Justin D. Littell

University of Akron, Akron, Ohio

Experimental and Analytical Characterization of the 

Macromechanical Response for Triaxial 

Braided Composite Materials

NASA/CR—2013-215450

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Justin D. Littell

University of Akron, Akron, Ohio

Experimental and Analytical Characterization of the 

Macromechanical Response for Triaxial 

Braided Composite Materials

NASA/CR—2013-215450

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NASA/CR—2013-215450 iii 

Contents 

Summary ....................................................................................................................................................... 1

1.0 Introduction ........................................................................................................................................... 1

2.0 Literature Review ................................................................................................................................. 3

2.1 Polymer Matrix Material Testing .................................................................................................. 4

2.2 Composite Material Testing .......................................................................................................... 5

2.2.1 Composite Material Static Testing .................................................................................... 5

2.2.2 Composite Material Interface Testing ............................................................................... 6

2.3 Composite Modeling Overview .................................................................................................... 7

2.3.1 Macroscale Composite Modeling Approaches ................................................................. 8

2.3.2 Microscale Constitutive Modeling Approaches ................................................................ 8

2.4 Material Property Selection .......................................................................................................... 9

2.5 Current Research ......................................................................................................................... 10

3.0 Investigations Into Composite Constituent Material Response .......................................................... 10

3.1 Experimental Setup ..................................................................................................................... 11

3.2 Optical Measurement Use for Data Collection ........................................................................... 11

3.3 Specimen Designs ....................................................................................................................... 13

3.4 Test Procedure ............................................................................................................................ 14

3.5 Results ......................................................................................................................................... 14

3.5.1 Tensile Results ................................................................................................................ 14

3.5.2 Compression Results ....................................................................................................... 18

3.5.3 Shear Results ................................................................................................................... 21

3.5.4 Cyclic Load-Unload Results ........................................................................................... 24

3.5.5 Examination of Results ................................................................................................... 31

3.6 Constituent Testing Summary ..................................................................................................... 33

4.0 Investigations of Triaxial Braided Composite Material Response ..................................................... 33

4.1 Material Background .................................................................................................................. 33

4.2 Specimen Geometries ................................................................................................................. 35

4.3 Test Equipment ........................................................................................................................... 37

4.4 Experimental Results .................................................................................................................. 37

4.4.1 Examination of Global Stress-Strain Data ...................................................................... 37

4.4.2 Examination of Local Deformations and Failure ............................................................ 47

4.5 Composite Testing Summary ...................................................................................................... 72

5.0 Development of Macromechanical Triaxial Braided Composite Computer Model ........................... 72

5.1 Material Background .................................................................................................................. 73

5.2 Composite Microstructure........................................................................................................... 73

5.3 Triaxial Braided Composite Model Development ...................................................................... 75

5.3.1 Development of Braid Geometry .................................................................................... 75

5.3.2 Composite Material Property Implementation ................................................................ 76

5.3.3 Development of Material Failure Parameters ................................................................. 81

5.4 Finite-Element Model Implementation for Prediction of Static Tests ........................................ 86

5.4.1 T700/PR520 Fiber/Resin Material Response .................................................................. 87

5.4.2 T700/E862 Fiber/Resin Material Response .................................................................... 90

5.5 Conclusions ................................................................................................................................. 92

6.0 Triaxial Braided Composite Impact Simulations ................................................................................ 92

6.1 Background ................................................................................................................................. 92

6.1.1 Material Testing .............................................................................................................. 92

6.1.2 LS–DYNA Introduction .................................................................................................. 92

6.2 Finite-Element Model Development ........................................................................................... 93
NASA/CR—2013-215450 iv 

6.3 Simulation Results ...................................................................................................................... 94

6.4 Conclusions ................................................................................................................................. 98

7.0 Concluding Remarks .......................................................................................................................... 99

7.1 Summary of Results .................................................................................................................... 99

7.2 Future Work .............................................................................................................................. 100

7.2.1 Constituent Testing ....................................................................................................... 100

7.2.2 Composite Testing ........................................................................................................ 101

7.2.3 Composite Modeling ..................................................................................................... 101

References ................................................................................................................................................. 102

 
NASA/CR—2013-215450 1 

Experimental and Analytical Characterization of the 

Macromechanical Response for Triaxial 

Braided Composite Materials 

Justin D. Littell 

University of Akron 

Akron, Ohio 44304 

Summary 

Increasingly, carbon composite structures are being used in aerospace applications. Their highstrength, high-stiffness, and low-weight properties make them good candidates for replacing many 

aerospace structures currently made of aluminum or steel. Recently, many of the aircraft engine 

manufacturers have developed new commercial jet engines that will use composite fan cases. Instead of 

using traditional composite layup techniques, these new fan cases will use a triaxially braided pattern, 

which improves case performance. The impact characteristics of composite materials for jet engine fan 

case applications have been an important research topic because Federal regulations require that an engine 

case be able to contain a blade and blade fragments during an engine blade-out event. Once the impact 

characteristics of these triaxial braided materials become known, computer models can be developed to 

simulate a jet engine blade-out event, thus reducing cost and time in the development of these composite 

jet engine cases. The two main problems that have arisen in this area of research are that the properties for 

these materials have not been fully determined and computationally efficient computer models, which 

incorporate much of the microscale deformation and failure mechanisms, are not available. 

The research reported herein addresses some of the deficiencies present in previous research 

regarding these triaxial braided composite materials. The current research develops new techniques to 

accurately quantify the material properties of the triaxial braided composite materials. New test methods 

are developed for the polymer resin composite constituent and representative composite coupons. These 

methods expand previous research by using novel specimen designs along with using a noncontact 

measuring system that is also capable of identifying and quantifying many of the microscale failure 

mechanisms present in the materials. Finally, using the data gathered, a new hybrid micromacromechanical computer model is created to simulate the behavior of these composite material systems 

under static and ballistic impact loading using the test data acquired. The model also quantifies the way in 

which the fiber/matrix interface affects material response under static and impact loading. 

The results show that the test methods are capable of accurately quantifying the polymer resin under a 

variety of strain rates and temperature for three loading conditions. The resin strength and stiffness data 

show a clear rate and temperature dependence. The data also show the hydrostatic stress effects and 

hysteresis, all of which can be used by researchers developing composite constitutive models for the 

resins. The results for the composite data reveal noticeable differences in strength, failure strain, and 

stiffness in the different material systems presented. The investigations into the microscale failure 

mechanisms provide information about the nature of the different material system behaviors. Finally, the 

developed computer model predicts composite static strength and stiffness to within 10 percent of the 

gathered test data and also agrees with composite impact data, where available. 

1.0 Introduction 

Increasingly, carbon composite structures are being used in aerospace applications. Their highstrength, high-stiffness, and low-weight properties make them good candidates for replacing many 

aerospace structures currently made of aluminum or steel. As reported by Boeing, 50 percent of the 

new 787 “Dreamliner” commercial wide-body passenger jet consists of composite materials (Ref. 1). 
NASA/CR—2013-215450 2 

The new 787 is also using General Electric’s (GE’s) new GENx turbofan engine. Both the blade and the 

engine case in this new GENx turbofan engine are made of composite materials. Similarly, other jet 

engine manufacturers such as Williams International, Honeywell Aerospace, and Rolls-Royce, are 

developing their own composite engine cases. GE’s new GENx is a case already in production whereas 

Williams International’s FJ443 and Honeywell’s HTF7000 are demonstration cases currently in the 

design and testing stages. However, instead of being made with traditional unidirectional composite 

layups, these new fan cases are using a two-dimensional, triaxial braided composite architecture. 

A major concern for these companies is that the design of a jet engine case has to have the ability to 

contain a fan blade in the event that an engine blade-out event occurs. Federal Aviation Administration 

(FAA) Regulation, FAR Part 33 Section 94–Blade Containment and Rotor Unbalance Tests, requires that 

the engine case contain a fan blade released at full engine operating speed (Ref. 2). In an engine blade-out 

event, a fan blade becomes dislodged from the engine center hub and strikes the side of the engine case at 

a high velocity while the engine is at full operating speed. For composite engine cases, there are two main 

types of designs for containing engine blades, and these cases fall into either the hardwall or softwall 

category. An engine case with a hardwall design has sufficient wall thickness around the impact areas to 

allow the structure itself to resist the penetration and absorb the energy from a released blade. An engine 

case with a softwall design has an outer layer of Kevlar (DuPont) or Zylon (Toyobo Co., Ltd.) wrapped 

around the engine case in the most critical area of penetration. For softwall containment, the engine case 

is designed to allow the blade to penetrate the inner structure, which absorbs the majority of the blade 

energy, but the ultimate containment is accomplished by the outer wrap (Ref. 3). In both designs, engine 

case materials must provide sufficient impact resistance to prevent penetration by a titanium or composite 

fan blade operating at speeds in the range of 600 to 1000 ft/s (183 to 305 m/s). 

To pass these requirements, engine manufacturers must conduct destructive blade-out tests on 

operating engines. Because full-scale and subscale testing of aircraft engines during blade-out conditions 

is expensive and time consuming and because data are difficult to obtain, alternative methods for 

evaluating case designs are needed. Accurate computer models that simulate an engine blade-out test 

offer one attractive alternative for examining the dynamics of the system and diagnosing potential failure 

mechanisms that occur in a full-scale test. For these reasons, computer models can be used as analysis 

tools to complement testing where necessary. Once accurate models are developed, system parameters, 

such as blade speed and trajectory, material systems, and engine case geometry, can be changed with 

relative ease without having to rerun a full-scale test. Although computer models cannot replace full-scale 

testing, they can serve as tools to identify and mitigate potential problems before they arise in a full-scale 

test. However, developing accurate computer models for simulation requires understanding the details of 

the composite material systems in question. 

Carbon-fiber-reinforced composites offer weight savings in aircraft design while still maintaining a 

high strength-to-weight ratio. Material systems currently being examined for use in composite engine 

cases are two-dimensional triaxial braided carbon-fiber composites, which offer higher impact resistance 

than traditional unidirectional composite laminates. Because of these characteristics, the triaxial braided 

carbon-fiber materials are ideal for the hardwall engine case design. 

Traditional composite structures have stacked layers of unidirectional fiber lamina s to form the 

composite laminate. However, in two-dimensional triaxial braided carbon-fiber-composite material 

systems, each lamina layer consists of two sets of fiber bundles braided at ±° angles, which undulate 

over and under a 0° axial fiber. This alternating pattern 
K–° fibers provides the distinct 

braid pattern, and because each lamina layer has all three orientations of fiber bundles, material 

characteristics such as impact strength and delamination resistance are improved. 

In carbon-fiber polymer matrix composites, the carbon-fiber tows provide the stiffness and strength 

when the composite is loaded longitudinally to the fiber direction, whereas the polymer matrix binds the 

fibers together and provides much of the strength transverse to the fiber direction. The properties of the 

polymer matrix material also play a significant role in an impact situation, where the material is mainly 

loaded out of plane to the direction of the fibers. The mechanical properties of the polymer matrix are also 
NASA/CR—2013-215450 3 

of interest because the polymer is the major contributor to the strain rate dependency of the composite 

material. 

Furthermore, even for situations in which the different polymers may behave similarly when tested as 

constituents, the as-fabricated composite materials having different fiber-polymer combinations can still 

behave differently when under identical static or impact loading conditions. It is because of this 

discrepancy that the interaction, or interface, between the fibers and polymer matrix is of great 

significance and interest and must therefore be examined. 

Finally, although the testing of the composite constituents is of great interest, computer models 

accurately simulating the material response under a variety of loading conditions are also needed. As 

these computer models will ultimately serve as tools to simulate composite material response, they must 

not only be accurate enough to simulate the as-measured test conditions but must also be robust enough to 

be predictive in a variety of loading conditions. 

Because of the background just presented, the goal of this research is twofold: 

(1) To gain a fundamental understanding of the material response and failure mechanisms involved 

in composite materials commonly used in jet engine cases by developing test methods that can 

identify the initiation and propagation of factors, such as delaminations and fiber bundle splitting 

and/or matrix cracking under static loading conditions. 

(2) To use the measured two-dimensional, triaxial braided composite properties obtained from testing 

to create a macromechanical composite computer model capable of accurately simulating 

composite material response under static loading conditions. 

These goals will be accomplished by first developing test techniques to fully define and characterize 

the polymer resins used as the matrix materials by finding a complete set of material properties for 

various temperatures and various strain rates needed in polymer constitutive modeling. Then testing will 

be done to examine the modes of failures, such as delaminations and transverse fiber bundle failures that 

occur in the composite materials under static loading conditions. These static test techniques will 

incorporate optical measurement techniques as the main instrument for obtaining material response data. 

By measuring the factors involved with the initiation and propagation of failure, discussions will be 

included about the fiber-matrix interface and how it affects the overall composite material response. 

Next, a macromechanical finite-element model will be developed to simulate the composite material 

response. The stiffness, strength, and failure data gathered from the static testing in conjunction with 

classical composite analytical techniques will be used to create the material model, and the braid 

geometry will be simulated using a novel through-thickness integration point method. The model will 

then be implemented in a finite-element code (LSDYNA) for use in simulations of the static testing. 

Finally, preliminary results will be presented to show differences in the impact responses for different 

material systems. Preliminary results from the impact simulations will confirm that the developed model 

will predict different impact responses from different material systems. Since very limited composite 

impact data are available at the time of this writing, material response comparisons between impact tests 

and simulations will be qualitative in nature. 

2.0 Literature Review 

This section presents an overview of relevant, current research on the topics proposed in this study. 

This literature review is intended to give a background to some of the methods currently in use and to 

present comparisons and extensions as to the applicability of this research. Specifically, test 

methodologies and some applicable results for the polymer matrix materials will be presented first. Then 

previous research into the static testing of composite materials will be presented. Afterwards, an overview 

of the current modeling techniques for composites both from the micromechanical and macromechanical 

sides will be explored. Finally, a brief discussion on the material property selection commonly used in 

composite material model implementation will be presented. 
NASA/CR—2013-215450 4 

2.1 Polymer Matrix Material Testing 

In polymer matrix carbon-fiber composites, the carbon fibers are the main mechanisms that give the 

composite stiffness and strength in the fiber direction. The primary function of the polymer matrix is to 

give the composite strength in the transverse and shear directions by binding the fibers together when 

loaded off-axis. Polymers are rate-dependent, nonlinear, viscoelastic materials that respond differently 

when tested under different loading rates and temperatures (Ref. 4). Since polymers are rate-dependent 

materials, they account for the main differences in the responses of composite materials when loaded at 

different rates. Traditional viscoelasticity theories model the material as combinations of springs and 

dashpots in series, as with the Maxwell model, or in parallel, as with the Kelvin model, or in 

combinations thereof (Ref. 5). However, because of limitations in the prediction of material response 

under a variety of different conditions, there has been great interest in adapting closed-form analytical 

solutions from plasticity theories originally developed to predict metallic material response to accurately 

predict the response of the polymer under a variety of loading rates and temperatures. Many researchers 

have attempted to develop closed-form analytical constitutive models that can predict polymer material 

response. Examples of some of the analytical solutions can be found in Bordonaro (Ref. 6), Goldberg 

(Ref. 7), and Karim and Hoo Fatt (Ref. 8). These constitutive models use data from tensile, compressive, 

and shear tests at different strain rates to quantify various internal state variables based on the individual 

constitutive law being used. As the composite materials will be used in environments where both low and 

high strain rates along with elevated temperatures (simulating jet engine operation) are present, polymer 

material properties acquired from strain rates ranging from 105

 to 102 s1 and temperatures ranging from 

room temperature to 93 C (200 °F) are needed. Therefore, it is necessary to obtain a complete set of 

tensile, compressive, and shear properties in a wide range of strain rates and temperatures to fully 

characterize the material. Thus, it is of great interest when determining material properties of composites 

to first determine the material properties of the polymer. To do so, a complete set of material response test 

data is needed. 

There are many techniques to test for the material properties of polymers, and standard guidelines 

exist to give properties needed for modeling or design. For low-strain-rate testing, the American Society 

for Testing of Materials (ASTM) Standard D638 (Ref. 9) suggests that long dog-bone specimen 

geometries serve as the basis for finding tensile properties, and ASTM Standard E2207 (Ref. 10) suggests 

that long thin-walled tubes be used for conducting shear testing on polymers. In both ASTM cases, the 

specimen deformation is measured by a strain gauge, and the reaction load is obtained from the test 

machine. With these data, a full stress-strain curve can be obtained. For testing polymer resins at high 

strain rates (greater than 102

 s1), a split Hopkinson bar (SHB) is commonly used. Details on the SHB 

technique can be found in Frantz (Ref. 11). 

In numerous cases because of material availability, manufacturing ability, or test constraints, many 

researchers have proposed novel specimen designs to obtain material properties of polymer resins. Gilat, 

Goldberg, and Roberts (Ref. 12) used very small dog-bone-shaped specimens for tensile tests and short 

hollow cylinders for shear tests. Specimens were glued onto tabs to permit their insertion into the test 

machine. However, many of the shear specimens failed prematurely because of imperfect bonding of the 

specimen to the tabs or at strain gauge bonding locations, whereas many of the tensile specimens failed as 

a result of stress concentrations arising from the edges in the square gauge section. Bordonaro (Ref. 6) 

examined Nylon 66 (Alliance Polymers, Inc.), VICTREX PEEK (Victrex), and Ultem PolyEtherImide 

(PEI) (Boedeker Plastics) and tried to categorize these polymers and develop constitutive equations using 

the viscoplasticity theory based on overstress. There, novel specimen designs were proposed, and tension, 

compression, and torsional tests were conducted using MTS biaxial extensometers (MTS Systems 

Corporation). However, no elevated temperature effects were considered. Liang and Liechti (Ref. 13) 

proposed rectangular dog-bone specimens for tension and flat plates for compression; however, strain rate 

and temperature effects were not considered. Behzadi and Jones (Ref. 14) conducted compression tests on 

small resin cylinders under a variety of strain rates and temperatures, but tensile and shear tests were not 

done. Kontou (Ref. 15) examined the effects of temperature on tensile properties of epoxy resins using a 
NASA/CR—2013-215450 5 

laser extensometer. Buckley et al. (Ref. 16) conducted static and high-strain-rate SHB tests for epoxy 

resins in compression. 

Many techniques for testing polymers have been proposed; however, none is fully robust and able to 

give a complete set of tensile, compressive, and shear properties at different temperatures and at various 

strain rates ranging from very low (105

 s1) to very high (102 s1). The deficiencies that arise from the 

lack of a complete set of test data must be remedied so that advanced constitutive models (such as the one 

discussed in Goldberg (Ref. 7)) can be accurate enough for all of the conditions considered. 

2.2 Composite Material Testing 

The next step in understanding the nature of composite material behavior is to find the properties 

of the carbon fiber. Having both the properties of the carbon-fiber fabric and polymer matrix, 

micromechanics-based equations and techniques such as classical laminated plate theory (CLPT) can be 

used to find the effective properties of the composite structure. However, it is impractical and many times 

impossible to measure all of the needed properties of the carbon fibers directly, so material properties of 

the as-made composite are measured instead. Also, by testing composite coupons, insight above and 

beyond what is observed just by knowing the constituent behavior can be gathered about the response of 

the constituent materials in an as-fabricated condition. The knowledge gained from testing can provide 

valuable information about the fiber-matrix interface and the ways in which the interactions between the 

fiber and matrix affect material response. 

2.2.1 Composite Material Static Testing 

Generally, when material properties of a full composite material need to be known, standardized tests 

can be used. ASTM D3039 (Ref. 17) gives specific guidelines on testing unidirectional or balanced 

composite laminates in tension; ASTM D3410 (Ref. 18) and D6484 (Ref. 19) provide guidelines on 

conducting compression tests; and ASTM D5379 (Ref. 20) and ASTM D3518 (Ref. 21) give guidelines 

on measuring shear properties in a composite laminate. ASTM suggests using either bonded strain gauges 

or extensometers to measure strain and load cells on the test machine to measure force. These standards 

call for rectangular-shaped specimen geometries and were originally designed and used for unidirectional 

composites; however, they also include basic specimen geometries for balanced and symmetric laminates. 

These test methods are primarily designed to give basic material properties, such as overall tensile or 

compressive strength and an effective Young's modulus, and are widely used in industry (Ref. 22). Since 

there is a wide variety of composite material systems and a wide range of uses for these composites, there 

are standardized databases that provide specific guidelines for testing as well as properties for some of the 

more common carbon-fiber composite material combinations. These databases include Composite 

Materials Handbook 17 (Ref. 23), NASA’s Advanced General Aviation Transport Experiments (AGATE) 

(Ref. 24), and the FAA’s Material Qualification Guidelines (Ref. 25). In these databases, most of the test 

data have been obtained by ASTM guidelines, or specimen designs similar to ASTM guidelines have 

been used. 

Others have also attempted to further quantify composite material behavior by developing their own 

test methods or by testing materials not currently in the above-mentioned databases. At NASA Langley 

Research Center, Masters and others did extensive investigations specific to two-dimensional, triaxial 

braided composite materials (Refs. 26 to 30). In Reference 29, notched and unnotched tests for twodimensional braided composites in tension and compression were conducted to obtain basic material 

properties. In further research, Masters’s (Ref. 28) recommendations for standard strain gauge sizes and 

overall criteria for testing woven composite materials were developed to account for the heterogeneity 

exhibited in the composite. Also, Moiré interferometry was used to demonstrate that heterogeneity exists 

in the displacements of the axial and transverse specimen directions (Ref. 28), but no further discussions 

on this heterogeneity are presented. Instead, it was concluded that the heterogeneity of the composite 

specimen demands that strain gauges be at least the length of a unit cell in order to neglect the local 
NASA/CR—2013-215450 6 

effects of fibers or resin pockets. It was also concluded that specimen width makes little difference in 

material properties as long as the coupon specimen is wider than the unit cell width. 

Others have investigated using noncontact measurement techniques as opposed to strain gauges or 

extensometers to measure the mechanical properties of composite materials. Grediac (Ref. 31) gives an 

overview of some of the most popular, which include speckle photography, image correlation, geometric 

Moiré, Moiré interferometry, and electronic speckle pattern interferometry. Of these methods, few have 

been used to measure the material properties of composite materials. Gliesche (Ref. 32) used image 

correlation to measure the strength and in-plane shear properties of ±45° woven cloth. Axial and 

transverse strains were not measured from the full-field strains but rather were averaged over an arbitrary 

section to smooth out the heterogeneities from the material. However, Gliesche did prove that the 

averaged strain values agree well with strain gauge measurements. Although stress-strain curves are 

presented, the authors offered no discussion of the amount of heterogeneity in the composite. Hale 

(Ref. 33) used Moiré interferometry to examine strains on woven laminate edges and concluded that 

Moiré interferometry was extremely sensitive to the heterogeneity on the free edge and to fiber 

misalignment between the layers of lamina. He does mention, though, that Moiré interferometry is a 

valuable tool for measuring surface strains on the faces of laminates. Fergusson et al. (Ref. 34) used 

optical measurement techniques to determine strain fields on composite sandwich structures under fourpoint flexure. Although he determined that these techniques could provide meaningful full-field strain 

measurements under test, the techniques provided data that gave way to problems with their four-point 

flexure test of composite sandwich structures. Fergusson’s conclusions are important because they 

demonstrate that optical measurement techniques provide unique data and illustrate potential flaws in test 

methods that may otherwise go unnoticed. 

Because of the unique nature of the braided composite material systems, many of the techniques 

originally developed for unidirectional composite laminates may not be sufficient for data collection. 

Thus, a discussion of the merits of these test methods is needed. Also, many previous researchers have 

used full-field measurement techniques such as optical measurements and Moiré interferometry to 

examine braided and woven composites; however, no discussions were presented that gave insight into 

the causes of localized specimen deformations and failures. Furthermore, previous research has not 

elaborated on potential failure mechanisms that occur in triaxial braided composite materials that lead to 

heterogeneities in the material response. It is in this area that the results of current research will be 

presented in an attempt to explain the complex nature of the triaxial braid and the way it affects the 

material response. 

2.2.2 Composite Material Interface Testing 

One potential characteristic that may account for differences in the material properties of fabricated 

composite structures and the material properties of similar constituents is the fiber-matrix interface. An 

interface in a composite material is a defined area where the fibers and matrix material meet, and its 

properties depend greatly on the bonding characteristics between the fiber and matrix material. The 

physical characteristics of the fiber fabrication, fiber surface treatments, matrix fabrication, composite 

cure time and temperature, and other variables will affect the interface properties. Whereas the goal of 

this research is not to identify, characterize, or assign a value to a specific interface parameter for a 

composite material, it is to address the need for an understanding of the way in which the interface affects 

material response. Since the interface plays an important role in the composite material response, a review 

of the current techniques to attempt to characterize an interface is presented. 

Researchers agree that a fiber-matrix interface is of great importance in composite material response. 

A great deal of research has been done to define the material properties of the fiber-matrix interface. Test 

methods have been developed to try to characterize the fiber-matrix interface on a micromechanical level 

by looking at a single fiber or single tows of fibers. Some of these methods are discussed in detail in 

Drzal, Herrera-Franco, and Ho (Ref. 35) and include some methods such as fiber pullout, single fiber 

fragmentation, and microdebond or microindentation techniques. Sometimes a material parameter called 

interfacial shear strength (ISS) is sought. Although these are novel approaches to quantify an interface 
NASA/CR—2013-215450 7 

property, they are largely used in either micromechanical composite modeling confined to a single unit 

cell or ply or in developing composite constitutive equations. Researchers (Refs. 36 and 37) have also 

sought to correlate the value of ISS determined from these micromechanical tests to failure types in 

macromechanical coupon testing. For compression testing, it was determined that a low value of the ISS 

(representing a weak fiber-matrix interface) caused a delamination failure in the composite; medium 

values of the ISS caused fiber microbuckling; and high values of ISS caused fiber compressive failure. In 

axial composite coupon testing, the ISS did not affect the composite strength or stiffness dramatically, but 

rather affected the mode of composite failure. Composites with a weak ISS demonstrated a progressive 

failure mode; those with an intermediate ISS demonstrated fiber “brushing” or “brooming”; and those 

with a strong ISS demonstrated a brittle or abrupt failure. In transverse coupon testing, the stiffness of the 

composite was largely unaffected by the value of the ISS, but the strength and strain at failure changed 

with the approximate ratio of the ISS. 

Others have taken a different approach to quantify the fiber-matrix interface. Unlike micromechanical 

interface testing or simulations, macromechanical interface testing attempts to find and quantify an 

average interface property based on data from coupons or structural subsections. These tests are done on a 

macromechanical scale with composite coupons; however, the value of ISS must be obtained by indirect 

methods. Haselbach and Lauke (Ref. 38) attempted to use acoustic emission to identify fiber breaks, 

matrix cracking, and fiber-matrix debonding, and Todoroki and Tanaka (Ref. 39) used an electric 

resistance charge method to identify fiber-matrix debonding. Some researchers (Ref. 40) have also 

attempted to determine a macromechanical ISS with some micromechanical methods: The microdroplet 

pullout technique was used to quantify an “interface relevance” parameter, and it was shown that the 

strength of the interface affects the failure modes of the composite. However, a value gained from the 

microdroplet test could not be directly used as a parameter in material modeling. 

Macromechanical interface testing has not been done largely because common measurement sensors 

(strain gauges, acoustic emission, and ultrasonic vibration) cannot accurately measure or predict the 

behavior of a macromechanically heterogeneous composite interface. The results obtained from these 

methods can sometimes be hard to obtain because interpretation of the data comes from indirect 

techniques to measure a physical property of the material. 

Although there have been numerous novel approaches to micromechanically and macromechanically 

characterize the fiber-matrix interface, the complete characteristics are still unknown, and the fiber-matrix 

interface property is a subject in which further research is being conducted. Even though it is not the goal 

of the current research to quantify an interface parameter in the composite materials tests, discussions are 

presented regarding the different degrees of interface strength and the way they affect composite material 

response. 

2.3 Composite Modeling Overview 

This section discusses the current modeling techniques for composites. The discussion comprises two 

categories. The first focuses on the constitutive modeling and other macroscale approaches that have been 

developed to categorize and predict overall composite material response but to neglect (to varying 

degrees) the microstructural behavior of the composite. These methods use various forms of CLPT as 

their basis; their approaches tend to account for the composite material response in an overall manner and 

neglect many of the fine details that are found in the microscale approaches. 

The second approach contrasts the first approach because it examines composites in a microscale 

modeling approach. In this approach, usually a small representative volume element (RVE) or repeating 

unit cell (RUC) of the composite is typically examined. In this approach, all of the finer details are 

considered and investigated. In many cases, the individual fibers, matrix, fiber undulation angles, and 

fiber-matrix interface are all explicitly modeled and examined. The goals of this approach are generally 

not to predict the overall composite material response but to investigate the micromechanical mechanisms 

influencing items such as overall composite strength and stiffness in a single RUC in addition to failure 

mechanisms, such as matrix cracking, fiber failure, and fiber-matrix debonding. 
NASA/CR—2013-215450 8 

2.3.1 Macroscale Composite Modeling Approaches 

Traditional constitutive modeling approaches for composite laminates use as their basis analytical 

micromechanics equations to obtain ply effective properties and CLPT. Discussions of traditional 

composite micromechanics methods and CLPT can be found in Christensen (Ref. 41). Many macroscale 

composite material models included in commercial finite-element codes (ABAQUS, NASTRAN, and 

LSDYNA) rely on CLPT. 

The composite material models built into these codes use CLPT calculations to build the composite 

laminate based on entered values for material moduli, Poisson’s ratios, and lamina directions and stackup 

sequence. These material models are then implemented into two-dimensional shell or three-dimensional 

brick elements. 

Although CLPT works well when defining laminate material properties based on stacked layers of 

unidirectional composite lamina, it cannot be directly used with braided or woven composites because a 

clear distinction cannot be made for each individual layer. Research has attempted to refine traditional 

CLPT methods specifically to woven or braided composites, and an overview is given in Tan, Tong, and 

Steven (Ref. 42). Examples include Raju and Wang (Ref. 43) and Byun (Ref. 44), who have developed 

CLPT equations specifically for woven composites by including fiber undulation. Others have developed 

their own methods for predicting elastic constants for the braided composite by including specific aspects 

of composite geometry. Tanov and Tabiei (Ref. 45) developed a four-cell model for woven composites. 

They divided the unit cell into a number of subcells and modified CLPT equations for each of the subcells 

by including the fiber undulations. Byun (Ref. 44) developed an approach to modeling triaxial braided 

composites by using the braid geometry and rule-of-mixtures approaches to calculate the material 

properties of the composite. Donadon et al. (Ref. 46) developed a three-dimensional constitutive model 

based on CLPT for woven laminates, and Huang (Ref. 47) developed a “bridging model” for woven 

composites based on undulations and composite geometry. Another model developed by Ishikawa and 

Chou (Ref. 48) called the “mosaic model” simplified woven composites by breaking up a unit cell into 

squares of unidirectional lamina. In this model, laminate properties were found by assembling the 

unidirectional lamina by rules developed from CLPT. Others created computer models having the fiber 

tows modeled as beams. Dano, Gendron, and Picard (Ref. 49) modeled two-dimensional, triaxial braided 

composite static tensile coupons using beam elements for the carbon fiber and shell elements for the 

polymer matrix material. Similarly, while conducting many tests on triaxial braided composites, Masters 

et al. (Ref. 27) developed two finite-element models for composite stiffness. The first of these models was 

called the “diagonal brick model,” which used a brick of resin as the outlining element with bar elements 

representing the carbon-fiber braid. Pastore and Gowayed (Ref. 50) developed what they called a “fabric 

geometry model,” which also modeled the triaxial braid as rods. There, they simulated the triaxial braided 

fiber architecture using local transformation matrices to simulate the undulation angles and a “stiffnessaveraging” micromechanics approach to develop global material constants from constitutive fiber and 

resin properties. 

In macroscopic modeling approaches, the developed models predicted the overall material response to 

varying degrees of success. However, most models have been developed to correlate one particular test 

condition and are usually not extended to predict results under a variety of different test conditions. These 

macromechanical models also failed to predict the behavior of one single fiber tow or resin pocket or the 

response of the fiber-matrix interface. This is the area in which microscale composite material modeling 

plays an important role. 

2.3.2 Microscale Constitutive Modeling Approaches 

Although the macroscale composite models were good at predicting overall composite behavior, they 

were deficient in predicting material response from a single fiber tow or resin pocket. The micromechanical 

finite-element models account for this deficiency. 

One main concern for researchers is that traditional CLPT and macromechanical approaches neglect 

the fiber-matrix interface. With these micromechanical models, many researchers have included a fiber-
NASA/CR—2013-215450 9 

matrix interface to more accurately define the composite material response because the interface typically 

has a strong effect on strength and failure modes in the composite specimen. Subramanian, Reifsnider, 

and Stinchcomb (Ref. 51) developed a micromechanical model that included an “efficiency” parameter 

developed from a concentric cylinders model. Using this efficiency parameter showed good correlation 

between predicted tensile strengths and analysis. However, this model was used for unidirectional 

composites only. Sun and Pan (Ref. 52) introduced a “bonding layer,” which was inserted between layers 

of fiber and matrix. Both these methods had up to 25 percent error in the transverse direction. Xie et al. 

(Ref. 53) developed a cohesive zone model to simulate the mode 1 fracture in two-dimensional, triaxial 

braided composite materials. The cohesive zone model used one-dimensional nonlinear spring elements 

connected between the fiber and matrix and simulated crack initiation and propagation of cracks under 

static mode 1 fracture. However, a dense mesh and a large number of elements were needed for the 

simulation to correlate to test data. Tsai, Patra, and Wetherhold (Ref. 54) modeled a fiber pullout test 

using contact parameters for cohesive debonding and frictional sliding as the interface. 

As the examples in the previous paragraph illustrated, attempts to micromechanically define an 

interface parameter normally led to a computer model having a large number of elements and were 

therefore inadequate for use in a macroscopic modeling approach. This discrepancy is where the main 

problem in simulations lie: many of the microscale models include parameters such as braid geometry and 

a fiber-matrix interface parameter that tend to improve the material response; however, these models are 

sufficiently large that they cannot be used on the macroscale level, which includes subcomponents or 

large structures. In contrast, the macromechanical braided composite models that exist can predict overall 

structural composite material response, but they cannot produce detailed results because they fail to 

include the micromechanical details. A macromechanical modeling approach needs a model that will 

account for the features found in the microscale approaches and also be able to predict macroscale 

behavior of the triaxial braided composite material response and failure for many composite material 

systems. The approach must at the same time minimize mesh sizes and computational time. 

2.4 Material Property Selection 

This section discusses the various ways of incorporating the composite material properties into model 

development. Even though all of the above-described approaches have merit in modeling braided 

composite materials, the overall laminate material properties used in these models must be found. Many 

of these approaches that explicitly model the fiber and matrix also implement the constituent properties 

directly into the model development. Thus, the constituent properties for the fiber and matrix must be 

known. This type of material implementation can be categorized as a “bottom-up” approach, where the 

fiber and matrix material properties are the basic, or bottom, parameters and serve as the building blocks 

for laminate equation development. 

As opposed to the bottom-up approach, researchers have used some of the theories described above 

and developed different methods for material property incorporation by using as-tested composite 

material properties. This group of theories can be thought of as a “top-down” approach, which uses full 

composite laminate material parameters obtained from material testing and develops equations that try to 

back out, or identify, the material properties for either the basic fiber and matrix constituents or a single 

ply of lamina. Chen and Kam (Ref. 55) developed a novel way to identify the material properties of 

angle-ply laminates by first measuring the axial and transverse strains during testing and then using error 

functions to minimize error when comparing these values with theoretical values. Ng (Ref. 56) also uses 

the top-down approach to back out unidirectional lamina properties from a stacked laminate. 

Both approaches have merits and limitations. When using constituent (fiber and matrix) properties, if 

a particular material parameter is unavailable, many times the value is assumed or gathered from 

literature. Although the results of these approaches match experimental data well, they can lead to 

adjusting an assumed material value to make the results match test data. This method is in contrast to 

using optimization approaches. Many times, certain types of overall composite material properties cannot 

be measured, which is the whole justification for using optimization. Usually, there are more variables 
NASA/CR—2013-215450 10 

than equations, and optimization schemes choose the unknown variables so that the total error from all of 

the equations is minimized. Even though this approach has a good basis in that it uses actual material test 

data, the final numbers developed are a combination of the equation development presented and solutions 

from a numerical solver, which have inherent errors associated with them. They do not find a closed-form 

solution to the problem. 

The next section discusses a model development approach that will use conventional composite 

analysis methods formulation of the material properties in a macroscale model. This model will be 

capable of predicting an overall material response that will implement test data without using 

optimization schemes or assumed values for properties. 

2.5 Current Research 

Previous research has not identified a solution for the testing of the composite constituent, the 

polymer resin, under a variety of strain rates and temperatures. Previous research has also not accurately 

characterized triaxial braided composite material response or offered information about the nature of local 

deformation and failure mechanisms that affect the composite material response. Test methods developed 

in this study are capable of capturing the resin matrix constituent properties at a variety of strain rates and 

temperatures for use in constitutive models. They are also capable of capturing the composite material 

response and identifying some of the local deformation and failure mechanisms. In addition, unlike 

previous research, these test methods captured the needed information through direct measurements. 

Both the developed test methods for the polymer resin and fabricated composite materials utilized a 

noncontact digital image correlation technique. The noncontact measurement techniques offered 

advantages over conventional techniques in that they were able to explore micromechanical failure 

mechanisms such as transverse fiber failure and delaminations. It will be shown that the developed 

measurement techniques provide all of the data needed for inclusion into material models used in 

computer simulations. 

The material parameters needed in macromechanical finite-element models were obtained via CLPT 

and traditional composite micromechanics techniques as the data reduction scheme. Although numerous 

braided composite micromechanical and macromechanical computer models have been developed, none 

uses measured full-field braided composite test data as a basis for material property inclusion. The model 

developed in this research has diminished the gap between micromechanical and macromechanical 

computer models through a micro-macromechanical hybrid approach. The computer models were used to 

predict triaxial braided composites under static loading. 

Finally, the qualitative results that will be presented show predictions of different impact responses 

based on different material systems. 

3.0 Investigations Into Composite Constituent Material Response 

As discussed in Section 2.0, the first step in understanding the nature of the composite material 

response is to examine the behavior of the polymer resin. Because the rate dependence in a composite 

material comes mainly from the rate dependence in the polymer resin, the resin data cannot be overlooked 

when trying to analytically characterize and observe the composite material response. Furthermore, one 

way of characterizing the polymer material response is by developing polymer resin constitutive models 

in which the resin response can be quantified in closed-form equations using various internal state 

variables. However, characterizing this material requires a complete set of tensile, compressive, and shear 

test data so that effects from the hydrostatic stress are accounted for, and internal parameters in the 

constitutive models can be identified and quantified. The previous methods described in Section 2.0 were 

deficient in producing appropriate data needed for the analytical models. Therefore, this issue is addressed 

by developing a test method to fully characterize a polymer in tension, compression, and shear for strain 

rates ranging from 105

 to 101 s

1

 and temperatures ranging from room temperature to 80 °C (176 F) for 

a selected resin, Epon Resin 862 (Momentive Specialty Chemicals, Inc.). 
NASA/CR—2013-215450 11 

3.1 Experimental Setup 

Epon 862 (E862 (Momentive Specialty Chemicals, Inc.)) is a thermoset resin with low viscosity. It 

recently has been examined as a potential candidate for producing composite fan cases. Also, because of its 

wide availability, it was an ideal candidate for the development of the test method and data collection 

techniques. 

To characterize the strain rate dependence of the E862 resin, displacement rates of 19105

 cm/min 

(7.5105

 in./min), 19103 cm/min (7.5103 in./min), and 1.9 cm/min (0.75 in./min)—corresponding to 

strain rates of 105

, 103, and 101 s1, respectively—were used for tension and compression tests, whereas 

6.875102

 deg/min, 6.875 deg/min, and 11.458 deg/s twist rates (corresponding to strain rates of 

1.6105

, 1.6103, 1.6101 s1) were used for torsion tests. All three tests (tension, compression, and 

shear) were conducted so that the effects of hydrostatic stresses could be quantified and examined as the 

strain rate was changed. Engineering stress versus strain was measured for all tests to preserve 

consistency between the tensile, compressive, and shear results. Stress-strain curves were determined at 

room temperature (~20), 50, and 80 °C (~68, 122, and 176 F). 

The constitutive modeling approach will also attempt to simulate polymers undergoing unloading. To 

investigate damage accumulation at various loading stages, load-unload tests also were conducted under 

tension, compression, and torsion for three strain rates and three temperatures. It was noticed that polymers 

produce a nonlinear unloading curve, caused by a combination of reversible and irreversible deformation 

mechanisms (Ref. 57). To account for the differences in nonlinearities in the unloading portion of the 

material response curve, the specimens were unloaded at three specified points: (1) maximum, or saturation, 

stress, (2) halfway between the elastic region and the saturation stress, and if there was specimen availability 

(3) approximately 2 percent strain to confirm an elastic unload. The specified load set points were 

determined from the previously conducted load-to-failure tests. 

Testing was conducted in an MTS 858 tabletop test machine with an MTS computer controller and an 

MTS 622.20C01 axial-torsional load cell. All tests were conducted in displacement (stroke) control. 

3.2 Optical Measurement Use for Data Collection 

For previous studies and data presented in literature, strain data were primarily collected by placing 

strain gauges on the polymer specimen. The strain gauge, in many cases, caused premature specimen 

failure, as demonstrated in Reference 12. Therefore, a different approach was used for the data collection. 

Instead of placing strain gauges on the specimens, a noncontact optical measurement technique was used. 

The optical measurement system has advantages over conventional strain gauges in that it does not 

require the sensor to be physically attached on the surface of the specimen, thus eliminating potential stress 

or strain concentrations, which typically lead to premature specimen failure. Another advantage is that it can 

be used on all shapes and sizes of specimen geometries, eliminating constraints usually needed with strain 

gauges. Finally, unlike conventional strain gauges, the noncontact measurement technique delivers 

displacements in all three coordinate directions (specimen transverse, x; specimen longitudinal, y; and 

specimen out-of-plane, z), allowing calculations of components of field strains: axial, transverse, and shear. 

Also, by directly measuring the axial and transverse strains, a Poisson’s ratio was directly measured. 

The optical measurement system is a commercially available system produced by GOM (Ref. 58) and 

consists of two digital cameras connected to a computer having specialized software capable of pattern 

recognition. The entire procedure for using the system is documented in the users manual (Ref. 59) and is 

summarized in this section for completeness. 

After determining the size of the test object in question, appropriate lenses are chosen and fitted on 

the cameras. The cameras are then calibrated using the software by taking pictures of specialized 

calibration blocks in various orientations. The calibration procedure allows the software to correct for 

minor height and angle differences between the cameras and also corrects any distortions present in the 

camera lenses. When the calibration procedure is completed, the software displays information about the 

size of the calibrated volume of space that is available to the user. Figure 3.1 is a schematic of the 

calibrated volume using the stereocamera setup. 
NASA/CR—2013-215450 12 

The user then applies a random black and white stochastic speckle pattern to the test specimen and 

positions it in the calibrated volume identified by the cameras (noted by the dotted box in Fig. 3.1). The 

specimen is then loaded and imaged specified intervals during the loading process. Once the test is 

completed, the user has a time history of stereo-images. These images are used to measure displacements 

and calculate strains. 

During postprocessing, the computer calculates the change in the pattern on the specimen relative to a 

painted but unloaded reference picture. It then determines the displacements and rotations in the pattern 

based on the unloaded picture. Strain can then be computed using calculated displacements and reference 

distances. 

When testing specimens at higher temperatures, a specially designed transparent temperature chamber 

was used. This chamber served as a closed isothermal environment capable of heating specimens up to 

176 °C (350 F) but still allowed the use of the noncontact optical measurement technique. The 

temperature chamber outer walls were made of a borosilicate glass with a low thermal expansion 

coefficient. The chamber was heated by connecting it to a laboratory compressed air line containing an 

inline heater that heated the air before it reached the chamber. 

To account for heat losses around the ends of the chamber and near the grips, special resistance 

heaters were placed near the top and bottom grips. The temperature chamber was calibrated by first 

setting temperature set points on the chamber controller and placing five thermocouples inside the 

chamber at various locations. As the temperature chamber ramped to reach the target set points, readings 

from the thermocouples were plotted and the time for the chamber to reach equilibrium temperature was 

recorded. When testing specimens in the chamber at high temperatures, the test was started only after the 

chamber had reached an equilibration temperature. 

To account for minor differences in light reflection through the clear thermal chamber glass, the 

cameras were calibrated through the glass. Calibrating through the glass removed the distortions in the 

measurements caused by the heating and defects in the glass. 

The setup used in the polymer testing consisted of Vosskühler CCD1330 cameras with 50-mm 

Schneider C-mount lenses. The calibrated volume for the cameras was approximately 10 by 8 by 8 mm, 

and the optical measurement system could resolve displacements on the specimen down to approximately 

104

 to 103 mm. The optical measurement system was also capable of capturing the value of the loading 

from the test machine through an external analog input channel. Thus, by using the synchronized 

computed strain value and the input load value, stress-strain curves were generated. 
NASA/CR—2013-215450 13 

3.3 Specimen Designs 

Specimens were cut from stock sheets of E862 resin plates that were manufactured and molded to be 

0.6096 m (2 ft) tall by 0.6096 m (2 ft) wide by 0.638 cm (0.25 in.) thick using a resin transfer molding 

(RTM) process. The catalyst used was Epikure W (Hexion Specialty Chemicals) with a cure cycle of 2.5 

h at a temperature of 176 °C (350 °F) under 1.03 MPa (150 psi) of pressure. In machining, rectangular 

bars were cut from the stock panels that were approximately the specimen length. These bars were then 

machined down to the required 6.0325-cm (2.3750-in.) length and were turned down to a 0.584-cm 

(0.230-in.) diameter using a CNC (computer numerical controlled) lathe. The gauge section was then cut 

out on a lathe and finished. The result was a tightly controlled specimen geometry with a very smooth 

surface finish. This precise machining method allowed for minimal variation between specimens. 

Tolerances for all specimen dimensions were ±1.310–4 cm (5.0105

 in.). The small specimen geometry 

allowed many specimens to be made from one stock sheet of resin, thereby reducing plate-to-plate 

variability. 

ASTM standard D638 Section 6.3 Rigid Rods (Ref. 9) was consulted for specimen geometry, and the 

specimens ultimately used in this study kept the similar length-to-width ratios as given in ASTM D638. 

However, smaller specimen geometries were chosen because it was difficult to make the large resin 

specimens needed for ASTM D638 out of the E862 resin because of cracking, bubbling, and warping in 

the stock plates. These cylindrical specimens had a gauge section 0.3175 cm (0.1250 in.) in length by 

0.3175 cm (0.1250 in.) in diameter, a large transition radii, and long 2.54-cm (1-in.) ends used in 

gripping. These specimens were ideal because they were small enough to manufacture many from the 

same resin plate, and they could also be used for high-rate SHB testing. ASTM D638 suggests a specimen 

gauge-length-to-gauge-diameter ratio of 2 or greater to achieve a uniaxial state of stress within the gauge. 

Although the specimens did not achieve these ratios, the geometry suggested does allow for a uniform 

state of stress within the gauge, which has been verified by finite-element analysis. A schematic of a 

tensile specimen is shown in Figure 3.2. Note that the compressive specimens used had the same 

dimensions as those of the tensile specimens, minimizing machining costs. 

For compressive tests, by using the optical measurement system to capture a time history of the 

loading, the onset of buckling was identified. This information was used to identify the region of stable 

and usable data. 

Shear specimens were designed similarly to the tensile specimens with modifications needed to meet 

shear specimen requirements. The transition radii were reduced to 0.3175 mm (0.0125 in.) and the gauge 

section outside diameter was enlarged to 0.5207 cm (0.2050 in.). A hole was drilled in the specimen 

leaving an inside diameter of 0.3619 cm (0.1425 in.), which gave a wall thickness of 0.762 mm 

(0.0300 in.). These dimensions ensured that a thin-walled tube assumption could be used during the data 

reduction. A schematic of the specimen are shown in Figure 3.3(a), and a digital microscopic image of the 

gage cross section is shown in part (b),which shows a highly uniform thin wall that was achieved by the 

precise specimen fabrication, an advantage of using CNC machining to create specimens. 
NASA/CR—2013-215450 14 

3.4 Test Procedure 

The specimens were painted with the stochastic pattern and then placed in the test machine and 

tested by pulling or twisting at the specified rates described in Section 3.1. The optical measurement 

system collected the test data by taking pictures at specified intervals during the test. Typically, the 

testing at 101

 s1 lasted approximately 10 s, and the acquisition rate was 10 Hz. The testing at 103 s

1

lasted approximately 20 min, and the acquisition rate was approximately 0.1 Hz. The lowest strain rate 

testing at 105

 s1 lasted up to 18 h, so data collection was much slower. For these tests, data were taken 

every 6 to 10 min. The above-described procedure usually gave about 100 to 150 discrete data collections 

for each of the rates tested. A final postfailure picture was also taken for completeness. 

3.5 Results 

Sections 3.5.1 to 3.5.4 present the results obtained using the techniques described in Section 3.4. 

Section 3.5.1 describes the tensile test results; Section 3.5.2, the compression results; Section 3.5.3, the 

shear results; and Section 3.5.4, the load-unload results. 

3.5.1 Tensile Results 

Typical tensile results obtained from the optical strain measurement technique are shown in 

Figures 3.4 and 3.5. Figure 3.4 shows axial strain results from a specimen shortly before specimen failure. 

One can see the strain uniformity around the perimeter of the specimen and gradual variation of the strain 

along its length, with the highest strain in the middle of the gauge section, which ensured failure at the 

midpoint. 

Figure 3.4 shows a gauge section midpoint strain of 25 percent, whereas the outer portions of the 

gauge section had a strain between 15 and 16 percent. Also, Figure 3.4 shows bands of uniform strain 

wrapping along the perimeter of the specimen. With the knowledge that the bands of strain within the 

camera field of view extended around the perimeter of the entire specimen, the strain was assumed to be 

uniform along the entire specimen perimeter based on the uniformity of the data. 

Figure 3.5 shows the failure of a tensile specimen with axial strain computed on the bottom portion of 

the specimen. The failure occurred in the middle of the gauge section, which was desired since the 

specimens were fabricated to achieve this result. Also note that the optical measurement system computed 

a permanent plastic deformation of 6.17 percent in the specimen after the failure. Although these data 

have not been used in constitutive model development, knowing the permanent plastic strain after 

specimen failure is an advantage of using an optical measurement system. 
NASA/CR—2013-215450 15 

To plot the stress-strain curves, between seven and nine points were picked in the areas of highest 

strain in the middle of the specimen gauge section. The strain was averaged for these points. Figure 3.6 

shows the points that were averaged for an example tensile test. 

In Figure 3.6, note that the nine points averaged for the final stress-strain material response curve for 

the specimen come from the area of highest strain located in the middle of the gauge section. This method 

of averaging was used to eradicate any erroneous results due to distortions for a particular location in the 

dot pattern. Use of the average point data from the areas of highest strain was consistent throughout all 

conducted tests. 
NASA/CR—2013-215450 16 

This same method of point averaging was used for tensile, compressive, and shear testing. Stress was 

found for the tensile and compressive tests by using the value of the load and dividing it by the original 

undeformed cross-sectional area, giving the final material response curves in engineering stress. Figures 

3.7 to 3.9 show tensile data obtained at the various test conditions. Each curve represents the averaged 

material response for a single test in each of the figures. 

The polymer clearly displayed rate effects, as evidenced by the material response curves for three 

rates at room temperature shown in Figure 3.7. The highest strain rate tested (101

 s1) showed an ultimate 

stress increase of 16 percent over the medium rate (103

 s1), whereas the difference between the ultimate 

stresses for the middle strain rate and the lowest strain rate (105

 s1) tested was 17 percent. 

Figure 3.8 shows the temperature dependence of the material at the medium strain rate tested. The 

polymer exhibited softening at higher temperatures. The lowest temperature tested, room temperature 

(~20 C, 68 F), showed an ultimate stress increase of 28.7 percent over the 50 °C (122 F) data, and the 

50 °C data showed an ultimate stress increase of 26.8 percent over the 80 °C (176 F) data. Also, the 

ultimate failure strain showed dependence on temperature. The average ultimate failure strains for room 

temperature, 50 °C, and 80 °C were 0.3, 0.38, and 0.46, respectively. These results correspond to 

increases of 26 percent going from room temperature to 50 °C and 21 percent going from 50 to 80 °C. 

Figure 3.9 shows the polymer temperature dependence at the highest strain rate (101

 s1). Again, the 

polymer exhibited a softening phenomenon at the higher temperatures. The room temperature data 

showed an 18-percent increase over the 50 °C data, and the 50 °C data showed a 29-percent increase over 

the 80 °C data. As with the medium-rate temperature-dependence data, the high-rate temperature data 

showed clear failure strain dependence on temperature. The average failure strains for the room 

temperature, 50 °C, and 80 °C data were 0.23, 0.36, and 0.47, respectively. These results correspond to 

changes of 55 percent going from room temperature to 50 °C and 36 percent going from 50 to 80 °C. 
NASA/CR—2013-215450 17 

Figures 3.8 and 3.9 show that the temperature played a greater role in the polymer material response 

than did the strain rate. The data showed the differences in the ultimate stress to be 28.7 percent when 

going from room temperature to 50 °C (a 150-percent increase in temperature) and 26.8 percent when 

going from 50 to 80 °C (a 60-percent increase in temperature). In comparison, the data in Figure 3.7 

showed that the stress differences were only 16 percent when the strain rate was increased 10 000 percent 

from the middle to the highest strain rate and were 17 percent when the strain rate was increased another 

10 000 percent from the lowest to the middle strain rate. 
NASA/CR—2013-215450 18 

All the curves exhibited the same trends in the material response, whether it was under high-rate, 

high-temperature loading or low-rate, low-temperature loading. The curves ramped up linearly until an 

upper yield point was reached. Next, there was a drop in load that caused the material response curves to 

decrease to a certain saturation stress. During this drop in load, there was localized necking in the gauge 

section of the specimen. While in the perfectly plastic region, the localized neck propagation spread 

throughout the gauge section. The material response behaved in the perfectly plastic manner until it 

started to rise again at the end of the loading, right before failure. The hardening that occurs near the ends 

of the curves presented in this section corresponds to a sufficient amount of localized polymer molecules 

aligning in their chain direction, which causes a rise in loading (Ref. 60). The trends in these data also 

agree with trends found in Reference 6. 

Finally, note that multiple overlapping curves in Figures 3.7 to 3.9 show the repeatability of test data 

attributed to the specimen design and strain measurement system. 

3.5.2 Compression Results 

The compression specimen geometries used were identical to the tensile specimens. However, 

material behavior in compression differs from that in tension because the specimens exhibited buckling in 

compression. Nevertheless, having the optical measurement system allowed the user to capture a test 

history and observe the strain in the specimen before and during buckling. Typical compression results 

showed that buckling in the compression specimens began to occur at around 20 percent strain. Although 

the curves for full stress versus strain until failure are presented in this section, when developing 

constitutive models, normally the data are only used until the saturation stress. Therefore, the data after 

buckling were not used in the constitutive models but are presented herein for completeness. Before the 

onset of buckling, the gauge section of the specimen “fattened” or barreled until approximately 20 percent 

strain was reached; then, as a result of either geometric eccentricities or slight grip misalignment, the 

specimen buckled. Figure 3.10 exemplifies a specimen exhibiting a postbuckling response. 
NASA/CR—2013-215450 19 

However, looking at the stress-strain curves in Figures 3.11 to 3.13, one can see that buckling occurs 

after the stress plateau is reached, which means that the specimen geometries allow the stress to reach 

saturation before the onset of buckling. Since engineering stress versus strain is plotted in these figures, 

the compressive curves tend to rise after the buckling point because the deformed area increases, whereas 

the original undeformed area of the calculated stress remains constant. 

Figure 3.11 shows the rate dependence of the resin under compression loading. Neglecting the rise in 

the stress-strain curves at strains above 15 percent due to barreling and buckling, the ultimate stresses in 

the material responses are 93, 106.8, and 126 MPa (13 485, 15 486, and 18 270 psi) for the 105

, 103, and 

101

 s1 strain rates, respectively. This result corresponds to a 15-percent increase when going from 105 to 

103 s

1

 and to an 18-percent increase when going from 103 to 101 s

1

. These curves are also 35, 32, and 

34 percent higher than the ultimate tensile stress (shown in Fig. 3.7) for the 105

, 103, and 101 s1 strain 

rates, respectively. The consistency of the greater ultimate stress in compression with that in tension for 

the three rates signifies that the hydrostatic stress effects play a role in the specimen response. 

Figure 3.12 shows the temperature dependence in the material response in compression for the 103

 s1

strain rate. Again, as with the tensile testing, as the temperature became higher, the ultimate stress for the 

resin became lower. The ultimate stresses for room temperature, 50 °C, and 80 °C are 106.8, 83, and 

60 MPa (15 486, 12 035, and 8700 psi), respectively, corresponding to a decrease of 29 percent when 

going from room temperature to 50 °C and 34 percent when going from 50 to 80 °C. The values of ultimate 

strain could not be found because of the buckling phenomena that occurred in the material response; 

however, the figure shows that the onset of buckling began much earlier in the room temperature specimen 

than in the higher temperature specimens. 

Figure 3.13 shows the temperature dependence in the material response in compression for the 10–1 s–1 

strain rate. The data at the highest strain rate confirmed what was found for the temperature dependence at 

the lower strain rate (103 s

1

) tested. The ultimate stresses for room temperature, 50 °C, and 80 °C (122 and 

176 F) are 126, 102, and 76 MPa (18 270, 14 790, and 11 020 psi), respectively. The changes in ultimate 

stress correspond to the changes in ultimate stress in the lower rate tested. The ultimate stress decreases by 

24 percent when going from room temperature to 50 °C and decreases by 35 percent when going from 50 to 

80 °C. These values are similar to those seen in the lower rate testing: in the lower rate testing, the decrease 
NASA/CR—2013-215450 20 
NASA/CR—2013-215450 21 

in stress is 29 percent between room temperature and 50 °C and is 34 percent between 50 and 80 °C. This 

result shows that the temperature dependency of the material is not dependent on the strain rate. 

The specimen compressive material response curves are different from the response under tensile 

conditions. Instead of reaching an upper and a lower yielding point, the specimens reached yielding at a 

plateau point before rising at the onset of buckling. 

3.5.3 Shear Results 

Engineering stress was plotted against torsional shear strain. Engineering stress was used to keep 

consistency in the data gathered. As with the tensile and compressive tests, points were picked in the 

middle of the gauge section and averaged to obtain a final stress-strain curve. Figure 3.14 shows the fullfield shear strain calculations at approximately 50 percent strain. 

As Figure 3.14 shows, there was a region of uniform shear strain along the perimeter of the specimen 

throughout the gauge section, and it is assumed to be uniform around the entire specimen. Because the 

optical measurement system only computed and displayed shear strain values as engineering shear strain, 

these values were multiplied by 2 to achieve the correct tensorial shear strain. 

In many cases, the shear specimen broke catastrophically once it reached 70 percent strain as a result 

of the extreme angle of twist on the specimen. Figure 3.15 shows a shear specimen failure. 

Again note that in Figure 3.15, postfailure strains that represent a permanent plastic deformation 

were able to be measured on the failed specimen. As with the tensile and compressive tests, plots of 

engineering shear stress  versus tensorial shear strain curves are presented in Figures 3.16 to 3.18. 

Engineering shear stress was found by 

 J

Tc

  (3.1) 

where the variable T represents the torque exerted on the specimen, the variable c is the outer radius of the 

gauge section, and J is the polar moment of inertia. To plot the shear stress-strain curves, the assumption 

that the torque and corresponding shear stress are uniform throughout the entire wall had to be made. 
NASA/CR—2013-215450 22 

The shear stress-strain curves in Figure 3.16 exhibit the same trends as the tensile and compressive 

material response curves, with the highest ultimate stress occurring at the highest strain rate tested 

(1.6101

 s1). Going from the lowest rate (1.6105 s1) to the medium rate (1.6103 s1) show an increase 

of 19 percent in the ultimate stress, and going from the medium rate to the highest rate show an increase of 

16 percent. These increases are consistent between both the tensile and compressive results. When going 

from the lowest to the medium rate tested, the tensile results show a 17-percent increase, and the 

compressive results show a 15-percent increase. When going from the medium to the highest strain rates, 
NASA/CR—2013-215450 23 

the tensile results show a 16-percent increase, and the compression results show an 18-percent increase. The 

data prove that effects of strain rate are equal between tension, compression, and torsional testing. 

Figure 3.17 shows the effects of temperature at the medium strain rate (1.6103

 s1) tested. Again, 

trends agree between both the tensile and compressive results. When going from room temperature to 

50 °C (122 F), the ultimate stress decreases by 17 percent, and when going from 50 to 80 °C (176 F), 

the ultimate stress decreases by 38 percent. However, no conclusions can be drawn about the ultimate 

strain, as all three temperatures show that the specimens failed at approximately 0.7 ultimate strain. 
NASA/CR—2013-215450 24 

Figure 3.18 shows the effects of temperature at the highest strain rate (1.6101

 s1) tested. The 

ultimate stress decreases by 13 percent when going from room temperature to 50 °C and decreases by 

33 percent when going from 50 to 80 °C. As with the medium-rate temperature results, ultimate strain 

comparisons could not be made because, again, all specimens fail catastrophically once 0.7 strain was 

reached. Comparing these results with the medium-rate results shows that the strain rate did not have an 

effect on the temperature results in that the percent decreases between the temperatures were similar for 

the two strain rates. 

3.5.4 Cyclic Load-Unload Results 

Load-unload tests in tension, compression, and shear were also conducted at strain rates of 1103

 s1 

and 1101 s1 under room temperature and elevated temperature conditions—to show the inelastic 

unloading and hysteresis of the resin. The unloading modulus decreased as the specimen was unloaded at 

higher strains because of the accumulation of plastic strain and damage in the specimens. Also, the slope 

of the unloading curve can be compared with the slope in the elastic region. The difference in these values 

can help to categorize damage parameters, which are also used in constitutive modeling. 

Figures 3.19 to 3.32 each contain multiple curves that represent different tests in which the specimens 

were unloaded at different points while in their plastic regime. Although a full data analysis is provided 

by Goldberg et al. (Ref. 57), it is summarized herein for completeness. 

Tensile load-unload-reload curves are shown at a strain rate of 103

 s1 in Figure 3.19 and at a strain 

rate of 101

 s1 in Figure 3.20. The unload points for both figures were 2, 5, 10, and 12 percent. Both 

figures show the nonlinearities in the unload portion of the curves, which grows more pronounced at the 

higher unloading points. Also note that in the 2- and 5-percent unloading curves, all the strain is 

recovered, signified by showing the curve returning to zero strain. However, in the 10- and 12-percent 

unloading points, most—but not all—of the strain is recovered. Finally, note that the average slope of the 

unloading curve decreases as the point of unloading increases. 

Upon reloading, the curves have their same original loading modulus and reach the original saturation 

stress. 
NASA/CR—2013-215450 25 

Figure 3.21 shows compression load-unload-reload curves at the 103

 s1 strain rate, and Figure 3.22 

shows load-unload-reload curves at the 10–1 s–1 strain rate. Unloading points were set at 2, 5, 8, and 

10 percent. These curves show results similar to those for the tensile curves. At 2 and 5 percent, nearly all 

the strain was recovered, whereas the 8- and 10-percent unloading curves show permanent plastic strain 

upon unload. Also, as the unloading point was increased, the value of the average unloading modulus was 

decreased. Upon reload, the slope of the curve follows the original loading modulus and returns to the 

original unloading point, following the original loading curve. The effects of hydrostatic stress on the 

material response are evident in the compression stress-strain curves. Also note that there is a significant 

amount of hysteresis present in the specimens unloaded at larger strains, which can be seen by comparing 

the loading and unloading portions of the curves. This hysteresis represents energy lost while loading and 

unloading the specimen. 
NASA/CR—2013-215450 26 

Comparing tensile and compressive load-unload-reload curves at a similar strain rate reveals the 

effects of the hydrostatic stresses. Using as examples Figure 3.20 (tensile load-unload-reload response at 

the 110–1 s–1 strain rate) and Figure 3.22 (compressive load-unload-reload response at the 1101

 s1

strain rate) reveals the differences. The compressive ultimate stress levels reach a higher value than the 

tensile stress levels, and the slope of the unloading curve was less in compression than what it was in 

tension. As a result of this reduction in slope, the compressive unloading curve crosses the zero stress axis 

at a lower strain than do the tensile curves. The compressive stresses also reach a lower value at the point 

of maximum unloading than do the tensile curves. It was these differences that signified that hydrostatic 

stress plays an important role in the material response and was one of the reasons why both tensile, 

compressive, and shear testing was done. For completeness, the full set of load-unload-reload data are 

included in Figures 3.23 to 3.32. 
NASA/CR—2013-215450 27 
NASA/CR—2013-215450 28 
NASA/CR—2013-215450 29 
NASA/CR—2013-215450 30 
NASA/CR—2013-215450 31 

3.5.5 Examination of Results 

Examining the data in the stress-strain plots in the previous sections reveals that the stresses increase 

significantly with strain rate, particularly in the nonlinear range. All these curves show an initial linear 

response to approximately 2 percent strain and then go nonlinear after this initial region. These figures 

also show the consistency in the data gathered. 

Although not used in the constitutive modeling development as described in Goldberg, Roberts, and 

Gilat (Ref. 4), the Young’s modulus, Poisson’s ratio, and shear modulus determined from the 

experimental results are listed in Table 3.1 as a check to confirm that the test method developed produced 

acceptable results. The Young’s modulus was determined from the tensile and compressive tests, and the 

shear modulus was determined from the torsion tests. These values were measured for all the strain rates 
NASA/CR—2013-215450 32 

and temperatures examined. Linear regression lines were used to compute the Young’s modulus, shear 

modulus, and Poisson’s ratio. The Young’s and shear moduli were measured as the slope of the stressstrain curve between 0 and 1 percent strain, and the Poisson’s ratio was measured as the ratio of average 

negative transverse strain to the average axial strain between 0 and 1 percent strain. Averaged values were 

used when multiple tests were conducted. Table 3.1 summarizes the results. 

The data in Table 3.1 show that the Young’s modulus increases as the strain rate increases, and 

decreases as the temperature increases for both tension and compression tests. The shear modulus also 

increases as the strain rate increases and decreases as the temperature increases. The Poisson’s ratio 

stayed at a constant value of approximately 0.4±0.03 for all the tension tests, whereas in some 

compression tests it was measured to be as low as 0.35. Shear modulus values measured from the torsion 

tests were compared with the theoretical computed values from the tension and compression data using 

  	  
  2 1

E G  	  
  2 1E G (3.2) 

where G is the calculated shear modulus, E is the measured axial modulus, and 
 is the measured 

Poisson’s ratio. Comparing rows 1 to 3 (tensile data at strain rates of 105

, 103, and 101 s1 at room 

temperature) with rows 15 to 17 (shear data at strain rates of 1.6105

, 1.6103, and 1.6101 s1 at room 

temperature) show this agreement. Rows 1 to 3 give calculated shear modulus values of 881, 957, and 

1032 MPa (127 745, 138 765, and 149 640 psi), respectively; rows 15 to 17 give measured shear modulus 

values of 801, 977, and 1002 MPa (116 145, 141 665, and 149 640 psi), respectively. The differences 

between these values were 9, 2, and 2 percent, respectively. 

TABLE 3.1.—E862 RESIN MATERIAL PROPERTIES 

Test condition Young’s 

modulus, 

GPa 

Poisson’s 

ratio 

Shear modulus 

(measured), 

MPa 

Shear modulus 

(calculated), 

MPa 

Temperature,a 

C 

Strain rate Load 

1 RT 10–5 Tension 2.52 0.43 – 881 

2 RT 10–3 Tension 2.77 0.41 – 957 

3 RT 10–1 Tension 2.89 0.40 – 1032 

4 50 10–3 Tension 2.28 0.40 – 814 

5 50 10–1 Tension 2.57 0.40 – 917 

6 80 10–3 Tension 1.95 0.40 – 696 

7 80 10–1 Tension 2.58 0.38 – 934 

8 RT 10–5 Compression 2.71 0.39 – 974 

9 RT 10–3 Compression 2.72 0.35 – 1007 

10 RT 10–1 Compression 2.96 0.40 – 1057 

11 50 10–3 Compression 2.09 0.35 – 774 

12 50 10–1 Compression 2.29 0.35 – 848 

13 80 10–3 Compression 1.66 0.37 – 615 

14 80 10–1 Compression 1.90 0.35 – 703 

15 RT 1.610–5 Shear – – 801 – 

16 RT 1.610–3 Shear – – 977 – 

17 RT 1.610–1 Shear – – 1002 – 

18 50 1.610–3 Shear – – 768 – 

19 50 1.610–1 Shear – – 823 – 

20 80 1.610–3 Shear – – 692 – 

21 80 1.610–1 Shear – – 718 – 

a

RT is room temperature. 
NASA/CR—2013-215450 33 

Rows 8 to 10 in Table 3.1 give compression data at room temperature at the three strain rates. 

Comparing these calculated shear modulus values from the compression tests with measured shear 

modulus values in rows 15 to 17 also show good agreement: The calculated shear modulus values of 974, 

1007, and 1057 MPa (141 230, 146 015, and 153 265 psi) differ by 21, 3, and 5 percent from values of 

801, 977, and 1002 MPa (116 145, 141 665, and 149 640 psi), respectively. 

When comparing the tensile and shear data at higher temperatures, the differences at 50 °C (122 °F) 

are 11 and 6 percent at 101

 and 103 s

1

 strain rates, respectively, and the differences at 80 °C (176 °F) are 

30 and 1 percent at 101

 and 103 s

1

 strain rates, respectively. The 30-percent difference in the high-rate 

data represents an anomaly in the data. The averaged tensile modulus values for the 10–1 s–1 strain rate at 

80 °C represents an average of 2.9 and 2.2 GPa (420 607.3 and 319 081 psi). By neglecting the 2.9-GPa 

(420 607.3-psi) test and only using the 2.2-GPa (319 081-psi) value for data comparison, the difference 

between the tensile calculated and the shear measured modulus is only 12 percent. 

3.6 Constituent Testing Summary 

The test method developed and the low-rate test data presented can provide an understanding of the 

mechanical behavior of this material and guidance for the development and characterization of 

constitutive models. Once formulated, these material models can be implemented in micromechanical 

computer models as user materials. Conversely, for quick approximations of material response, data can 

also be easily implemented in tabular form into computer model material models. 

Section 4.0 will discuss test methods that were developed for composite coupons as well as the results 

that provided information about the material response and the interactions between the carbon fibers and 

the resin matrix. 

4.0 Investigations of Triaxial Braided Composite Material Response 

Triaxial braided carbon-fiber preforms, as opposed to traditional laminated composite layups, have 

enabled composite structures with complex shapes to be designed and fabricated with a fiber architecture 

optimized locally for overall performance. One potential mechanism that may account for the difference 

in performance between braided composites and traditional composites is the load transfer between fiber 

bundles within the braid in triaxial braided composites. Hence, a more detailed investigation of the 

deformation and failure processes in triaxial braid composites is presented in this section. The composite 

test methods developed not only examine overall material response by presenting a series of stress-strain 

curves, but also provide information about the nature of progressive composite failure by developing a 

methodology using optical measurements to directly measure the local failure mechanisms. 

4.1 Material Background 

Four fiber/resin material systems were examined for this research. The four material systems all had 

the same fiber but were infused with a different resin. Toray’s T700 carbon fibers (Toray Industries, 

Inc.) were infused with four different resin systems—CYCOM PR 520 (Cytec Industries, Inc.), 5208 

(Cytec), Epon 862 (Momentive Specialty Chemicals, Inc.), and Hercules 3502 (Hexcel Corporation)—

that were used to fabricate the finished composite panels. The Toray fiber was a high-strength, standard 

modulus fiber used in applications where tensile strength was needed. The fibers are known to behave as 

linear elastic material exhibiting an abrupt or brittle failure when the maximum failure strain and stress 

are reached. Table 4.1 gives the properties of the T700 fiber as reported by Toray. 

The Cytec CYCOM PR520 resin is a one-part toughened thermoset resin with a cure temperature of 

179 °C specifically designed for resin transfer molding (RTM) processes. The Cytec 5208 resin is an 

untoughened thermoset resin with a cure temperature of 177 °C (350 F). The Epon 862 resin, which is 

discussed in the previous section, is a low-viscosity, high-flow thermoset resin ideal for RTM. The 

Hexcel 3502 resin is a general purpose thermoset resin with a cure temperature of 177 °C. The resins 

were chosen because they could withstand elevated temperature applications and were usable up to 
NASA/CR—2013-215450 34 

104 °C (220 F) temperature environments. Table 4.2 lists the mechanical properties of each resin as 

reported by the manufacturer (unless noted). 

The triaxial braid fiber geometry was formed at A&P Technology, Inc., in Cincinnati, Ohio. Triaxial 

braided performs in the shape of 38.79-cm- (15.27-in.-) diameter tubes were used to create the 0°, 60°

architecture for these panels. There were 24 000 individual axial carbon fibers in the axial (0°) fiber bundles 

(representing a designation of 24k wide), and there were 12 000 individual carbon fibers in the bias (60°)

fiber bundles (12k wide). The finished composite panels were quasi-isotropic in their overall material 

response properties. An RTM process was used to produce flat composite panels 61 cm (2 ft) long by 61 cm 

(2 ft) wide by 0.318 cm (0.125 in.) thick. Three layers of the flattened braided tube were placed in the RTM 

mold with 0° (axial) fibers aligned, and resin was injected and cured at North Coast Composites in 

Cleveland, Ohio, under conditions specified by each resin manufacturer. The cured composite panels had 

six layers of braid (two layers per flattened tube) and had a total thickness of 0.318 cm. 

Figure 4.1 shows an example of the standard 0°, ±60° fiber braid architecture not infused with resin—

a triaxial braid with the axial fibers aligned vertically (only partially visible, noted by the arrows). A 

single unit cell is highlighted; the entire composite material can be recreated by aligning repeating 

patterns of this single unit cell. The unit cell in the triaxial braid geometry contains two axial fiber tows 

underneath a –60 and +60 layer with areas between the axial tows where the bias fibers cross. 

TABLE 4.1.—COMPOSITE FIBER PROPERTIES 

 Tensile strength, 

MPa 

Young’s modulus, 

GPa 

Failure strain, 

percent 

Density, 

g/cm3

Toray T700 fiber 4900 230 2.1 1.80 

TABLE 4.2.—COMPOSITE RESIN PROPERTIES 

Resin Tensile strength, 

MPa 

Young’s modulus, 

GPa 

Density, 

g/cm3

Cytec CYCOM PR520 82 4.0 1.256

Cytec 5208 50 3.8 1.263a 

Hexcel 3502 33 3.6 1.266 

Epon 862b 61 2.7 1.200a 

a

Measured value. 

b

Momentive Specialty Chemicals, Inc. Values reported at 2.5 h cure time. 
NASA/CR—2013-215450 35 

TABLE 4.3.—FIBER VOLUME FRACTIONS 

IN COMPOSITE MATERIAL SYSTEMS 

Material systema 

(fiber/resin) 

Fiber volume fraction, 

percent 

T700/E862 55.6±2.42 

T700/PR520 55.9±0.18 

T700/3502 59.9±4.64 

T700/5208 53.0±3.30 

a T700, Toray Industries, Inc. 

 Epon 862, Momentive Specialty Chemicals, Inc. 

 CYCOM PR 520, Cytec Industries, Inc. 

 3502, Hexcel Corporation. 

 5208, Cytec Industries, Inc. 

The nominal fiber volume fraction for the fabricated panels was 56 percent. An acid digestion 

technique procedure was used in accordance to ASTM D3171 (Ref. 61) on representative composite 

samples from each of the material systems, and the results are shown as an average with ±1 standard 

deviation in Table 4.3. 

4.2 Specimen Geometries 

Test specimens were cut from the panels using an abrasive waterjet technique, which was used to 

minimize machining times. Straight-sided tensile test specimens were cut in accordance with ASTM 

D3039 (Ref. 17). Rectangular 30-cm- (12-in.-) long by 3.579-cm- (1.409-in.-) wide dimensions were 

chosen for tensile test specimens. These dimensions were chosen such that the width contained at least 

two unit cells and the length conformed to ASTM length to width ratios. Compression test specimens 

were also prepared in accordance to ASTM D3410 (Ref. 18), with specimen dimensions of 15 cm (6 in.) 

in length by 3.579 cm in width. The compression specimens allowed for a long gripped region with short 

(3-cm, or 1-in.) gage section as specified by ASTM. 

Both ASTM 3039 tensile and ASTM 3410 compression specimens were cut in two ways for testing. 

For tests designated “Axial,” the specimens were cut such that the axial (0) fibers were parallel to the 

axis of loading. For tests designated “Transverse,” the specimens were cut such that the axial (0) fibers 

were oriented perpendicular to the direction of loading. Figure 4.2 illustrates the geometries of the axial 

and transverse tension specimens along with the fiber orientations for each test. 

Shear specimens were prepared using a modified version of the ASTM D5379 standard (Ref. 20). The 

modified design extended the gripped region of the specimens such that bending resistance was improved 

while the specimen was under load. The ASTM standard specimen design was also modified by 

extending the gage section of the specimen to include one entire unit cell. Figure 4.3 shows a schematic 

and dimensions of the shear specimen geometry. 

 
NASA/CR—2013-215450 36 
NASA/CR—2013-215450 37 

4.3 Test Equipment 

All specimens were tested in an MTS axial-torsional 858 test machine capable of loading to 

22 680 kg (50 000 lb). All tests were conducted under displacement (stroke) control at rates of 

0.635 mm/min (0.025 in./min). All strain measurements were taken using an optical measurement system. 

A V-Notched Rail Shear test fixture was used to facilitate the testing of the shear specimens. This fixture 

was manufactured by Wyoming Test Fixtures (SN WTF–NR–4). The optical measurement technique 

used for gathering the material property data was the same as the one described in Section 3.0. As with 

the previous testing, the synchronized load and strain curves were recorded by the optical measurement 

system. Stress-strain curves were calculated from the synchronized load and strain measurements. 

4.4 Experimental Results 

The next sections present the experimental results obtained from the material testing. Section 4.4.1 

explains the procedure for collecting the material property data needed for the generation of the global 

material response curves and the results obtained, and Sections 4.4.2 to 4.4.5 will explain the local failure 

mechanisms that influenced the global material response. 

4.4.1 Examination of Global Stress-Strain Data 

Figure 4.4 shows an example of the full-field axial strain distribution acquired using the optical 

measurement system during an example axial tension test. The field of view captured the entire 3.579-cm 

specimen width and approximately 5 cm (2 in.) of the specimen height. 
NASA/CR—2013-215450 38 

By using the optical measurement system to obtain material response data, any individual point 

within the field of view could be picked and individual results (strains and/or displacements) could be 

examined. The global strains used in the specimen material response curves were found by creating a 

“digital strain gage” using individual data points from the full-field results on the specimen. The digital 

strain gage was created from four points on the surface of the specimen. The global axial strain was 

obtained by measuring the relative displacement between the black and yellow points (approximately 

1.9 cm (0.75 in.) apart) in Figure 4.4 and dividing it by the original distance, which was measured at the 

beginning of the test. Similarly, transverse strain was obtained by measuring the relative displacement 

between the red and blue points (also approximately 1.9 cm apart) and dividing it by their original 

distance, also measured before the test. A distance of 1.9 cm between the points was chosen to average 

strain concentrations present in a particular area of the specimen, which was in agreement with guidelines 

proposed by Masters (Ref. 28). Global strains in the axial and transverse directions were also used to 

calculate a global Poisson’s ratio. 

Also note that in Figure 4.4 there are areas of yellow and red surrounded by areas of green. These 

areas of yellow and red represent regions of localized high strain concentrations. Factors contributing to 

these strain concentrations will be examined in Sections 4.4.2 to 4.4.5. 

4.4.1.1 Tensile Testing Results 

Representative global stress-strain curves for the four material systems were plotted using the method 

described above for both axial and transverse specimen tests. Representative global stress-strain curves 

are presented in Figures 4.5 to 4.8. 

Material modulus values were extracted from each of the specimen’s stress-strain curves by taking 

the slopes of the curves between 0 percent and the closest data point acquired at 0.2 percent strain. Also, 

failure strains and strengths were extracted from the global stress-strain curves. Table 4.4 shows the 

moduli, strengths, and failure strains for the material systems. A minimum of five tests were conducted to 

obtain the tensile results. In the cases of limited material availability, only four tests were conducted. For 

the T700/PR520 fiber/resin material system’s transverse tests, only two tests were conducted. The results 

reported in Table 4.4 are a specimen average ±1 standard deviation. 
NASA/CR—2013-215450 39 
NASA/CR—2013-215450 40 

TABLE 4.4.—TENSILE RESULTS FOR FOUR COMPOSITE MATERIAL SYSTEMS 

Material systema 

(fiber/resin) 

Tensile propertyb

Axial Transverse 

Strength, 

MPa 

Modulus, 

GPa 

Failure strain, 

percent 

Strength, 

MPa 

Modulus, 

GPa 

Failure strain, 

percent 

T700/E862 800±6 46.9±1.6 1.78±0.08 462±36 41.6±1.3 1.44±0.09 

T700/PR520 1046±34 47.6±1.0 2.16±0.09 599±3.3 42.0±2.3 1.69±0.19 

T700/3502 608±56 47.2±2.0 1.51±0.14 336±11 40.6±4.1 1.00±0.15 

T700/5208 693±46 47.5±1.0 1.51±0.10 310±15 41.3±4.5 0.85±0.05 

 aT700, Toray Industries, Inc. 

 Epon 862, Momentive Specialty Chemicals, Inc. 

 CYCOM PR 520, Cytec Industries, Inc. 

 3502, Hexcel Corporation. 

 5208, Cytec Industries, Inc. 

b

Values are shown as an average with ±1 standard deviation. 

Table 4.4 shows that the T700/PR520 material system had the highest strength in both the axial and 

transverse directions, with the next highest being the T700/E862 system. The two lowest material systems 

were the T700/5208 and the T700/3502 systems. The T700/PR520 material system had an axial strength 

30 percent higher than the T700/E862 system and 60 and 70 percent greater than the T700/5208 and 

T700/3502 systems, respectively. Likewise, the T700/PR520 material system had a transverse strength 

30 percent greater than the T700/E862 system while having a transverse strength 80 and 90 percent 

greater than the T700/3502 and T700/5208 systems. The axial failure strain in the T700/PR520 material 

system was approximately 2.1 percent. This failure strain value corresponds to the ultimate failure strain 

in the carbon fibers reported by Toray, which are shown in Table 4.1, and indicate that in the T700/PR520 

material system, the fibers dominated the composite axial failure strain, with little or no influence from 

the resin. However for the other three materials, the axial failure strain of the composite was less than the 

failure strain of the T700 fiber. The T700/E862 material system showed failure strains 25 percent less 
NASA/CR—2013-215450 41 

than the ultimate fiber failure strain, while the T700/5208 and T700/3502 systems were 35 percent less 

than the ultimate fiber strain. 

Also, the T700/PR520 material system’s axial material response curve was perfectly linear until failure. 

The T700/E862 and T700s/5208 material systems’ axial stress-strain curves started to show a nonlinear 

response starting at approximately 1.25 percent strain. For the lowest strength material, T700/3502, the 

material response curve starting showing nonlinear behavior at approximately 1.0 percent strain. 

The explanation for the above observed and described material response in the axial direction was 

that in the three weaker material systems (T700/E862, T700/5208, and T700/3502) damage accumulation 

was occurring, which accounted for the nonlinear behavior in the axial material response curves. This was 

contrasted by the T700/PR520 material system, which showed classical fiber-dominated axial composite 

behavior until fiber failure. In the T700/PR520 material system, the composites’ stiffness was linear 

elastic, and the composite exhibited brittle failure. The results from the tensile tests showed that the 

T700/PR520 material system had higher damage resistance, which implied that T700/PR520 had a 

stronger fiber-resin interface. With the other three material systems, however, the damage that occurred 

accumulated in the composite and played a role in the material response. In general, axial composite 

material response is a result of damage-causing factors such as matrix cracking, fiber breaking, and/or 

layer delaminations. Some or all of these classical damage mechanisms occurred in the three lower 

strength material systems, and it was these mechanisms that accounted for the nonlinearities encountered 

in the axial material response. Some of these damage-causing mechanisms will be examined in the 

following sections. 

For composite material response in the transverse direction, the matrix material played a more 

important role in the material response. Unlike the axial direction, where there were continuous axial 

fibers that extended from the top grip to the bottom grip and throughout the entire length of the gage 

section and along the loading direction, the transverse composite coupon specimen geometries oriented 

the axial fibers transversely to the direction of loading. Because there were no continuous axial or bias 

fibers extending throughout the entire gage section, the primary load-carrying mechanisms in the 

composite were the matrix and fiber-matrix interface. The differences in transverse strengths as shown in 

Table 4.4 were attributed to differences in the matrix material and the fiber-matrix interface. For example, 

the PR520 resin had an ultimate tensile strength 64 percent greater than the 5208 resin, and accordingly, 

the data show that the T700/PR520 material system had a transverse tensile strength approximately 

48 percent higher than the T700/5208 system. The other materials exhibited the same trends. The PR520 

resin had a 34 percent greater strength than the E862 resin and 148 percent greater than the 3502 resin. 

The transverse tensile strength data show that the T700/PR520 material system had a strength 29 percent 

greater than the T700/E862 system and 93 percent greater than the T700/3502 system. 

The global transverse stress-strain curves for T700/5208 showed that the slope of the curve became 

nonlinear early in the test at approximately 0.2 percent strain. This was opposed to the T700/PR520 

material system, in which the transverse curve started to behave nonlinearly at about 0.6 percent strain. 

Again, the difference in the point in which these curves became nonlinear was attributed to damage 

occurring much earlier in the weakest T700/5208 material system than in the strongest T700/PR520 

system. The other two material systems fell within this envelope. 

The differences in the material moduli between the material systems in both the axial and transverse 

directions were negligible and fell within the experimental scatter. This was expected since all material 

systems used the same fiber, and the modulus values for the different resins were similar. Finally, a 

Poisson’s ratio was found by taking the ratio of transverse to axial strain in both the axial and transverse 

test specimens’ stress-strain curves to 0.2 percent. These data are presented in Table 4.5. For the data 

labeled Axial Poisson’s ratio, the data was taken from the axial tests, and for data labeled Transverse 

Poisson’s ratio, the data was taken from the transverse tests. An average ±1 standard deviation from each 

of the material systems is reported. 

The Poisson’s ratios of the material systems were also approximately the same in the axial direction 

and fell within the experimental scatter. In the transverse direction, with the exception of T700/5208, the 

Poisson’s ratios also fell within experimental scatter of each other. Also, the Poisson’s ratios in the 
NASA/CR—2013-215450 42 

transverse directions matched those in the axial direction. These results validated that the material elastic 

properties are consistent with those of a quasi-isotropic material. 

4.4.1.2 Compression Testing Results 

Because of material availability, only two tests were run in each direction for the compression 

specimens of each material system. Figures 4.9 to 4.12 show the global stress-strain material responses 

for both the axial and transverse directions. 

TABLE 4.5.—AXIAL AND TRANSVERSE 

POISSON’S RATIOS FOR FOUR 

MATERIAL SYSTEMS 

Material systema 

(fiber/resin) 

Poisson’s ratiob

Axial, 

12

Transverse, 

21

T700/E862 0.30±0.03 0.29±0.02 

T700/PR520 0.31±0.02 0.30±0.003 

T700/3502 0.32±0.04 0.30±0.04 

T700/5208 0.29±0.03 0.27±0.006 

a

T700, Toray Industries, Inc. 

 Epon 862, Momentive Specialty Chemicals, Inc. 

 CYCOM PR 520, Cytec Industries, Inc. 

 3502, Hexcel Corporation. 

 5208, Cytec Industries, Inc. 

b

Values are shown as an average with ±1 standard 

deviation.

 
NASA/CR—2013-215450 43 

 
NASA/CR—2013-215450 44 

TABLE 4.6.—COMPRESSIVE RESULTS FOR FOUR COMPOSITE MATERIAL SYSTEMS 

Material systema 

(fiber/resin) 

Compressive propertyb 

Axial Transverse 

Strength, 

MPa 

Modulus, 

GPa 

Failure strain, 

percent 

Strength, 

MPa 

Modulus, 

GPa 

Failure strain, 

percent 

T700/E862 327 41.4 1.01 303.5 42.7 0.87 

T700/PR520 378 41.9 1.80 346 39.0 1.10 

T700/3502 321 41.8 0.86 243 41.1 0.61 

T700/5208 249 44.6 0.56 191 38.6 0.49 

a

T700, Toray Industries, Inc. 

 Epon 862, Momentive Specialty Chemicals, Inc. 

 CYCOM PR 520, Cytec Industries, Inc. 

 3502, Hexcel Corporation. 

 5208, Cytec Industries, Inc. 

b

Values are shown as an average with ±1 standard deviation.

Material modulus values were determined from the global stress-strain curves between 0 percent and 

the data point collected closest to 0.2 percent strain. Also, failure strength and strain values were obtained 

from the global stress-strain curves. The modulus, strength, and failure strain values were taken from the 

test’s average. 

The compression material response showed that the axial moduli are approximately the same for the 

four material systems. Also, the material response data showed that the transverse moduli are 

approximately the same between the four material systems. The material moduli are similar between the 

four systems because in compression, the main material carrying the load is the matrix material. The 

results in Table 4.6 reflect the similarities in the resin moduli. The axial strength data showed that the 

T700/PR520 material system is the strongest material with the T700/E862 system being the second 

strongest. The T700/PR520 system was approximately 18 percent stronger than T700/3502 and 

52 percent stronger than T700/5208. Examining the transverse strength data, the T700/PR520 system was 

14 percent stronger than T700/E862, 40 percent stronger than T700/3502, and 80 percent stronger than 

the T700/5208 material system. The trends in these results agreed with the tensile results, and showed that 

T700/PR520 is the strongest material, followed by T700/E862, T700/3502, and finally T700/5208. 
NASA/CR—2013-215450 45 

Examining the global stress-strain curves, the stronger T700/E862 and T700/PR520 material systems 

exhibited significant nonlinear behavior before failure in the axial direction. The inelastic regions occur 

because the interface strength between the fiber and resin is sufficiently high enough to allow for the resin 

to reach an inelastic region before the specimen failure occurs. The two weaker material systems did not 

display any significant nonlinear behavior, but rather failed before this regime was reached. This 

indicated that the interface between the fiber and resin is weak enough and allows for fiber microbuckling 

to occur before this inelastic regime in the resin is reached, which typically causes composite failure as 

shown in Reference 62. 

Figure 4.13 shows the microbuckling phenomena on the macroscale for the weakest material system 

tested, T700/3502, as captured by the optical measurement system. 

This local buckling occurred because the weak fiber-matrix interface allowed for fiber movement 

within the composite, which caused microbuckling in the fibers before the inelastic region of the resin 

was reached. This behavior was common to the two weaker material systems; however, it was absent 

from the stronger systems. The same phenomena occurred in the transverse testing, although the 

specimens buckled at an earlier global stress. 

4.4.1.3 Shear Testing Results 

A minimum of four tests were conducted for each material system for the shear specimens. Two tests 

were conducted with the axial fibers running parallel to the direction of loading, and two were conducted 

with the axial fibers running perpendicular to the direction of loading. Figure 4.14 shows example shear 

stress-shear strain material response curves for the material systems. 

All three material systems’ material response curves show nonlinear behavior starting at 

approximately 0.2 percent strain. This was due to the fact that in shear testing, as in compression testing, 

the main loading-carrying mechanisms are the resin and the fiber-resin interface. The strength and 

modulus values for each material system were determined from the curves and are presented in Table 4.7. 

The two orientations yielded similar results, and the results reported are for a four-specimen average 

±1 standard deviation. 
NASA/CR—2013-215450 46 

TABLE 4.7.—SHEAR RESULTS FOR FOUR 

COMPOSITE MATERIAL SYSTEMS 

Material systema 

(fiber/resin) 

Shear propertyb 

Strength, 

MPa 

Modulus, 

GPa 

T700/E862 257±10 32±1.1

T700/PR520 307±6.8 34.9±0.6 

T700/3502 224±30 33.7±1.2 

T700/5208 200±20 33.5±0.7 

a T700, Toray Industries, Inc. 

 Epon 862, Momentive Specialty Chemicals, Inc. 

 CYCOM PR 520, Cytec Industries, Inc. 

 3502, Hexcel Corporation. 

 5208, Cytec Industries, Inc. 

b

Values are shown as an average with ±1 standard deviation.

Table 4.7 shows the strength and modulus results for the three material systems. Trends in this table 

followed the tension and compression results. The T700/PR520 material system had the highest strength. 

It was higher than the T700/E862 system by 19 percent and higher than the T700/5208 system by 

53 percent. Also, like with the other testing, the differences in the materials’ moduli were negligible, 

which was expected since the resin moduli were similar. Since a nonstandard specimen geometry was 

used in shear testing, the failure of the specimen was also examined. 

Figure 4.15 shows a picture of a shear specimen failure. The shear specimen is still gripped in the test 

machine, with the failure occurring in the gage section between the notches (circled). The nonstandard 

specimen geometry with the extended ends and longer notched gage section forced the failure of the 

material between the notches. The figure confirms that the shear specimen used in testing gave the desired 

failure surface and was sufficient to use for material property collection. 
NASA/CR—2013-215450 47 

4.4.2 Examination of Local Deformations and Failure 

The full-field strain data in Figure 4.4 is presented to demonstrate the use of the point averaging 

method to obtain overall composite material response. However, it also shows an example of the 

occurrence of local strain concentrations typically present in the composite specimens, noted by the areas 

of yellow and red that appeared on the surface of the specimen. An examination of the full-field material 

strain in all test results revealed that such concentrations were present in all of the material systems, and 

the material response curves suggested that classical damage mechanisms occurring in the composite 

affected the material response. This section presents a closer look into the full-field strain data, 

providing further insight into the differences in the global material properties reported in the tables in 

Sections 4.4.1.1, 4.4.1.2, and 4.4.1.3. 

However, because of specimen availability, not all techniques were used on all of the material 

systems, but rather the techniques were developed on example composite specimens to provide insight 

into material responses. Comparisons were done on a subset of the material systems, typically between 

strong (representing a high failure stress) and weak (representing a low failure stress) materials. 

4.4.2.1 Development of Strain Overlay Techniques 

Because the localized strain occurring in the specimen leads to global damage in the composite, the 

areas of strain concentrations were of interest to determine the types of damage present. Since the 

composite specimens were painted with the contrasting speckle pattern as described earlier to yield the 

full-field results, direct correlations between the full-field results and composite braid geometry locations 

could not be made because the braid geometry was covered by the painted speckle pattern. Full-field 

overlay techniques were developed to mitigate this problem by mapping the postprocessed full-field strain 

results onto the unpainted composite specimen. The step-by-step process by which to overlay the strain 

onto an axial specimen is shown in Figure 4.16 on an axial tensile specimen from the T700/PR520 

material system. Figure 4.16 shows the data obtained in a representative axial composite coupon at the 

last data point collected before specimen failure. Part (a) shows the unpainted picture of the composite 

coupon taken before testing was begun. Part (b) shows the postprocessed global axial strain data obtained 

from the full-field measurement software after testing was completed. Part (c) shows the postprocessed 

strain data only. The overlay technique maps the full-field strain data onto the unpainted specimen via a 
NASA/CR—2013-215450 48 

two-step process. The first step mapped the picture in part (b) onto the one in part (a) by matching the 

visible fiber locations and datum marks placed on the specimen. The second step mapped the picture in 

part (c) onto the one in part (b) by matching the common strain result locations. The picture in part (b) 

was then removed, leaving the final overlay with pictures from parts (a) and (c) only. Finally, the opacity 

on part (c) decreased such that the fiber bundles in part (a) were visible. Note that by using common 

datum marks, the deformed pictures could be stretched to match the unloaded specimen picture. 

Figure 4.17 shows the final overlay picture after the process was completed. This final image was then 

used to determine locations of the strain concentrations on the surface of the specimen because both the 

full-field strains and fiber bundle locations were visible. 

The overlay in Figure 4.17 shows that the majority of the axial strain was approximately 2.19 percent 

(represented by the majority of the picture showing the strain in green), which is in agreement with the 

T700/PR520 axial failure strain data in Table 4.4. However, as Figure 4.17 shows, areas of high strain 

were present, as indicated by the yellow and red areas. The overlay technique shows the areas of lines of 

high strain present were in the middle of and running parallel to the surface bias fiber layers, which 

consisted of a mixture of the bias fiber bundles and surrounding resin matrix material. These areas of high 

strain could have been indicative of a transverse fiber bundle failure that was exposed by having the 

surface bias fibers “split” apart. These areas were located directly over the subsurface axial fibers, which 

are indicated by the black arrows in Figure 4.17. 

These results were confirmed by examining a bias fiber bundle under a scanning electron microscope 

(SEM). Figure 4.18 shows a +60 bias fiber bundle of the T700/5208 material system removed from a 

tested axial specimen. Loose fibers in the failed region of the specimen were removed and scanned, with 

care being taken to ensure that artificial defects were not introduced into the specimen by the removal 

process. 
NASA/CR—2013-215450 49 

Figure 4.18 shows that in axial testing, the bias fiber bundles exhibited the splitting phenomena 

mentioned in the previous paragraph, as indicated by the arrows. These results confirm the observations 

obtained from the optical measurement system. The bias bundle splits are parallel to the direction of the 

fiber orientation. The strain data obtained from the optical measurement system at the locations of splits 

could be used for investigations of the fiber-matrix interface and local transverse failure strength 

(described in Sec. 5.0, “Development of Macromechanical Triaxial Braided Composite Computer 

Model”). Also note that the particular fiber bundle shown in Figure 4.18 was taken from the middle layer 

of the braid. This also confirms that even though the optical measurement system was only able to 

measure surface strains, the measured surface strain data was representative of all layers throughout the 

composite architecture. 

The areas of high strain that occurred in the middle of the bias fiber bundle region developed from the 

load transfer between the subsurface axial and surface bias fiber bundle region consisting of fiber bundles 

and surrounding resin. As the subsurface axial fiber bundles underwent axial extension during testing, 

they also affected the surface bias fiber bundle region. The transfer of load between the subsurface axial 
NASA/CR—2013-215450 50 

and surface bias fiber bundles occurred through the areas of resin material between the two fiber bundles, 

the fiber bundle-resin interface, and the interface between the resin and individual fibers that make up the 

fiber bundle. These areas of high strain are indicative of matrix cracking, which caused the surface bias 

fiber bundles to “split” and occurred when the strain was equal to the local ultimate transverse tensile 

strain of the area consisting of the bias fiber bundles and surrounding resin. 

Another way to measure ultimate transverse strain of these regions around the fiber bundles is to 

examine the regions of high strain that occurred in a transverse tensile test, in which the axial fiber 

bundles were oriented perpendicular to the direction of the applied load. The high strains that develop in 

the region surrounding the axial fiber bundles represent a strain equal to the ultimate fiber bundle 

transverse tensile strain. Figure 4.19 shows an overlay of a transverse tension test. 

Figure 4.19 shows the areas of high strain that developed on the subsurface axial fiber bundles 

(circled), which were visible between the surface bias fibers. The strain on the surface was assumed to be 

the same as the strain on the regions of the visible subsurface axial fiber bundles and surrounding resin. 

This assumption was verified by digital microscopic imaging. 

Figure 4.20 shows a digital microscopic image of the side (edge) view of a transverse tensile 

specimen. The areas of dark grey represent the axial fibers, and the areas of white represent the bias 

fibers. The circled areas in Figure 4.20 show the fiber bundle splits that occurred in the axial fibers. The 

fiber bundle splits were present in not only the fibers captured by the optical measurement system, but 

also in the subsurface fibers. The digital microscopic picture confirmed the data seen by the optical 

measurement system that in transverse tensile tests the axial fiber splits were a major damage-causing 

mechanism. 

Figure 4.21 shows an in-plane shear strain overlay on the gage section of a shear specimen. A 

uniform shear strain field was present in the middle of the gage section, which indicated that the local 

fiber bundle transverse “splits” or failures did not appear under shear loading. Instead, because of the 

loading direction, the specimen behaved homogeneously. 
NASA/CR—2013-215450 51 
NASA/CR—2013-215450 52 

The notched region in Figure 4.21 represents the gage section for the shear tests. A uniform area of 

approximately 0.012 shear strain developed in the gage section, which is represented in the yellow color 

in Figure 4.21, and a very small red area of slightly higher (approximately 0.016) shear strain developed 

between the gage sections notches. There are a few areas of strain concentrations represented by the 

diagonal red lines; however, these lines are not part of a regular repeating pattern and represent a local 

defect in the specimen. The main areas of high strain occur at the ends of the gage section represented by 

the red parallel diagonal lines show that there is slight cracking due to the notched edges. The area outside 

of the gage section (represented in green and blue) represent the gripped portion of the specimen. These 

outer areas saw little strain and confirmed that, in shear testing, the majority of the specimen deformation 

occurred in the middle of the notched gage section. 

4.4.2.2 Examination of Transverse Fiber Bundle Failures 

Section 4.4.2.1 shows the strain overlay techniques developed, which determined that there were 

areas of local fiber bundle failure. This section expands on the observations of transverse fiber bundle 

failures and how they related to the global material response. Specifically, the concept that the transverse 

fiber bundle failures initiated the damage propagation and progression in the composite coupon are 

elaborated in this section. 

To reiterate the concept of the transverse fiber bundle splitting representing a transverse fiber bundle 

failure, Figure 4.22 shows the fiber bundle splits for the highest strength T700/PR520 material system 

that have developed in the transverse tensile specimen. The circled area in Figure 4.22 shows areas of 

high axial strain (in red) on the axial fibers orientated transversely to the loading in the picture, which are 

areas of high strain that represent matrix cracking. The matrix cracking caused the subsurface axial fiber 

bundles to split apart. With this knowledge, a random sampling of points on an example transverse tensile 

specimen was chosen for further examination. 

Figure 4.23 demonstrates this principle by showing local strain results for four randomly picked 

points on the fiber bundle splits. Figure 4.23(a), shows the locations and labels of four example 

subsurface axial fiber bundle failures. Figure 4.23(b) shows the local strain at each of the individual 

chosen points plotted versus global composite stress for the specimen. A sudden increase in local strain at 

each chosen point without a significant increase in global specimen stress represents a fiber bundle failure 

(noted by the arrows on Fig. 4.23(b)). The value of the strain after the fiber bundle failure was examined 

carefully: the optical measurement system produced some erroneous results due to extreme distortions in 
NASA/CR—2013-215450 53 

the speckle pattern from the split at the chosen locations. Values of local strain or stress obtained after the 

split occurred were not used as material property information because of these extreme distortions in the 

speckle pattern. However, the value of the stress and strain immediately before the fiber failure was found 

and used as material parameters representing the effective transverse failure strain value of a fiber bundle 

and surrounding resin in a triaxial braided composite material. The mean value of strain at transverse 

failure was approximately 1.4 percent, with values ranging from 1.0 to 1.8 percent for the T700/PR520 

material system. 

The value of the global stress in which the first fiber bundle failed in Figure 4.23(b) was 

approximately 350 MPa. Comparing this value of stress to the global transverse tensile curve in Figure 

4.6, one can note that 350 MPa was the approximate stress value in which the transverse tensile curve 

became nonlinear, suggesting that the transverse fiber bundle failures were causing the damage in the 

transverse tensile material response curves. Similarly, the same technique for examining the fiber bundle 

split locations was used on the low-strength T700/5208 material system and is shown in Figure 4.24. 

The mean strain value for transverse fiber bundle failure in the T700/5208 system was approximately 

0.5 percent, with values ranging from 0.4 to 0.7 percent strain (noted by the black arrows in Figure 4.24(b). 

The data show that transverse fiber bundle failure occurred at a lower strain in the T700/5208 system, 

leading to a lower ultimate failure strain than for the T700/PR520 system. These data also suggest that either 

the fiber-resin interface for the T700/5208 system was weaker than that of the T700/PR520 system or the 

ultimate strength of the resin was playing a major role in the material response. 

The global composite stress at which the transverse fiber bundle failures started to occur was 

150 MPa, which was a lower global stress value than for the T700/PR520 material system. Again, when 

comparing this global stress value to the transverse global material response curve in Figure 4.8, the data 

show that the global material behavior became nonlinear at approximately 150 MPa. These observations 

verify the data presented for T700/PR520, in that the transverse fiber failures were causing damage in the 

composite material systems. 

Note that the values reported in Figures 4.23 and 4.24 are different than the composite transverse failure 

strain values reported in Table 4.4. The overall composite specimen failure is reported in Table 4.4, whereas 

the initiation of transverse fiber bundle failure, represented by the onset of fiber bundle splitting, is being 

reported in this section. By using the optical measurement system, the transverse failure of both the 

individual fiber bundles and the composite coupon were found. This led to an important conclusion about 

the composite material response in the transverse tests: In transverse tensile testing, the fiber bundles began 
NASA/CR—2013-215450 54 

to split at the transverse fiber bundle failure strain, but the overall composite failed at the ultimate failure 

strain. Between the initiation of fiber bundle splitting and overall composite failure, the fiber bundle splits 

propagated throughout the composite, representing damage accumulation. Once the damage accumulation 

reached a critical value, the composite specimen then failed. 

Also, Figures 4.22, 4.23(a), and 4.24(a), show that areas of low strain represented by dark blue 

sections developed along the free edges of the specimens. In the transverse specimens, this characteristic 

in the material response was common and occurred because the bias fibers terminated at the free edge of 

the transverse specimen. These areas of low strain were present because the bias fiber bundles at the 

edges of the specimens did not carry load from the test. 

The full-field strain pictures and the transverse tensile data led to another important conclusion: For 

triaxial braided composite materials, standard coupon geometries may be inadequate for the determination 

of strength and elastic properties. For the quasi-isotropic assumption for the material properties of the 

composite to be valid, the strengths in both the axial and transverse direction should be equal. The data 

collected from this and the previous sections invalidated this assumption. The data show that strengths are 

56 percent weaker for the T700s/PR520 fiber/resin system and 47 percent weaker for the T700s/5208 

system in their transverse directions compared with their axial directions. 

Alternative specimen designs have been proposed to eliminate the above deficiencies. One alternative 

specimen design that has been proposed is a “bowtie” or notched specimen geometry (Ref. 63), in which 

all of the axial and bias fibers located in the gage section could be gripped during the test. The other is a 

tubular specimen geometry, in which axial and bias fiber bundles extend along the entire specimen length 

and perimeter. Filament-wound tubular specimen geometries have been explored for obtaining shear 

properties by Foley, Roylance, and Houghton in Reference 64, but tubes containing the triaxial braid 

architecture have not been explored in detail. 

The matrix cracking causing the fiber bundle splitting on the axial tensile specimens was examined 

next. Because of the differences in strength values between the strong T700/PR520 and weak T700/5208 

material systems and the differences in the stress in which the fiber bundle splits begin to occur, the 

propagation of the fiber bundle splitting phenomenon was examined further through a series of time 

history snapshots. The three pictures for each system represented the specimen at a certain time during the 

history of loading. These three different points presented in Figure 4.25 represent (1) the onset of fiber 

bundle splitting, (2) the fiber bundle splitting that was occurring at a common stress value between the 

two material systems, and (3) the extent of fiber bundle splitting that occurred at the last data point 

collected before failure. 
NASA/CR—2013-215450 55 

For the T700/5208 material system, the onset of fiber bundle splitting occurred earlier during the test, 

which corresponded to a lower global stress value than for the T700/PR520 material system, and is 

represented by the top set of pictures in Figure 4.25. Also, the amount and extent of fiber bundle splits, as 

shown in the bottom set of pictures, was much greater in the weaker T700/5208 system. These two factors 

were also indications that the ultimate fiber-resin interface strength was lower in the T700/5208 material 

system than in the T700/PR520 system. The fiber-matrix interface was the main component holding the 

fibers to the matrix, indicating that the interface in the T700/5208 material system was weaker than that of 

the T700/PR520 system. The fiber bundles split apart earlier in the test and grew more abundant, giving 

rise to stress concentrations in the fiber bundles and ultimately weakening the composite. The results 

reported in Table 4.4 agree with these conclusions. 
NASA/CR—2013-215450 56 

4.4.2.3 Examination of Subsurface Delaminations 

In this section, the optical measurement system was used to examine and determine the extent of a 

different type of damage mechanism: subsurface fiber layer delaminations. To examine this type of 

damage mechanism, out-of-plane displacements were captured by the optical measurement system and 

examined in situ during testing. Note that to examine the areas of possible delaminations, the field of 

view from the optical measurement system was enlarged by reconfiguring the cameras and lenses to 

measure approximately 20 cm (8 in.) of the specimen height by the entire 3.579 cm (1.409 in.) of the 

specimen width. Any areas exhibiting large relative out-of-plane displacements coincided with areas of 

possible delamination. To verify delamination, results were compared with an ultrasonic through 

transmission (UTT) nondestructive evaluation (NDE) technique. Although UTT testing was not the scope 

of this work, a brief explanation of how UTT works will be presented to familiarize the reader with this 

NDE technique. A full explanation can be found in Reference 65. 

For UTT an acoustic emitter was placed on one side of the specimen and a receiver was placed on the 

other side. The emitter then emitted a sound pulse, which was caught by the receiver. The transmitterreceiver system scanned the entire specimen, and the results of the scans were processed by a computer, 

showing the results as a full-field specimen visualization. The system was similar to the optical strain 

measurement system; the user can look at full-field postprocessed data. However, this technique differs 

such that the UTT must scan the specimen small areas at a time and cannot be done while the specimen is 

under loading. The UTT postprocessed data are also different because absolute measurements in the 

material response could not be made. Instead, relative degrees of the received signals are represented on a 

grayscale. A white color in the postprocessed visualizations indicates that the receiver captured the entire 

pulse emitted by the transmitter, meaning there were no subsurface defects in the material that scattered 

the transmitted wave. As more of the transmitted wave is scattered by passing through changes in local 

fiber architecture or local subsurface damage such as fiber delamination, the darker the postprocessed 

UTT images become. A black area in the UTT postprocessed data indicates that very little of the emitted 

sound wave was actually collected by the receiver. 

The two material systems that were used to examine possible subsurface layer delaminations were a 

stronger material system, T700/E862, and a weaker material system, T700/3502. Four specimens from 

each material system were tested in both their axial and transverse directions. Each of the four specimens 

was tested to a different value of loading: 25, 50, 75, and 90 percent of its ultimate strength as determined 

from Section 4.4.1.1. Testing was conducted by loading the specimen at 0.635 mm/min (0.025 in./min) 

while taking pictures at specified intervals between 2 and 6 s, depending on the value of ultimate loading. 

Once the end value of load was reached, the loading was held constant, and a final loaded picture was 

taken by the optical measurement system. Finally, the specimen was unloaded, and a final unloaded 

picture was taken to compare with the pretest specimen data. 

4.4.2.3.1 Subsurface Delaminations in the Axial Direction 

The T700/E862 material system’s axial tensile specimens were examined first. The UTT and out-ofplane optical measurements were taken before the test to establish baseline conditions, with which 

posttest results could be compared. Baseline conditions using the optical measurement system were 

established by gripping and taking a picture of an unloaded specimen, then computing the out-of-plane 

displacements. These baseline pictures also established the relative grip misalignment in the test machine. 

Figure 4.26 shows the baseline results from the optical measurement system. Here, the baseline 

measurements made by the optical measurement system indicate that the specimens that were used for the 

25-, 75-, and 90-percent ultimate strength tests exhibit a uniform field of very small out-of-plane 

displacements, with the exception of their bottom right corners. This small region of high displacement 

was due to the grip misalignment in the machine and was accounted for when examining the posttest 

results. The 50-percent specimen shows areas of high out-of-plane displacement near the top and low outof-plane displacement near the bottom. This anomaly was due to a grip misalignment in the test fixture 

and was accounted for when examining the posttest results. To establish the UTT baseline conditions, 

specimens were scanned in an unloaded state before the test. 
NASA/CR—2013-215450 57 

Figure 4.27 shows that the baseline scans made by the UTT system captured repeating patterns of 

white and dark areas in the specimen. These areas represent different locations within the fiber braid. The 

dark areas indicate areas where the bias fiber bundles met, and the white areas represent areas where the 

axial fibers are present. The braid architecture can also be seen by noting that the alternating white and 

dark parallel lines running in the –60° and +60° directions represented the bias fiber bundles present in 

the specimens. 

After the baseline conditions were established, the test was run and the posttest results were 

examined. Figure 4.28 shows the out-of-plane displacement results gathered from the optical 

measurement system at the final load for the axial tests conducted for the T700/E862 material system, and 

Figure 4.29 shows the UTT results. Figure 4.28 shows the four axial tests conducted on the T700/E862 

material system, and Figure 4.29 shows the UTT scans of the same specimens. The optical measurement 

data in Figure 4.28 are shown at the point of maximum load. Ultrasonic through transmission pictures are 

shown in a posttest unloaded state. By comparing Figures 4.28 and 4.29, one can see that similarities exist 

between the results from the optical measurement system and UTT. First, by looking at the baseline 

optical measurement data and UTT scans for the specimens loaded to 25 and 50 percent, the posttest 

results show identical images to the baseline results, indicating that there were variations that were 

normally present in the composite. Also note that the anomaly present in the 50 percent specimen during 

the baseline optical measurements was accounted for and was not present in the postprocessed results. 

However, when the 75 and 90 percent specimen results were examined, major differences between the 

posttest and baseline results became evident. Figure 4.30 shows comparisons of the UTT and optical 

measurement data for the 75 and 90 percent specimens. 
NASA/CR—2013-215450 58 
NASA/CR—2013-215450 59 
NASA/CR—2013-215450 60 

When the material system was tested at 75 percent of ultimate loading, the optical measurement’s 

out-of-plane data show areas of high out-of-plane deformation surrounded by regions exhibiting behavior 

similar to the baseline data, indicating a local delamination. Figure 4.30 also shows that strong 

correlations exist between the optical measurement system and the UTT NDE techniques for the 

specimen loaded to 75 percent of its ultimate load. This conclusion is important because it shows that in 

future testing, delaminations causing damage in the composite materials can be captured by examining 

the out-of-plane deflection obtained from the optical measurement system, without having to conduct an 

extra NDE test. The results from the specimen loaded to 90 percent of ultimate load verify these results. 

Out-of-plane deformation occurred on the highest loaded specimens, which indicates that delamination 

occurred at higher loadings. 

To verify that the subsurface delaminations were present, regions of high out-of-plane deformation 

were cut from the specimens and examined under a digital microscope. Figure 4.31 shows the location of 

the section that was examined in the axial T700/E862 material system loaded to 90 percent of ultimate 

load. The optical measurement and UTT data showed that the specimen had a possible delamination in 

the middle of the section. Figure 4.32 shows a digital microscopic image of the section described in 

Figure 4.31. 
NASA/CR—2013-215450 61 

Figure 4.32 highlights the area shown to have a possible delamination as identified by both the optical 

measurement system and UTT technique. The axial fibers, which were orientated out of the plane of the 

picture, are shown in dark grey and the bias fibers are shown in light grey. The large black areas 

surrounding the axial fibers are the edges of the axial fibers. The indicated area in Figure 4.30 

corresponds to the area of a possible delamination as seen by the optical measurement system and the 

UTT. The indicated area in Figure 4.32 shows damage in the subsurface bias fiber, which was caused by 

the surface axial fiber as pulled away from a subsurface bias fiber in its lower right corner. This was the 

out-of-plane deformation picked up by the optical measurement system and UTT. 

Figure 4.33 shows where the 25, 50, 75, and 90 percent loading points occurred on the global stressstrain material response curve for T700/E862. The black curve depicts a typical axial material response. 

The four stress levels are marked with a red line. Finally, a perfectly linear material having the same 

modulus as T700/E862 is marked with the dotted blue line. The material response curve starts to behave 

in a nonlinear fashion at approximately 75 percent, or more specifically, where the subsurface 

delaminations begin to appear and are captured by the optical measurement system and UTT. Below the 

75 percent stress level, the curve behaves in a linear manner, which corresponds with the lack of damage 

as seen by the UTT and the optical measurement systems. The conclusion garnered from this data 

supports the theory that the subsurface delaminations are damage mechanisms that occur in the axial 

direction, causing the stress-strain curve to become nonlinear. 
NASA/CR—2013-215450 62 

Next, the same procedure was repeated on the weaker T700/3502 material system’s axial test 

specimens. Baseline pictures from the optical measurement system and pretest scans from the UTT were 

taken. As before, the specimens were loaded to 25, 50, 75, and 90 percent of ultimate strength as 

determined by the material response curves presented in Section 4.4.1.1 and then unloaded. 

The baseline optical measurement system pictures confirmed that the untested specimen shows very 

little displacement, and the baseline UTT scans show similar results to Figure 4.27: repeating patterns in 

the braid architecture were found, with no anomalies present. Therefore, the tests were run and the 

posttest results are presented. Figure 4.34 shows the out-of-plane displacement results from the optical 

measurement system at maximum load. 

The T700/3502 material system starts to show a small amount of out-of-plane displacements when 

the specimen was loaded to 50 percent of ultimate strength. The specimen shows pronounced out-of-plane 

displacements at 75 and 90 percent of its ultimate load. Again, to verify these conclusions, the specimens 

were also scanned with the UTT. 

Figure 4.35 shows the results of the UTT scans. At 25 percent of ultimate load, the scans only show 

the normal variation in braid pattern. However, slight amounts of dark areas appear at the bottom of the 

specimen loaded to 50 percent of ultimate load. At 75 and 90 percent, large dark areas were clearly 

present, indicating delaminations. Figure 4.36 shows the comparisons of the optical measurement’s outof-plane deformation and the UTT scans. The optical measurement’s out-of-plane deflection results show 

good agreement with that from the UTT. As with the T700/E862 material system, T700/3502 was 

examined with digital microscopic imaging. 
NASA/CR—2013-215450 63 
NASA/CR—2013-215450 64 

Figure 4.37 shows the section from the 90 percent specimen used for digital microscopic imaging. 

The optical measurement and UTT data show that the specimen had a possible delamination in the middle 

of the section. Figure 4.38 shows the digital microscopic image of the section cut from the specimen. The 

dark grey areas represent the axial fibers, which are orientated out of the plane of the picture, and the light 

grey areas are the bias fibers. The dark outlines around the axial fiber represent the edge of the fibers. The 

indicated area is an area that corresponds to a possible delamination, as observed by the optical 

measurement system and the UTT. Figure 4.38 shows damage to the subsurface bias fiber directly 

underneath the axial fiber as well as a small gap between the two. This gap is the data point picked up by 

the optical measurement system and the UTT. 

However, the digital microscopic imaging pictures are not as conclusive as either the optical 

measurement or UTT data. There are two possibilities for this discrepancy: The first possibility is that 

since the delaminations are very localized in the braid architecture, the sections cut from the specimen 
NASA/CR—2013-215450 65 

might not have captured the spot of maximum delamination but rather were cut in an area slightly away 

from the delamination, which only captured the propagation. The second possibility is that the area in 

question became unusable in the process of cutting and preparing the areas where possible delaminations 

occurred from the composite. By cutting the specimen, the delaminated fiber bundle could have been able 

to “relax,” or set back into its original position in the braid architecture, closing the gap seen by the 

optical measurement system and UTT. Because of these reasons, digital microscopic imaging was used 

only as a third check on the data. In many cases, when trying to observe nonvisible damage in tested 

material systems, UTT techniques are accepted methods of detecting subsurface damage occurring in 

materials and have been widely reported. Thus, the correlations between the UTT and optical 

measurement system provide a way to measure and detect subsurface delaminations leading to damage 

accumulation in the composite specimens. 

As with the stronger T700/E862 material system, Figure 4.39 shows the material response curve for 

the T700/3502 material system in the axial direction with four stress levels are marked by a red line. A 

theoretical material having a perfectly linear modulus the same as T700/3502 is added as a dotted blue 

line for reference. The figure shows that the nonlinearities in the material response starts to occur around 

50 percent ultimate load, which corresponds to the first detectable subsurface delamination damage. 

Beyond this region, the delaminations are clearly present in the material, leading to the conclusion that in 

the axial tensile direction, the subsurface delaminations were damage mechanisms occurring in the axial 

direction that caused the nonlinearities in the global material response curves. 

Using the data gathered in this section along with that gathered in Section 4.4.2.2 and the global 

material response curves in Section 4.4.1.1, an understanding of the composite response in the axial 

direction can be described: Under loading, the axial fibers in the composite specimens are the main loadcarrying mechanisms. The fiber-matrix interface dictates when the surface bias fiber bundle splitting 

begins to occur, which is a good indication of the interface strength; however, the nonlinearities in the 

global material response curves begin to appear once the subsurface delaminations appear. The composite 

coupon’s ultimate failure is dependent on the fiber-matrix interface: the interface influenced the ultimate 

failure strain of the axial fiber bundles. A stronger interface causes a clean fiber-matrix separation and 

allows for the fibers to reach their ultimate failure strain, as shown with the T700/PR520 material system. 

A weaker interface allows for the matrix to degrade the fiber ultimate strength by bringing concentrations 

to the fiber bundles, while also allowing for fiber layer delaminations to occur more frequently and at 

earlier stages in the loading. 
NASA/CR—2013-215450 66 

4.4.2.3.2 Subsurface Delaminations in the Transverse Direction 

Recall that in transverse tensile testing, the axial (0°) fibers did not extend throughout the gage 

section, but rather were oriented perpendicular to the direction of loading. As pointed out in the previous 

section, the transverse fiber bundle failures in the axial fibers were one of the causes of the nonlinearities 

occurring in the global stress vs. strain material response curve. However, out-of-plane displacements 

were also examined to determine whether subsurface delaminations played a role in the material response. 

Testing was done in the same fashion as the axial testing: four different specimens were loaded to 

four different loading levels, 25, 50, 75, and 90 percent of ultimate strength, as determined by the overall 

material response testing presented in Section 4.4.1.1. To start, baseline UTT scans and optical 

measurement pictures were taken for posttest comparisons. 

Figure 4.40 shows the baseline optical measurement system out-of-plane displacements for the 

T700/E862 material system and indicates that the specimens exhibit a uniform field of very small out-ofplane displacements, with the exception of their bottom right corners. As with the axial tests, this small 

region of high displacement was due to the grip misalignment in the machine and accounted for when 

examining the posttest results. Again, as with the axial test, the UTT baseline conditions were established 

by scanning the specimens in an unloaded state before the test. 

Figure 4.41 shows that the baseline scans made by the UTT system again captured white and dark 

areas in the specimen. These areas represent different locations within the fiber braid. Again, the dark 

areas indicate areas where the bias fiber bundles met, and the white areas represent areas where the axial 

fibers are present. The braid architecture can also be seen, by noting that the alternating white and dark 

parallel lines running in the –30° and +30° directions represent the bias fiber bundles present in the 

specimens, which in the transverse test, run 60 to the horizontal axis. Also the areas of parallel black and 

white lines running in the horizontal direction represent the axial fiber bundles. After the baseline 

conditions were established, the test was run and the posttest results were examined. 

Figure 4.42 shows that the high localized areas of out-of-plane deformation seen in the axial tests are 

not present in the transverse testing, even at the highest loaded conditions. The majority of the results 

show a uniform field of little displacement, with slightly higher areas around the bottom right corner of 

the specimens. This slightly higher area of displacement was due to the slight grip misalignment present 

in the machine. To verify the results seen by the optical measurement system, the specimens were 

scanned with the UTT. 
NASA/CR—2013-215450 67 
NASA/CR—2013-215450 68 

The UTT scans (Fig. 4.43) confirmed the results seen by the optical measurement system. The UTT 

scans completed on the tested transverse specimens show only patterns normally present, created by the 

braid architecture. This led to the conclusion that delaminations did not occur and did not influence the 

material response in the transverse tensile composite coupon as they did with the axial tension specimens. 

For completeness, the T700/3502 material system was also tested. Figure 4.44 shows the results from 

these four tests. 

Figure 4.44 shows that for specimens at 25, 50, and 75 percent loading, the results agree with the 

T700/E862 results. The 90-percent specimen however, showed results that indicated possible 

delaminations. As with all of the testing done in this section, the specimens labeled 90 percent were 

loaded to a nominal 90-percent ultimate stress level as determined by an average from the specimens 

tested for the generation of material response curves in Section 4.4.1.1. However, the specimen tested in 

Figure 4.44 began to fail before 90 percent of the average ultimate strength was reached, representing the 

low end of the standard deviation of the data. The 90-percent picture in Figure 4.44 shows the specimen at 

the onset of ultimate failure, more likely at 99 percent of its ultimate strength. Had this specimen been 

loaded higher than 279 MPa (40 470 psi), the specimen would have failed completely, leaving both the 

optical measurement and UTT results unusable. Thus, the test was stopped at the initial onset of ultimate 

failure, which is being shown in Figure 4.44. Again, these results were verified with UTT scans, as shown 

in Figure 4.45. 
NASA/CR—2013-215450 69 
NASA/CR—2013-215450 70 

UTT scans confirmed the results shown by the optical measurement system. Only the 279-MPa 

specimen showed signs of out-of-plane displacements, whereas the others showed only normal deviations 

in the braid pattern. Figure 4.46 compares the two results. 

The specimen loaded to 279 MPa presents a unique data point because it was the only specimen 

tested in the transverse direction that was able to be captured at the onset of specimen failure and showed 

any sort of damage occurring. The specimen failure was first detected by visible inspection after the test 

was completed; the areas of high out-of-plane displacement on the edges are areas in which the specimen 

showed visible cracks on the surface. The conclusion drawn from this test was that in transverse testing, 

specimens show that only right before failure did they exhibit out-of-plane displacements, which start 

along the specimen edges and propagate throughout the entire gage width. In order to understand the 

failure process, such detailed examination of the onset of failure in the transverse specimens is necessary. 

Finally, digital microscopic imaging was used to examine the onset of the specimen failure at the 

microscopic scale. Figure 4.47 shows the two sections used for the microscopic imaging. Both are areas at 

the onset of specimen failure. Section “A” was cut such that the face of the viewing surface was parallel to 

the direction of applied load, whereas Section “B” was cut such that the face of the viewing surface was 

perpendicular to the direction of applied load. Figure 4.48 presents Section A from the specimen and shows 

clear damage in the axial fiber bundles, which was represented by the vertical cracks present in the axial 

fiber bundles. As described in Section 4.4.2.2, the cracking present in the axial fiber bundles represents the 

fiber bundle splitting, and is the main damage mechanism occurring in the transverse tensile tests, leading to 

nonlinearities in the global material response curve. Figure 4.49 shows Section B from the 90-percent 

transverse specimen. The circled areas show cracks on the specimen surface causing the delaminations seen 

by the out-of-plane displacement measurements from the optical measurement system. 
NASA/CR—2013-215450 71 
NASA/CR—2013-215450 72 

By using Figures 4.48 and 4.49 and the material response data, a full understanding can now be 

obtained of how the transverse tensile specimens fail. The damage in the specimen starts from the 

initiation of the axial fiber bundle splits. The onset of these splits causes the global material response 

curve to become nonlinear. The damage accumulation in the composite is the result of the fiber bundle 

split propagation. At the onset of specimen failure, the fiber bundle splits are great enough to cause 

surface cracks near the edges of the composite, leading to the out-of-plane displacements seen in 

Figure 4.47. The final failure in the composite occurs when the surface cracks extend from one edge of 

the composite to the other, leaving no path for the load to travel. Once the surface crack reaches both 

edges of the composite coupon, the coupon fails. 

4.5 Composite Testing Summary 

This section presents the composite material testing that has been completed using optical 

measurement techniques, which capture some important characteristics of triaxial braided composite 

materials normally undetectable using conventional methods. Composite coupon testing has been 

completed, and global stress-strain material response curves have been presented. The global material 

response data shows that optical measurement techniques can be utilized in static testing to obtain 

material properties of triaxial braided composite materials. 

The data also show that the local deformations of the composite specimens can be examined and 

quantified. By utilizing some of the overlay techniques developed, precise locations for areas of high and 

low strain were determined. Also, material parameters such as matrix cracking causing transverse fiber 

bundle failure and delaminations in the braid architecture were examined. 

The use of the optical measurement system provided insight into the nature of the premature failure of 

the weaker material systems and led to preliminary conclusions about the fiber-matrix interface in 

general. The results obtained by the optical measurement system suggest that a weak interface causes 

initiation of transverse fiber failure sooner than a strong interface. A weak interface also distributes the 

load more evenly than a strong interface, and properties like fiber splitting grow more abundant because 

of this load distribution. Also, a weak interface causes premature failures in the axial fibers and fiber layer 

delaminations resulting in nonlinear behaviors in the stress-strain response curves. However, the interface 

characteristics did not influence the modulus of the overall composite because the modulus values are 

taken from the very beginning of the stress-strain curves. 

The optical measurement system, along with confirmations from UTT scans, was able to show that 

some of the damage causing mechanisms in the composite tests for the axial direction was delaminations 

within the fiber braid layers. The stronger T700/E862 fiber/resin material system started to show signs of 

delamination at approximately 75 percent of its ultimate stress, and the weaker T700/3502 material system 

showed signs of delamination at approximately 50 percent ultimate stress. It was at these points that the 

global specimen material response curves became nonlinear. In the transverse direction, the optical 

measurement system was able to capture the large out-of-plane deformations at the onset of failure. 

The information presented in this section not only provides a greater insight into the nature of 

specimen response, but also will provide critical material parameters used when developing a computer 

model, which will be presented in the next section. 

5.0 Development of Macromechanical Triaxial Braided Composite 

Computer Model 

The previous chapters describe test methods developed and implemented to measure the material 

response of the constituents and coupons of triaxial braided composites. Also, mechanisms affecting the 

overall material response have been presented. While the full-field data presented provides a unique 

insight into the nature of the material response, it can also be utilized in the development of a finiteelement-based approach to model braided composites. The methods described in this chapter provide a 
NASA/CR—2013-215450 73 

systematic approach that utilizes the full-field material response data and braid geometry for 

implementation into a finite-element model. Information from the experiments is used along with the 

current material models available in LS–DYNA (Ref. 66), a commercially available transient dynamic 

finite-element code, to simulate the influence of the braided architecture on the failure process of the 

testing completed. 

5.1 Material Background 

Two material systems from the tested composite coupons described in Section 4.0, “Investigations of 

Triaxial Braided Composite Material Response” were simulated. The T700/PR520 and T700/E862 

fiber/resin material systems were chosen because they were the highest strength material systems studied as 

shown by the test data and are therefore of the greatest interest for use in composite structures. As described 

in the previous sections, the fiber was Toray’s high-strength, standard-modulus T700 fiber, and the resins 

were CYCOM PR520 (Cytec Industries, Inc.) and Epon 862 (Momentive Specialty Chemicals, Inc.). 

5.2 Composite Microstructure 

The method for modeling the composite braid architecture is presented first. Figure 5.1 shows the 

composite braid architecture and highlights the unit cell geometry common to the material systems tested. 

A unit cell is considered to be the smallest repeating volume of the composite where the behavior of the 

unit cell can be considered to be representative of the composite as a whole. For the analysis technique 

developed, a single unit cell was also divided into four subcells, labeled A through D. Figure 5.1(a) shows 

the fiber orientation in a single layer of a braided preform. In Figure 5.1(b), part I, shows a magnification 

of one unit cell for one layer of braid of the composite. Part II is a top view of a geometric representation 

of the three-dimensional model of the braid architecture, and part III shows a side view of the geometric 

representation. The +60 fibers are represented in green, while the –60 fibers are represented in red, and 

the 0 fibers are represented in blue. Finally, part IV shows the braid architecture in a homogenized 

condition by using the layers of the composite braid, and dividing them up into layers of unidirectional 

composites within each subcell. The full composite architecture was represented by placing each of the 

stacked unidirectional layers comprising each subcell adjacent to each other to make a complete unit cell. 

Because of the nature of the braiding scheme, the fiber layup was different in each of the individual 

subcells. As shown by the subcell illustrations in Figure 5.1(b), part II, subcell A contains a –60° fiber 

above of a 0° fiber, which is above a 60° fiber on the bottom (represented by red). Subcell B contains only 

a –60° fiber above a 60° fiber; subcell C contains a 60° fiber above a 0° fiber on top of a –60° fiber. 

Finally, subcell D contains a 60° fiber above a –60° fiber. This braid architecture in each of the subcells 

shown in Figure 5.1(b), part II, was represented by stacking these fiber directions as layers through the 

thickness, as shown in Figure 5.1(b), part IV. A single unit cell with braid orientation was represented as a 

series of subcells with layers of unidirectional fiber tows stacked through the thickness. The unit cell with 

subcell geometries as defined here was the basis for the modeling technique. 

When making the finished composite material, six layers of braid (representing the fabricated 

composite) were used. Figure 5.2 shows a cross section of a finished composite panel, with the full six 

layers of braid present, that was obtained from digital microscopic imaging. 

Figure 5.2 shows a side view cross section of a digital microscopic picture of a finished composite 

panel. Upon examination of the microscopy pictures the phenomena known as fiber shifting, or the 

relative position of the unit cells through the specimen thickness, was observed. Fiber shifting was 

incorporated into the model because if the assumption was made that all of the subcells were in the same 

relative position throughout the thickness, then subcells B and D (having only +60 and –60 fibers as 

shown in Figure 5.1) would potentially be overly weak due to the lack of axial (0°) fibers. Also, shifting 

was included to account for the assumption of quasi-isotropy (by shifting the subsequent layers of 

subcells, each of the subcells of the full six-layer finished composite would have an equal number of 0°, 

 –60°, and 60° fibers). In Figure 5.2, the dark areas represent the cross sections of the axial fiber bundles, 
NASA/CR—2013-215450 74 

as they are orientated perpendicular to the cut, while the white areas represent bias fiber bundles, and are 

orientated at 30° to the cross-sectional cut. The small areas of grey between the fiber bundles represent 

resin-rich pockets. Subcell designations shown in the figure were picked to represent the subcells for the 

topmost layer of braid. Subsequent layers were shown to have significant misalignments under the 

topmost layer. These relative changes in position for subsequent layers through the thickness suggested 

that subcell shifting was prevalent enough such that it needed to be accounted for when modeling. Subcell 

shifting is accounted for in an idealized way when modeling the braid geometry; the analysis method 

shifted the unit cell by one subcell for each of the layers through the thickness of the composite, which 

will be described in detail in Section 5.3.1, “Development of Braid Geometry.” 
NASA/CR—2013-215450 75 

5.3 Triaxial Braided Composite Model Development 

The commercial transient dynamic finite-element code, LS–DYNA (Ref. 66), was used to analyze the 

triaxial braided composites discussed in this paper. LS–DYNA was used because of its ability to simulate 

impact events, which is the ultimate goal of this modeling technique, and will be discussed in Section 6.0. 

Both the triaxial braid geometry and the material properties obtained from testing were incorporated 

into the model. First, the methods for approximating the composite braid architecture will be discussed, and 

then the methods developed for the utilization of the test data within the finite-element model will be 

presented. 

5.3.1 Development of Braid Geometry 

The idealized full six-layer composite geometry that will be simulated in the finite-element model is 

shown in Figure 5.3. The model developed is an extension of the model first developed by Cheng (Ref. 67). 

Cheng’s original methodology will be modified because Cheng did not include the fiber shifting phenomena 

observed and described in the previous section. 

As Figure 5.3 shows, the shifting of the unit cell under the topmost layer was accounted for in the braid 

geometry. Subcell A, represented in pink, was in the leftmost portion of the unit cell on the top layer; 

however, subsequent layers underneath the top layer show that it has shifted to the left by one subcell. 

In LS–DYNA, each subcell was modeled as a Part, which is the LS–DYNA term for a discrete entity. 

All subcells were modeled using a shell element since the length and width of the composite structures 

being examined were much greater than the thickness. Each Section card contained properties such as 

element thickness, which represented the thickness of the entire composite specimen; number of 

integration layers, which defined the number of fiber layers through the cross section; and integration 

layer orientation, which described the angle of the fiber at each particular layer. Thus, the Section card in 

each of the subcells included 15 integration points, which represented the 15 layers of fibers through the 

thickness of the composite. Finally, separate Integration cards were used for each subcell. The Integration 

card was referenced by each individual subcell Section cards. The Integration card included parameters 
NASA/CR—2013-215450 76 

such as individual fiber layer position through the thickness of the section, and relative weight for each of 

the layers. For ease of the material model equation development, the analysis method assumed that each 

of the 15 fiber layers had the same thickness, which spaced all of the fiber layers equally throughout the 

thickness. To account for the differences in sizes between the 24k axial and 12k bias fiber bundles, the 

axial layers were weighted twice the amount as the bias layers. 

For example, looking at Figure 5.3, Subcell A was modeled as Part 1, which had a corresponding 

Section 1. Section 1’s integration layers reflected the braid geometry seen in Figure 5.3. Going from 

bottom to top in subcell A, the orientation of the fibers were as follows: –60°, 60°, 60°, 0°, –60°, –60°, 

60°, –60°, 0°, 60°, –60°, 60°, 60°, 0°, –60°. All layers were equally spaced, and the normalized weights 

on the axial (0°) fibers were double that of the bias (60°) layers. 

5.3.2 Composite Material Property Implementation 

The constitutive material model within LS–DYNA that was employed for all of the subcells was a 

continuum-damage-mechanics-based orthotropic material model, based on a model developed by 

Matzenmiller, Lubliner, and Taylor (Ref. 68). This material model assumes that applied deformation 

causes damage initiation and progression, which is captured by a stiffness reduction in the material. The 

stiffness reduction is accounted by in	
	
	
	,11, 22, 12, which 

represent damage in the axial, transverse, and shear directions, respectively, into the compliance matrix in 

the constitutive equation. Detailed evolution laws govern the relationship between applied deformation 

and values of the damage variables. A detailed discussion about general uses of this material model in 

LS–DYNA is presented in Schweizerhof et al. (Ref. 69). 

The continuum-damage-based material model used for the computer model was called 

MAT_LAMINATED_COMPOSITE_FABRIC (Mat 58) within LS–DYNA as a Material card for each of 

the individual parts. For the elastic portion of the analysis, which will be described first, each layer’s 

effective unidirectional ply properties needed to be entered as part of the model input. 

The unidirectional laminate properties needed for the material models are as follows: axial modulus 

(E11), transverse modulus (E22), in-plane shear modulus (G12), and in-plane Poisson’s r
21). The 

methods for obtaining the effective unidirectional ply-level properties (E11, E2221, G12) that are needed 

for each integration layer in each of the subcells are developed in this section. Cheng (Ref. 67) used 

carbon fiber and resin matrix properties, along with classically based composite micromechanics 

approaches for material property implementation, which represented a bottom-up approach. The method 

developed in this section also differs from Cheng in that it will take a top-down approach. The key feature 

of the approach is that the required properties were “backed out” from coupon-level test data obtained and 

presented in Section 4.0 by using classical laminated plate theory (CLPT) and classical composite 

micromechanics techniques. A discussion of these techniques can be found in References 41, 70, and 71. 

Many of the specimen geometries and boundary conditions utilized for the model development were the 

same as those used in the composite testing described in Section 4.0. The analytical technique started by 

first examining results from a transverse tensile test, in which the specimen geometry was taken from the 

ASTM D3039 standard (Ref. 17). In this test, the axial (0) fibers are oriented perpendicular to the 

applied load Px as shown in Figure 5.4. To represent the transverse tensile test in the model, the four 

subcells of the unit cell were orientated parallel to the direction of the load (Fig. 5.4). 
NASA/CR—2013-215450 77 

The development of the technique required some assumptions. By first assuming that all six layers of 

braid in the specimen carried the same load, the total load gathered from the test was divided by the 

number of layers in the composite to determine the load Px in each layer of braid. Next, the assumption 

was made that all of the unit cells along the width of the specimen carried equal loading, so the load was 

also divided by the number of unit cells along the width, which gave the total load for each unit cell. This 

means that the analysis technique was developed for the unit cell shown in Figure 5.1 (bottom right), not 

the full 15-layer composite geometry shown in Figure 5.3. The full 15 layers of the braid architecture 

were implemented in the LS–DYNA Section card. Note, that CLPT also required traction Nx, so the total 

load was taken to be per unit length, which meant that it was also divided by the width of each unit cell. 

Equation (5.1) shows the final traction value used in the analysis: 

 	 #Layers
 #Unit cells
 Width  x x P N (5.1) 

The traction Nx next had to be partitioned among each of the subcells in the unit cell. For this process, 

and for the methods described in the remainder of this section, uniform stress (or load) and uniform strain 

assumptions that have been applied in micromechanics methods in the past (Ref. 41) need to be applied 

between the subcells. For example, in the ASTM 3039 transverse tensile test configuration, the load Nx

was assumed to be equal in all of the subcells: 

D

x Cx Bx A Nx  N  N  N (5.2) 

The subscript x in Equation (5.2) represents the direction of loading, and the superscript represents the 

subcell name. Next, the volume average of the load in the y-direction in each of the subcells Ny was 

assumed to be equal to 0 since there was no applied load in that direction. 

*  *  *  *  0 D

y

D

f

C

y

C

f

B

y

B

f

A

y

A Vf N V N V N V N (5.3) 

Each Vf represents the volume fraction of its subcell as compared to the volume of the entire unit cell, 

and not the fiber volume fraction of the as-fabricated composite. Note that because subcell C had the 

same volume fraction as subcell A and subcell D had the same volume fraction as subcell B, 

Equation (5.3) can be rewritten: 

2* *  2* *  0 B

y

B

f

A

y

A Vf N V N (5.4) 

Next, CLPT was used to relate Nx and Ny in each subcell to the strains in the subcell. Although on a 

local level the laminate orientations in each subcell were not symmetric, when accounting for all six 

layers in the composite on a global level, the composite was assumed to be symmetric. This assumption 

was verified by looking at the full-field strain data. By examining the out-of-plane deflections on the 

composite specimens during testing, care was taken to ensure that out-of-plane bending did not occur. 

Knowing that out-of-plane bending did not occur, the assumption was made that the B constitutive matrix 

normally associated with CLPT, which would account for the out-of-plane bending, was set equal to 0. 

Furthermore, on the local level only the in-plane strains were needed and obtained from the test data, so 

the D matrix normally associated with CLPT was not analyzed. The laminate orientations were assumed 

to be balanced on the global level, so the A16 and A26 components of the A matrix from CLPT were set 

equal to 0. To summarize, in-plane normal loads were assumed to be a function of in-plane normal 

strains, and shear loads are assumed to be a function of shear strains; that is, the strains were uncoupled. 

These are commonly used when examining composite material response using CLPT and have been 

widely reported. The assumptions above can be used to rewrite the CLPT in equation form, as shown in 

Equation (5.5): 
NASA/CR—2013-215450 78 





































































A

xy

A

y

A

x

A

A

A

A

A

A

xy

A

y

A

x

A

A

A

A

A

N

N

N

66

0

0

0

22

12

0

12

11

 (5.5) 

In Equation (5.5), the superscript A represents the subcell name. Similarly, the constitutive equations 

for subcells B, C, and D were written. Expanding the matrix in Equation (5.5) above for Nx and Ny, 

Equations (5.6) and (5.7) were obtained for subcell A and Equations (5.8) and (5.9) were obtained for 

subcell B: 

A

y

A A x A A Nx  A11 *  A12 * (5.6) 

A

y

A A x A A Ny  A12 *  A22 * (5.7) 

B

y

B B x B B Nx  A11 *  A12 * (5.8) 

B

y

B B x B B Ny  A12 *  A22 * (5.9) 

Noting that subcells A and C both had the same layers of 0° fibers, layers of 60° fibers, and layers of 

–60° fibers, only subcell A was examined. Similarly, since subcells B and D had the same number of 60° 

and –60° layers, only subcell B was examined. 

The A matrix terms were expanded by using CLPT, and are represented in Equation (5.10): 



k

ij ij k A Q *t (5.10) 

In Equation (5.10), t is the thickness of the k

th layer. The expansion of the Aij matrix was specifically 

written for subcells A and B is shown in Equations (5.11) and (5.12): 

A Q t Q t Q t A * * * 60

11

0

11

60

11 11       (5.11a) 

A Q t Q t Q t A * * * 60

12

0

12

60

12 12       (5.11b) 

A Q t Q t Q t A * * * 60

22

0

22

60

22 22       (5.11c) 

A Q t Q t B * * 60

11

60

11 11

     (5.12a) 

A Q t Q t B * * 60

12

60

12 12

     (5.12b) 

A Q t Q t B * * 60

22

60

22 22

     (5.12c) 

In Equations (5.11) and (5.12), the Q terms are the transformed stiffness terms for a unidirectional 

ply in the structural axis system. Note that the Q terms for the 0 fiber are not present in subcell B 

because 0 fibers are not present in subcell B. The Q terms were then decomposed into their 

representative Q terms, which represent the stiffness for a unidirectional ply layer in the material axis 

system for the axial, transverse, and shear directions. In general, 
NASA/CR—2013-215450 79 

66

2 2

12

2 2

22

4

11

4

11 Q  m *Q  n *Q  2*n *m *Q  4*m *n *Q (5.13a) 

 	 66

2 2

12

4 4

22

2 2

11

2 2

12 Q  m *n *Q  m *n *Q  m  n *Q 4*m *n *Q (5.13b) 

66

2 2

12

2 2

22

4

11

4

22 Q  n *Q  m *Q  2*n *m *Q  4*m *n *Q (5.13c) 

In Equation (5.13), m represents the cosine of the braid angle and n represents the sine of the braid 

angle. Thus Equation (5.13) was substituted into Equations (5.11) and (5.12) noting that the values for m

and n changed for the different bias directions. 

There are six unknown variables in the equations derived above for the transverse test 

configuration—Q11, Q12, Q22, Q66, A Ny , and B Ny —and only five equations available for finding the 

unknown variables—Equations (5.4) and (5.6) to (5.9). Representative subcell strains in both the axial 

and transverse directions were directly measured from the optical measurement system described in 

Section 4.0. The main advantage of the method described is that by using the above-developed equations 

and the optical measurement system’s results, strain was not an unknown; rather, strains in each of the 

subcells for both directions were known. 

Figure 5.5 shows an example of the subcell strains in both the axial and transverse direction for both 

subcells A and B, as measured by the optical measurement system. Since the optical measurement system 

computed strain over the full specimen, multiple subcells were visible. The local subcell strains presented 

were representative samples of the many subcells measured. 
NASA/CR—2013-215450 80 

In an axial tension test, the axial (0°) fibers were oriented to the direction of loading. This was 

represented by orienting the four subcells perpendicular to the direction of loading. 

An important point to note for the discussion that follows is that the composite was once again 

assumed to be loaded in the “x-direction.” That means that in terms of the unit cell orientation the axis 

orientation was switched 90° from the transverse loading case. In other words, what was considered to be 

the y-direction previously was now the x-direction, and vice versa. In axial tension testing, only one 

uniform stress assumption needed to be applied for the model development. Since the unit cell was being 

pulled in the x-direction, the effective force in the y-direction must have been equal to 0. The force in the 

y-direction in each of the subcells was also assumed to be equal. Expressed as equations, these 

assumptions translated to 

    0 D

y

C

y

B

y

A Ny N N N (5.14) 

The CLPT equations were expressed for the y-direction only for the case of an axial tension test. Note 

that the Aij terms were not the same as they were for the transverse tension testing, as the angles for m and 

n have changed by 90° because the orientation of the unit cell has changed by 90°. 

A

y

A A x A A Ny  0  A12 *  A22 * (5.15) 

B

y

B B x

B B B Ny  0  A *  A * 12 22 (5.16) 

By taking into account the 90° change in angle in the Aij terms, there were seven equations 

(Eqs. (5.4), (5.6) to (5.9), (5.15), and (5.16)) and only six variables (Q11, Q12, Q22, Q66, a Ny , and b Ny ) for 

the transverse tensile test. Now 6 out of the 7 equations can be used for the solution and the 7th equation 

can be used for verification. 

Since the ultimate goal was to find the unidirectional ply material properties required for the material 

model, the Q terms were decomposed as follows: 

12 21

11

11 1 v *v

E Q  (5.17) 

12 21

22

22 1 v *v

E Q  (5.18)

12 21

21 11

12 1 *

*

v v

v E Q  (5.19) 

Q66  G12 (5.20) 
NASA/CR—2013-215450 81 

In Equations (5.17) to (5.20), the unidirectional-ply-level axial modulus (E11), transverse modulus 

(E22), in-plane shear modulus (G12), and in-plane Poisson’s ratios (v12 and v21) were the unknown 

variables. Again, there were more unknowns than equations. The final equation came from elasticity 

theory: 

21

22

12

11

v

E

v

E  (5.21) 

Knowing the Qij from above and using Equations (5.17) to (5.21), E11, E22, G12, v12, and v21 were 

found. These values were the effective unidirectional engineering properties of the composite ply at each 

integration point in the finite-element model. 

By using the measured subcell strains and values of load from the test data as the inputs into the 

material model, representative material properties were found. Because the values of strain and load were 

measured from fabricated composite coupons, the model’s effective unidirectional-ply-level properties 

included items such as the interface effects between the fibers and matrix and also inherent localized 

deficiencies present in real fabricated composite materials such as resin rich pockets. Thus, the material 

model does include many of the micromechanical properties and deficiencies present in the fabricated 

composite materials, but utilizes them macromechanically. 

5.3.3 Development of Material Failure Parameters 

Ply-level material properties were one portion of what the material constitutive model in LS–DYNA 

required as inputs. The other requirement was that the initial ply-level unidirectional failure strengths for the 

composite needed to be found. The initial failure criteria implemented within the LS–DYNA material model 

was based on the Hashin (Ref. 72) failure criteria and has the parameters specified in Table 5.1 as input. 

Failure values were extracted from the composite test data based on the requirements in Table 5.1. 

Observations were made on the full-field strain data from the various axial and transverse tensile and 

compressive tests conducted. The T700/PR520 fiber/resin material system will be used for an example of 

how the material properties needed were obtained. 

The simplest parameters to observe were the axial tensile values. The main assumption for extracting 

the axial tensile strength from these results was that the braided composite was effectively acting as a 

unidirectional laminated composite, and therefore the axial tensile strength obtained during the test could 

be extrapolated to be the axial tensile strength of a unidirectional layer. The LS–DYNA strain at axial 

tensile strength, E11T, was found by observing the strain in an axial tensile specimen at failure. The LS–

DYNA axial tensile strength XT was found by recording the ultimate tensile strength that occurred at the 

ultimate strain. Figure 5.7 shows a representative example of an axial tension test. 

TABLE 5.1.—FAILURE VALUES NEEDED IN LS–DYNA 

FINITE-ELEMENT MATERIAL MODEL 

Parameter Description 

E11T Strain at longitudinal tensile strength 

E11C Strain at longitudinal compressive strength 

E22T Strain at transverse tensile strength 

E22C Strain at transverse compressive strength 

GMS Strain at in-plane shear strength 

XT Longitudinal tensile strength 

XC Longitudinal compressive strength 

YT Transverse tensile strength 

YC Transverse compressive strength 

SC Shear strength 
NASA/CR—2013-215450 82 
NASA/CR—2013-215450 83 

In compression, the full-field strain data show that the composite behaved as a homogenous material. 

Unlike tensile tests, there were no areas of high and low strain, but rather a uniform strain field was 

present in the composite. Knowing this, the LS–DYNA strain at axial compressive strength, E11C, was 

found by observing the strain in an axial compression specimen at failure. The LS–DYNA axial 

compressive strength XC was found by recording the ultimate compressive strength that occurred at the 

ultimate compressive strain, even after the inelastic deformation, which is represented by the plateau in 

the material response curve. Figure 5.8(a) shows the uniform strain field present in an axial compression 

specimen, as measured by the optical measurement system, and Figure 5.8(b) shows the material 

response, with material parameters used. 

Similarly, for compression in the transverse direction, the composite acted as a homogenous material. 

The LS–DYNA transverse tensile strength YC and strain at transverse compressive strength, E22C, were 

obtained from the material response from a transverse compression test. Figure 5.9(a) shows the uniform 

strain field present in a transverse compression specimen, and Figure 5.9(b) shows the stress-strain 

response from a transverse compression test. 

Finding the transverse tensile values was not as well defined. Since the failure strength input that was 

required was that of an effective unidirectional composite, the transverse tensile strengths could not be 

directly determined by looking at the composite coupon stress-strain because the bias fibers significantly 

contributed to the composite failure strength. Instead a different approach was used. By using the fullfield strain measurement technique and examining the stress that caused the onset of fiber bundle 

splitting, YT was assumed to be this stress. For reference, a discussion on transverse fiber bundle failures 

is presented in Section 4.4.2.2, and states that a fiber bundle split was a result of the matrix cracking, 

causing the fiber bundles to split in their transverse direction, representing a transverse failure of layers in 

the composite. However, the composite failed once the overall composite material response reached its 

failure strain, assumed to be E22T. Between the onset of the splitting in the individual fiber bundles (YT) 

and specimen failure (E22T), damage accumulated in the composite, which was demonstrated by the 

nonlinearities in the overall specimen response curves, shown in Section 4.4.1.1. As each of the individual 

fiber bundles reached their failure stress and split, their load-carrying capability diminished. The load 

from the failed fiber bundles was then distributed to other nonfailed fiber bundles in the specimen. As the 

other fiber bundles begin to carry the extra load from the failed bundles, they, in turn, began to fail. When 

the number of fiber bundle failures reached a critical value the composite specimen then failed at its 

ultimate failure strain, E22T. 
NASA/CR—2013-215450 84 

The transverse failure caused by the fiber bundle splitting was represented in by setting the transverse 

tensile stress limiting parameter (SLIMT2) equal to 1 in the material model. Setting this parameter to 1 

made each individual layer for each of the subcells in the model behave in an elastic-plastic manner in the 

transverse direction. In the elastic region, the fiber bundles carried load until they reached their ultimate 

stress value YT, and split. They then went into a plastic region. The plastic region represented the region 

in which each layer could not carry any more load and simulated the loading on the layer after a fiber 

bundle split occurred in the composite test. It allowed for the overall composite specimen to still carry 

load, even though individual fiber bundles could not. This meant that even though some of the individual 

fiber bundles failed, the overall specimen stress vs. strain material response continued to grow until the 

final strain assumed to be E22T, took place. In the transverse direction, the material response for a single 

layer would be as shown in Figure 5.10. 

Figure 5.11(a) shows the full field strain measurement on a representative transverse coupon, and the 

global coupon stress versus local fiber bundle strain from a transverse tension test. When the transverse 

fiber bundle reached its failure stress, highlighted in Figure 5.11(b), the SLIMT2 parameter controlled the 

layers’ material response until the composite reached its ultimate failure strain. 

The material response curve of the localized area around a fiber bundle split should not be used after 

the fiber bundle split because of distortions in the speckle pattern caused by the split. Even though the 

fiber bundle splits do appear in the composite coupon in a regular fashion, the split itself caused 

discontinuities in the painted pattern, thus rendering it unusable. Accordingly, data obtained after the 

highlighted region in Figure 5.11(a) were not used after the value of YT was obtained. As a result, the 

value of E22T used in the analysis was the value of the transverse composite specimen failure. The value 

for E22T was taken from the overall composite stress-strain response and not from the failure value at the 

first fiber bundle split. The overall composite failure strain in the test specimen was representative of a 

composite coupon failure from the accumulated damage created by the fiber bundle split propagations. 

The overall composite transverse stress versus strain response is shown in Figure 5.12. 
NASA/CR—2013-215450 85 
NASA/CR—2013-215450 86 

Shear parameters were found using shear testing according to ASTM D5379 (Ref. 20). Figure 5.13 

shows the orientation of the unit cell under shear loading. Each of the subcells carried the same shear 

stress, and if the assumption was made that all thicknesses in each layer were the same, each layer for 

each subcell took the same shear stress. Knowing this, the shear data measured from the test were directly 

implemented into the model as unidirectional layer material parameters. A representative shear stress 

versus strain response is shown in Figure 5.14. 

5.4 Finite Element Model Implementation for Prediction of Static Tests 

The modeling approach described in the previous section was developed into an LS–DYNA finiteelement model. Four shell elements, each having the dimensions of one subcell, were used as the basis for 

the finite-element model mesh. From this generic finite-element model, appropriate specimen geometries 

were created by using repeated patterns of the four-subcell layout. 

To check the validity of the braided modeling approach used for analysis, two static finite-element 

models were created in LS–DYNA, one simulating an axial tensile test, and the other simulating a 

transverse tensile test. Both geometries were based on ASTM 3039 geometries. Figure 5.15 shows the 

geometries. 

The fixed end in the model was constrained in all three displacement and rotation directions. The 

loading was applied at a constant velocity 0.635 mm/s (0.025 in./s), which was consistent with the test 

conditions. The red elements represent subcell A, the blue elements represent subcell B, the green 

elements represent subcell C, and the yellow elements represent subcell D. The unit cell orientations for 

both of the modeling conditions are highlighted for reference. In the axial test conditions the unit cell was 

oriented perpendicular to the direction of applied loading, which oriented the axial layers parallel to the 

direction of loading. In the transverse test conditions, the unit cell was oriented parallel to the direction of 

applied loading, which oriented the axial layers perpendicular to the direction of loading. These 

orientations were consistent with the test conditions. 
NASA/CR—2013-215450 87 

Axial and transverse tensile tests were simulated in LS–DYNA and overall stress versus strain 

material response plots were output for each test. The stress-strain plots for the LS–DYNA simulations 

were compared against the experimental stress-strain curves obtained as discussed in Section 4.0. The 

next two sections divide up the two material systems tested: Section 5.4.1 discusses results obtained from 

the T700/PR520 material system, and Section 5.4.2 discusses results obtained from the T700/E862 

material system. 

5.4.1 T700/PR520 Fiber/Resin Material Response 

Simulations were run using the data from the T700/PR520 material test as inputs in the finite-element 

model. Table 5.2 shows the parameters and values obtained from the developed method and used in the 

material model. 

Figure 5.16 shows material response curve comparisons of a sample axial test and LS–DYNA 

simulations, which show good agreement. Table 5.3 compares the results of the LS–DYNA simulation 

and average test results. 
NASA/CR—2013-215450 88 

TABLE 5.2.—T700/PR520 FIBER/RESIN MATERIAL 

PARAMETERS USED FOR LS–DYNA MODEL 

Material parameter (LS–DYNA name) Value 

Axial modulus (EA), GPa ................................................................. 51.3 

Transverse modulus (EB), GPa ......................................................... 25.0 

In-plane shear modulus (GAB), GPa ................................................ 19.0 

In-plane Poisson’s ratio (PRBA) ..................................................... 0.071 

Axial tensile failure strain (E11T)................................................. 0.0216 

Axial compressive failure strain (E11C) ......................................... 0.018 

Transverse tensile failure strain (E22T) ........................................ 0.0168 

Transverse compressive failure strain (E22C) ................................ 0.011 

In-plane shear failure strain (GMS) ................................................ 0.012 

Axial tensile stress at failure (XT), MPa .......................................... 1045 

Axial compressive stress at failure (XC), MPa ............................... 377.1 

Transverse tensile stress at failure (YT), MPa ................................... 362 

Transverse compressive stress at failure (YC), MPa.......................... 345 

In-plane shear stress at failure (SC), MPa ....................................... 307.3 

Stress-limiting parameter for axial tension (SLIMT1) ........................... 0 

Stress-limiting parameter for transverse tension (SLIMT2) ................... 1 

Stress-limiting parameter for axial compression (SLIMC1) .................. 0 

Stress-limiting parameter for transverse compression (SLIMC2) .......... 0 

Stress-limiting parameter for shear (SLIMS) ......................................... 0 

TABLE 5.3.—COMPARISON OF T700/PR520 FIBER/RESIN 

TEST AND LS–DYNA SIMULATION 

AXIAL TENSION DATA

 Axial tensile propertya 

Strength, 

MPa 

Modulus, 

MPa 

Test 1050±34 4.7104

±1.1103

LS–DYNA 903 5.1104

Error, percent 12 7

a

Values are shown as an average with ±1 standard deviation. 
NASA/CR—2013-215450 89 

The axial test results show that the material modulus for the simulation correlates well with the 

material modulus for the test; however, the strength obtained with the simulation was low compared to 

the test data. One reason for this discrepancy is that the value chosen for axial strength (XT) was only 

based on the axial fibers, which is consistent with the assumptions used, and did not take into account the 

bias fibers. Modifying these assumptions to include the bias layers may have brought the strength to more 

closely match the test data. Another reason is that the material model used in LS–DYNA was a continuum 

damage model. Damage could have been occurring in the axial layers leading to a reduced strength in 

these layers not shown by the test data. Also, interactions between each layer could have been causing 

localized stress concentrations in the LS–DYNA model that may be not present in the test. However, the 

model’s results show good agreement with the test data in that both response curves show linear behavior 

until failure. 

Figure 5.17 shows the results in the transverse direction. The transverse results also showed good 

correlation between the test results and the simulation. Table 5.4 shows the comparisons. 

The simulations captured the nonlinearities due to damage accumulation in the composite usually 

encountered with transverse testing. However, the strength values for the simulation were higher than the 

test. This could have been due in part to the value picked for the transverse strength of the fiber bundle 

split. More detailed investigations are needed to determine if the first fiber bundle split should be used for 

the analysis, or if a median value of stress based on the number of fiber bundle splits should be used. 

TABLE 5.4.—COMPARISON OF T700/PR520 FIBER/RESIN 

TEST AND LS–DYNA SIMULATION 

TRANSVERSE TENSION DATA 

 Transverse tensile propertya 

Strength, 

MPa 

Modulus, 

MPa 

Test 8.69104

±4.3102 4.3104±1.6103

LS–DYNA 647 3.9104

Error, percent 8 9 

a

Values are shown as an average with ±1 standard deviation. 
NASA/CR—2013-215450 90 

5.4.2 T700/E862 Fiber/Resin Material Response 

Simulations also were run using the data from the T700/E862 tests. Table 5.5 shows the parameters 

used in the material model, and Table 5.6 shows the result comparisons between the tests and simulations. 

Figure 5.18 shows the material response curves for both the LS–DYNA simulation and an example 

axial tension test. Good agreement is seen between the simulations and test data. However, one can see 

that the nonlinearities occurred in the test data, particularly at higher strains. These nonlinearities may 

have been caused by the delaminations occurring in the composite at higher strains, as discussed in 

Section 4.4.2.3, “Examination of Subsurface Delaminations.” However, because of the limitations in the 

shell element model formulation, the computer model cannot currently simulate a delamination failure 

mechanism. However, using the failure data that was obtained from the testing, the model and test data 

did agree within 10 percent for both the modulus and ultimate strength. 

Figure 5.19 shows the transverse material response curves, and Table 5.7 presents a comparison of 

the data. 

TABLE 5.5.—T700/E862 FIBER/RESIN MATERIAL 

PARAMETERS USED FOR LS–DYNA MODEL 

Material parameter name (LS–DYNA name) Value 

Axial modulus (EA), GPa ................................................................. 51.3 

Transverse modulus (EB), GPa ......................................................... 25.0 

In-plane shear modulus (GAB), GPa ................................................ 19.0 

In-plane Poisson’s ratio (PRBA) ..................................................... 0.071 

Axial tensile failure strain (E11T)................................................. 0.0178 

Axial compressive failure strain (E11C) ....................................... 0.0058 

Transverse tensile failure strain (E22T) ........................................ 0.0144 

Transverse compressive failure strain (E22C) .............................. 0.0086 

In-plane shear failure strain (GMS) .............................................. 0.0095 

Axial tensile stress at failure (XT), MPa ......................................... 809.4 

Axial compressive stress at failure (XC), MPa .................................. 320 

Transverse tensile stress at failure (YT), MPa ................................... 196 

Transverse compressive stress at failure (YC), MPa.......................... 303 

In-plane shear stress at failure (SC), MPa .......................................... 257 

Stress-limiting parameter for axial tension (SLIMT1) ........................... 0 

Stress-limiting parameter for transverse tension (SLIMT2) ................... 1 

Stress-limiting parameter for axial compression (SLIMC1) .................. 0 

Stress-limiting parameter for transverse compression (SLIMC2) .......... 0 

Stress-limiting parameter for shear (SLIMS) ......................................... 0 

TABLE 5.6.—COMPARISON OF T700/E862 FIBER/RESIN 

TEST AND LS–DYNA SIMULATION 

AXIAL TENSION DATA 

 Axial tensile propertya 

Strength, 

MPa 

Modulus, 

MPa 

Test 807±25 4.7105

±1.6103

LS–DYNA 5.19 5.1104

Error, percent 6.8 8.8 

a

Values are shown as an average with ±1 standard deviation. 
NASA/CR—2013-215450 91 

Because of the large amount of scatter in the strength test data, the average error was over 10 percent; 

however, if the highest value of strength obtained from testing was used in the comparison, the error was 

10 percent. As with the T700/PR520 material system, the transverse strength was again overpredicted by 

the computer simulation. This data suggested that the value used for the transverse fiber bundle strength 

was again picked too high. This may have been due in part to the fact that fiber bundle splits could have 

been occurring within the composite, and therefore were not visible to the measurement system before the 

fiber bundle splits appeared on the surface. However, as with the tension data, the cumulative error 

between the tests and simulations was within 10 percent. 

TABLE 5.7—COMPARISON OF T700/E862 FIBER/RESIN 

TEST AND LS–DYNA SIMULATION 

TRANSVERSE TENSION DATA

 Transverse tensile propertya 

Strength,

MPa 

Modulus,

MPa 

Test 460±36.3 4.1104

±1.3103

LS–DYNA 7.7104

 3.9104

Error, percent 14 6.6

a

Values are shown as an average with ±1 standard deviation. 
NASA/CR—2013-215450 92 

5.5 Conclusions 

This section shows the development of a macromechanical computer model used for the prediction of 

composite material response. The macromechanical model includes aspects from the composite braid 

geometry as well as the material property data from test composite materials. Axial and transverse tensile 

tests have been simulated on two example fiber/resin material systems, T700/E862 and T700/PR520, with 

stress-strain curves presented. The macromechanical composite computer model predicts the tensile 

response of the materials to within 10 percent accuracy. 

6.0 Triaxial Braided Composite Impact Simulations 

As described in Section 1.0, “Introduction,” the composite materials presented in this research are 

primarily going to be used in impact situations, in which the impact resistance of these materials must be 

known and quantified. This chapter presents preliminary investigations that use the developed composite 

computer models for impact simulations for the detection and prediction of impact velocity thresholds and 

failure depictions. Two fiber/resin material systems, which have been extensively investigated in earlier 

chapters, are going to be used for impact simulations: T700/E862 and T700/PR520. This section will 

discuss the test setup, composite impact geometry of the finite-element model, the material properties 

used, and also the rationale for conducting simulations with a soft projectile. It will also show preliminary 

results for the two material systems and compare to the test data, when available. 

6.1 Background 

The following sections present background information on the triaxial braided composite testing 

approach and the LS–DYNA finite-element software utilized in this study. 

6.1.1 Material Testing 

There has been ongoing research at the NASA Glenn Research Center to efficiently screen different 

triaxially braided composite material systems for use in containment applications. The screening process 

involves impacting a triaxially braided composite plate with a soft projectile made of gelatin from a gas 

gun in the ballistic velocity regime. Gelatin was picked as the projectile because it was an efficient way of 

transferring a maximum amount of its kinetic energy into strain energy in the composite panel. This 

process was an effective way in determining the composite material’s threshold velocity, which is the 

lowest velocity at which the projectile penetrated the composite panel. Penetration was established when 

the gelatin could be seen exiting the back of the composite panel. 

The screening process has been partially completed on the four fiber/resin material systems examined 

and presented earlier: T700/E862, T700/PR520, T700/5208, and T700/3502. However, only the top two 

performing material systems, T700/E862 and T700/PR520, will be examined in this section to compare 

threshold velocities and examine differences in material response. 

6.1.2 LS–DYNA Introduction 

In order to conduct impact simulations for the above-mentioned materials, a commercial finiteelement code, LS–DYNA, was utilized. A detailed explanation of LS–DYNA can be found in Reference 

73, but a brief summary is presented here for completeness. 

LS–DYNA is a commercially available nonlinear transient explicit finite-element code commonly 

used in impact and crashworthiness applications by the automotive and aerospace industries. The main 

solver in LS–DYNA uses a central difference explicit time integration to solve transient dynamic impact 

problems. LS–DYNA has a large material library (>150 material models), much of which is based on 

constitutive laws developed by researchers, and a robust set of contact laws to handle complex 

interactions between objects. It is capable of computing traditional structural impact problems in 

Lagrangian space (used in Sec. 5.0, “Development of Macromechanical Triaxial Braided Composite 
NASA/CR—2013-215450 93 

Computer Model”), in which the finite-element mesh is fixed to and deforms with the structures, but 

LS–DYNA also has features which allow it to solve fluid-structure interaction problems (e.g., a structure 

landing in water) using a combination arbitrary Lagrangian-Eulerian (ALE) meshing technique. The ALE 

technique will be utilized in the computer models presented for the composite impact problems. In the 

ALE space, the fluid material (representing the gelatin) is allowed to flow freely and is remapped within 

the mesh at each time step. Thus, the material exhibits large deformations within the mesh without 

causing extreme deformations within the elements or time step. 

6.2 Finite Element Model Development 

The composite impact finite-element model used the same material and section properties that have 

been described in Section 5.0, a 0.6-m by 0.6-m by 3.18-mm (2-ft by 2-ft by 0.125-in.) panel geometry. 

Figure 6.1 shows the geometry of the composite subcell model. The alternating patterns of pink, blue, 

green, and yellow represent the four subcells used to simulate the composite braid geometry. To simulate 

the test conditions in an impact test, the four sides of the panel were constrained in all three displacement 

and all three rotation directions. 

Fundamental studies on gelatin impacts were originally done by Wilbeck (Ref. 74). Wilbeck 

showed that the gelatin material exhibited extreme deformation at the velocities under investigation. For 

LS–DYNA implementation, because the gelatin was a low-strength, low-stiffness, and high-flow 

material, it was modeled using a null formulation in which its pressure-volume relation, which simulated 

the shock wave throughout the gelatin at impact, was modeled using an equation of state relationship. A 

propriety set of material parameters were used for the gelatin in this study. The gelatin was given an 

initial velocity (representing the impact velocity from the test), and the run time was set to 210–3 s, with 

output results written at 510–5 s. The finite element model consisted of a total of 243 209 nodes, 16 320 

composite shell elements, and 41 040 solid elements for the gelatin formulation. To simulate the contact 

between the gelatin and the composite, the *CONSTRAINED_LAGRANGE_IN_SOLID contact card 

was used. The model was run on a single precision version of LS–DYNA 971. Figure 6.2 shows the 

LS–DYNA model compared to the test setup. 
NASA/CR—2013-215450 94 

Testing was done at the NASA Glenn Research Center Impact Ballistic Lab by NASA personnel and 

is described in Reference 3. In the test setup, a composite panel was fixed into a steel frame normal to the 

end of the gas gun barrel. The gelatin was placed in the gun barrel such that the longitudinal axis of the 

gelatin projectile was in the direction of flight, and the flat end made contact with the composite panel. 

Calibrated high-speed cameras were used to track and measure the gelatin’s position and velocity before 

impact. This velocity measurement was the number used when determining an impact threshold velocity, 

and also when correlating simulation speeds to test speeds. The optical measurement system was also 

used on the nonimpacting side of a subset of the composite panels tested. The optical measurement 

system measured maximum out-of-plane deflection as well as axial and transverse surface strains on the 

panel. These measurements, along with the failure patterns were the main parameters compared to the 

simulations. 

6.3 Simulation Results 

The penetration threshold for the simulations of the material system was determined by examining the 

lowest velocity causing element failure in the model. Element failure occurred when all of the integration 

points in the element (representing each of the different fiber layers) failed. However, if only a partial 

number of the layers failed, the element remained in the model. These partially failed elements contained 

a reduced modulus because the failed layers did not contribute to the overall stiffness in the element. 

For T700/E862, the lowest velocity that caused element failure, and thus was the penetration 

threshold, was 143 m/s (470 ft/s). Figure 6.3 depicts these results with part (a) showing containment at 

(140 m/s) 460 ft/s and part (b) showing results from a 143 m/s impact velocity, which depicts penetration. 

A pressure wave can be seen in both parts of Figure 6.3. Figure 6.3(b), shows element failure. The 

failure depicted shows that the composite panel opened both along the axial fiber direction (global y in 

the figure) and transversely to the axial fiber direction (global x in the figure). This failure depicts the 

composite behaving more as a quasi-isotropic material, which was primarily caused by the inclusion of 

the fiber shifting phenomena into the model. However, the failure data cannot be validated because, at the 

time of this writing, no test data exists at the penetration threshold of this particular material system. 

At the time of this writing, the only two test data points available for T700/E862 were at 141 m/s 

(463 ft/s) and at a much higher 226 m/s (741 ft/s). The T700/E862 test data showed containment when 

tested at 141 m/s and showed penetration for 226 m/s. The LS–DYNA results fell within this band and 

agreed with these results. The LS–DYNA was also run at 226 m/s to compare the failure results. 
NASA/CR—2013-215450 95 

Figure 6.4 compares the failures of the T700/E862 composite panel at 226 m/s. Note that the test 

picture presented is at a 45° off-axis angle to the rear of the panel. The simulation picture in Figure 6.4(b) 

has attempted to emulate this view. The test data shows a penetration by hole in the middle of the panel 

(circled). This hole was also present in the computer simulation, which can be seen in Figure 6.4(b), 

which mimicked the failure in Figure 6.3(b). 

Similarly, the LS–DYNA models were run for T700/PR520. Two data points were available from the 

testing of the T700/PR520 composite panels; the first test showed containment below threshold at 186 m/s 

(609 ft/s), and the second test showed penetration at 194 m/s (637 ft/s). The computer model predicted a 
NASA/CR—2013-215450 96 

penetration velocity threshold of 192 m/s (630 ft/s), which agreed well with the test data. Since the optical 

measurement system was also used on the impacted panels, items such as maximum out-of-plane deflection 

and axial and transverse strains at failure were compared between the test data and simulation. 

Comparisons were first done for the velocity of 186 m/s, which was below the penetration threshold. 

The simulation predicted a maximum out-of-plane deflection of 4 cm (1.57 in.) in the middle of the panel, 

whereas the test data obtained from the optical measurement system showed that the actual deflection was 

4.3 cm (1.68 in.). The axial strains in the middle of the panel were compared next. The maximum values 

obtained from the test data were 1.67 and 1.49 percent for the global axial and transverse strains, 

respectively. The simulation showed that the maximum axial strain value was 1.74 percent and the 

transverse strain value was 1.75 percent. 

Figure 6.5 shows the comparisons between the test and simulation at the time in which the maximum 

axial strain occurred. Both images show very low far-field strain. The simulation accurately reflects the 

concentration seen in the impact location. The next item to note is that both pictures show a concentrated 

area of high strain in the middle of the panel, which is in the impact location. One difference between the 

pictures is that whereas the test data show concentric circles of gradually increasing strain, the simulation 

shows a small oval of concentrated strain in the center. This difference could be attributed to one main 

reason: the resolution on the test data is not great enough to capture the highly localized areas of strain 

seen in the simulation because of the limitations in camera speed resolution. However, for the results on 

maximum out-of-plane deflection and axial and transverse strains, there were good correlations between 

the test data and simulation results. 

Next, comparisons were done between the test and simulation data above the penetration velocity 

threshold. The simulation was run with the gelatin projectile having a velocity of 194 m/s to match with 

the test, and only comparisons in the failure shapes were done. Items such as failure strain and maximum 

out-of-plane deflection were not able to be compared because of the removal of the elements for the 

simulation and distortions of the dot pattern for the test in the regions in question. Figure 6.6 compares 

the failures shape of the composite panels. 
NASA/CR—2013-215450 97 

Examining the test data, the initiation of the failure occurred in the middle of the panel. The failure 

propagated in the vertical direction, parallel to the axial fibers, and the panel failed when the propagation 

reached the boundaries. This failure showed the panel “unzipping,” or transversely failing, along the axial 

fiber direction. The simulation results match both the initiation and propagation of the failure, but differed 

in the final failed picture. In the simulation, the failure initiated in the middle of the panel. It then 

progressed in the vertical direction, parallel to the axial fibers; however, by the time the panel failure 

occurred, there were both axial and transverse failures. The axial failures occurred in the horizontal 

direction to the left and right of the middle of the panel, and caused the final “diamond” shape to occur in 

the failed panel. 

Limited examinations were able to be conducted on some of the failed elements in the model. The 

time history of the axial strain was further examined for the first failed element in the middle of the panel. 

Figure 6.7 shows the axial strain time history for an element in the middle of the composite model. 

Notice that the failure occurs when the E11T parameter is reached. Since the failure occurred between the 

two points in which the output results were written (between 5.010–4 and 5.510–4 s), the result can be 

assumed to be between the two. Since the SLIMT1 parameter is set to 0 in the model, the element 

immediately fails and the load-carrying capacity of the element goes to 0. 
NASA/CR—2013-215450 98 

Both of the material systems examined in this research show failures different from what was 

reported by Cheng (Ref. 67). Cheng saw a “barn door” failure, which was represented by a transverse 

failure occurring in the middle of impacted region, with failures in the bias fiber direction leading toward 

the sides of the panel. The differences in failure modes can be attributed to a variety of factors, with the 

main one being that the fiber shifting was employed in this composite model to account for the real 

composite layups seen in the digital microscopic imaging, as shown in Sections 4.0 and 5.0. The fiber 

shifting made the composite material behave as a quasi-isotropic material much more than by stacking 

layers of subcells on top of each other. Another main difference is that Cheng examined different material 

systems than the ones examined for this study, which could affect the panel’s material responses greatly. 

Finally, whereas measured material properties are used in this model development, Cheng employed 

classical mechanics of composite materials models to obtain the effective unidirectional properties for the 

model, which may have led to some inaccuracies in material property determination. 

6.4 Conclusions 

Conclusions drawn from the impact simulations presented in this chapter are limited because of the 

lack of test data for the materials. Using the measured material properties for the static models originally 

presented in Section 5.0, simulations were conducted on the two highest strength material systems under 

impact loading. The results show that for the T700/E862 fiber/resin material system, the threshold 

velocities and failure depictions for the simulations did agree with the test data that were available. 

Because there was a defined threshold for the T700/PR520 material system, more extensive 

investigations were conducted. The T700/PR520 simulation predicted a penetration threshold of 192 m/s 

(630 ft/s), which was in good agreement with the 194 m/s (637 ft/s) penetration threshold measured in 

testing. When examining the out-of-plane displacement and strains for the simulation below the 

penetration threshold, results also matched up well with the test data. Finally, when comparing the failure 

surface above threshold, the simulation predicted the initiation and propagation well, but did not match 

the final failed shape.
NASA/CR—2013-215450 99 

7.0 Concluding Remarks 

The research presented in this report presents investigations into the nature of triaxial braided 

composite material response and composite constituent response with implementations into finite-element 

computer models for simulation. 

7.1 Summary of Results 

The work is summarized here to remind the reader of the important points demonstrated throughout 

the research. 

Section 3.0, “Investigations Into Composite Constituent Material Response,” proposed a unique way 

to measure the mechanical response of matrix materials used in triaxial braided composites with an 

optical measurement system using unique, nonstandard specimen geometries. Utilizing the test method 

presented, tension, compression, and shear results for pure load-to-failure and load-unload-reload tests 

were obtained on an example material for a variety of strain rates and temperatures. The results showed 

that the resin is both rate and temperature dependent for all of the loading conditions. The results also 

show the effects of hydrostatic stress when examining the differences between the tensile and 

compressive results as well as a damage accumulation, represented by a reduced modulus on the 

unloading portion of the load-unload curve. The results obtained were important because many resin 

constitutive models in development need all of the data acquired in this report, but also provide a first 

insight to the rate and temperature dependence of the material. 

In Section 4.0, “Investigations of Triaxial Braided Composite Material Response,” the material 

properties for four example composite material systems were determined. As with the resin testing, 

optical measurement techniques were used to measure the triaxial braided composite material response. 

By using this method, the nature of each different material system’s microscale and macroscale behavior 

was categorized and quantified. The optical measurement technique was able to obtain global stress 

versus strain material response curves, and also able to identify local failure mechanisms present within 

the different composite material systems, which led to the differences in the global material response 

curves. The results led to the conclusion that there were different damage mechanisms affecting the 

material properties. 

For the composite testing in the axial tensile direction, the load transfer between the loaded axial 

fibers and bias fibers accounted for the surface bias fiber bundle splits that occurred and were captured by 

the optical measurement system. The fiber bundle splits in the bias fibers caused strain concentrations in 

the axial fiber bundles, which led to the axial fibers failing prematurely, causing a reduced strength in the 

material. Also, the results showed that the nonlinearities seen in the global axial material response curves 

were a result of damage in the form of subsurface delaminations, which were previously very difficult to 

be measured in situ. 

In the transverse tensile direction, since there were no continuous fibers extending throughout the 

entire gage section, the resin played a major role in the material response. The main damage-causing 

mechanism was the fiber bundle splitting that occurred in the axial fibers. Failure in the transverse tests 

was a result of edge delaminations that occurred and quickly propagated along the bias fibers. 

All of the characteristics described above led to the ultimate failure in the composite specimens; 

however, the results indicate that differences in the fiber-matrix interface properties allowed for the 

specimens to fail at different strain levels. The data show that the T700/PR520 fiber/resin material system 

had the strongest interface, and the T700/3502 system had the weakest interface. 

In compression, the stronger two material systems exhibited inelastic behavior prior to failure. This 

inelastic behavior occurred because the fiber-matrix interface was sufficiently strong enough to hinder the 

microbuckling phenomena. The two weaker material systems exhibited microbuckling, which occurred 

because the weak fiber-matrix interface was not strong enough to hold the fiber bundles together under 

the compressive loading. 
NASA/CR—2013-215450 100 

Shear testing showed that a modified ASTM specimen design was viable for use in the collection of 

shear data. The modified specimen design allowed for a uniform region of high strain in the gage section 

and between the grips. Under shear loading, specimens did not exhibit fiber bundle splitting or other 

microscopic failures; rather, the specimens failed catastrophically when the ultimate strain was reached. 

Along with being an integral tool in determining and quantifying material response properties for the 

composite material systems investigated, the data obtained from the optical measurement system were 

also used for developing a finite-element-based analytical model to simulate the responses of the triaxial 

braided composites. 

In Sections 5.0, “Development of Macromechanical Triaxial Braided Composite Computer Model,” 

and 6.0, “Triaxial Braided Composite Impact Simulations,” a triaxially braided finite-element-based 

analytical computer model was created and utilized to simulate the static and impact response of 

composite coupons and panels. The computer model simulates the braid geometry by dividing the unit 

cell into four subcells and stacking the layers of braid using a novel through-thickness integration 

technique. The properties needed for the material model were obtained from the coupon tests performed 

using the optical measurement data and classical composite micromechanics techniques. The created 

computer model predicted strength and stiffness to within 10 percent error for the static tests and 

predicted a ballistic penetration threshold consistent with data available from impact tests. 

Generalizing, the work presented can provide a more fundamental understanding of braided 

composite materials. The nature of the resin matrix testing allows for insight into the main rate-dependent 

behavior of the composite materials, while also giving preliminary predictions about strength and stiffness 

in the finished composite material system. Secondly, by using both the constituent and composite test data 

acquired, a greater understanding of the role of the resin, interface, and fiber properties can be gained. 

Finally, by collecting all of the data from the composite and resin matrix, computer models can ultimately 

be developed that can give a more accurate prediction on static and impact strength by including the rate 

dependence of the resin while also using some of the microscopic failure parameters seen in the finished 

composites. 

Even though the scope of this work is limited to one material for the constitutive testing and four 

material systems for the composite testing, the methods described can be used on any type of fiber or 

matrix for use in other triaxial braided composite material systems. The methods developed can be used 

on a wide range of material systems to determine the composite constituent properties, the composite 

macroscopic response material response, and also microscopic failure properties that affect the 

macroscopic response. 

Finally, the computer model and method for implementation of the composite properties can be 

generalized to include any number of fiber layers, any fiber angle, and thicknesses with relative ease 

without changing the methodology developed. 

7.2 Future Work 

The methods and data presented in this work provide a fundamental basis for understanding the 

behavior of triaxial braided carbon fiber composites. However, this work is not a conclusive end to an 

understanding in these materials. The reader is reminded that work is ongoing and must still be done to 

fully understand the complex nature of these materials. 

7.2.1 Constituent Testing 

The test method described in Section 3.0 describes an efficient method for testing the composite 

matrix constituent under a variety of loading rates and temperatures. Example results have been presented 

on one example matrix material, Epon 862 resin (Momentive Specialty Chemicals, Inc.). However, for 

composite materials made with other matrix materials, other materials must be tested as well. There is 

work in progress as of this writing to use the test method on a second composite matrix material of 

interest, Hexcel’s 3502. 
NASA/CR—2013-215450 101 

7.2.2 Composite Testing 

Although the work presented in Section 4.0 gives insights into the nature of composite material 

response, future work can expand on these issues. For example, only rectangular ASTM 3039 specimens 

were used for the testing in this report. The results in Section 4.4.2.2 showed that areas of low strain 

occurred on the edges of the transverse specimens, indicating that these edge areas did not contribute 

significantly to the overall composite material response. Alternative specimen designs should be 

investigated to remedy this problem. One idea would be to use a notched specimen in which continuous 

bias fibers extend throughout the entire gage section. Bowman, et al. (Ref. 63) have briefly investigated 

this problem by proposing notched “bowtie” specimens and have presented material response curves on 

similar materials; however, the optical measurement technique to collect the strain data was not used so 

full-field results were not available. Also, a braided tubular specimen design that has no terminating fibers 

in its gage section would be an ideal specimen design, although the complexity in the fabrication of this 

specimen design makes it the most undesirable to manufacture. 

Next, the work in this research presents fabricated composite panels having a thickness of 3.18 mm 

(0.125 in.) and six layers of the braided preform through the thickness. In order to investigate failure 

mechanisms such as fiber bundle splitting and fiber-resin matrix interaction, tests could also be done on 

one layer of fabricated braid, such that interactions between the braided preform layers are removed. 

Also, testing one layer of braid will validate assumptions made in the composite modeling section. 

Also, only in-plane testing (tensile, compression, and shear) was done for the materials studied. 

However, when composite materials undergo impact loading, out-of-plane deformation is generally the 

main item of interest. Knowing this, out-of-plane testing such as three-point-bending tests (e.g., ASTM 

D2234 (Ref. 75)) should be examined to see if items such as failure strain and transverse fiber bundle 

failures can be examined. 

Finally, as the test method and analysis technique presented quantifies composites mainly under static 

loading with limited implementations into the dynamic regime, ballistic impact testing using full-field 

optical measurement techniques must be performed to gain insight into the nature of items such as 

transverse fiber bundle failure and other mechanisms occurring in the ballistic range. Once ballistic 

testing has been completed on a variety of materials under a variety of test conditions, the finite-element 

models can be modified using the ballistic data to better predict impact response. 

7.2.3 Composite Modeling 

The analytical approach to composite modeling is a first step in trying to develop a macromechanical 

composite finite-element model using composite test data. Once some of the above tests have been 

completed, the finite-element model can be adjusted to incorporate the new test data. Also, although the 

finite element model uses data such as transverse fiber bundle failures, when looking at the composite 

material response simulations, the fiber bundle splits do not appear because of the nature of the large 

mesh size. Also, fiber bundle layer delaminations were examined in both the axial and transverse tensile 

tests; however, the model cannot predict the delaminations, because shell elements cannot predict items 

such as transverse shear failures. However, the shell element model can be expanded to include either an 

explicit interface layer (with its own material properties, which must be found using a combination of the 

above-mentioned tests) or use some more advanced techniques to determine if integration layers in the 

model can be adjusted to include delaminations. One potential mechanism that has been investigated by 

Tabiei (Ref. 76, LS–DYNA Composite Materials Training Course) is to use a 

*CONTACT_TIEBREAK_... LS-DYNA parameter to simulate the delaminations between layers. 

However, as of this writing, the *CONTACT_TIEBREAK command in LS–DYNA can only be used 

between stacked shell elements and not between integration layers. 

Finally, investigations must be done to examine the differences between the failure shapes for the 

impact simulations. While the numbers used in the material model for simulation lead to good correlation 

between the tests and simulations, they may need to be adjusted to incorporate the impact data. Because 
NASA/CR—2013-215450 102 

the finished composite material will be rate dependent, as shown with the resin data, some of the numbers 

gained from the static testing used may be deficient for the implementation into the impact regime. 

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4. TITLE AND SUBTITLE

Experimental and Analytical Characterization of the Macromechanical Response for Triaxial 

Braided Composite Materials 

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Littell, Justin, D. 

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14. ABSTRACT

New aircraft engines are being developed that use fan cases made of composite materials instead of metallic materials. Triaxially braided 

composites are one system under investigation as a possible replacement candidate; however, the impact properties for these materials have 

not been fully determined, and computationally efficient computer models are not available. The research reported herein attempts to bridge 

these deficiencies by addressing the mechanical response of triaxial braided composite materials and their constituents. First, new test 

methods are presented for the polymer resin constituent of the composite, accurately quantifying the resin under a variety of strain rates and 

temperature for three loading conditions. The tests use novel specimen designs along with a noncontact measuring system capable of 

identifying and quantifying many of the microscale failure mechanisms present in the materials. These methods are then extended to the 

composite material test specimens. The results for the composites reveal noticeable differences in strength, failure strain, and stiffness for 

the different material systems presented. Investigations into the microscale failure mechanisms provide information about the nature of the 

different material system behaviors. Finally, using the data gathered, a hybrid micro-macromechanical computer model is created to 

simulate the behavior of these composite material systems under static and ballistic impact loading using the test data acquired. The model 

predicts composite static strength and stiffness to within 10 percent of the gathered test data and also agrees with composite impact data. 

15. SUBJECT TERMS

Photographic measurement; Composite materials; Static tests; Computer simulations 

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