Materials and Design 53 (2014) 706–718

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Materials and Design

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Technical Report

Low-velocity impact damage of woven fabric composites: Finite elementsimulation and experimental verification

0261-3069/$ - see front matter � 2013 Elsevier Ltd. All rights reserved.http://dx.doi.org/10.1016/j.matdes.2013.07.068

⇑ Corresponding author at: Mechanical Engineering Department, Faculty ofEngineering, University Malaya, 50603 Kuala Lumpur, Malaysia. Tel.: +60 379674447; fax: +60 3 79675282.

E-mail addresses: el_khozami@rocketmail.com, mohsenegypt@um.edu.my (M.A.Hassan).

M.A. Hassan a,b,c,⇑, S. Naderi a,c, A.R. Bushroa a,c

a Mechanical Engineering Department, Faculty of Engineering, University Malaya, 50603 Kuala Lumpur, Malaysiab Mechanical Engineering Department, Faculty of Engineering, Assiut University, 71516 Assiut, Egyptc Center of Advanced Manufacturing and Material Processing, AMMP Center, University Malaya, 50603 Kuala Lumpur, Malaysia

a r t i c l e i n f o

Article history:Received 17 May 2013Accepted 18 July 2013Available online 2 August 2013

a b s t r a c t

This paper addresses the response of Glass Fiber Reinforced Plastic laminates (GFRPs) under low-velocityimpact. Experimental tests were performed according to ASTM: D5628 for different initial impact energylevels ranging from 9.8 J to 29.4 J and specimen thicknesses of 2, 3 and 4 mm. The impact damage processand contact stiffness were studied incrementally until a perforation phase of the layered compoundsoccurred, in line with a force–deflection diagram and imaging of impacted laminates. The influence thatimpact parameters such as velocity and initial energy had on deflection and damage of the test specimenswas investigated. Finite Element Simulation (FES) was done using MSC. MARC� was additionally carriedout to understand the impact mechanism and correlation between these parameters and the induceddamage. The simulation and experimental results reached good accord regarding maximum contact forceand contact time with insignificant amount of damage.

� 2013 Elsevier Ltd. All rights reserved.

1. Introduction

The application of composite materials in industrial structuresis projected to increase over the next couple of decades. The dy-namic mechanical behavior of composite materials is consideredone of the most important properties by structural engineers. Forinstance, plastic behavior and damage under low-velocity impactcan possibly ensue during production, maintenance, repair, or thelifetime of structural composite components. A number of factorswhich can seriously damage composites include tool drop, flyingdebris, foreign object damage, etc. However, damage from low-velocity impact is not visible to the naked eye but may affect thematerial’s residual mechanical properties.

Recently, numerous researchers have been studying the impacteffects on composite laminates. The investigations can be dividedinto three categories: (1) dynamic response of composite lami-nates, (2) contact mechanism in composite structures by impactload and (3) damage modes and failure in composites. Findiket al. [1] and Findik and Tarim [2] have experimentally investigatedthe impact performance of some polymer-based composites and

observed the contact mechanism as well as dynamic response ofcomposite laminates. Other researchers have focused their studieson damage recognition, type and mode. Unal et al. [3] investigatedinfluence of adding talc and kaolin fillers on the mechanical prop-erties of nylon 6. But they did not mention about a delaminationmodel of different fiber reinforced plates that always occurred instretched form or almond shape. Findik et al. [4] studied the effectsof impact on mechanical properties of glass fiber reinforced polyes-ter matrix plates using optical and scanning electron microscopes.They also looked into how a toughened matrix could enhance theimpact characteristics of epoxy composites. Zhou and Greaves [5]studied the damage resistance and tolerance of glass fiber-rein-forced plates with a range of thicknesses. The damage of four dif-ferent fiber-reinforced composite plates following standard dropweight impact at various impact energies was studied by Hossein-zadeh et al. [6]. All plates were modeled using ANSYS LS-DYNA un-der similar conditions to those from the real tests. They alsocalculated the threshold damage value for each composite. Titaet al. [7] developed experimental and numerical approaches forfailure analyses of thin composite laminates under low-velocityimpact. Zhang et al. [8] investigated Impact behaviors at low veloc-ity of composite laminates reinforced with fabrics of differentarchitectures.

Bellingardi and Vadori [9] examined the behavior of compositelaminate plates subjected to low-velocity impact loading. Thetests produced three kinds of results, namely rebound, stop, or

Fig. 1. A schematic picture of stacking sequence.

Table 1Geometric properties and number of layers for test specimens.

Fabricmaterial

Area density (gr/m2)

Length(cm � cm)

Number of layer fordifferent thickness

2 mm 3 mm 4 mm

E-glass 400 12 � 12 3 5 6

Fig. 3. Geometry of impactor with hemispherical head (diameter = 12.7 mm).

M.A. Hassan et al. / Materials and Design 53 (2014) 706–718 707

perforation, all based on the potential energy initially supplied tothe dart by fixing its dropping height. It was deduced that if the en-ergy absorbed by the specimen was not excessively high, theimpactor would experience rebound.

The FE-numerical approaches appear to be the best techniquefor analyzing the behavior of composite laminate plates sincethey are fairly accurate, less expensive and less time consuming.Belingardi and Vadori [10] examined the effect of thickness onbehavior of laminated composites under low-velocity impactloading based on saturation energy. The damage processes wascharacterized by using the ratio between the dissipated energyand the initial impact energy. They developed a linear relationfor the dependence of the first damage force and maximum forcevalues, of the saturation energy and of the plate flexural stiffnesswith respect to the laminate number of layers. However, the rela-tion is valid only in the examined range and cannot begeneralized.

Choi [11] developed a finite element equation for solving thelow-velocity impact response and damage of composite laminatesunder initial in-plane load. He assumed that damage areas of theplates can be approximately predicted from the value of the straincomponent of the bottom layer of the laminate. Yet this assump-tion needs to be verified by further experiments.

Iannucci and Willows [12] proposed the application of theenergy based damage mechanics to model impact onto wovencomposite materials. They implemented their approach into

Fig. 2. Fixtures and sample loc

explicit dynamic DYNA3D code for plane stress condition. Re-sults revealed that their model is valid for problems specific toimpact on thin carbon composite structure. But it does not con-sider the local variability and scatter in the force time responsesince it links damage and fracture in a representative volumeconcept.

Mitrevski et al. [13] studied the influence of impactor shape andtensile biaxial preload on the impact response of thin glass fiberreinforced polyester laminated. The overall damage area was mea-sured using a back illumination technique. The maximum force,absorbed energy and damage area were mostly unchanged bythe preload. However, further work is needed to study the effectof level of preload under negative biaxial stress ratio.

Ghasemnejad et al. [14] implemented The Charpy impact test toinvestigate the energy absorbing capability of delaminated com-posite beam. The test was also simulated using LS-DYNA finite ele-ment software. Experiential and numerical results indicated thatthe energy absorption could be proper criteria to improve impactdamage response of composites. Wang et al. [15] investigated

ations under the fixtures.

Fig. 4. Schematic of drop weight machine.

Fig. 5. Schematic of force–deflection curve after impact for (a) non-perforated sample (closed form), and (b) perforated sample (open form).

Fig. 6. Loading and unloading phases in schematic force–deflection in woven fibercomposite by different impact energy.

708 M.A. Hassan et al. / Materials and Design 53 (2014) 706–718

low-velocity impact and residual tensile strength to carbon fibercomposite laminates by numerical and experimental methods.According to their analysis results, degradation of residual tensilestrength was utilized to judge the damage amount for impactedcomposite laminate.

In general, as per work previously mentioned, the shape of theimpacted region did not show proper coincidence with those ob-tained from the experiments. But the simulations were able to pre-dict the onset of damage as it was verified well by test results. Thismay be attributed to the deviation in the quality of compositematerial models that are implemented in FE-commercial software.As per work previously mentioned, the experimental and classicalmechanics approaches seem to be very costly and highly compli-cated for studying GFRP laminates under impact. Damage fromlow-velocity impact is not visible to the naked eye but may affectthe material’s residual mechanical properties. Thus damage shouldbe assessed during and after the impact. The main goal of this pa-per is therefore to study the response of woven composite GFRPlaminates under low-velocity impact in an efficient and economi-cal manner. To understand how the damage process can be as-sessed, based on FE-simulation, and how it correlates to theforce–deflection curve, a velocity–deflection curve and image ofimpacted plates with different thicknesses and impact energiesare scrutinized. Bending stiffness and damage are assessed duringand after the impact.

Fig. 7. Finite element model with solid elements.

M.A. Hassan et al. / Materials and Design 53 (2014) 706–718 709

MSC.MARC finite element software was used to simulate theimpact behavior of glass fiber/epoxy since it has well establishedorthotropic composite material models. The obtained simulationresults were verified with the experimental force–time curves ob-tained with the free-fall drop dart machine. Finally, the results arediscussed and evaluated.

2. Materials and methods

2.1. Preparation of specimens

Different methods of sample preparation have been highlightedby Yetgin et al. [16]. In this investigation, epoxy resin reinforcedwith woven E-glass fiber was employed. The hand layup processwas used to stack the plies which were cured at room temperaturefor over 24 h. Cross-ply glass fibers in each layer run in the x and ydirections, and the stacking sequence of layers is shown in Fig. 1. In

Fig. 8. F–d diagrams for impact energies of 9.8 and 19.6 J on

order to study the behavior of thin and thick plates under impactload, samples were fabricated in thicknesses of 2, 3 and 4 mm.The number of layers was increased depending on the thicknessof the laminates. Table 1 lists the number of layers and the sam-ples’ geometric properties.

The test specimens were cut into squares (12 � 12 cm). Theplates’ surfaces were burnished for transparency to properly visu-alize the inner damage with the naked eye.

2.2. Impact test configuration

The equipment used in this research is a free-fall drop dart ma-chine which has a load cell with a capacity of 10 KN. The impactor’sheight and weight are changeable to facilitate obtaining differentinitial impact energies. The composite plates have clamped bound-aries with several square fixtures of different sizes that hold thesamples in various dimensions. Fig. 2 illustrates a sample fittedinto a square fixture.

According to ASTM: D5628 [17], the impactor head is hemi-spherical with a diameter of 12.7 mm (Fig. 3). The impactor wasmade from steel 4340 to warrant high rigidity. Fig. 4 indicates a gen-eral schematic picture of the drop weight machine. A data acquisi-tion system, acceleration transducer and load cell connected to theimpactor were applied to record the force–deflection (F–d) curvesimultaneously during the impact process. The velocity curvesversus deflection are also obtained from the force–acceleration

samples with thicknesses of: (a) 2 mm, and (b) 3 mm.

Fig. 9. Photographs of impacted and non-impacted samples with 2 mm thicknessafter impact with different impact energy and damage propagation values in the45� direction in woven fiber laminate. (a) Initial energy = 9.8 J, and (b) initialenergy = 19.6 J.

Fig. 10. Photographs of impacted and non-impacted samples with 3 mm thicknessafter impact with different impact energy and damage propagation values in the45� direction in woven fiber laminate. (a) Initial energy = 9.8 J, and (b) Initialenergy = 19.6 J.

Fig. 11. F–d graph for sample with 4 mm thickness and impact energy: (a) 9.8 J, (b)19.6 J, and (c) 29.4 J.

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Fig. 12. F–d graph for sample with 4 mm thickness and impact energy: (a) 9.8 J, (b) 19.6 J, and (c) 29.4 J.

M.A. Hassan et al. / Materials and Design 53 (2014) 706–718 711

diagram by calculating the first integration of acceleration; deflec-tion is obtained from the second integration of acceleration. Theintegration process is done offline using a small code written inMATLAB software.

The minimum impactor height is 10 cm and minimum weight is7 kg including the tup mass. Height is increased by 10 cm incre-ments at each step. The pneumatic brake system prevents theimpactor from making multiple impacts following the first impactwith the test specimen. The height of the impactor ranges from 10to 30 cm the mass of 10 kg is constant.

If an object with mass m impacts a composite plate with avelocity v the impact energy of impactor Ei as Belingardi and Vado-ri [10] considered can be expressed by:

mgh ¼ 12

mv2 ¼ Ei ð1Þ

2.3. General behavior of GFRPs under low-velocity impact

The history diagrams for impact force, deflection, impactorvelocity and absorbed energy were studied to assess the behavior

Fig. 13. F–d diagram in loading phase with impact energy of 9.8 J for: (a) 2 mm, (b)3 mm, and (c) 4 mm thickness.

Table 2Bending stiffness for different thickness (in parentheses an amount of kb per numberof layers).

Thickness (mm) 2 3 4

Kb (ton/(ms)2) 0.29 (0.097) 0.38 (0.076) 0.57 (0.095)

712 M.A. Hassan et al. / Materials and Design 53 (2014) 706–718

of woven fiber composites subjected to low-velocity impact.Perforation and threshold of the perforation phase are character-ized by the shape and trend of energy–deflection as well as

force–deflection curves. Images of the impacted samples are alsopresented to raise awareness of the different damage modes. Thenumerical results were gained from a finite element impact modelof E-glass epoxy laminates with different thicknesses including im-pact behavior, maximum contact force and contact time. Thenumerical and experimental force–time curves are compared forthree impact energy levels.

Fig. 5 shows a typical graph for force deflection of non-perfo-rated and perforated samples. If perforation does not occur a closedcurve is obtained (Fig. 5a), whereas an open curve is observed inthe presence of perforation (Fig. 5b). During the loading phase ofimpact both graphs manifest the same trend. From the generalshape of the diagrams the damage mode and corresponding behav-ior of the composite can be interpreted. In the closed case, the areaunder the curve is the deformation energy that initially becomesprogressively transferred from the impactor to the laminate andthen returned from the plate to the rebounding impactor. The areaincluded inside the loop refers to the energy absorbed during theimpact. For instance, initial energy Ei and absorbed energy Ea aretwo characters capable of evaluating the damage process in com-posite structures after one impact test. Ei is defined as the kine-matic energy before an impact incident and Ea is the amount ofabsorbed energy at the end of impact loading, which is equal tothe area bounded by the F–d curve. The shaded areas visible inFig. 5a and b represent the amount of absorbed energy in non-per-forated and perforated samples, respectively.

Fig. 6 depicts loading and unloading phases of the closed force–deflection curve of woven fiber composites under different impactenergy levels (rebounding with no perforation). The absorbed en-ergy is calculated by deducing the impactor energy after rebound-ing from the initial impact energy. This energy can also be achieveddirectly from the energy–time diagram, something that will be ex-plained in the next sections. It is worth noting that for small impactenergy the absorbed energy of the closed-form curve is not signif-icant. If a lot of energy is absorbed by the specimen, the F–d dia-gram becomes an open form. The stiffness of the specimen as aplate is calculated from the linear relationship between force anddeflection in the loading phase, which will further be discussedin Section 4.

3. Finite element simulation model

This section provides details regarding the finite element simu-lation model used to analyze the impact phenomenon. The re-sponse of glass fiber epoxy composite laminates under low-velocity impact was modeled with MSC.MARC� MENTAT�. Three-dimensional solid elements with eight nodes were used for the dis-cretization of the square specimen laminates. The nodes at thespecimen’s periphery were fixed in all directions. ORTHOTROPICmaterial was selected for modeling the material properties ofcomposites.

The impactor of the hemispherical nose with 12.7 mm diame-ter is discretized with an 8-node solid element similar to thatused for the composite laminate. The impactor is constrained tomovement within 5 degrees of freedom (x and y translation and3 rotation), and is allowed to move only in the z direction. Theimpactor is treated as a rigid elastic body with effective densityof 7860 kg/m3, Young’s modulus of 200 GPa and a 0.3 Poisson’s

Fig. 14. Experimental force–time curve for different impact energies and thicknesses: (a) 2 mm, (b) 3 mm, and (c) 4 mm.

M.A. Hassan et al. / Materials and Design 53 (2014) 706–718 713

ratio. An automatic contact condition is assigned between thecomposite target and impactor to accommodate impact initiationand progress. It starts with a point on the surface contact sincethe impactor touches the composite plate and progresses as asurface-to-surface contact. A contact criterion based on 0.01 mmof normal distance between the contact surfaces is adopted forthe simulation.

The time step is one of the most crucial parameters, which nor-mally causes divergence in non-linear finite element analysis.Choosing an adequate time step is another fundamental stage inthe simulation process. Modal analysis indicates that 2 � 10�8 s

is the minimum time required to prevent divergence of the solu-tion process. The FE-model of the impactor and composite lami-nate is shown in Fig. 7.

4. Results and discussion

4.1. Force–deflection diagram

Fig. 8 illustrates the F–d diagram for GFRP laminates withthicknesses of 2 and 3 mm. Two damage modes clearly exist. A

Fig. 15. FE-simulation results for force–time curve under different impact energies and thicknesses: (a) 2 mm, (b) 3 mm, and (c) 4 mm.

Fig. 16. Maximum contact force–banding stiffness for glass/epoxy laminate forimpact energies of 9.8 J and 19.6 J.

714 M.A. Hassan et al. / Materials and Design 53 (2014) 706–718

drastic fall in contact force in the F–d diagram pertains to the firstdamage mode involved in this situation. The F–d diagram has aclosed structure due to low initial impact energy (9.8 J). Here,the impactor rebounds since in the downward part of the graphthe force value and deflection decrease concurrently in theunloading phase. This damage mode includes matrix cracks andbending of fibers that are visible on non-impacted surfaces. Fiberfractures are attributed to bending deflection and fiber separationfrom the matrix that lead to diminished specimen bending stiff-ness. This is reflected in the plateau area of the F–d graph (anearly constant force value with changes close to a particularamount).

Fig. 8a indicates an open curve form of the Force–deflectiondiagram for impact energy of 19.6 J. Increasing the energy levelresults in rising maximum force at the impact moment. Neverthe-less, for 2 mm thickness where perforation occurred, the forcepeak is less than the impacted plate by 9.8 J of energy. The reasonis that perforation causes a drastic decline in bending stiffness. Inthe unloading phase, force alters sharply and causes unstablebehavior of the perforated laminate. In Fig. 8b the graph doesnot have a completely open form for 3 mm plate thickness and19.6 J of impact energy. In this state, the laminated plate is atthe threshold moment when the plate is about to be perforated.In the first instant of the unloading phase, deflection grows andthen it decreases. For a clearer view of the impact process,

photographs of the damaged laminates with 2 and 3 mm thick-nesses were taken (Figs. 9 and 10, respectively). The impactedsurface (front) and the non-impacted (back) show damage

Fig. 17. Variation of deflection versus time under different impact energies for thesamples: (a) 2 mm, (b) 3 mm, and (c) 4 mm.

M.A. Hassan et al. / Materials and Design 53 (2014) 706–718 715

propagation for 9.8 and 19.6 J of energy. Composite behaviorchanges when thickness is increased up to 4 mm, and conse-quently, impact response alters.

The F–d diagram for 4 mm thickness is presented in Fig. 11. Inthe unloading phase, force value variation is insignificant in thethin plates (2 and 3 mm) since the contact force is imposed ontoall lower and upper layers. Also, all layers are affected by the sameforce magnitude so the contact force will increase proportional tothe deflection (Fig. 11). After the laminate absorbs sufficient en-ergy, the damage mechanism will be activated and cause a de-crease in bending stiffness and contact force. For thick plates(4 mm), the layers are in contact with the impactor head fromthe upper to the lower layer respectively, causing a tremendousdrop in force value. Unlike the thinner plates, there is a plateau re-gion around the peak force. When the initial impact energy in-creases to 29.4 J, the impactor rebounds without perforating thesurface of the plate. The photographs of the damaged laminate inFig. 12 confirm this. The first feature of the material behavior is re-lated to the slope of the force versus displacement diagram, secondand third factor are first damage load and maximum load [10]. Firstdamage indicates the damage initiation point while maximum loadsignifies the end of crack initiation and the start of damage propa-gation [18]. For [0/90o] fibers, the laminate is reinforced in 0� and90� directions, thus the plate is weaker in the 45� direction; conse-quently, the damage propagates in these directions as illustrated inFigs. 9, 10 and 12. Bending stiffness Kb is defined as the slope of theline that fits the loading section of the F–d curve. Kb is a materialconstant that does not depend on impact energy. Fig. 13 portraysthe loading segments of the F–d curves for different impact veloc-ities and plate thicknesses of 2, 3 and 4 mm. It is clear that thebending stiffness Kb increases as the thickness and number of lay-ers increase. In turn, the response of low-velocity impact is affectedtoo. Table 2 lists the bending stiffness versus number of layers,which is almost constant at 0.1 ton/ms2.

4.2. Force–time diagram

The contact force can be defined by the reaction force betweenthe plate and the impactor. In the experiments, this force was re-corded by the load cell while the other parameters includingvelocity and deflection were calculated using the history of forceas discussed in [19]. Fig. 14 illustrates the force–time curve forthree thicknesses and the range of impact energies. For instance,when the impact energy is low (9.8 J), the obtained curve is par-abolic and variations in force value with time are insignificant.MSC.MARC� runs were conducted with three impact energiesand thicknesses. The force–time plots were compared with theexperimental results. Fig. 15 shows the force–time diagrams,which resulted from the finite element simulation analysis. Theseresults agree with those presented by Tita et al. [7] and Mitrevskiet al. [13]. The behavior of E-glass/epoxy laminates can beinterpreted through this diagram. As Fig. 15 indicates, the FE sim-ulation model overestimates the maximum load carrying capacitywhen the damage is significant and the impact time is below theexperimental values. The failure criteria employed in theproposed FE-model is not accurate for the laminates because per-foration is deemed the dominant damage mode. The FE resultssignify that the modeled material is slightly stiffer than the actualone.

The maximum force increases slightly as initial impact energyincreases. The same as for the F–d curves, a drastic fall in contactforce is observed after 8 ms due to bending fracture of fibers inthe lower surface (non-impacted). The maximum force value alsoincreases with augmenting thickness. Fig. 16 shows the maximumamount of force with respect to bending stiffness for impactenergies of 9.8 J and 19.8 J. It indicates a linear relationship for

glass/epoxy laminate with respect to impact. The impacted plateof 2 mm thickness is perforated, so the force value decreases byincreasing the energy level. As seen in Figs. 14 and 15, the maxi-mum load increases with increasing impact energy. This indicatesthat the maximum impact load of the laminates has not yetreached a saturation level where considerable damage or perfora-tion would occur. The contact time shortens as thickness increasesand the obtained curve is parabolic; however, the time for peakforce is almost constant at roughly 8 ms.

4.3. Deflection–time diagram

Fig. 17 illustrates the deflection–time (d–t) diagram for 2, 3 and4 mm sample thicknesses. Deflection is obtained from recordingthe vertical displacement of the impactor nose. But indentation iscalculated as the difference between the displacements of impac-tor tip and that of the top surface of plate where the indenter is

Fig. 18. Variation of velocity versus time under different impact energies for the samples: (a) 2 mm, (b) 3 mm, and (c) 4 mm.

716 M.A. Hassan et al. / Materials and Design 53 (2014) 706–718

considered rigid body [20]. The maximum deflection is observedapproximately at the instant of greatest contact force with a smalldelay. After the impactor reaches the peak deflection point, it con-tinues to shift to the left side of the time axis. Contrary to the F–tdiagram, the location of the peak value is constant for differentthicknesses, but for the d–t curve, the maximum deflections timesare 10.8, 9.7 and 9 ms respectively for 2, 3 and 4 mm thicknesses(impact energy is 9.8 J). In Fig. 17a, the d–t curve demonstratesthat the impactor does not rebound to the initial place for the

perforated plate and finally, the curve ascends for the perforatedlaminate in the d–t diagram.

4.4. Velocity–time diagrams

Fig. 18a–c show velocity versus time at various impact energylevels at 2, 3, and 4 mm thicknesses in order to combine the depen-dency of the energy parameters and force threshold values on the

Fig. 20. Ratio of return velocity to initial velocity versus plate thickness for differentimpact energies.

M.A. Hassan et al. / Materials and Design 53 (2014) 706–718 717

impact velocity (Belingardi and Vadori [9]). Each graph’s maximumvelocity is at the beginning of the impact event.

When there is no perforation and the laminate has maximumdeflection, the velocity value reaches zero for the reboundedimpactor, after which the impactor moves in the reverse directionand velocity grows. For the perforated sample, the velocity doesnot change sign because the impactor does not rebound but in-stead keeps going through the laminates. For the impacted lami-nate with 19.6 J of energy, the velocity is near zero at thethreshold of perforation.

4.5. Velocity–deflection diagram

Impactor velocity versus deflection is illustrated for differentimpact energies in Fig. 19a–c. As with the v–t curve, the maximumvelocity value is detected just before the incident. The velocity–deflection diagram (v–d) is parabolic when the impactor returns,and velocity is at a maximum when deflection is zero. If the signof velocity changes, the impactor will reverse in direction and thenwill return to its original point. Fig. 19a denotes the v–d graph for a

Fig. 19. Velocity–time diagram for the samples: (a) 2 mm, (b) 3 mm, and (c) 4 mm;(follow-up of curve is estimated).

perforated plate by initial impact energy of 19.6 J. The curve is uni-directional as the velocity value decreases and deflection rises.

The impactor is stopped by a pneumatic automatic brake in-stalled on the machine in order to avoid multiple impacts. Conse-quently, data is recorded until the impactor returns to its originalplace. Thus, one portion of the v–d curve is estimated and is shownby the dotted line. Return velocity can be evaluated with thisapproximation.

The slope of the v–d curve indicates disparities of strain rate (d _ewhich has a higher value in the loading phase as opposed to theunloading phase when the impactor returns from the surface. Ini-tial velocity (vi) and return velocity (vr) are given in Fig. 20. The ra-tio of return velocity to initial velocity (vr

v i) decreases while the

amount of impact energy increases; otherwise the drop in the dia-gram is associated to the damaged composite plates.

The amount of vrv i

ranges between 0 and 1, meaning that:

0 6v r

v i6 1 ð2Þ

When vrv i

equals 1, the impact is completely elastic. If vrv i

equals 0 or isalmost zero, the laminate is at the threshold moment of perforation(Fig. 19b).

For comparison, the return velocities calculated from Fig. 19a–care shown in Fig. 20. It is clear that for a given constant energy le-vel the return velocity vr of the impactor and velocity ratio vr

v iin-

crease as the composite laminate becomes thicker. Since thevalue of vr

v idescribes the laminate behavior under impact, it can

be considered an index for the expected amount of damage.

5. Conclusions

The behavior of woven fabric composite laminates under low-velocity impact was experimentally investigated. Bending stiffness,impact force, impact velocity, deflection, and damage were as-sessed during and after the impact. The experimental results re-vealed that the response of the glass fiber reinforced plasticlaminates (GFRPs) to low-velocity impact is very sensitive to thick-ness and impact energy level. The results are primarily presentedfor perforated laminates as well as at the perforation threshold.The damage process was studied by investigating the F–d graphfor a range of thicknesses. Variations in bending stiffness and max-imum impact force were used to assess the damage to GFRPs. Theimpact mechanics of fiber glass/epoxy composite under low-veloc-ity were also simulated using MSC.MARC� MENTAT�. The simu-lated force–time data was then contrasted against theexperimental results. The predicted load carrying capacity wasfound to be slightly lower than the experimental values, whereasthe contact time was overestimated. The result discrepancies are

718 M.A. Hassan et al. / Materials and Design 53 (2014) 706–718

attributed to insufficient information on the real mechanical prop-erties and contact conditions.

Acknowledgments

The authors would like to acknowledge the support provided byUniversity of Malaya and the Ministry of Higher Education, Malay-sia with the high impact research (HIR) grant number HIR-MOHE-16001-00-D000027.

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