Strain rate behavior of composite materials

Strain rate behavior of composite materials

H. M. Hsiaoa and I. M. Danielb ,*aMaterials Science Department, Research and Technology, Hexcel Composites,Dublin, CA 94568, USAbRobert R. McCormick School of Engineering and Applied Science,Northwestern University, Evanston, IL 60208-3020, USA

The effect of strain rate on the compressive and shear behavior of carbon/epoxy composite materials wasinvestigated. Strain rate behavior of composites with fiber waviness was also studied. Falling weight impactsystem and servohydraulic testing machine were used for dynamic characterisation of composite materials incompression at strain rates up to several hundred per second. Strain rates below 10 s¹1 were generated using ahydraulic testing machine. Strain rates above 10 s¹1 were generated using the drop tower apparatus developed.Seventy-two-ply unidirectional carbon/epoxy laminates (IM6G/3501-6) loaded in the longitudinal and transversedirections and [(08/908)2/08] s crossply laminates were characterised. Off-axis (30 and 458) compression tests ofthe same unidirectional material were also conducted to obtain the in-plane shear stress–strain behavior. The 908properties, which are governed by the matrix, show an increase in modulus and strength over the static values butno significant change in ultimate strain. The shear stress–strain behavior, which is also matrix-dominated, showshigh nonlinearity with a plateau region at a stress level that increases significantly with increasing strain rate. The08 and crossply laminates show higher strength and strain values as the strain rate increases, whereas the modulusincreases only slightly over the static value. The increase in strength and ultimate strain observed may be related tothe shear behavior of the composite and the change in failure modes. In all cases the dynamic stress–strain curvesstiffen as the strain rate increases. The stiffening is lowest in the longitudinal case and highest in the transverse andshear cases. Unidirectional and crossply specimens with fiber waviness were fabricated and tested. It is shownthat, with severe fiber waviness, strong nonlinearity occurs in the stress–strain curves due to fiberwaviness with significant stiffening as the strain rate increases.q 1998 Published by Elsevier Science Ltd. Allrights reserved

(Keywords: strain rate effects; dynamic response; compressive testing of composites; falling weight impact)

INTRODUCTION

Some applications of composite materials involve dynami-cally loaded components and structures. The analysis anddesign of such structures subjected to dynamic loadings,ranging from low-velocity impact to high-energy shockloadings, requires the input of high strain rate properties.Numerical simulations, such as finite element analysis,need an accurate description of such effects as strain rate,loading history, deformation, internal damage, and wavepropagation.

Related work on dynamic characterisation of compositematerials has been relatively limited compared to quasi-static tests due to the difficulty of high strain rate testing anddata interpretation. Most of the dynamic work conducted sofar has involved lateral impact testing of compositelaminates, but with less emphasis on constitutive propertiescharacterisation. In order to develop more sophisticatedconstitutive models and failure criteria under dynamic

loading and to assess their adequacy, experiments con-ducted over a wide range of strain rates, in which a singledominant stress component can be extracted, are veryimportant.

The various dynamic test methods used to date havedifferent advantages and limitations. The use of aservohydraulic machine is common and convenient. How-ever, the conventional hydraulic machine is limited to lowerstrain rates, below 10 s¹1, because of inertial effects of theload cell and grips. Chou et al.1 designed a special open/closed loop hydraulic machine to study the dynamiccompressive behaviour of neat resins over a range from10¹4 to 103 s¹1. The data presented show approximatelythree times increase in strength and are twice higher ininitial modulus over static values for PMMA resin. The dropweight impact test has many advantages, it is inexpensive,can accommodate different specimen geometries and allowseasy variation of strain rate. However, the system is verysensitive to the contact conditions between the impactor andspecimen and to spurious noise from ringing and vibrations.Dynamic tests using such a device on composite materialswere first conducted by Lifshitz2 in 1976. He observed a

Composites Part B29B (1998) 521–5331359-8368/98/$ - see front matter

q 1998 Published by Elsevier Science Ltd.All rights reservedPII: S1359-8368(98)00008-0

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* Corresponding author. Tel: +1 847 4915649; fax: +1 847 4915227;e-mail: [email protected]

significant strength increase under impact on balancedangle-ply laminates. Montiel and Williams3 used aninstrumented drop tower to determine compressive proper-ties of 48-ply graphite/PEEK [02/90]8s composites for strainrates up to 8 s¹1. The results indicate that at high strain rateloading, the strength increases by 42% and the ultimatestrain increases by 25%. There only appears to be a smallstrain rate effect on the initial modulus. Groves et al.4 alsodeveloped a drop tower system to generate strain rates from10 to 1000 s¹1. The split Hopkinson pressure bar (SHPB)technique permits testing at higher strain rates exceeding1000 s¹1. Contact surface conditions are very critical as inthe drop weight testing. Specimens must be short tominimize wave propagation effects. However, this raisesquestions on the homogeneity and uniaxiality of the inducedstress in the specimen. Most of the high strain ratecompressive properties reported to date have been obtainedby this technique, e.g., Sierakowski et al., El-Habak,Harding, Lifshitz and Leber, Weeks and Sun, and Powerset al. 5–10. Sierakowski et al.5 investigated steel/epoxycomposites in compression up to 1000 s¹1. They observedvery different failure modes in static and dynamiccompressive tests on cylindrical specimens. The initialmodulus remains unchanged but the strength increases by100% in the dynamic tests. Harding7 studied two wovenglass/epoxy material systems in compression up to 860 s¹1

using cylindrical and thin strip specimens. He concludedthat there is a significant increase in the initial modulus,strength and ultimate strain with increasing strain rate forwoven glass/epoxy composites. Amijima and Fujii11

studied glass/polyester plain woven and unidirectionalcomposites in compressive tests of cylindrical specimens.The increase in strength is shown to be higher for the wovencomposites than for the unidirectional ones. Tests using thinring specimens under dynamic internal or external pressure

can minimize the wave propagation effects, but they areexpensive and complex and cannot be used for thickcomposites. Daniel and LaBedz12 developed a test methodutilizing a thin graphite/epoxy ring (six to eight plies thick)composite specimen loaded by an external pressure pulseapplied explosively through a liquid. They obtainedcompressive properties at strain rates up to 500 s¹1. The08 properties show some increase in initial modulus over thestatic values but no change in strength. The 908 propertiesshow much higher than static modulus and strength.Reviews on high strain rate studies for composite materialscan be found from the articles and books by Greszczuk andSierakowski13–15.

This paper discusses the application of a drop weightsystem and a servohydraulic testing machine for dynamiccharacterisation of carbon/epoxy composites. Strain ratebehavior of composites with fiber waviness was alsostudied. The results presented cover strain rates fromquasi-static to several hundred per second. Strain ratesabove 10 s¹1 were generated using a drop towerapparatus.

EXPERIMENTAL PROCEDURES

Material selection and specimen fabrication

Seventy-two-ply thick unidirectional and crossply lami-nates were selected to investigate the strain rate effect in thisstudy. The material used was IM6G/3501-6 carbon/epoxycomposite (Hexcel Corp.). The prepreg layup was cured in apress/autoclave by a three-step curing cycle especiallydeveloped for thick composites16. The void content, asdetermined by digital image analysis of photomicrographs,was less than 1% in all panels tested.

Strain rate behavior of composite materials: H. M. Hsiao and I. M. Daniel

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Figure 1 (a) Impact specimen configurations; (b) specimen holding and guide fixture

Drop tower apparatus

A drop tower was designed and built for dynamiccompressive testing of thick composites at strain ratesranging from 10 to several hundred per second17. It consistsof two 2.54 cm (1 in) diameter and 3 m (10 ft) long guiderods which are 17.8 cm (7 in) apart. The drop weight isguided along the rods through two bearing assemblies. It israised and released using an electromagnet connected to acable. A 5000g quartz accelerometer (Kistler Instr. Corp.)is mounted at the center of the drop weight on the topsurface.

Figure 1a shows the dynamic compression test specimenconfiguration for the drop tower. A 72-ply compositespecimen 2.54 cm (1 in) long and 1.27 cm (0.50 in) widewas bonded to a similar high-strength steel specimen. Thelatter was made of 4140 steel with a yield stress of1660 MPa (240 ksi) under quasi-static loading. Steel endcaps were bonded at the outer ends. Each end cap consistedof a 513 513 6.4 mm (23 2 3 0.25 in) plate with a 8.7312.7 mm (0.353 0.50 in) rectangular cutout at the centerbonded to a similar 1.27 cm (0.50 in) thick plate without acutout. Curing of the adhesive in the end caps was done byplacing the specimen between the impactor and the baseplate, which increased the uniformity of surface contactduring impact. Close tolerances were achieved for flatnessand perpendicularity on the contact faces to minimise out-of-plane specimen bending.

In all cases the specimens were end-loaded. A fixture wasdesigned to hold and guide the specimen during impact(Figure 1b). Uniform end loading was accomplishedthrough the use of this guide system to constrain all butthe vertical motion of the specimen. The specimen with theend caps was mounted in such a way that the top of the endcaps protruded by 6 mm (0.25 in) above the top of the guidesystem. Axial strain gages were mounted on both sides of

the composite and steel specimens, connected to a bridgeconditioner, amplified by an HP amplifier and recorded by afour-channel digital processing oscilloscope (Norland 3001)at sampling intervals of 1–10ms. For strain rates below10 s¹1 the servohydraulic testing machine was used, alongwith the specimen, guide fixture and data acquisition systemdescribed here.

The dynamic impact force was measured in two differentways. Initially, it was measured with an accelerometermounted on the top of the drop weight. The dynamic forceand hence applied stress was obtained from the acceler-ometer reading multiplied by the mass of the impactorassembly, which included the drop weight, bearingassembly, and top end cap. This was checked against thevalue obtained more directly from strain readings on thesteel portion of the specimen. The axial strain in the steelspecimen (load cell), mounted in series with the compositespecimen, was multiplied by its modulus (207 GPa; 30 Msi)for more accurate determination of the dynamic force. Forthe specimen dimensions used, the time required for a stresswave to travel the length of the steel specimen isapproximately 5ms and that for the composite specimenvaries between 3 (08 specimen) and 11ms (908 specimen).Valid results were obtained since the test durations in thedrop tower tests, usually on the order of several hundred to1000ms, were much longer than the above stress wave traveltimes. In most cases the force results obtained from theaccelerometer reading were in agreement with thoseobtained from strain readings in the steel specimen.Discrepancies occurred near the end of the stress–straincurve, with the accelerometer reading giving a lower forcevalue. This was attributed to wave propagation effectsinside the impactor and vibrations of the entire system.Because of the signal noise from the accelerometer, forcedeterminations based on steel strain readings were judged tobe more reliable and thus used in all cases.

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Figure 2 Acceleration of 4.66 kg (10.27 lb) mass impacting a unidirectional IM6G/3501-6 carbon/epoxy specimen in the transverse direction and measuredaxial strains in composite and calibration steel specimens (height of drop, 2.44 m (8 ft))

The major problem in the use of a drop tower apparatus isthe presence of vibration stress waves superimposed on thestress–strain curves. In this study rubber sheets, from2.54 mm (0.1 in) to 7.62 mm (0.3 in.) thick, were placedover the top end cap to minimise ringing due to impact. Thisabsorber dampened the spurious noise in the accelerationand strain histories caused by apparatus vibrations and steel-to-steel contact. It also served to distribute the load on thespecimen more uniformly. Fiber-cork vibration dampingpads were placed between the floor and the entire drop towerapparatus to reduce the undesirable wave reflections. It isnoted that, without damping the system, the acceleration,load and strain measurements are distorted through oscilla-tions, which include rigid body accelerations of the systemand shock waves resulting from impact. To separate thesetwo sources, a fast Fourier transform (FFT) analysis can beapplied to decompose the frequency of the raw data18,19.The lower frequency data are attributable to rigid bodyacceleration, whereas the higher frequency data result fromacoustic waves. The high frequency data can then be culledfrom the raw data, resulting in a smooth stress–strain curvewhich contains rigid body acceleration only.

RESULTS AND DISCUSSION

Transverse compressive behavior of unidirectionalcomposite

Strain rate tests were performed on the drop tower and thehydraulic testing machine. Tests conducted on the droptower used a mass of 4.66 kg (10.27 lb) falling from a heightof 2.44 m (8 ft), producing strain rates from 10 to severalhundred per second. The impactor acceleration and thespecimen strains (steel and composite) were recorded.Typical acceleration versus time and specimen strain versus

time plots are shown inFigure 2. Dynamic stress–straincurves of such a test are shown inFigure 3, where they areplotted based on both acceleration and steel calibrationstrain measurements. The two curves agree for the mostpart, except near the end where the acceleration measure-ments tend to underestimate the force (stress). Forcedeterminations based on steel strain readings were judgedto be more reliable and thus were used in all cases.Specimen strains versus time plots, such as the one shown inFigure 2, were used to determine the strain rate. Because ofthe absorbers used in dynamic testing, the initial part of thestrain–time curve was not truly indicative of the effectivestrain rate experienced by the specimen. However, thestrain rate seemed to reach a nearly constant value at a strainlevel of approximately 10%–20% of the ultimate strain inall cases. The strain rates were thus determined bydifferentiating the strain–time curve at strain readingsabove 20% of the ultimate rain. The strain rate obtained bythis method for the case shown inFigure 2 wasapproximately 60 s¹1.

Transverse stress–strain curves to failure under quasi-static and high strain rates are shown inFigure 4. Thiscomparison shows a significant strain rate effect. Thetransverse strength, which is a matrix-dominated property,shows nearly a two-fold increase from the quasi-staticvalue. The initial modulus follows a similar trend, althoughnot as pronounced, with an increase of up to 37%. Theultimate strain shows no strain rate effect at all, whichimplies that it can be used as a failure criterion in analysisunder dynamic loading.Figure 4also shows that the stress–strain behavior is a function of strain rate. The materialstiffens (with a reduction in matrix ductility) as the strainrate increases. This stiffening behavior is very significant inthe nonlinear region. Two possible reasons for thisphenomenon are proposed. The first one is the viscoelasticnature of the polymeric matrix itself and the second one is


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Figure 3 Transverse compressive stress–strain curves for unidirectional IM6G/3501-6 carbon/epoxy at a strain rate of 60 s¹1 (the curves were based on bothacceleration and steel calibration strain measurements)

the time-dependent nature of accumulating damage. Atslower rates damage accumulates more gradually, such thata well-defined nonlinear region occurs near the end of thestress–strain curve. At higher rates, however, damage doesnot have enough time to develop and thus the damageaccumulation process has a diminishing effect on the stress–strain curve as the strain rate increases. A similarphenomenon was also observed on the transverse compres-sive behavior of AS4/APC2 carbon/PEEK under quasi-static and high strain rates of loading (Figure 5). However,PEEK-based resin is more ductile in the nonlinear region ofthe stress–strain curves compared to the 3501-6 epoxy-based resin.

In-plane shear behavior of unidirectional composite

The off-axis compression test was used to obtain the in-plane shear behavior of the unidirectional composite. A 108off-axis specimen is usually chosen to minimize the effectsof longitudinal and transverse stress components,j1 andj2,on the shear response. However, under compressiveloading, it is not practical to employ the 108 off-axis testsince a long specimen is required. Therefore, off-axisspecimens of 15, 30, 45 and 608 were first tested underquasi-static compressive loading to check the consistency ofshear stress–strain curves obtained from different off-axisangles. These results, shown inFigure 6, reveal that the

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Figure 4 Transverse compressive stress–strain curves for unidirectional IM6G/3501-6 carbon/epoxy under quasi-static and high strain rate loading

Figure 5 Comparison of transverse compressive stress–strain curves between AS4/APC2 carbon/PEEK and IM6G/3501-6 carbon/epoxy under quasi-staticand high strain rate loading

shear stress–strain curves obtained from different off-axisspecimens agree well within both the linear and nonlinearranges. This implies that the superposition principle stillholds and the shear component can thus be decoupled fromthe applied uniaxial stress. It should be noted that theexperimental results tend to overestimate the ultimateproperties due to interaction of the transverse compressivestress across the fibers; nevertheless the elastic propertiesand overall shear stress–strain curve can be obtainedfrom the off-axis test accurately. In this study, 30 and 458off-axis specimens were used to investigate the strain rateeffect on the in-plane shear behavior of the unidirectionalcomposite.

Shear property characterisation conducted on the droptower used the mass of 4.66 kg (10.27 lb) falling from a

height of 2.44 m (8 ft).Figure 7 shows the shear stress–strain curves obtained from 30 and 458 off-axis specimensunder quasi-static and high strain rates of loading forcomparison. It appears that the shear stress–strain curvesobtained from these two different angles agree well for thesimilar strain rate in either the static or dynamic domain.This characterisation also reveals a strong strain rate effect.The shear stress–strain behaviour, which is also matrixdominated, shows high nonlinearity with a plateau region ata stress level that increases significantly as the strain rateincreases. The yield point of the curve also increases withincreasing strain rate. The strength increases sharply withstrain rate from the quasi-static value by up to 80%. Theinitial modulus follows a similar trend, although not aspronounced, with an increase up to 18%.


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Figure 7 Comparison of shear stress–strain curves obtained from 308 and 458 off-axis tests under quasi-static and high strain rate compressive loading

Figure 6 Comparison of in-plane shear stress–strain curves obtained from different off-axis tests under quasi-static compression

Longitudinal compressive behavior of unidirectionalcomposite

In this study the end loading principle was adopted totesting thick composites since it is widely accepted and,more importantly, easy to use for dynamic compressivetesting. Test methods based on the end loading principleinclude the ASTM D695 test (SACMA SRM 1-88), theEuropean version ICSTM test20, and the DTRC test21.Recently a new compression test method for thickcomposites (NU method), based on the concept of combinedshear loading and end loading, was developed22. It wasfound that the pure end loading method tends to

underestimate the longitudinal compressive strength andstrain values of thick composites due to premature end-crushing failure (Figure 8). By using the NU test method,longitudinal compressive strengths of 1660 MPa (240 ksi),which are significantly higher than those measured by theend loading methods, are obtainable experimentally forthick composites under quasi-static loading. Therefore,experimental results from compression tests have to beinterpreted with extra care. Longitudinal compressivestrengths obtained at different strain rates can only becompared when the same loading method is used.

Unidirectional specimens were loaded in the fiberdirection with a mass of 17.31 kg (38.16 lb) falling from a

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Figure 9 Longitudinal compressive stress–strain curves for unidirectional IM6G/3501-6 carbon/epoxy under quasi-static and high strain rate loading

Figure 8 Comparison of compressive stress–strain curves between combined shear/end loading (NU test method) and pure end loading under quasi-staticloading

height of 2.44 m (8 ft) on the drop tower.Figure 9displaysthe longitudinal stress–strain curves to failure under quasi-static and high strain rates of loading. It clearly shows thestiffening behavior in the nonlinear range that is notobservable from the end loading results alone. The stress–strain curve stiffens as the strain rate increases, although themagnitude of the change is much smaller compared to thetransverse and shear behavior. The initial modulus showsonly a slight increase with strain rate. The strength andultimate strain are significantly higher than the static valuesby up to 79% and 74%, respectively. The increase instrength and ultimate strain observed may be related to theshear behavior of the composite and the change in failure

modes. It is known that longitudinal compressive failure isintimately related to, and governed by, the in-plane shearresponse of the composite, even in the presence of theslightest initial fiber misalignment23–25. Any compressivefailure observed follows some form of initial shear failure ofthe composite. The longitudinal compressive strength isexpressed as

F1c ¼ (jx)max¼tp

f þ gp

wheref is the initial fiber misalignment; andt*, g* arevalues of shear stress and strain as defined inFigure 10.

Figure 10shows a measured shear stress–strain curve for


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Figure 11 Compressive stress–strain curves for [(08/908)2/08] s crossply IM6G/3501-6 carbon/epoxy under quasi-static and high strain rate loading

Figure 10 Graphical determination of longitudinal compressive strength (f ¼ initial fiber misalignment)

an IM6G/3501-6 carbon/epoxy composite with an illustra-tion of a graphical determination oft* and g*. Thecompressive strength corresponds to the valuest* and g*,where the tangent to the shear stress–strain curve equals theslopet*/(f þ g*). It is apparent fromFigure 10that, if thein-plane shear behavior stiffens substantially with increas-ing strain rate, then this would lead to the increase inlongitudinal compressive strength.Figures 7 and 10combined give a good explanation of the increase inlongitudinal strength and ultimate strain observed during thetests. This relationship can also be used to explain thesignificant increase in the compressive strength of wovencomposites under impact. It is found that a woven compositeis more sensitive to strain rate than a unidirectional one, andthat different woven composites have different strain rateeffects due to the reinforcement structure11,26. Plain-weavecomposites show a higher strain rate effect than satin-weave, unidirectional or multidirectional ones. This isattributed to the higher shear-dependence in the plain-weavecase than in the other cases.

In addition, for high strain rate testing, the duration ofloading is short enough that material failure occurs prior tothe onset of fiber microbuckling. This suggests that a changein failure modes occurs as the strain rate increases. Themicrostructure change during the high rate testing should bestudied in depth to elucidate the contribution of differentdamage mechanisms to the dynamic behavior of compositematerials.

Compressive behavior of crossply composite

Crossply specimens of [(08/908)2/08] s layup were loadedwith a mass of 11.34 kg (25 lb) falling from a height of2.44 m (8 ft). Stress–strain curves to failure under quasi-static and high strain rates of loading are shown inFigure 11for comparison. It shows that the material stiffens as thestrain rate increases, and the magnitude of the change isslightly higher than in the longitudinal case. The initialmodulus shows only a slight increase with strain rate. Thestrength and ultimate strain are significantly higher than thestatic values by up to 67% and 57%, respectively. The strainrate sensitivity of the strength, initial modulus and ultimatestrain of the crossply composite follow similar trends as theones observed under longitudinal compression. Therefore,compressive behavior of a crossply composite is dominatedby the 08 layers.

Compressive behavior of composite with fiber waviness

Fiber waviness is a type of manufacturing defectoccurring during processing. It results from wet hoop-wound filament strands under the pressure exerted by theoverwrapped layers during the filament winding process. Itoccurs also in the manufacture of the fiber tows, in theprepreg tape impregnation process, or in the subsequentlayup and curing process. Fiber waviness has been shown toaffect significantly the compressive behavior of compositematerials27–30.

Techniques were developed for fabrication of composite

specimens with different types of controlled waviness31.One hundred and fifty-ply unidirectional specimens withuniform through-the-thickness sinusoidal waviness(Figure 12a) and 72-ply [(08/908)2/08w] s crossply specimenswith central layer waviness (Figure 12b) were fabricated tostudy their strain rate behavior.A and L in Figure 12represent the amplitude and period of the wavy fiber,respectively. The degree of waviness is characterised by theamplitude to period ratio,A/L. The A/L ratio of unidirec-tional and crossply specimens studied here is 0.0425 and0.02, respectively.

The presence of fiber waviness can significantly degradethe compressive properties of composite materials.Figure 13 illustrates the predicted stiffness and strengthreduction as a function of waviness parameterA/L alongwith the experimental result for unidirectional compositeswith uniform fiber waviness (quasi-static case)29. It appearsthat both major Young’s modulus and compressive strengthdegrade seriously as the fiber waviness increases. Com-pressive strength is much more sensitive to fiber wavinessthan the major Young’s modulus, especially whenA/L issmall. Figure 14 illustrates the predicted stress–straincurves under uniaxial static compressive loading as afunction ofA/L for the same wave pattern30. It demonstrateshow material nonlinearity increases with increasing fiber

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Figure 12 (a) Representative volume and coordinates for a unidirectionalcomposite with uniform fiber waviness. (b) Representative volume andcoordinates for a [(08/908)2/08w] s crossply composite with central layerwaviness

waviness. Since it is shown that the stress–strain curvestiffens with increasing strain rate and decreasing fiberwaviness, it is interesting to understand the combinedeffects of fiber waviness and strain rate on the compressivebehavior of composite materials.

Unidirectional and crossply specimens with fiber wavi-ness were loaded with a mass of 11.34 kg (25 lb) fallingfrom a height of 2.44 m (8 ft).Figure 15 shows thecompressive stress–strain curves for unidirectional speci-mens with uniform fiber waviness (A/L ¼ 0.0425) underquasi-static and high strain rates of loading. The specimenstested failed prematurely due to the fiber discontinuities onthe specimen surfaces (Figure 12a), and thus the strength

and ultimate strain cannot be compared in this particularcase. The dynamic stress–strain curves stiffen slightly overthe static ones up to the load level applied. This result agreeswell with the predictions based on the numerical incre-mental analysis by the authors32. However, it was suggestedfrom the same analysis that the strain rate effect becomessignificant at higher loads due to larger shear componentinvolved (Figure 16). Figure 16 is the replot ofFigure 15along with the predictions made by the incremental analysis.It is shown that, with this type of severe fiber waviness (A/L¼ 0.0425), strong nonlinearity occurs in the stress–straincurves due to fiber waviness with significant stiffening asthe strain rate increases.


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Figure 14 Predicted stress–strain curves as a function of waviness parameterA/L for unidirectional IM6G/3501-6 carbon/epoxy with uniform fiber wavinessunder quasi-static compressive loading

Figure 13 Predicted stiffness and strength reduction of unidirectional IM6G/3501-6 carbon/epoxy under quasi-static compressive loading as a function ofwaviness parameterA/L for uniform-waviness model

Figure 17shows the compressive stress–strain curves forcrossply specimens with and without central layer waviness(maximumA/L ¼ 0.02) under quasi-static and high strainrates of loading. The waviness in this case is localised andmuch milder compared to the previous case (Figure 12).Therefore, the strain rate sensitivity of the strength,ultimate strain, initial modulus, and stress–strainbehavior of this wavy crossply composite follows similartrends as its nonwavy counterpart with slightly highermagnitude.

SUMMARY AND CONCLUSIONS

A systematic investigation was conducted of the effect ofstrain rate on the compressive and shear behavior ofcomposite materials. Unidirectional carbon/epoxy lami-nates (IM6G/3501-6) with fibers at 0, 30, 45 and 908 withloading direction and [(08/908)2/08] s crossply laminateswere characterised at strain rates up to several hundred persecond. Unidirectional specimens with uniform fiberwaviness and [(08/908)2/08w] s crossply specimens with

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Figure 15 Compressive stress–strain curves for unidirectional IM6G/3501-6 carbon/epoxy with uniform fiber waviness (A/L ¼ 0.0425) under quasi-staticand high strain rate loading

Figure 16 Predicted compressive stress–strain curves by incremental analysis and experimental results for unidirectional IM6G/3501-6 carbon/epoxy withuniform fiber waviness (A/L ¼ 0.0425) under quasi-static and high strain rate loading

central layer waviness were fabricated to study their strainrate behavior.

The transverse compressive strength increases sharplywith strain rate to nearly double the quasi-static value at thehighest rate. The initial modulus follows a similar trend,although not as pronounced, with an increase up to 37%.The ultimate strain shows no strain rate effect at all, whichimplies that it can be used as a failure criterion for analysisunder dynamic loading. The stress–strain behavior is also astrong function of strain rate. The material stiffenssignificantly as the strain rate increases.

The 30 and 458 off-axis compression tests wereconducted to investigate the strain rate effect on the in-planeshear behavior of unidirectional composites. Shear stress–strain curves obtained from these two different angles agreewell for the similar strain rates in either the static ordynamic domain. The shear stress–strain behavior showshigh nonlinearity with a plateau region at a stress level thatincreases significantly as the strain rate increases. The yieldpoint of the curve also increases with increasing strain rate.The shear strength increases sharply with strain rate fromthe quasi-static value by up to 80%.

Longitudinal compressive properties were obtained forstrain rates up to 110 s¹1. The initial modulus increases onlyslightly with strain rate over the static value. The strengthand ultimate strain are significantly higher than the staticvalues by up to 79% and 74%, respectively. The increase instrength and ultimate strain observed may be related to thestiffening of the composite in-plane shear behavior underdynamic loading and the change in failure modes. Thestress–strain curve stiffens slightly as the strain rateincreases. Compressive properties of a crossply compositewere also obtained. The results show increases in strengthand ultimate strain but only a slight increase in initialmodulus. The stress–strain curve stiffens as the strain rateincreases and the magnitude of the change is slightly higherthan in the longitudinal case. The strain rate sensitivity of

the strength, initial modulus and ultimate strain of thecrossply composite follow similar trends as the onesobserved under longitudinal compression. Therefore, com-pressive behavior of crossply composite is dominated by the08 layers.

Unidirectional and crossply specimens with fiber wavi-ness were fabricated and tested. The dynamic stress–straincurves of unidirectional specimens stiffen slightly over thestatic ones up to the load level applied. This result agreeswell with the predictions based on the numerical incre-mental analysis. However, it was suggested from the sameanalysis that the strain rate effect becomes significant athigher loads due to larger shear component involved. It isshown that, with this type of severe fiber waviness, strongnonlinearity occurs in the stress–strain curves due to fiberwaviness with significant stiffening as the strain rateincreases. The waviness in crossply specimens is localisedand much milder compared to the unidirectional ones. Theobtained strain rate sensitivity of this wavy crossplycomposite follows similar trends as its nonwavy counterpartwith slightly higher magnitude.

ACKNOWLEDGEMENTS

The work described in this paper was sponsored by theOffice of Naval Research. We are grateful to Dr. Y. D. S.Rajapakse of ONR for his encouragement and cooperation.

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Figure 17 Compressive stress–strain curves for crossply IM6G/3501-6 carbon/epoxy with and without central layer waviness (maximumA/L ¼ 0.02) underquasi-static and high strain rate loading

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Strain rate behavior of composite materials

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