series materials: results for failure of 6PCF-XX series

panels during CAI testing.

258
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Compression After Impact Experiments and Analysis on Honeycomb Core 

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McQuigg, Thomas D.

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A better understanding of the effect of impact damage on composite structures is necessary to give the engineer an ability to 

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Composite structures; Damage tolerance; Impact damage; Honeycomb cores; Sandwich panels; Finite element analysis; 

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