International Journal of Fatigue 48 (2013) 266–279

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International Journal of Fatigue

journal homepage: www.elsevier .com/locate / i j fa t igue

Progressive fatigue damage simulation method for composites

Yuri Nikishkov, Andrew Makeev ⇑, Guillaume SeonDepartment of Mechanical and Aerospace Engineering, University of Texas at Arlington, Arlington, TX, USA

a r t i c l e i n f o a b s t r a c t

Article history:Received 15 May 2012Received in revised form 8 November 2012Accepted 10 November 2012Available online 21 November 2012

Keywords:CompositesMatrix failureFatigue damageFinite element simulations

0142-1123/$ - see front matter � 2012 Elsevier Ltd. Ahttp://dx.doi.org/10.1016/j.ijfatigue.2012.11.005

⇑ Corresponding author. Address: 500 W First St., A+1 817 2729448; fax: +1 817 2722952.

E-mail address: makeev@uta.edu (A. Makeev).

The main objective of this work is to show the ability of solid finite element-based techniques to accu-rately predict the onset and progression of matrix cracks and delaminations in composites under fatigueloading. The specific objectives are: (a) to develop fatigue failure simulation method for multi-directionalcarbon/epoxy laminate articles in a finite element code; and (b) to correlate the failure predictions withtest data. The failure prediction models presented in this work use stress-based fatigue failure criteriacombined with fatigue damage accumulation and are not based on initial flaw assumptions. The verifi-cation test articles include 88-ply IM7/8552 carbon/epoxy composite laminate coupons with wavy plies,and 16-ply IM7/8552 carbon/epoxy open-hole tensile coupons. Available stress–strain relations and fail-ure progression algorithm are built in finite element models; and fatigue material properties are used topredict fatigue damage onset and progression. The fatigue model predictions and subsequent test corre-lations are presented.

� 2012 Elsevier Ltd. All rights reserved.

1. Introduction

One of the goals of this work is to inform the engineering com-munity of recent development in the advanced structural methodsthat could enable more accurate fatigue life predictions for com-posite structures. Currently, the engineers do not have appropriatetools to assess life of composite structures quickly enough for effi-cient use in the structural designs. In particular, such tools are crit-ical to the aerospace industry to achieve the ability to design andbuild a fatigue-critical, flight-critical composite part right the firsttime (achieve at least 80% yield). The first-time yield is estimatedabout 20–30%, and 70–80% in production. New composite part de-signs are currently sized for static in-plane properties; and the fa-tigue qualification occurs too late in the development process.Therefore, one cannot afford to redesign the part for eliminationof the fatigue performance issues.

As indicated by Lorenzo and Hahn [1], fatigue failure in a com-posite laminate starts with matrix cracking and interlaminar dam-age that does not immediately affect laminate’s residual capabilityand useful life. Defining composite failure as the onset of delami-nation growth from assumed initial delamination flaw might proveoverly conservative due to branching of the initial delaminationthrough matrix ply-cracks into other interfaces that typically oc-curs in multi-directional tape laminates. Prediction of damage pro-gression to significant (detectable) size that accounts for theinteraction of in-ply and interlaminar matrix-dominated failure

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modes is necessary for accurate assessment of fatigue part condi-tion. A comprehensive fatigue structural analysis methodologythat captures multi-stage failure modes and their interaction incomposites, and predicts initiation and progression of structuraldamage to detectable size without a priori assumptions of the ini-tial damage or the damage path is required.

The motivation for this work is the need in the development ofcomputational fatigue damage analysis techniques for compositematerials that are based on three-dimensional finite elementmethod. Continuum-based orthotropic material models combinedwith three-dimensional finite element method have achieved wideacceptance in the engineering community as a reliable tool forstress analysis for the most complex combinations of geometry,material system or layup. This work appends these techniqueswith progressive fatigue damage analysis that uses stress-basedmatrix failure criteria to simulate matrix failures and delamina-tions. The proposed analysis method does not require initial flawsfor damage predictions; and the method is able to predict the onsetand development of a large number of cracks typical for compositelaminates. Predictions are based on experimentally measured sta-tic and fatigue material properties used by failure criteria. Theobjective of this work is to show the ability of solid finite ele-ment-based techniques to accurately predict the onset and pro-gression of matrix cracks and delaminations to detectable lengthunder fatigue loading. The specific objectives are: (a) to develop fa-tigue failure simulation method for multi-directional carbon/epoxycomposite articles in a finite element code; and (b) to correlate fail-ure predictions with test data.

The first application of stress-based failure criteria to fatiguefailure analysis was proposed by Hashin and Rotem [2] and then

Y. Nikishkov et al. / International Journal of Fatigue 48 (2013) 266–279 267

used for predicting fatigue failure of angle ply laminates [3]. Themethod was based on adjusting material strengths according toS–N curves for constant amplitude loading. For variable amplitudeloading, in addition to linear damage accumulation (Palmgren–Miner rule [4]), a number of cumulative damage rules based onresidual life approach were proposed specifically for composites,such as Broutman and Sahu [5], and Hashin and Rotem [6]. A re-view of analysis methods for variable amplitude fatigue loadingis available in [7]. An alternative to residual life was a methodintroduced by the ‘‘wear-out’’ model [8] that used residualstrength as measure of fatigue degradation of the material. A re-view of methods based on residual strength and their comparisonwith tests can be found in [9]. Hashin also demonstrated thatmethods based on residual life and residual strength are equivalentif Hashin–Rotem damage accumulation rule is used [10].

Another approach of estimating fatigue life under variable load-ing is based on measurements of residual stiffness. One of its firstapplications was the critical-element model by Reifsnider andStinchcomb [11]. Shokrieh and Lessard [12] combined fatigue fail-ure analysis based on residual stiffness with stress-based failurecriteria based on residual strength measurements. Their approachrequired large number of tests to characterize fatigue behavior ofa unidirectional material. Methods to decrease the number of testswere later proposed by Shokrieh and Taheri-Behrooz [13]. How-ever, oftentimes residual stiffness shows significant drop onlyshortly before failure so that the prediction methodologies basedon residual stiffness are highly dependent on the experimentalqualification of rapidly decreasing stiffness. For low cycle fatiguein general, it has been shown [14] that failure is typically of a ‘‘sud-den death’’ type so that the residual strength remains equal to sta-tic strength before reducing drastically at failure.

Finite element simulations of fatigue failure have been pro-posed extensively during the last decade. In addition to works byShokrieh et al. [12,13], Tserpes et al. [15] used the Hashin’s fatiguefailure prediction method at the element level combined withgradual and sudden stiffness degradation to simulate failure. Lianand Yao [16] have conducted extensive test program and FEA sim-ulations based on stiffness degradation and assumed proportionalresidual strength degradation to predict failure using quadraticstress-based criteria. Other examples of using progressive failureapproach can be found in works by Basu et al. [17] that providedfailure predictions in laminated panels using 2D FEA; and Hufnerand Accorsi [18] that demonstrated FEA-based simulations foropen-hole tensile tests of woven composites and experimental ver-ification using digital image correlation.

Improvements in computational power of desktop computersalso led to recent increase of interest to stress-based failure initia-tion and FE simulations of damage progression in composites. Dáv-ila et al. [19] proposed the set of LaRC criteria that depend onmaterial fracture toughness and account for all failure modes incomposites. Maimí et al. [20,21] used these criteria to propose pro-gressive damage development in composite laminates and Cama-nho and Lambert [22] successfully applied them to bolted joints.Authors of this work used the LaRC criterion for transverse matrixtension in the models with fiber-aligned meshes to obtain detailedpredictions of matrix damage in quasi-isotropic laminates understatic loading [23]. Camanho and Dávila [24] used the same failuretheories with cohesive elements to successfully predict delamina-tion failures in the pre-defined locations.

This work introduces the fatigue damage progression algorithmthat combines stress-based fatigue element failure (based on S–Ncurves) and damage accumulation due to variable stress conditionsat the 3D solid elements in the FE mesh. Matrix cracks and delam-inations initiate at locations determined by failure criteria andthen develop due to fatigue degradation of the material and accu-mulation of damage. Sudden degradation of material properties at

failed elements leads to variable stress conditions during fatiguesimulations; the effect of variable stress is captured by damageaccumulation. Simulation of both matrix and interlaminar damageis essential for accurate predictions of damage progression due to astrong interaction between the two damage modes as matrixcracks in different plies are connected through delaminationsforming common failure surfaces. A practical goal of this algorithmis the prediction of number of loading cycles required for matrixcracks or delaminations to reach the size that can be detected bymeasurements.

Similarly to other methods based on the residual life approach,this method is limited to load ratios for which the experimental S–N curves are available. Intermittent element failures require recal-culation of stress distribution in the non-failed elements; aftereach stress recalculation the analysis is performed with the sameS–N curves assuming that the effects of transition to the readjustedstate of stress are negligible for the damage progression simula-tion. Degradation of interlaminar tensile and shear stiffnesses inunidirectional specimens occurs late in the fatigue life as no signif-icant changes in modulus have been observed during more than90% of the fatigue life. Based on such observations static stiffnessproperties were considered appropriate for the proposed simula-tion method as it typically steps through the number of cyclestoo large to include stiffness changes.

Computational models used for simulations are implemented inuser-defined procedures of the ABAQUS finite element software[25]. Fatigue damage propagation simulations are conducted for88-ply IM7/8552 carbon/epoxy tape laminates with wavy plies,and 16-ply IM7/8552 tape quasi-isotropic open-hole tensile(OHT) coupons. Model predictions and subsequent test correla-tions are presented. Three-dimensional volumetric visualizationby X-ray Computed Tomography (CT) is used to inspect damagemode interactions in tested specimens.

2. Simulation method

This section presents the foundations of the damage simulationmethod user in this paper. The method is based on the followingprinciples:

� Microscopic damage: accounted for by material non-linearitymeasurements.� Fatigue failure criterion: stress-based failure criteria relate stres-

ses to material strength reduced with cycles based on S–Ncurves.� Failure simulation: element failure is simulated by reducing

stiffness in the directions defined by failure criterion.� Progressive fatigue damage algorithm: fatigue failure criterion

and damage accumulation are combined to detect fatigue fail-ure under variable stress conditions.� Failure mode interaction: matrix failure and delaminations are

detected by the same damage simulation algorithm used inthe appropriate material directions.

2.1. Microscopic damage

Tests show that composite materials demonstrate highly non-linear shear stress–strain response before detectable matrix-plycracking. Physically, shear non-linearity can correspond to micro-cracks in the matrix. Makeev et al. [26] used full-field deformationmeasurement to generate accurate shear stress–strain responseapproximation for IM7/8552 carbon/epoxy tape in the form oflog-linear Ramberg–Osgood equation:

c13 ¼ s13=G13 þ ðs13=K13Þ1=n ð1Þ

268 Y. Nikishkov et al. / International Journal of Fatigue 48 (2013) 266–279

In this equation index 1 corresponds to the fiber direction and index3 to the interlaminar direction of the material. An n = 0.2 value gen-erated in [26] results in the 5th-order non-linearity in the interlam-inar shear stress–strain response. This paper assumes the samenon-linear shear stress–strain response in the 1–2 in-ply principalmaterial plane.

2.2. Failure criteria for macroscopic matrix damage

Stress-based failure criteria are used to establish failure initia-tion in a single element. This work uses two failure criteria forthe transverse matrix cracking as shown on Fig. 1 (left): the Hashinfailure criterion [2]:

r22

S22

� �2

þ s12

S12

� �2

¼ 1; r22 > 0

s12

S12

� �2

¼ 1; r22 6 0

ð2Þ

and the LaRC failure criterion [27] based on the Hahn and Johannes-son proposal [28] to account for material’s fracture toughness in themixed-mode fracture criterion:

ð1� gÞr22

S22þ g

r22

S22

� �2

þ vðs12ÞvðS12Þ

¼ 1; r22 > 0

vðs12ÞvðS12Þ

¼ 1; r22 6 0ð3Þ

where g ¼ GIc=GIIc , and GIc, GIIc are Mode I and Mode II fracturetoughness values and vðs12Þ is a shear component of the strain en-ergy density that adjusts the criterion for the non-linear shearstress–strain response [29]:

vðs12Þ ¼ 2Z

s12dc12ðs12Þ

As proposed by Hashin and Rotem [2], the quadratic stress-basedcriterion can be used for fatigue predictions by assuming that thein-plane shear and tensile strengths used in the criterion followthe material S–N curves:

S22 ¼ S22;staticaTðlogNÞ�bT

S12 ¼ S12;staticaSðlogNÞ�bSð4Þ

where S22,static and S12,static are static in-plane tensile and shearstrengths. Note that the reduction of strengths based on uniaxialS–N curves assumes constant cycling stress ratio for all stress com-ponents, no phase lag, and linear stress–strain material response forthe in-plane stresses. Mixed-mode quadratic failure criteria such asEq. (2) are also limited to positive load ratios [30]. In Eq. (3) con-stant mixed-mode ratio g = 0.3521 calculated from the mean frac-ture toughness values [22] is assumed as the available fatigue

Fig. 1. Schematic views of the transverse crack (left) and de

data for the Mode II energy release rate component exhibit largescatter [31].

Eq. (4) are substituted into failure criteria (Eqs. (2) and (3)) tocalculate number of cycles to failure for all elements in the FEmesh. An element that shows the smallest number of cycles to fail-ure corresponds to the location of macroscopic damage initiation.After the first element failure, stress distribution is recalculatedand the following failures are based on the combination of fatiguefailure criterion prediction and accumulated damage, as detailed inSection 2.5.

2.3. Delamination simulation

Simulating delamination failures is important for accurate dam-age predictions even if the specimen failures are dominated by ma-trix cracking. Significant interactions between matrix ply-crackingand interlaminar damage modes are confirmed by tests andnumerical results obtained in this work. Successful implementa-tion of mixed-mode failure criteria for detecting delaminations insolid FEM models was demonstrated for wavy laminates [26] andfor unidirectional specimens with porosity defects [32].

Delamination is simulated by failing the thin layer of elementslocated at the laminate ply boundary. Material properties of thedelamination layer are assumed to be the same as the propertiesof the one of the adjacent plies; it is the failure simulation thatmakes a difference by assuming a crack that propagates betweenthe plies. The delamination plane is denoted as 1–2 material planeon Fig. 1 (right); and the Figure shows delamination layer (darkgray, not to scale) for a fragment of a ply element. In this model,delamination is represented by matrix failure in the 1–2 materialplane such that the failure is determined by the same failure crite-ria (Eqs. (2) and (3)) with material directions 2 and 3 interchanged.The delamination layer is in three-dimensional stress state and allthree stress components acting on the plane normal to materialdirection 3 must be accounted for in the criterion; e.g. the LaRC cri-terion (Eq. (3)) takes the following form:

ð1� gÞr33

S33þ g

r33

S33

� �2

þ vðs13ÞvðS13Þ

þ vðs23ÞvðS23Þ

¼ 1; r22 > 0

vðs13ÞvðS13Þ

þ vðs23ÞvðS23Þ

¼ 1; r22 6 0ð5Þ

Transverse interlaminar shear strength S23 is calculated from thetransverse compressive strength using [19]:

S23 ¼ S22C=2tana0 ð6Þ

where a0 = 53� is the typical fracture plane angle for compressivefailures [19].

lamination crack (right) with respect to material axes.

Y. Nikishkov et al. / International Journal of Fatigue 48 (2013) 266–279 269

2.4. Failed element state simulation

When failure criterion indicates failure in an element it is as-sumed that crack is ‘‘smeared’’ over its volume. An element staysbroken for the rest of the analysis after failure. Failed state of asolid element is simulated by the loss of element stiffness inthe plane of cracking as defined by the initiation criterion. Fol-lowing this assumption, the element loses tensile stiffness inthe transverse material direction (2) as well as shear stiffness inthe (1–2) and (2–3) planes. Using the approach proposed byKachanov [33] the stiffness modulus decreases with damageincreasing:

EðdSÞ ¼ ð1� dSÞE ð7Þ

where dS represents scalar damage variable that changes from zero(no damage) to one (fully damaged). For more details on the stress–strain relationship in the damaged elements, see [23]. Quick loss ofstiffness due to damage variable dS should not be confused with fa-tigue damage accumulation due to variable stress conditions de-scribed in Section 2.5.

A number of damage evolution laws were proposed in works[15–18,20–21] both to simulate material response to micro- andmacro-cracking. In this work it is assumed that the damage vari-able dS goes from zero to one as fast as practically possible to allowfor convergence of the numerical procedure. This technique is sim-ilar to ‘‘sudden stiffness degradation’’ in [15]. The damage variableis expressed as:

dSðtÞ ¼

0; t < tf

ð1� kf Þt�tf

Dtr; tf 6 t 6 tf þ Dtr

1� kf ; t > tf þ Dtr

8>>><>>>:

ð8Þ

where t represents the time parameter in the quasi-static FE analy-sis. tf corresponds to the time parameter for which the elementfailed; Dtr is the time of damage relaxation determined from con-vergence requirements; and kf is the remaining stiffness ratio thatis small enough to simulate full element failure. The time variablecan be proportional to the applied load in the quasi-static analysisor to the loading cycles in the fatigue analysis. In the fatigue dam-age progression algorithm proposed in Section 2.5 the time param-eter corresponds to the algorithm steps such that the step size isproportional to the number of elements failed in the increment.Convergence of the equilibrium iterations also requires that thenon-linear adjustment of the shear moduli continues until the ele-ment is fully damaged.

2.5. Fatigue damage progression algorithm

Fatigue damage progression algorithm is based on the combina-tion of the fatigue failure initiation criterion and damage accumu-lation due to variable stress conditions under fatigue cycling. Atany cycle the fatigue failure criterion is assumed to provide predic-tion of the number of cycles to failure for the undamaged elementunder fixed peak stress. Elements accumulate damage based on thepeak stress levels during the fatigue simulation. Then the com-bined failure includes the effect of previously accumulated damageunder different stresses and the stress-based fatigue failure predic-tion for the peak stress just before failure. Linear damage accumu-lation [4] is used in this work; however, the algorithm below canbe used with any damage accumulation rule that defines failurefor arbitrary sequence of cyclic stresses and is based on the numberof cycles to failure. Finally, in this work the simulation was stoppedwhen damage (longest surface matrix crack) reached the selecteddetectable size; an ultimate failure criterion or any other stoppingcriteria can also be used.

Fatigue damage progression algorithm proceeds as follows:

1. Apply peak fatigue load to the model. Obtain stresses at zerocycles.

2. For each element solve the algebraic equation for the number ofcycles obtained by substituting fatigue curves (Eq. (4)) for thestrength values in a failure initiation criterion.

FðrðkÞel ; SðNfelÞÞ ¼ 1 ð9Þ

where F(r,S) denotes stress-based failure criterion, r(k) is currentstress state in the element and S(Nf) are strengths adjusted using fa-tigue curves (Eq. (4)). The equation is solved numerically for Nf

which is the number of cycles to failure for the undamaged materialin the current stress state. For the failure criteria used in this work(Eqs. (2) and (3)) this equation has monotonic derivatives, whichguarantees that Eq. (9) always has single root.1. For each element find progressive failure cycle Npf based on the

linear accumulation of damage [4] from the previous steps andassuming that failure occurs when damage reaches criticalvalue.

Npfel ¼ ðd

f � dðk�1Þel ÞNf

el ð10Þ

In this work df is assumed equal to unity.4. Find minimum Npf noted as N(k) for the first element failure.5. Advance cycle counter by N(k); for each non-failed element cal-

culate current fatigue damage using linear damage accumula-tion principle [4]:

dðkÞel ¼ dðk�1Þel þ NðkÞ

Nfel

ð11Þ

d = 0 at zero cycles.6. Fail the element and recalculate stresses r(k+1).7. Continue from step 2 until a detectable damage size is reached

or the ultimate failure criterion is satisfied. Note that this stop-ping criterion defines the extent of fatigue cycling simulationbut does not affect the damage propagation.

To speed up the calculations it is advisable to fail multiple ele-ments in a single iteration. In this case, at step 4 the elements aresorted by cycles to failure; a desired number of elements with thesmallest cycles are failed, and the cycle counter is advanced by thelargest cycle to failure.

Since typical number of cycles in a step is too large to includestiffness changes; and to keep fatigue material properties limitedto minimum, the simulations below assume no stiffness degrada-tion until macroscopic damage is detected (see Section 3.2 for briefdiscussion).

2.6. Computational procedure

2.6.1. Fiber-aligned mesh approachNumerical methods that simulate damage by reducing material

stiffness are known to produce mesh-dependent results [34].Dependence of crack development on the mesh orientation wasdemonstrated in the earlier work by the authors [23] for the staticanalysis of the OHT coupons. It was shown that typical circumfer-entially-structured mesh with the smallest in-plane size of an ele-ment equal to 0.12 mm (4.7 � 10�3 in.) and total 707529 DOF thatprovides accurate stress predictions, not only was not able todetermine accurate failure loads but also could not capture correctdamage progression due to circumferential mesh constraining thecracks to radial orientations and restricting their growth underincreasing load.

270 Y. Nikishkov et al. / International Journal of Fatigue 48 (2013) 266–279

To overcome crack growth dependence on the mesh orienta-tion, the fiber-aligned mesh approach was proposed [23]. In thisapproach the finite element mesh for each ply is structured suchthat the element edges are parallel to the fiber directions. Simula-tion of damage propagation under static loading performed in [23]demonstrated excellent correlation of matrix crack lengths and ori-entations with tests. Section 4.2.1 shows convergent results for fa-tigue crack lengths at the surface of the OHT specimen with respectto the element size in the fiber-aligned mesh.

Since ply meshes are incompatible at the interfaces, mesh tieconstraints [25] are used to hold the mesh assembly together.Mesh tie constraints introduce additional equations that relate dis-placements of ply boundary nodes to the displacements of theadjacent ply nodes located within the specified distance. Algebraicconstraints do not guarantee correct stresses in the vicinity of con-strained surfaces, and the fiber-aligned model has to be verified toproduce convergent stresses used by failure criterion. Section 4.2.1demonstrates such verification for the numerical example de-scribed in this work.

2.6.2. Failure simulation in the FE softwareFE simulations were conducted using ABAQUS software, version

6.10 [25]. Each element in the FE model used the unidirectionalmaterial properties. Material orientations were specified for all ele-ments in the FE mesh according to the layup and local ply wavi-ness. Transverse orthotropic material properties in the coordinatesystem of Fig. 1 and the shear non-linearity behavior were codedin the ABAQUS subroutine UMAT [25] for all elements in the mod-el. The user-defined subroutine UMAT allows providing customstresses as a function of trial strains and, optionally, the Jacobianmatrix for the equilibrium iterations. The custom subroutineUMAT was also used to calculate the damage variable in the ele-ments and determine element failures per fatigue algorithm in Sec-tion 2.5. Damage and failure status were stored as state variablesfor each element during the steps of the fatigue progression algo-rithm. Finally, the stiffness of failed elements and resulting stresseswere calculated in the subroutine UMAT per Section 2.4.

3. Material properties

This section presents material properties of IM7/8552 carbon/epoxy tape used in the FE simulations.

3.1. Static properties

Table 1 lists stiffness and strength properties according to [26],and fracture toughness values per [22]. Note that secant-intercept

Table 1Material properties for IM7/8552 carbon/epoxy tape.

Tensile modulus, E11 171 GPa (24.8 msi)Tensile modulus, E22 = E33 8.96 GPa (1.3 msi)Poisson’s ratio, m12 = m13 0.32Poisson’s ratio, m23 0.5Shear modulus, G12 = G13 5.31 GPa (0.77 msi)Shear modulus, G23 = E22/(2 � (1 + m23)) 2.99 GPa (0.433 msi)Secant-intercept modulus, K12 = K13 260 MPa (37.8 ksi)Secant-intercept modulus, K23 = K12 � G23/G12 147 MPa (21.3 ksi)Exponent, n 0.203In-ply and interlaminar tensile strength,

S22 = S33

98.6 MPa (14.3 ksi)

In-ply and interlaminar shear strength, S12 = S13 113 MPa (16.4 ksi)Transverse compression strength, S22C 300 MPa (43.5 ksi)Mode I fracture toughness, GIc 0.2774 kJ/m2

(1.584 psi in.)Mode II fracture toughness, GIIc 0.7889 kJ/m2

(4.505 psi in.)

modulus and exponent refer to an approximation of the shearstress–strain response given in Eq. (1).

Refs. [26,35–36] illustrate the details of the techniques to mea-sure the interlaminar constitutive properties. The in-ply transversecompression strength value was generated based on compressiontests of 90� coupons machined from a 6.35 mm-thick (0.25 in.) uni-directional panel. This value agrees with the Fill compressionstrength of 305 MPa (44.2 ksi) published by the prepreg manufac-turer [37].

3.2. Fatigue properties

The interlaminar tensile and shear S–N curves used in this workare generated in [38] based on curved-beam (CB) and short-beamshear (SBS) tests, respectively [36,38]. See Ref. [38] for more detailson test setup and calculation of stresses. Power laws (Eqs. (12) and(13)) approximate the average fatigue curves corresponding to 0.1load ratio.

s13

S13¼ 1:2487ðlog NÞ�0:4123 ð12Þ

r33

S33¼ 0:9001ðlog NÞ�0:3504 ð13Þ

Eqs. (12) and (13) are used to predict fatigue failure onset based onfailure criteria (Eqs. (2) and (3)) listed in Section 2.2.

The fatigue models developed in this work assume that matrix-dominated shear and tensile stress–strain constitutive relations forIM7/8552 carbon/epoxy are not dependent upon cycles until closeto matrix failure. Such assumption is based on monitoring inter-laminar stress–strain response in a number of SBS and CB teststhroughout fatigue history using the digital image correlation(DIC) technique [39]. No significant modulus change as a functionof cycles has been observed during more than 90% of the number ofcycles to delamination failure. It is worth noting that in the pre-sented examples as well as in the potential applications, matrix-dominated shear/tensile failures would occur well before changesin the other stress–strain constitutive properties are expected.

4. Finite element simulations and comparison with tests

This section presents finite element simulation results based onthe fatigue damage modeling presented in Section 2. The followingfinite element-based simulation results are provided and com-pared with tests:

� Fatigue failure simulation predictions are compared with testsfor thick tensile laminates with waviness defects.� Simulated matrix cracks and delaminations compared with sur-

face cracks detected by DIC technique.� Surface strains from simulations compared with strains

obtained from DIC of tested specimens.� Three-dimensional damage interaction demonstrated by com-

paring with CT scans of the fatigued specimens.� Crack length and sub-surface delamination fatigue develop-

ment compared with tests.� Crack length predictions compared with tests for different peak

loads and cycles of loading.

4.1. Fatigue of laminates with waviness defects

4.1.1. Fatigue tests and finite element models88-ply [(±453/02)3/(±454/02)/(±454/04/±454)/(02/±454)/(02/

±453)3]T IM7/8552 carbon/epoxy tape laminates were selected toverify the accuracy of the interlaminar fatigue failure models inthe presence of fiber waviness. Fiber waviness is a manufacturing

Y. Nikishkov et al. / International Journal of Fatigue 48 (2013) 266–279 271

defect oftentimes present in thick composites parts; it is attributedto non-uniform molding pressure during part manufacturing. Fiberwaviness was shown to significantly affect composite specimenfailure strength and fatigue life in the experimental [40] and ana-lytical [41] works. The laminate thickness was 15.7–16.3 mm(0.62–0.64 in.); width is 3.56 mm (0.14 in.); length is 3.6 mm(6 in.) and gage (untabbed) length is 74.9 mm (2.95 in.). Three cou-pons (B4, B5, and B6) were subject to fatigue constant amplitudeload at 10 Hz frequency and 0.1 load ratio. The peak loads for allthree tests are provided in Table 3. Tests were stopped shortly afterfailure onset to capture quick delamination propagation. Fig. 2shows digital images of the three coupons B4, B5, and B6 withthe sample finite element model for coupon B4. The DIC technique[39] was used to monitor the peak strains at 500-cycle intervalsduring fatigue loading. A clear visible delamination onset was de-tected in the B4 and B5 coupons. For the B6 coupon, the first onsetwas not detectable in the individual images but traceable though aslight shift in the speckle pattern during a movie replay of the dig-ital images.

The finite element mesh shown in Fig. 2 was used for fatigueanalysis of B4 coupon. The structured rectangular mesh was gener-ated based on spline smoothing of points extracted manually fromthe digital photographs of the specimens. The FE meshes for twoother coupons were built individually based on their digitalimages.

4.1.2. Ply-termination analysisPlane stress finite element simulations are capable of providing

excellent predictions of static failure loads [26] and cycles to

Fig. 2. Surface images of B4–B6 coupons an

Ply-terminations

0 +45

Fig. 3. Surface photograph of the coupon with waviness (left

fatigue failure initiation [38]. However, plane stress models mostlycould not predict correct ply-group location of fatigue failure. Onereason could be ply-terminations in the ±45� ply-groups at failure-critical locations as shown in [42]. Fig. 3 shows ply-terminations inthe B4 coupon.

The finite element models were modified to account for suchdiscontinuities. The ply-terminations with the neat resin proper-ties were built in the finite element meshes for all three coupons.The following linear isotropic constitutive properties listed in Ta-ble 2 were assumed for the neat resin:

Fatigue simulation shows that the ply-termination elementsfailed at low cycles. Following their failure, it was assumed thatthey lose tensile stiffness in the load direction and shear stiffness.The ply-termination discontinuities built in the FEM enable theshift in the delamination locations to correct 0/+45 ply-interfaces.

4.1.3. Progressive fatigue failure predictionsSimulation methods that account for three-dimensional stress

state and progressive damage development are necessary for pre-dictions of crack development observed in tests. Fatigue damageprogression algorithm for delamination analysis described in Sec-tion 2 was used for these predictions. Fig. 4 shows the three-dimensional finite element meshes for coupon B4 used for theanalysis of the wrinkled specimen with and without ply-termina-tions modeling.

Fig. 5 compares 3D finite element model predictions with testfor coupon B4. The axial strain contours obtained from DIC analysisof test data at 750,000 cycles show crack initiation just belowwrinkle number 4. The crack development follows the wrinkle at

d finite element mesh for B4 coupon.

Ply-terminations

0 +45

) and finite element mesh with ply-terminations (right).

Table 28552 Resin stiffness and strength properties.

Tensile modulus, GPa (msi) 4.67 (0.677) (IM7/8552 prepreg data sheet[34])

Poisson’s ratio 0.3Ultimate strength, MPa (ksi) 79.3 (11.5) (1.7% Elongation to failure [34])

272 Y. Nikishkov et al. / International Journal of Fatigue 48 (2013) 266–279

first and then goes through the cross-ply to the main wrinkle. The3D FE model without ply-terminations predicts crack initiation atthe top of wrinkle 5. Including ply-terminations in 3D FE analysisallows for accurate predictions of crack initiation location anddevelopment for coupon B4 when using both Hashin and LaRC fail-ure criteria as shown in Table 3.

Table 3 compares ply-termination analysis results to the analy-sis without ply terminations and tests for the three coupons. Thetable shows cycles to failure and failure locations predictionaccording to the Hashin and LaRC criteria compared with tests;location is either at wrinkle (Fig. 5, center) or at ply termination(such as ‘‘p/t at 4/5’’ means ply termination between wrinklesnumber 4 and 5). For B5 coupon, introduction of ply terminations

Fig. 4. 3D finite element meshes: base wavy model

1 2 3 4 5 6 7 8 9 1 432

Fig. 5. Comparison of crack location obtained from test at 750,000 cycles (left) and 3D Fwith ply-terminations at 750,000 cycles (right) for coupon B4.

Table 3Comparison of tests and failure predictions for models with ply terminations.

Specimen B4 B5Peak load 9875 N (2200 lbs) 8674

Criterion Model Cycles to failure Failure location Cycles

Hashin No p/t 3,800,000 4th Wrinkle 230With p/t 796,000 p/t at 4/5 200

LaRC No p/t 710,000 4th Wrinkle 290With p/t 450,000 p/t at 4/5 230

Test 750,000 p/t at 4/5 <1000

increases number of cycles to failure. Stress concentrations at theply terminations re-directs and ‘‘smoothes’’ the forces flux aroundthe wrinkle leading to a reduction of the stress concentration at thecritical wrinkle location, which is similar to higher fatigue lifedemonstrated by the coupon with two holes aligned in the loadingdirection comparing to the same coupon with a single hole.Although the fatigue failure initiation is at the resin pocket, thedamage propagates from the main wrinkle. For B6 coupon, includ-ing ply terminations leads to significantly earlier failure. Using theLaRC criterion with ply terminations analysis leads to excellentcomparison of a first damage onset with test results. The Hashinand LaRC failure criteria again lead to significantly different predic-tions; the LaRC criterion predictions provide better correlationwith tests.

The three-dimensional progressive fatigue failure analysis dem-onstrates good correlation with tests for tensile laminate articleswith waviness defects. Both cycles to failure and location of failurepredictions were improved after the FE model was modified to ac-count for ply-termination defects. More accurate three-dimen-sional geometric evaluation and structural analysis ofmanufacturing defects are required to further improve correlationswith tests.

(left) and model with ply-terminations (right).

1 2 3 4 5 6 7 88765

E model predictions by base wavy model at 1,000,000 cycles (center) and by model

B6N (1950 lbs) 6894 N (1550 lbs)

to failure Failure location Cycles to failure Failure location

4th wrinkle 196,000 4th Wrinkle4th wrinkle 154,000 4th Wrinkle

4th wrinkle 73,000 4th Wrinklep/t at 4/5 56,000 4th Wrinklep/t at 4/5 50,000 p/t at 3/4

Y. Nikishkov et al. / International Journal of Fatigue 48 (2013) 266–279 273

4.2. Fatigue of OHT coupons

4.2.1. Fatigue tests and finite element models16-Ply quasi-isotropic IM7/8552 carbon/epoxy tape open-hole

tensile (OHT) coupons have been manufactured and tested to theASTM Standard D7615 [43] specifications. The coupon dimensionsare 38.1 � 190.5 � 2.642 mm (1.5 � 7.5 � 0.104 in.). The hole-diameter is 6.35 mm (0.25 in.). Two quasi-isotropic layups wereused: [45/0/�45/90]2S (layup 1) and [45/90/�45/0]2S (layup 2).Layup 1 coupons were subject to constant amplitude load at10 Hz frequency, up to 1,000,000 cycles. The minimum load was2.22 kN (500 lbs) and the maximum load was 22.2 kN (5000 lbs).Layup 2 coupons were subject to constant amplitude loads rangingfrom 21.4 kN (4800) lbs to 24.9 kN (5600 lbs), same load ratio of0.1, up to the number of cycles that resulted in approximatelythe same length of the ultimate surface crack. Damage patternsand surface strains obtained using DIC technique [39] are com-pared with numerical simulations.

A three-dimensional solid finite element-based model wasbuilt. Half of the coupon through-the-thickness (8 plies) was con-sidered in the analysis to reduce the computational effort. Symme-try boundary conditions were applied. Boundary conditions alsoincluded fixed displacements at the bottom end, and fixed trans-verse displacements and uniform axial (vertical) displacementswith applied tensile force at the top end. The finite element modelused 8-noded three-dimensional linear elements with reducedintegration (C3D8R elements in ABAQUS) [25]. Each element hada single integration point so that the damage is activated for thewhole element. Reduced integration elements have been shownto adequately represent the stress state with respect to modelingdamage [23]. Appropriate number of elements per ply was deter-

Fig. 6. Photograph of a test specimen (layup 1, left) a

Fig. 7. Sub-model with the fiber-aligned mesh (left) a

mined by a stress convergence study [23]. Fig. 6 shows the globalfinite element model and a sample test photograph.

Sub-modeling [25] was used to simplify mesh generation and toallow sufficient mesh size for convergence of transverse stresses.The sub-model with plies in different colors and its location areshown on Fig. 6 (right). Displacement boundary conditions wereused in the sub-model. The global mesh used a circumferential ele-ment concentration near the hole in the coupon. The smallest finiteelement size in the global mesh was 0.25 mm (0.01 in.) resulting in33243 DOF. The sub-models used for comparison with tests hadthe outer radius equal to three times the hole radius and the small-est element size of 0.124 mm (4.9 � 10�3 in.). Base sub-modelwithout delamination layer used 4 elements per ply resulting in92288 elements and 363120 DOF; the sub-model with delamina-tion layer used 5 elements per ply, 112476 elements and 426666DOF. In the latter sub-model, 4 elements per thickness of eachply were used to simulate matrix failure (Section 2.2) and oneadditional element was used to simulate delamination failure (Sec-tion 2.3). Note that the material orientations at all elements in oneply were the same; the difference between elements used for sim-ulation of matrix failures and delaminations was only in failure in-dex calculation. The size of delamination element layer wasselected as 10% of the ply thickness. The sub-model was an assem-bly of fiber-aligned structured meshes connected by mesh tie con-straints. Fig. 7 demonstrates the sub-model with the fiber-alignedmesh visible for the 1st sub-surface ply and the model through-the-thickness structure.

As noted in Section 2.6 the incompatible fiber-aligned meshinterfaces led to introduction of tie constraints between the plies.The quality of stress calculations in the sub-model was substanti-ated by a convergence study. Figs. 8 and 9 show failure index plots

nd global and sub-model for FE analysis (right).

nd model through-the-thickness structure (right).

Fig. 8. Convergence of the failure index for through-the thickness mesh (left) and in-plane mesh (right) and comparison with the sub-model at 20% radius from the holesurface.

Fig. 9. Convergence of the failure index for through-the thickness mesh (left) and in-plane mesh (right) and comparison with the sub-model at the surface ply.

Fig. 10. Comparison of the longest surface crack fatigue growth for different crackwidths e in FE simulations.

274 Y. Nikishkov et al. / International Journal of Fatigue 48 (2013) 266–279

for global meshes of increasing density and the sub-model meshselected for analysis. The Figures show excellent approximationof stresses in the sub-model at the location of damage as comparedto convergent global solution.

A convergence study was performed for the in-plane elementsize that simulates width of the matrix cracks in the sub-model(see Section 2.6). Fig. 10 shows comparison of the longest surfacecrack fatigue growth for different element sizes in the FE mesh.The comparison shows converging predictions with the elementsize decreasing. The crack obtained on the mesh with the smallestsize, e = 0.105 mm, had smaller length prediction for the same cy-cles than the mesh with e = 0.124 mm; however, the symmetriccrack on the other side of the whole had higher predictions. Bothare shown on Fig. 10.

The simulation starts by finding static stresses for the maxi-mum fatigue load. The damage progression algorithm describedin Section 2.5 continues by failing the preset number of elementsin one step of the algorithm, determining the fatigue cycles com-pleted, and recalculating the stresses as a result of the elementdamage. Using higher number of failed elements per step enablesfaster simulation but increasingly ignores the progressive effectsof stress recalculation resulting in less conservative predictions.Fig. 11 compares fatigue growth of the longest surface crack (usingthe LaRC failure criterion with delamination simulation) for differ-ent number of failed elements per algorithm step. Convergentbehavior is observed with number of failed elements per step

decreasing. Based on Fig. 11, 50 elements were selected to fail inone step for FE meshes used in the simulations below.

Fig. 11. Comparison of the longest surface crack fatigue growth for differentnumber failed elements per algorithm step.

Y. Nikishkov et al. / International Journal of Fatigue 48 (2013) 266–279 275

The elements failed during the simulation are interpreted asmacroscopic cracks. The relaxation time defined by Eq. (8) was se-lected as Dtr = 0.4 Dtstep, where Dtstep is the initial step size; tf wasselected as tf = ti�Dtr/2, where ti is the start of the step; andremaining stiffness ratio was selected as kf = 10�6. This parameterselection results in full element failure in one step of the algorithm,which maximizes the effect of element failure on stress redistribu-tion. Note that the step size’s only meaning is in relation with thenumber of elements to fail and the relaxation time; if equilibriumiterations fail to converge then the step size (time increment inABAQUS terms) is automatically reduced by the FE software, whichresults in proportionally smaller number of elements failing in onestep and more gradual stiffness degradation in failed elements asdefined by Eq. (8).

4.2.2. Comparison of surface strains and cracks with testsThis section presents first of the methods of the fatigue progres-

sion algorithm validation that is based on DIC measurements of thelongest surface crack and surface strains. The matrix crack in thesurface 45� ply shown on Fig. 12 grows steadily with the numberof cycles and ultimately destroys the specimen.

The comparison of matrix cracks from FE results and test data isshown on Fig. 12. The DIC image shows two major cracks on eachside of the coupon as well as smaller cracks on the right side. FEdamage plot displays elements colored to show their failure cycles

DIC Crack Length Measurement

Fig. 12. DIC image with overlapped shear strain (left) and FE

from low (blue to green color, N < 100,000) to high (orange to redcolor: 100,000 < N < 1,000,000). Fig. 12 also shows the method ofsurface crack length measurements in tests used for comparisonwith simulations in Fig. 17. In the simulations below, length ofthe longest crack in the surface ply was used for comparison.

Fig. 13 displays the comparison of surface strains at 1,000,000cycles. Area of high shear strain localization appears to be largerin the DIC results than in simulation, which is due to small in-planesize of the elements in simulation. As shown in Section 4.2.1, usinglarger elements leads to smaller surface crack lengths predictionsthan detected in tests. In static tests strain localizations correlatewell with simulations [23]; larger strain localizations on Fig. 13 ap-pear to be a fatigue phenomenon.

4.2.3. Three-dimensional damage interactionRecent feasibility assessments demonstrated the ability to de-

tect manufacturing and structural defects in composites with a Mi-cro-CT system [44]. The CT scans of the fatigued specimens are anexcellent tool for discovering the three-dimensional structure offailure surfaces and measuring the sub-surface matrix cracks anddelaminations. X5000 industrial CT system made by North StarImaging Inc. with a 225 kV Microfocus X-ray tube and Varian4030E series Flat Panel detector was utilized in this work.

Fig. 14 shows the FE predictions of matrix cracks and delamin-ations, and the CT scan of the specimen compared after 1,000,000cycles of fatigue loading. In the FE model, matrix cracks can be seenas lines of colored elements along the fiber direction on the surfaceof the specimen; they are also shown as colored squares at the in-ner hole surface and the through-the-thickness section of the mod-el. Delaminations can be seen at the same through-the-thicknesssurfaces as thin lines of colored elements between the plies. Colorsencode cycles to failure: elements in blue to green colors failed atlow cycles (N < 100,000) and elements in yellow to red colors failedat higher cycles (100,000 < N < 1,000,000). The CT scan data showsboth matrix cracks and delaminations as dark lines (due to lowerdensity) oriented along fiber directions or between the plies,respectively. Matrix cracks and delaminations in the two plies justbelow the surface of the specimen are clearly identified since theyremain open after unloading; a detailed inspection of the CT scanalso reveals matrix cracks of smaller widths in further sub-surfaceplies. Fig. 14 demonstrates excellent correlation of the locations ofthe major matrix cracks in the surface and sub-surface plies anddelaminations between these plies. Both the FE model and the CTscan show that matrix cracks and delaminations in the two topsub-surface plies demonstrate strong interaction and need to bemodeled simultaneously to account for their reciprocal effects.

FE simulation of fatigue damage progression can be an efficienttool for optimizing composite layups for fatigue performance.Figs. 15 and 16 show the comparison of matrix crack lengths and

FEM Crack Length Measurement

damage (right) for the OHT coupon at 1,000,000 cycles.

Fig. 13. Shear strain from DIC (left) and FE simulation (right) at 1,000,000 cycles.

Delaminations

Matrixcracks

Fatigue Model Test (CT Data)

Fig. 14. Detailed comparison of FE failure predictions (left) and CT scan of test specimen (right) for layup 1.

Delaminations

Matrix cracks

Shifts to zero-degree ply crack

Fig. 15. Matrix cracks in the surface ply and delaminations in the sub-surface interface for FE predictions (left) and CT scan (right) of fatigued layup 1 specimen.

276 Y. Nikishkov et al. / International Journal of Fatigue 48 (2013) 266–279

delamination sizes for the specimens with two different quasi-iso-tropic layups fatigued to 1,000,000 cycles. FE simulations showmatrix cracks as black lines along the fiber direction of the surfaceply and delaminations as gray-colored areas; the CT scan imagesshow cracks as thin lines in fiber direction and delaminations as

darker areas formed by the cracks in the two sub-surface plies.Figs. 15 and 16 again demonstrate excellent comparison with thesub-surface CT measurements for both location and size of dam-age. Both simulations and tests clearly show cracks shifting fromthe surface matrix to delamination in the 1st sub-surface interface

Fig. 17. Comparison of the ultimate crack length versus fatigue life for FEpredictions and test data.

Delaminations Delamination shifts to 90°ply crack

Matrix cracks

Fig. 16. Matrix cracks in the surface ply and delaminations in the sub-surface interface for FE predictions (left) and CT scan (right) of fatigued layup 2 specimen.

Fig. 18. Comparison of the sub-surface interface delamination versus fatigue life forthe FE predictions and test data.

Y. Nikishkov et al. / International Journal of Fatigue 48 (2013) 266–279 277

and to cracks in the 2nd sub-surface ply. The difference in delam-ination sizes and shapes between the two layups is due to differentfiber orientations at the 2nd sub-surface ply: 0� for layup 1 and 90�for layup 2.

4.2.4. Fatigue development of surface cracks and delaminationsThis section presents simulations of fatigue crack development

for different failure criteria and failure modeling, and comparesthem with tests. DIC technique allows for monitoring surfacestrains during the fatigue test. Strain monitoring is an efficientway to detect crack advances in the surface ply of a laminate with-out stopping the test. The test crack lengths were obtained byinspecting DIC images at the corresponding number of fatigue cy-cles and measuring length in the crack direction from the start(clearly visible at the images at higher cycles) to the point whereshear strain reaches the value determined by the actual extent ofthe crack (measured by microscope) in the final DIC image. Anexample of shear strain contours in the final DIC image is shownon Fig. 12 (left).

Fig. 17 presents FE fatigue growth predictions of the longestsurface crack for a layup 1 specimen. The Figure compares: (a) fa-tigue crack development on both sides of the hole measured fromDIC images; (b) predictions of the matrix crack development basedon the fatigue progression algorithm using the Hashin failure crite-rion and the LaRC failure criterion for damage initiation; and (c)

predictions that include delamination modeling as described inSection 2.3. The crack development predictions based on the LaRCfailure criterion provide better predictions overall but start to un-der-predict crack lengths at higher cycles. Taking ply delamina-tions into account leads to conservative predictions when cracklengths reach larger values, and the simulation is able to conserva-tively predict crack lengths for most of the fatigue test. The simu-lation based on the Hashin failure criterion predicted significantlysmaller crack lengths at high cycles; including delamination simu-lation shifted the predictions far to the conservative side resultingin about 1 mm longer cracks.

Fig. 18 shows progressive fatigue delamination development inthe 1st sub-surface interface for layup 1 and 2 specimens. For bothlayups the predictions of fatigue delamination growth based on theHashin failure criterion are almost twice as large as the predictionsbased on the LaRC failure criterion. CT scans of the tested speci-mens provide different assessment of delamination sizes for thetwo layups showing that the reason for different delaminationsizes is the interaction between matrix cracks in the surface andthe 1st sub-surface plies. For layup 1, large delamination area isformed by cracks in the 45� surface ply and sub-surface 0� ply asshown on Fig. 15, right. For layup 2, the delamination area isformed by the 45� crack and the 90� crack as shown on Fig. 16,right and Fig. 19, bottom. As far as simulation predictions, the dam-

4800 lbs 3,000,000 cycles 5200 lbs 400,000 cycles 5400 lbs 200,000 cycles

Delaminations

Delaminations Size

Size

FEM crack length measurement

CT scan crack length measurement

Fig. 19. Comparison of simulation predictions (top) and CT scans of tested specimens (bottom) for surface ply-cracks and sub-surface interface delaminations for layup 2specimens.

Table 4Comparison of largest surface crack lengths and delaminations for the OHT articles.

Peak load, kN (lbs) Cycles Simulation (LaRC) Simulation (Hashin) Test (average)

Crack len. (mm) Delam. size (mm) Crack len. (mm) Delam. size (mm) Crack len. (mm) Delam. size (mm)

21.4 (4800) 3,000,000 6.2 2.0 7.5 3.8 7.1 1.022.2 (5000) 1,000,000 6.2 1.7 6.8 3.5 6.4 1.023.1 (5200) 400,000 6.2 1.8 6.2 3.0 6.2 1.024.0 (5400) 200,000 6.2 1.8 6.8 3.4 6.3 0.924.9 (5600) 100,000 6.2 1.8 6.2 3.1 5.3 1.122.2 (5000) Layup 1 1,000,000 6.2 1.9 6.8 3.5 6.3 3.8

278 Y. Nikishkov et al. / International Journal of Fatigue 48 (2013) 266–279

age growth based on the Hashin criterion conservatively developsthe delamination along the major surface cracks leading to goodcorrelation with layup 1; the simulation based the LaRC criterionis consistent with layup 2 delamination growth limited by a stronginteraction with 90� ply cracks.

4.2.5. Comparison of fatigue damage growth at different peak loadsTo further validate the progressive fatigue failure analysis, five

OHT articles of layup 2 were tested at different peak loads and dif-ferent number of cycles such that the longest surface crack reachedapproximately the same length. The loads and cycles are shown inTable 4. Load ratio was maintained at 0.1. The three-dimensionalFE model for layup 2 was executed for the same peak loads and cy-cles, respectively. Predictions are compared with the CT scans of fa-tigued OHT articles.

Fig. 19 shows surface ply-cracks and sub-surface interface del-aminations for specimens at three different peak loads and fatiguecycles. In all cases, simulation predictions based on the LaRC failurecriterion demonstrate excellent agreement of crack and delamina-tion locations with tests; the delamination size predictions deter-mined as shown on Fig. 19 appear to exceed the sizes detected inCT scans. Similarly to results from Section 4.2.4, simulation predic-tions based on the Hashin criterion are more conservative for allspecimens. Table 4 shows the comparison of model predictions

based on the LaRC and Hashin criteria and the test data for allspecimens.

5. Conclusions

An engineering method to predict fatigue initiation and growthof matrix cracks and delaminations in tape composites is devel-oped in this work. The fatigue damage progression algorithm thatcombines stress-based fatigue element failure (based on S–Ncurves) and damage accumulation due to variable stress conditionswas introduced. FE-based simulations predict damage develop-ment to detectable size under fatigue loading conditions. Suddenstiffness degradation is implemented to simulate material failurein accordance with test data described in this paper. Interactionsof matrix cracking and delamination damage modes are shownto be an important factor in improving correlations of predictionsand tests.

Numerical examples provided in this paper show good qualita-tive and quantitative agreement of the FE simulations with the testdata. The simulations are able to predict locations of macroscopiccracks and their development through the fatigue life of the spec-imens. The fatigue damage progression algorithm that uses theLaRC criterion for matrix cracks and delaminations demonstratesexcellent predictions of damage development. Fatigue damage pre-

Y. Nikishkov et al. / International Journal of Fatigue 48 (2013) 266–279 279

dictions based on the Hashin criterion generally result in moreconservative predictions.

Three-dimensional visualization of volumetric specimen mod-els based on X-ray Computed Tomography provides unique insightin the damage mode interactions. CT scans allow unparalleledidentification and measurement of the sub-surface defects in thefatigued specimens resulting in the improved fidelity of test com-parisons. The CT visualization results show that delamination sizesare highly dependent on the interaction with cracks in the adjacentplies. Accurate simulation of delaminations should rely on the sim-ulation of matrix crack growth in all laminate plies and geometricfactors that limit the development of crack surfaces.

The proposed fatigue damage progression algorithm providesroom for improvement as it does not rely on the particular con-stant amplitude failure criteria or damage accumulation laws usedin simulations. One can select from a variety of stress or strain-based criteria as long as fatigue properties for the allowables areavailable. Linear accumulation hypothesis can be replaced withmore complex damage accumulation laws and damage-based fail-ure criteria. Gradual stiffness adjustment can be added to the fati-gue iterations when stiffness degradation is significant during thefatigue life. Finally, simple extension of the algorithm allows sim-ulations of the arbitrary fatigue load spectrum.

Acknowledgments

This work is sponsored by the National Rotorcraft TechnologyCenter, U.S. Army Aviation and Missile Research, Developmentand Engineering Center (ARMDEC) under Technology InvestmentAgreement W911W6-06-2-0002, entitled National RotorcraftTechnology Center Research Program, and the Office of Naval Re-search (ONR). Such support is gratefully acknowledged. The viewsand conclusions contained in this article should not be interpretedas representing the official policies, either expressed or implied, ofthe AMRDEC or the U.S. Government. The authors also thank Mr.Russ Fay at Boeing for manufacturing the open-hole tensile cou-pons; and Mr. Ed Lee from Bell Helicopter Textron for manufactur-ing the coupons with fiber waviness.

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