modeling of multilayer composite fabrics for gas turbine engine … · 2015. 7. 29. · modeling of...

Modeling of Multilayer Composite Fabrics for Gas TurbineEngine Containment Systems

J. Sharda1; C. Deenadayalu2; B. Mobasher3; and S. D. Rajan4

Abstract: An experimental and modeling system for the modeling of multilayer composite fabrics used in a gas turbine enginecontainment system is developed. Specifically, Kevlar 49 �17�17� and Zylon AS �35�35� fabrics are used in the study. The experimentalsetup is first used to obtain the material properties of these fabrics. Later, one or more layers of these fabrics is tightly wrapped arounda steel cylinder that simulates an engine containment housing. A steel penerator �or a blunt nose� is used in a static test by slowly pushingagainst the fabric. The resulting load-deflection data are used to compute a variety of parameters, including the energy absorption capacity.The material behavior obtained from the experimental study is then used as the constitutive model in a finite element simulation of thestatic test. The objective is to develop a procedure for understanding the relative strengths and weaknesses of different fabrics and to aidin the development of finite element modeling of actual fan blade-out events.

DOI: 10.1061/�ASCE�0893-1321�2006�19:1�38�

CE Database subject headings: Tensile strength; Stress analysis; Stress strain relations; Fabrics; Composite materials; Finite elementmethod; Containment.

Introduction

Traditional engine containment systems use metals, such as alu-minum and titanium, to provide for the safety of the vital airplanecomponents in the event of a catastrophic failure of the turbines.Contained gas turbine engines turn out to be safer in case of fanblade-out events by protecting the fuselage from damage arisingfrom high-energy trajectories of broken components. Strong me-tallic containment cases make the engine assembly much heavierand are costly to fabricate. A suitable alternative to the titaniumcontainment cases is an aluminum containment case protected bya composite fiber wrap, which is a lighter and stronger barrier.Composite fiber fabric wraps are widely used in the containmentsystems of gas turbine engines. Such systems are found to beespecially cost-effective for mitigating engine debris during a fanblade-out event. This is mostly because of its high strength perunit weight property, and low manufacturing cost compared withthe traditional metallic containment systems. One such commonlyused fabric is Kevlar �Dupont 2003� wrapped around the appro-priate area of the fan housing. Another such new high-performance composite fabric is Zylon, developed by Toyobo,Japan �Toyobo 2003�. Zylon consists of rigid-rod chain molecules

1Research Assistant; currently, Product Design Engineer, Motorola,Plantation, FL 33322.

2Research Assistant, Dept. of Civil and Environmental Engineering,Arizona State Univ., Tempe, AZ 85287-5306.

3Professor, Dept. of Civil and Environmental Engineering, ArizonaState Univ., Tempe, AZ 85287-5306.

4Professor, Dept. of Civil and Environmental Engineering, ArizonaState Univ., Tempe, AZ 85287-5306.

Note. Discussion open until June 1, 2006. Separate discussions mustbe submitted for individual papers. To extend the closing date by onemonth, a written request must be filed with the ASCE Managing Editor.The manuscript for this paper was submitted for review and possiblepublication on December 12, 2003; approved on September 6, 2004. Thispaper is part of the Journal of Aerospace Engineering, Vol. 19, No. 1,
January 1, 2006. ©ASCE, ISSN 0893-1321/2006/1-38–45/$25.00.
38 / JOURNAL OF AEROSPACE ENGINEERING © ASCE / JANUARY 2006

of poly�p-phenylene-2, 6-benzobisoxazole�. The fill yarns arerelatively straight, while the warp yarns are more crimped. Stressstrain curves generated from different tensile tests of Zylon indi-cate that weaving reduces the tensile strength of a yarn. Highlycrimped yarns have a significantly reduced strength and failurestrain.

Modeling a multilayer fiber fabric composite for engine con-tainment systems during a a fan blade-out event has been a diffi-cult task. Part of the reason is due to a lack of accurate modelingtechniques, resulting in the need to better understand the strength,energy absorption capacity, and hence usefulness of these wovencomposites for containment applications. Innovative techniqueshave been implemented to model the behavior of composite fabricmaterials utilizing the micromechanical approach and the homog-enization technique. Paley and Aboudi �1992� developed a modeldesigned for the analysis of a fibrous composite with a periodicstructure in which the repeating volume element consists of fourinteracting subcells. Ivanov and Tabiei �2001� used a model con-sisting of four subcells for the prediction of the elastic materialproperties. The model allows the warp and the fill yarns not to beorthogonal in the plane of the composite ply. Another model con-siders the two-dimensional extent of the woven fabric, and has aninterface with nonlinear finite element codes �Tabiei and Jiang1999�. This model is similar to the approaches proposed by Paleyand Aboudi �1992� mentioned earlier �Bednarcyk 2001�. Theseaveraging methods have also been applied to woven carbon/copper composites by Bednarcyk and Pindera �1999, 2000a,b�.Using the iso-stress and iso-strain assumptions, the constitutiveequations are averaged along the thickness direction for a repre-sentative volume cell. One of the major drawbacks of these ap-proaches is that they are applicable to matrix-based compositesand not dry fabrics.

The purpose of this work is to develop a methodology for thefinite element �FE� analysis modeling. First, simple tension testsare used in obtaining the material properties. Second, these tests
are used to develop the stress-strain relationship �or constitutive

modeling� suitable for use in a nonlinear finite element procedure.Third, to validate the developed constitutive modeling, statictests—that approximate the impact of a typical projectile on fab-ric wraps around a fan housing of an engine containmentsystem—are conducted using single and multiple layers of Kevlarand Zylon fabrics. Fourth, FE simulations of the static tests arecarried out. Specifically, the load deflection curves obtained bythe FE simulations are compared to the static test results in orderto validate the material modeling that can then be used for othertypes of fabrics or FE analysis �explicit analysis�.

Simple Tension Tests

Simple tension tests were used to construct the engineering stress-strain diagram up to ultimate strength in the principal material�warp� direction for the Kevlar 49 and Zylon AS fabrics �ASTM2000�. The cross-sectional area of each yarn was calculated bydividing the linear density of the yarn by its bulk density. Thetotal cross-sectional area of the specimen was defined as thecross-sectional area per yarn multiplied by the number of yarnsper unit length of fabric and the total width of the specimen. Thedimensional and physical properties of the two materials and thetest specimens are provided in Table 1. A detailed methodologyfor testing is described in an earlier report �Rajan et al. 2004�.

Perforated aluminum flat pieces with dimensions of63.5�63.5�0.635 mm �2.5�2.5�0.025 in. � thick were at-tached to both the ends of the specimen using commercial gradeepoxy, and held under the hydraulic pressure of frictional grips.Two specimens of each fabric type were tested. The tests wereconducted in a 245 kN �55 kips� servohydraulic test frame oper-ated under closed-loop displacement control with a constant rateof 2.5 mm/min �0.1 in. /min�. The overall deformation of thespecimen was measured by the stroke movement of the actuator,and continued until complete failure of the specimen wasachieved. Digital data acquisition was used to collect data every0.5 s. The load-deformation results were used to calculate thestress strain response.

The stress strain results are plotted for Kevlar and Zylon speci-mens in Fig. 1 and are shown in Table 2. In both fabrics, theinitial portion of the load-deflection graph shows a large increasein displacement �actuator stroke� for a very small increase load.Woven fabrics inherently have crimp �or waviness�, and in thisportion, the load essentially straightens the yarns by removing thecrimp. As the load increases, the yarn alignment leads to an in-crease of the slope of the load-deflection graph. The stress–strainresponse exhibits nonlinearity prior to the peak load, and a suddendrop in the stress beyond the ultimate strength that is character-istic of progressive yarn failure. This behavior is much more pro-nounced in the postpeak region of Zylon as compared to the Kev-lar specimen. The ultimate tensile failure of all the specimens isbrittle with little or no postpeak response. Gauge length was de-termined based on the average distance of the grip face to gripface. Energy absorbed by the fabric was calculated using two

Table 1. Basic Material Properties

Material Yarn countBulk density

�N/m3 �lb/ in.3��Lin�N/

Kevlar 49 17�17 1,440 �0.00530516� 0.0001671

Zylon AS 35�35 1,540 �0.00567358� 5.56�10

different measures. In the first method, the energy absorbed by the

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fabric was calculated from the total area under the stress–straincurve and represented as En1*. This included in initial nonlinearascending portion of the curve. Parameter En2* represents theenergy absorbed by linear approximation of the area under thestress strain curve extended from the modulus of elasticity slope.Comparison of these two measures indicates that there is an in-significant amount of energy dissipated in the initial straighteningof the yarns corresponding to 3.0 and 7.4% underestimation of theenergy absorbed for Kevlar and Zylon, respectively.

Static Ring Tests

The primary objective of static tests is to simulate the penetrationof a blunt object through the fabric-based engine containmentsystem. The secondary objective is to obtain load deformationresponse so that the FE material models can be validated. Thecomposite fabric was wrapped around a steel cylinder that simu-lated the engine housing. This section was rolled from a 25.4 mm�1 in.� thick A36 mild steel plate to the dimensions of: 813 mm�32 in.� outside diameter, 762 mm �30 in.� inside diameter, andwidth of 152 mm �6 in.�. The ring was assembled in two sections,a small and a large arc corresponding to 38° and 222° angles.These parts were connected by means of two side plates to a baseplate and the actuator. A small window was machined in the largearc to allow for the penetration of the blunt nose. Use of the ringas a two-part assembly allowed for easy installation of the speci-men in the loading fixture. A detailed view of the cylinder withside plates is shown in Fig. 2 and the schematic in Fig. 3.

The loading for all the tests was achieved by a blunt nosepenetrator as shown in Fig. 4. The dimension of steel nose was50.4 mm �2 in.� wide by 7.94 mm �5/16 in. � thick with a radius

sityn. ��

Cross-sectional areaper yarn �mm2 �in.2��

Specimen size�mm �in.��

57�10−7� 0.114838 �1.78�10−4� 63.5�304.8 �2.5�12�5�10−7� 0.0360644 �5.59�10−5� 63.5�304.8 �2.5�12�

Fig. 1. Stress strain curves for Kevlar and Zylon fabrics

ear denm �lb/ i

85 �9.4−5�3.17

AL OF AEROSPACE ENGINEERING © ASCE / JANUARY 2006 / 39

of 3.97 mm �5/32 in. � in the major direction and the corners. Thecross section of the base of the blunt nose was 2�2 in. The bluntnose assembly was initially set up inside the steel ring and thetests were conducted by its outward movement in a quasi-staticmanner thus applying the load. Failure was defined as the fullpenetration of the blunt nose through the single or multilayerfabric. Single and multilayer specimens for both Kevlar andZylon wraps were used. The specimen dimensions were 32 in. indiameter and 4 in. wide, and consisted of 1, 2, 4, 8, and 24 layerswrapped around the outside of the steel cylinder �Fig. 2�. The loadand deformation history were collected throughout the test andthe stiffness, total displacement, and energy absorption capacityof the structure were calculated from this response.

For multilayer specimens, a continuous fabric was wrapped ona custom-designed mandrel �Sharda 2002�. The last layer wasglued to the previous layer using 5-min epoxy. Overlap length forall single and multilayer specimens was 152 mm �6 in.�. Thespecimen was cured for 24 h before testing. To ensure minimal

Table 2. Summary of Test Results

Test IDPeak load�kN �lbs��

Elongation�mm �in.��

Tensile streng�MPa �psi�

Kevlar specimensKTest1 10.8 �2,419� 5.4 �0.214� 2,082 �301,95

KTest2 9.3 �2,085� 5.2 �0.204� 1,878 �272,45

Average 10.0 (2,252) 5.3 (0.209) 1,980 (287,20Standard deviation 1.05 (236) 0.18 (0.007) 144 (20,858

Zylon specimensZTest1 10.1 �2,276� 13.0 �0.510� 3,182 �461,55

ZTest2 9.2 �2,064� 12.0 �0.472� 2,893 �419,55

Average 9.65 (2,170) 12.5 (0.491) 3,037 (440,55Standard deviation 0.67 (150) 0.69 (0.027) 205 (29,696

Notes: Stress is obtained by dividing the peak load by the cross-sectionelongation at peak load by the specimen gauge length. Modulus of elasstress–strain graph.aEn1* denotes the energy absorbed by the fabric as calculated by the totabEn2* denotes the energy absorbed by the fabric as calculated by the linmodulus of elasticity slope.

Fig. 2. Static test setup


disturbance during the assembly process and proper alignment ofthe layers, a transfer ring with outside diameter of 813 mm �32in.� was manufactured. The rolled sample was slipped from themandrel onto a transfer ring in order to transport it to the testfixture. The specimens were covered with opaque plastic sheetingto minimize the degradation effects of moisture and ultravioletlight.

Test Setup

C Clamps were used to secure the fabrics to the loading fixture atpoints remote from the blunt head in order to avoid transferringthe entire load to the end joint. Several tests were conducted withand without clamps and indicated that clamping the specimen hadlittle effect on the integrity of the results. In consideration of thelarge displacements expected throughout the test, the effect offixity of the blunt nose loading mechanism with respect to thespecimen was also studied. It was expected that if the side loadswere not removed through the use of hinges, a stiff system would

Ultimatetensilestrain�%�

Modulus ofelasticity

��GPa� �ksi��

Energy absorbed per unit volume,�N cm/cm3�lb in. / in.3��

En1a En2a

3.06 118 �17,115� 2,516 �3,650� 2,475 �3,590�

2.92 128 �18,590� 1,782 �2,584� 1,737 �25,19�

2.99 123 (17,853) 2,149 (3,117) 2,106 (3,055)0.1 7.2 (1,043) 520 (754) 522 (757)

7.27 126 �18,242� 5,462 �7,923� 4,740 �6,875�

6.75 131 �18,960� 4,976 �7,217� 4,266 �6,188�

7.01 128 (18,601) 5,219 (7,570) 4,503 (6,532)0.37 3.5 (508) 344 (499) 335 (486)

tabulated in Table 1. Ultimate tensile strain is obtained by dividing theis taken as the maximum �linear� slope from the prepeak region of the

under the stress–strain curve.

proximation of the area under the stress-strain curve extended from the

Fig. 3. Schematic of test setup with clamps and hinges to removespurious side loads

th�

0�

3�

2))

0�

4�

2))

area asticity

l area

ear ap

be created which would result in side loads. Alternatively, anyrotation of the test assembly could result in loss of contact of thefull length of the blunt nose with the fabric, thus increasing thecontact pressure and premature failure of the specimen. In orderto make sure that the load applied is purely uniaxial in the z axis,all conditions of fixed-fixed, free-free, and fixed-free �x and ydirections� were evaluated using two perpendicular hinges at thenose and load cell. These hinges allowed for rotation in the twominor directions, and could be independently fixed against rota-tion. It was necessary to fix the end conditions at the blunt noseby fixing the load cell bearings that were placed orthogonal to thenose bearings. Even with the best-case efforts in ensuring that thetest setup was aligned, side loads were generated during the test-ing due to the tilting of the hinge at the bottom of the blunt nosehousing. A blunt nose housing, corresponding to fixed–fixed endconditions, was designed that is shown in Fig. 4.

Static Test Results

An MTS servohydraulic test machine with digital controller soft-ware was used. All the tests were conducted under actuator con-trol using a constant rate of travel of 10 mm/min �0.4 in./min�.The data were collected using digital data acquisition at a rate of2 Hz. A limiting deformation value of 101.6 mm �4 in.� was usedin all the one-layer tests. Figs. 5 and 6 show the response for one-,two-, four-, eight-, and 24-layer Kevlar and Zylon specimens,respectively. The values are normalized by the number of layers.It is observed that fabric slack exists for both Kevlar and Zylon

Fig. 4. Blunt nose housing

samples. In the case of Zylon, it is observed that up to 50 mm �2

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in.� of stroke travel under an insignificant amount of load �e.g., upto 1,112 N�. The initial region of the response curve is dominatedby a gradual increase in the load carrying capacity. This is con-sidered to be the region dominated by slack recovery as the re-corded deformation is due to the straightening of the yarns andgradual loading of the specimen to reach the stiffness of the fabricin tension. The ultimate load is reached in these samples in anabrupt manner after several yarns fracture. The fracture of theyarns prior to the peak load is observed as the incremental dropsin the load response. Fracture of a few yarns results in redistribu-tion of load to adjacent unbroken yarns. This excess load is suf-ficient to push the average stress on the yarns toward the ultimate

Fig. 5. Load-deformation response of one-, two-, four-, eight-, and24-layer Kevlar samples

Fig. 6. Load-deformation response of one-, two-, four-, eight-, and24-layer Zylon samples


tensile strength. There is an insignificant amount of postpeak re-sponse observed in these samples that is partly due to the insig-nificant magnitude of the frictional pullout of the yarns as com-pared to the overall load carrying capacity. Examination of Fig. 5indicates that the stiffnesses of the samples are quite comparable.The average value of the stiffness for the single layer specimensis 194 kN/m �1,108 lbs/ in. �, with a standard deviation of8.756 �50 lbs/ in. �, while the maximum load has an average of6.96 kN �1,564 lbs� and a standard deviation of 472 N �106 lbs�.The 24-layer Kevlar sample shows a different behavior since itsmode of failure is different than the others. The first noticeablefailure occurs at about 4.448 kN/ layer �1,000 lbs/ layer� followedby load redistribution. The failure of a few layers at a time con-tinues up until the peak which is then followed by a sudden dropin the load carrying capacity due to the full penetration of theblunt nose through all the layers. Examination of the failed speci-men shows that some of these failures are occur at some distanceaway from the point of application of the load �Fig. 7�a��.

Although the peak load seems to scale proportional to thenumber of layers �up to eight layers� for the Zylon specimens,these responses are highly nonlinear due to the progressivemechanism of failure, especially in multiple layer fabrics. By nor-malizing these curves and comparing the results, it is observedthat the two-layer specimen deviates from the one-layer curve atapproximately 65% of the ultimate strength of a single layer,whereas the four-layer specimen deviates from the two layer atabout 41% of its strength, and the eight layer deviates from thefour layer at about 27% of its strength. This indicates that thecontribution of outer layers to the stiffness of the overall assemblydiminishes with the number of layers. Significant displacement ofthe inner layers must take place before the outer layers are able tocarry any load. This also indicates the importance of parameters,such as the coefficient of friction between the layers, which isresponsible for the mechanical interlock and thus the transfer ofload from one layer to another. The amount of slack in all thesespecimens is significant to the level of up to 3 in. of travel dis-tance. However, the stiffnesses of the material do not appear to bedifferent during the early stages of loading. One- and two-layerspecimens have almost same stiffness up to the ultimate strengthof the first layer. This indicates that the two-layer Zylon is nottwice as stiff as the single-layer specimens, and the sample has tobe loaded to a significantly high level of its single-load carryinglevel for the second and subsequent layers to participate in loadsharing.

The energy absorbed per areal density and the normalized en-ergy absorbed per areal density graphs for both Kevlar and Zylonsamples are presented in Figs. 8 and 9. Zylon results show moreenergy absorption capacity than the corresponding Kevlar speci-

Fig. 7. Failure of the 24-layer specimens around the blunt nose: �a�Kevlar; and �b� Zylon

mens. The energy graphs predict the fabric capacities as linear in


nature, but the normalized curves show that there is no consis-tency in the energy absorption capacity of the fabrics. Fig. 9 rep-resents the maximum load normalized by areal density of bothKevlar and Zylon fabrics. Fig. 10 represents the stiffness versusnumber of layers as well as linearly extrapolated stiffness valuesfor Kevlar and Zylon.

Finite Element Modeling

The FE method was used to develop and validate a numericalmodel of the two fabrics used. The major objectives include de-velopment of a material model for Kevlar and Zylon fabrics basedon the simple tension tests, and their implementation in the finiteelement model of the static tests. The focus is on the capturing thebehavior of the fabrics up until the peak response. It was assumedthat Kevlar and Zylon fabrics exhibit orthotropic material behav-ior. The modulus of elasticity, E, Poisson’s ratio, �, and shearmodulus, G, are directional dependent resulting in a total of nineindependent material constants—E1, E2, E3, G12, G23, G13, �12,�23, and �13. Using a simplified approximation, the results from

Fig. 8. Energy absorbed/areal density/layer for 1 through 24-layerKevlar and Zylon samples

Fig. 9. Average normalized maximum load versus number of layersfor all tests

the simple tension tests are used to obtain the major modulus ofelasticity value, E1, and the rest of the material constants areadjusted. In the absence of a more sophisticated procedure, thematerial values used in the material model are assumed as fol-lows. The in-plane tensile moduli were taken as: E1=E2=E. Theout-of-plane tensile modulus was taken as E3=0.05E, The shearmoduli were taken as G13=G23=G12=0.2E. All the Poisson’s ra-tios are considered to be negligible and are taken as 0.01 to avoidnumerical problems. The motivation was that the fabric in thestatic tests would primarily be loaded in the �warp� direction, thedirection used in the simple tension tests to generate the stress–strain diagram for the two fabrics. An appropriate failure criterionis needed when the material behavior is considered beyond theelastic regime. In the current study, �principal� strain is used asthe failure criterion with its limiting value obtained from thesimple tension tests.

The ABAQUS/Standard �HKS 2002� FE program was usedusing static loads �load control� and large displacement theory. Inaddition, nonlinear stress–strain material behavior with smooth,finite sliding between the various contact surfaces was used. Lin-ear solid elements �eight-noded hexahedral and four-noded tetra-hedral elements� were used instead of higher-order elements �20-noded hexahedral and 10-noded tetrahedral elements� that wereavoided due to convergence problems during contact. Conver-gence studies using the developed model show that the linearelements were adequate in providing the required results. A non-linear stress–strain material behavior in the context of a FE analy-sis using ABAQUS requires a user-defined subroutine �ABAQUS/Standard User Manual, Volume III �HKS 2002��. The subroutineis used to define the mechanical constitutive behavior of a mate-rial and updates the stresses, the material Jacobian matrix,�� /��, and solution-dependent state variables to their valuesat the end of each increment. A piecewise linear approximation tothe nonlinear stress–strain relationship obtained from the simpletension tests for Kevlar and Zylon �see Fig. 2� are used up untilthe peak. Beyond the peak, the slope of the stress–straincurve istaken as a small fraction of the previous slope value �i.e., 1 /10�.The slope of the compressive stress–strain curve is also assumedto be the same as the postpeak tensile stress–strain curve. Toverify the user-developed material modeling subroutine for bothKevlar and Zylon, the displacement-control approach was used in

Fig. 10. Average stiffness per number of layers used for all tests�actual and linearly extrapolated�

the FE analysis and the results from the FE analysis matched the

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experimental values obtained from the simple tension tests upuntil the peak response.

Finite Element Analysis of Static Tests

The analysis was performed on a quarter model due to the inher-ent symmetry of the geometry and the loading �Fig. 11�. Thestatic FE model was set up based on the following components—steel cylinder of A-36 steel with an outer diameter 81.3 cm �32in.�, width 15.24 cm �6 in.� �Z direction�, and thickness 2.54 cm�1 in.�. The cylinder contains an opening or window that is in thecircumferential direction. The cold-rolled steel blunt nose �or pen-etrator� with dimensions reported earlier was constrained to movein radial direction, passes through the window in the cylinder andpushes the fabric thereby loading it. The steel cylinder and theblunt nose were modeled with elastic, isotropic material proper-ties with a modulus of elasticity of 200 GPa �29�106 psi�, and aPoisson’s ratio of 0.3. One concentric layer of FEs representing asingle fabric layer �either Kevlar or Zylon� for one through eightlayers of fabric wrapped circumferentially around the cylinderwas used. The number of layers of FEs is increased to 3 whenmodeling 24 layers of fabric.

The loading from the blunt nose is uniformly distributed andapplied in increments so as to track and construct the load versusblunt nose tip-displacement graph. The line of nodes correspond-ing to the location of the clamps was constrained from moving inall directions. In addition, the blunt nose is constrained to move inthe radial direction. The nodes at the bottom of the cylinder arealso constrained from moving in all directions. Two sets of con-tact surfaces are defined, the first is between the blunt nose andthe fabric, and the second is between the fabric and the steelcylinder. A finite-sliding interaction, which is the most generaland allows for arbitrary separation, sliding, and rotation of theparticipating surfaces, is assigned in both contact cases. The for-mulation is well suited to geometrically nonlinear analysis. Nofriction between the contact surfaces is considered.

Kevlar Model

Fig. 12 shows the comparison between the static test and theresults obtained from the FE analysis for the one-, two-, four-, andeight-layer Kevlar samples. The FE and experimental peak load

Fig. 11. Details of the quarter-model finite element mesh showingthe blunt nose, steel cylinder, and the fabric

and displacement values are quite close for all multiple layers.


The FE load-deflection graph follows the experimental graph veryclosely except for the initial portion. The FE simulation overpre-dicts the peak load for the single-layer model. This behavior oc-curs with some of the simulations and is due to the fact that theelements where the ultimate strain has been exceeded are still apart of the FE model. Since these elements are not deleted, theystill provide some stiffness to the overall response. It should benoted that these strain zones are localized.

The eight-layer model follows the previous trends exhibitedwith the one-, two-, and four-layer models. It appears that notonly the required amount of slack adjustment to bring the twographs close to each other increases with the number of fabriclayers, but also that there is less of a discrepancy between the twocurves in the initial portion of the graph. The 24-layer modelfollows some of the previous trends exhibited with the one-, two-,four-, and eight-layer models. The FE and experimental load anddisplacement values are quite close till about 67 kN �15,000 lbs�.While the peak loads are close, the FE peak displacement is muchless than the experimentally obtained value. Since the FE is muchstiffer in this case, a larger value of load is needed to achieve thesame level of deformation.

Zylon Model

Fig. 13 shows the comparison between the static test and theresults obtained from the FE analysis. The FE and experimentalpeak load and displacement values as well as the load-deflectiongraphs are quite close.

Fig. 14 shows the comparison between the static test and theresults obtained from the FE analysis for the 24 layers of Kevlarand Zylon both. For all the Kevlar and Zylon simulations, thefollowing observations were made.1. The FE simulations of both Kevlar and Zylon underpredict

the peak load, perhaps due to the inherent stiffness of the FEmodel. Termination of the FE analysis takes place when the:

Fig. 12. Comparison of the load-displacement graphs for one-, two-,four-, and eight-layer Kevlar models

�1� solution starts diverging due to the presence of negative


eigenvalues in the system stiffness matrix, or �2� contact sur-face between the fabric and the blunt nose cannot be resolvedat large displacement values.

2. The maximum tensile strain in the fabric occurs at the area incontact with the edge of the blunt nose. This is consistentwith the failure modes observed during the static tests thatinitiate at and around the blunt nose contact region. Thestrain gradient is very high near the edges of the blunt noseand decrease very rapidly away from the blunt nose. Strainvalues greater than the ultimate strain value are found in allthe FE simulations. This is because finite elements are not

Fig. 13. Comparison of the load-displacement graphs for one-, two-,four-, and eight-layer Zylon models

Fig. 14. Comparison of the load-displacement graphs for 24-layerZylon and Kevlar models

“deleted” when the ultimate strain values are exceeded.However, this high strain zone is very localized.

3. The highest compressive strains occur in the fabric at: �1� theend diametrically opposite the blunt nose, and �2� at the edgeof the fabric near the blunt nose. These compressive strainsare prominent only after the postpeak stiffness value hasbeen reached. A fabric draping effect is seen in the deformedplot that is more prominent with Zylon specimens than withKevlar specimens.

4. The FE load-displacement curves track the experimentallyobtained curve quite nicely up until the peak load. In the caseof Zylon, the stress–strain curve from T1-test performs betterthan the T2-generated curve. When the multiple-layer resultsare compared to the FE-obtained curves, the finite elementresults indicate a stiffer model or behavior. This is probablybecause in the FE analysis only one equivalent fabric layer ismodeled.

Conclusions

A methodology for experimentally testing and modeling dry fab-rics for engine containment systems is presented. The methodol-ogy has been successfully employed in characterizing twofabrics—Kevlar 49 and Zylon AS. A simple but effective FE ma-terial model has been developed and validated. The constitutivemodeling as described in this study along with other input, hasbeen successfully used in explicit FE simulations of actual enginecontainment systems using LS-DYNA FE software system�Gomuc 2003�.

Acknowledgments

The writers would like to thank the Federal Aviation Administra-tion �FAA� for sponsoring this research under Grant No.01-C-AW-ASU. Don Altobelli and Bill Emmerling are the FAAproject managers for the project. The cooperation and help fromresearch partners—Honeywell Engine Systems, Phoenix, SRI,

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Intl., Menlo Park, Calif., and NASA-Glenn, Cleveland, Ohio—are also appreciated.

References

ASTM. �2000�. “Standard test method for tensile properties of fiber-resincomposites.” ASTM-D-3039.

Bednarcyk, B. A. �2001�. “Discussion of ‘woven fabric composite mate-rial model with material nonlinearity for non-linear finite elementsimulation’ by Tabiei and Jiang.” Int. J. Solids Struct. 38, 8585–8588.

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