Christos C. Chamis

Glenn Research Center, Cleveland, Ohio

Levon Minnetyan

Clarkson University, Potsdam, New York

Micro-Energy Rates for Damage Tolerance

and Durability of Composite Structures

NASA/TM—2006-214037

January 2006
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Christos C. Chamis

Glenn Research Center, Cleveland, Ohio

Levon Minnetyan

Clarkson University, Potsdam, New York

Micro-Energy Rates for Damage Tolerance

and Durability of Composite Structures

NASA/TM—2006-214037

January 2006

National Aeronautics and

Space Administration

Glenn Research Center

Prepared for the

16th European Conference on Fracture

cosponsored by ASTM, JSEM, SMS, BSSM, AIAS, SEM, and EURASEM

Alexandroupolis, Greece, July 3–7, 2006
Available from

NASA Center for Aerospace Information

7121 Standard Drive

Hanover, MD 21076

National Technical Information Service

5285 Port Royal Road

Springfield, VA 22100

Available electronically at http://gltrs.grc.nasa.gov

This work was sponsored by the Fundamental Aeronautics

Program at the NASA Glenn Research Center.
NASA/TM—2006-214037 1

Micro-Energy Rates for Damage Tolerance and 

Durability of Composite Structures 

Christos C. Chamis 

National Aeronautics and Space Administration 

Glenn Research Center 

Cleveland, Ohio 44135 

Levon Minnetyan 

Clarkson University 

Department of Civil Engineering 

Potsdam, New York 13699 

Abstract 

In this paper, the adhesive bond strength of lap-jointed graphite/aluminum composites is examined by 

computational simulation. Computed micro-stress level energy release rates are used to identify the damage 

mechanisms associated with the corresponding acoustic emission (AE) signals. Computed damage regions 

are similarly correlated with ultrasonically scanned damage regions. Results show that computational 

simulation can be used with suitable NDE methods for credible in-service monitoring of composites. 

Introduction 

For effective structural health monitoring, it is important to quantify damage tolerance of a candidate 

structure. Since continuous fiber composites are able to arrest cracks and prevent self-similar crack 

propagation, composite structures have received a great deal of consideration for design with emphasis on 

damage tolerance. However, a number of design parameters such as fiber orientation patterns, choices of 

constituent material combinations, ply drops and hybridization, result in complex design options for 

composite structures. Thus, it is necessary to evaluate damage initiation in a composite structure and its 

fracture propagation characteristics for achieving a rational damage tolerant design. 

Compared with homogeneous materials, damage initiation and progression characteristics of fiber 

composites are much more complicated. Composite structures often contain some pre-existing or induced 

flaws in matrix and fibers after fabrication of composites. At lower stresses, matrix is likely to be cracked 

because of flaw-induced stress concentrations and cause the matrix flaws to propagate across the 

composite. With the use of established material modeling and finite element models, and considering the 

influence of local defects, through-the-thickness cracks and residual stresses, computational simulations 

have made it possible to evaluate the details of progressive damage and fracture in composite structures. 

In a computational simulation, damage evolution quantifier such as the damage volume, exhausted 

damage energy, and the damage energy release rate (DERR) are used to quantify the structural damage 

tolerance at different stages of degradation. Low DERR levels usually indicate that degradation takes 

place with minor resistance by the structure. Structural resistance to damage propagation is often 

dependent on structural geometry and boundary conditions as well as the applied loading and the 

state of stress. 

In certain cases such as the room temperature behavior of composites designed for high-temperature 

applications, internal damage initiated as microcracks in the matrix become enlarged to be externally 
NASA/TM—2006-214037 2

visible. Thus, matrix cracking and its effect on damage propagation/damage tolerance need be evaluated. 

Some simulations (refs. 1 and 2) have been successful in predicting damage tolerance and failure load of 

composite structure by considering ply stresses and the corresponding stress limits for matrix crack 

growth. In this paper, lap-jointed composite specimens subjected to uniaxial tension are investigated. 

Damage initiation, growth, accumulation, and propagation to fracture are studied. Since the complete 

evaluation of ply and subply level damage/fracture processes is the fundamental premise of computational 

simulation, a microstress level damage index is added for the identification and tracking of subply level 

damage processes. Computed damage regions are similarly correlated with ultrasonically scanned damage 

regions. Simulation is validated by comparison with test data from acoustic ultrasonic (AU) testing. 

Results show that computational simulation can be used with suitable NDE methods for credible inservice monitoring of composites. 

Methodology 

Computational simulation is implemented via integrating three modules: (1) composite mechanics, 

(2) finite element analysis, and (3) damage progression tracking. The composite mechanics module 

(ref. 3) is designed to analyze fiber composite structures with an updated composite mechanics theory. Its 

main function is to calculate ply and composite properties of laminates from the fiber and matrix 

constituent characteristics and the composite layup. Additionally, it determines the composite structural 

response and ply stresses from the FEM analysis results. In simulation, the composite mechanics module 

is called before and after each finite element analysis. 

The finite element analysis module is able to process linear and nonlinear static and dynamic analysis. 

Four–node anisotropic thick shell elements are usually used to model laminated composites (ref. 4). The 

finite element analysis module accepts laminate properties from the composite mechanics module and 

performs the structural analysis at each load increment. After structural analysis, the computed 

generalized node stress resultants and deformations are provided to the composite mechanics module. The 

composite mechanics module computes the developed ply stresses for each ply and checks for ply failure 

modes at each node. Failure criteria applied to detect ply failures are based on the maximum stress and 

modified distortion energy (MDE) criteria for combined stress effects (ref. 3). 

The overall evaluation of composite structural durability is carried out in the damage progression 

module (ref. 2) that keeps track of composite degradation for the entire structure. The damage progression 

module relies on the composite mechanics module for composite micromechanics, macromechanics and 

laminate analysis, and calls the finite element analysis module for global structural analysis. If excessive 

damage is detected, the incremental loads are reduced and the analysis is restarted from the previous 

equilibrium stage. Otherwise, if the increment of loads is acceptable, another finite element analysis is 

performed but the constitutive properties and the finite element mesh are updated to account for the 

damage and deformations from the last simulation. Simulation is stopped when global structural fracture 

is predicted. 

Method of Simulation 

The matrix in orthotropic composite plies is divided into two parts: regions A and B. Region A 

represents the area in which stress concentrations induced by the interaction of matrix and fiber do not 

create any effect in matrix. Region B represents the interaction zone between fiber and matrix. Figure 1 

shows the details of regional subdivision in transverse and normal directions of a composite ply with 

square array packing. 
NASA/TM—2006-214037 3

Considering the behavior of longitudinal stress σl11, transverse stress σl22, in-plane shear stress σl12, 

out-of plane shear stress σl23, temperature gradient ΔTl, and moisture Ml, Murthy and Chamis (ref. 3) 

present the complete set of equations for evaluating ply microstresses in regions A and B. For example, 

ply microstresses due to σl11 are given by: 

( )

( )

() () ( ) ( )

() () () ()

22 33 22 33 11

22 33 12 11 11

11 11 11 11

11 11 11

1

l

f

B f

f

B

f

B

m Bm

m l m l l

A

m

A

m

f f l l

m m l l

k

k

v v E E

E E

E E

σ − σ = σ = σ = σ = −

σ = σ = − σ

σ = σ

σ = σ

in which σm11 is the matrix longitudinal stress, σf11 is the fiber longitudinal stress, ( ) A

m22 σ is the matrix 

transverse stress in region A, and ( ) B

m22 σ is the matrix transverse stress in region B. If the ply is subject to 

combined stresses, its microstresses are obtained by simply superimposing results of all corresponding 

stress components. Ply transverse fractures usually begin in region B due to the elevated stress levels 

from stress concentration. Microstress level damage tracking is able to quantify the type of damage in the 

matrix by comparison of microstresses with constituent stress limits. A microstress damage index is 

defined as a binary number with 14 bits in the damage progression module. 

Simulation Results and Discussion 

In this paper, two unidirectional graphite/aluminum composite plates (fig. 2) with single lap joint 

under uniaxial tension are used to demonstrate the use of microstress damage index in computational 

simulation. The specimen has a length of L = 76.2 mm (3 in.), a width of W = 19.05 mm (0.75 in.) and a 
NASA/TM—2006-214037 4

thickness of H = 1.27 mm (0.05 in.). The fiber volume ratio is Vf = 0.60 and the void volume ratio is 

Vv = 0.01. The specimens are bonded with adhesive to produce a bond area of 0.75 by 0.75 in. The first 

adhesive type is an epoxy resin and the other is a graphite/epoxy prepreg tape. The specimen is assumed 

to be dry with zero moisture content. Additionally, two metal plates with dimensions of 2 by 0.75 in. are 

also bonded to the specimens with epoxy resin (fig. 2). The fiber and matrix properties used for 

computational simulation are given in tables 1 and 2. 

The finite element model as shown in figure 3 has 451 nodes and 360 Mindlin type rectangular 

elements. To represent the test setup described by Quattlebaum (ref. 5), nodes along the end of the 

specimen are restrained against translation to model the fixed boundary and nodes at the end of another 

specimen are constrained only moveable in the longitudinal direction. Axial tension load is applied at the 

moveable end. Moreover, nodes along the moveable end are tied by duplicate node constraints to enforce 

the uniform displacement of the clamped loaded edge. Computational simulation indicated a damage 

initiation load of 4555.06 N (1024 lb) for the lap joint with epoxy resin. The damage initiation mode was 

by ply longitudinal tensile failures in the 0° ply and the microstress damage indexes are activated for the 

SM1A(+), SM2A(+), SM2B(–), SM3A(+), SM3B(–), SM12A, SM12B, SM13A, and SM23A 

microfailure modes. The locations of damage initiation were at the lap joint area. After damage initiation, 

longitudinal tensile failures spread to the interface between lap joint and composite plate as the applied 

load reached 7584.35 N (1705 lb). Then, longitudinal tensile failures continuously spread at the lap joint 

with the load increasing to 7691 N (1729 lb). The microstress damage indexes were also activated for the 

SM1A(+), SM2A(+), SM2B(–), SM3A(+), SM3B(–), SM12A, SM12B, SM13A, and SM23A 

microfailure modes. Thereafter, longitudinal tensile failures developed at the lap joint and the interface 

between lap joint and the composite plate as the load increased. The lap joint continued to fracture rapidly 

and broke under the 44.096 kN (9913 lb) loading. Computational simulation indicated that substantial 

adhesive damage resulted in failure of the lap joint. 

For the lap joint with graphite/epoxy prepreg tape as its adhesive, the damage initiation load was 

36.45 kN (8193 lb) by ply longitudinal tensile failures in the 0° ply. The damage initiation took place at 

the edges of the lap joint adjacent to the composite plate. The microstress damage indices were activated 

for SM1A(+), SM2A(+), SM2B(–), SM3A(+), SM3B(–), SM12A, SM12B, SM13A, and SM23A 

microfailure modes. After damage initiation, longitudinal tensile failures spread to plies of the specimen 

as the applied load reached 42.52 kN (9558 lb). Subsequently, damage growth was limited mainly to the 

first two plies of interface between the edge of lap joint and the composite plate until the load was 

increased to 44.53 kN (10010 lb). At 44.75 kN (10060 lb), longitudinal tensile failures spread to plies 

around the edge of lap joint. The microstress damage indices were activated for SM1A(+), SM2A(+), 

SM2B(–), SM3A(+), SM3B(–), SM12A, SM12B, SM13A, and SM23A microfailure modes. With 

increasing load, fracture continued to develop at the edges of the lap joint and the specimen broke under 

the 52.49 kN (11800 lb) loading. Similar to the simulation for the lap joint bonded with epoxy resin. 
NASA/TM—2006-214037 5

TABLE 1.—AS-4 FIBER PROPERTIES 

Nomenclature Values

Number of fibers per end 10000 

Fiber diameter 0.00508 mm (0.200×10–3 in.)

Fiber density 4.04×10–7 Kg/m3

 (0.063 lb/in.3)

Longitudinal normal modulus 226.84 GPa (3.29×107

 psi)

Transverse normal modulus 13.72 GPa (0.199×107

 psi)

Poisson’s ratio (ν12) 0.200

Poisson’s ratio (ν23) 0.250

Shear modulus (G12) 13.79 GPa (0.20×107

 psi)

Shear modulus (G23) 6.89 GPa (0.10×107

 psi)

Longitudinal thermal expansion coefficient 1.0×10–6/°C (–0.55×10–6/°F)

Transverse thermal expansion coefficient 1.0×10–6/°C (0.56×10–6/°F)

Longitudinal heat conductivity 301 kJ-m/hr/m2

/°C (4.03 BTU-in./hr/in.2/°F)

Transverse heat conductivity 30.1 kJ-m/hr/m2

/°C (0.403 BTU-in./hr/in.2/°F)

Heat capacity 0.712 kJ/kg/°C (0.17 BTU/lb/°F)

Tensile strength 3.72 GPa (540 ksi)

Compressive strength 3.35 GPa (486 ksi) 

TABLE 2.—EPOXY MATRIX PROPERTIES 

Nomenclature Values

Matrix density 3.30×10–7 Kg/m3

 (0.0443 lb/in.3)

Normal modulus 3.45 GPa (500 ksi)

Poisson’s ratio 0.35

Coefficient of thermal expansion 0.77×10–4/°C (0.428×10–4/°F)

Heat conductivity 0.648 kJ-m/hr/m2

/°C (0.868×10–2 BTU-in/hr/in.2/°F)

Heat capacity 1.047 KJ/Kg/°C (0.25 BTU/lb/°F)

Tensile strength 68.99 MPa (10.0 ksi)

Compressive strength 241.59 MPa (35.0 ksi)

Shear strength 89.7 MPa (13.0 ksi)

Allowable tensile strain 0.02

Allowable compressive strain 0.05

Allowable shear strain 0.045

Allowable torsional strain 0.045

Void conductivity 16.8 J-m/hr/m2

/°C (0.225 BTU-in./hr/in.2/°F)

Glass transition temperature 216 °C (420 °F) 
NASA/TM—2006-214037 6

Figure 4 shows the relation between displacement and loading for lap joint with two different 

adhesives. It indicates the bonded strength of lap joint with graphite/epoxy prepreg tape is approximately 

1.19 times higher than that of the epoxy bonded joint, a little lower than experimental results by 

Quattlebaum (ref. 5). This is due to some difference in the material properties in simulation and 

experiment. On the other hand, the apparent linear relationship between the load and displacement 

depicted in figure 4 is not able to reflect the presence of internal damage initiation and growth processes. 

For epoxy and graphite/epoxy prepreg tape bonded specimens, figures 5(a) and (b) compare the 

change of microstress energy component SM1A(+) with increasing displacement. It shows that the peak 

of SM1A(+) for graphite/epoxy prepreg tape is quite later and higher than that of epoxy. This means 

cracking in region A for epoxy bonded joint is earlier than prepreg bonded joint. The difference in the 

damage energy amplitudes indicate that the prepreg bonded joint has a much higher energy of SM1A(+) 

damage. 

Figures 5(c) and (d) show the microstress energy component SM2A(+) as a function of displacement. 

From the plots, it is obvious that prepreg specimen can withstand higher transverse tensile stress in large 

displacement than epoxy specimen. It reflects that there is greater resistance against crack initiation in 

matrix for prepreg specimen. 

Figures 5(e) and (f) show the relation of microstress energy component SM2B(–) versus 

displacement. It is observed that the stress required to cause transverse debonding at the fiber-matrix 

interface for prepreg specimen is larger than that for epoxy specimen. The bond strength for epoxy 

specimen is not as strong as that for prepreg specimen. This is mainly due to the fiber bridging effects that 

impede crack propagation in the prepreg-bonded specimen. 

Figures 5(g) and (h) plot microstress energy component SM13A versus displacement. In the graph, 

the shear stress (out of plane) in region A for prepreg bonded joint is higher than that for epoxy bonded 

joint. It shows that there exist bridging fibers in prepreg specimen. 

Quattlebaum (ref. 5) presented the acoustic activity data obtained from epoxy resin and prepreg 

specimens with the same configuration as the computational simulation. Direct comparison of the 

acoustic emission signals with computed microstress level damage energies was not possible because the 

computed damage energy values had much fewer points than the experimentally measured acoustic 

emission data. The apparent reason for the mismatch of refinement between experimental and 

computational values is that microstress level damage tracking is not sufficient to capture the acoustic 

emission data from NDE testing. For correlation of current microstress level damage energy tracking with 

Quattlebaum’s test data, we used a curve fitting software, TableCurve2D v5 2000 (ref. 6), to find the 

fitted curve that envelops acoustic signals. 
NASA/TM—2006-214037 7
NASA/TM—2006-214037 8

Figure 6(a) shows the envelope curve for epoxy resin bonded specimen and figure 6(b) plots the 

envelope curve for prepreg bonded specimen. Experimental acoustic emission levels are marked with 

slight ticks as points through which curves are drawn in figures 6(a) and (b). The area under the envelope 

represents the total damage energy detected by the acoustic emission during the period monitored. Thus, 

we can correlate the microstress damage energy through computational simulation with the relative total 

damage energies represented by the envelope areas. The envelope area in figure 6(a) is 1.22986×10–3 and 

that in figure 6(b) is 1.30145×10–3. The ratio of the energies from figure 6(b) to that of figure 6(a) is 

1.058. Comparatively, the ratio of simulation results for damage energy shown in figure 7 is 1.168, which 

is 10 percent higher than the ratio computed from the NDE test results. 

Conclusions 

The failure patterns of the investigated fiber composite specimens and the available computational 

simulation results are found that: 

1. Microstress level damage tracking is able to evaluate the bond strength and monitor adhesive 

yielding. 

2. Microstress level computational simulation provides the details of damage initiation, growth, and 

subsequent fracture in composites. It represents a new approach for investigating damage mechanisms of 

composites. 
NASA/TM—2006-214037 9

3. Computational simulation shows a good correlation with AU signals in the cumulative sense. 

4. The demonstrated procedure is flexible and applicable to all types of constituent materials, 

structural geometry, and loading. Hybrid composites, as well as laminated, stitched, woven, and braided 

composites can be simulated. 

5. Computational simulation, with the use of established composite mechanics and finite element 

models can be used to predict the influence of microstresses, as well as loading and material properties on 

the durability of composite structures. 

References 

1. Zhang, H., Minnetyan, L., and Chamis, C.C. (2001), “Microstress Level Damage Evolution in 

Composite Structures,” 46th International SAMPE Symposium, Long Beach, CA. 

2. Minnetyan, L., Murthy, P.L.N., and Chamis, C.C. (1990), “Composite Structure Global Fracture 

Toughness via Computational Simulation,” Computers and Structures, 37, 2, pp. 175–180. 

3. Murthy, P.L.N., and Chamis, C.C. (1986), “Integrated Composite Analyzer (ICAN): Users and 

Programmers Manual,” TP–2515. 

4. Nakazawa, S., Dias, J.B., and Spiegel, M.S. (1987), “MHOST Users’ Manual,” prepared for NASA 

Lewis Research Center by MARC Analysis Research Corporation. 

5. Quattlebaum, G.J., and Raju, P.K. (1997), “Nondestructive Evaluation of Graphite/Aluminum 

Composites Using Acousto-Ultrasonics,” Proceedings of the ASME Noise Control and Acoustics 

Division. 

6. TableCurve2D v5 (2000), AISN software. 
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E–15394

WBS 561581.02.08.03

15

Micro-Energy Rates for Damage Tolerance and Durability

of Composite Structures

Christos C. Chamis and Levon Minnetyan

Acoustic emission; Joints; Microstresses; Damage mechanisms

Unclassified -Unlimited

Subject Category: 24

Prepared for the 16th European Conference on Fracture cosponsored by ASTM, JSEM, SMS, BSSM, AIAS, SEM, and

EURASEM, Alexandroupolis, Greece, July 3–7, 2006. Christos C. Chamis, e-mail: Christos.C.Chamis@nasa.gov,

NASA Glenn Research Center; and Levon Minnetyan, e-mail: levon@clarkson.edu, Clarkson University, Department of

Civil Engineering, 8 Clarkson Avenue, Potsdam, New York 13699. Responsible person, Christos C. Chamis, organization code R, 216–433–3252.

In this paper, the adhesive bond strength of lap-jointed graphite/aluminum composites is examined by computational

simulation. Computed micro-stress level energy release rates are used to identify the damage mechanisms associated

with the corresponding acoustic emission (AE) signals. Computed damage regions are similarly correlated with

ultrasonically scanned damage regions. Results show that computational simulation can be used with suitable NDE

methods for credible in-service monitoring of composites.