Finite element modeling of low velocity impact damage of composites
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https://www.eduzhai.net American Journal of M aterials Science 2013, 3(1): 1-7 DOI: 10.5923/j.materials.20130301.01 Finite Element Modeling of Composite Materials Subjected to the Low Velocity Impact Damage Djillali Be ida Maamar1, R. Ze nasni1,*, A. He bbar1, Jaime Vina Olay2 1M echanical Department, University of M ostaganem, Laboratory LMNPM ,BP 882, RP, 27000, M ostaganem, Algeria 2Department of M aterial Sciences, University of Oviedo, 33204, Gijon, Spain Abstract In this paper, the low velocity impact behavior of a composite material was investigated using the LS DYNA a fin ite element package. In order to investigate the damage produced by different impactors, three shape impactors were chosen (ball, cy linder, and truncated cone). The impactors impact the plate with a velocity of 6m/s. The co mposite was a carbon fiber/epoxy of sequence stacking[45/ 0/-45/ 90]s. All the impactors dropped the plate at the center. In order to study the effect of the inclination of the laminated plate, three different inclination angles were chosen (30, 45 and 60°). The loads, the impact energy, the d isplacements and the Von M ises stresses were co mputed and represented in a d ifferent graphs en function of the time of the impact. The truncated cone and a cylinder provide a higher impact forces and a displacements (great damaged zone). In the case of an angle of 30°, the ball produced a higher displacement and impact energy. Keywords Co mposite, Finite Element, Impactor Shapes, Laminate Inclination, Stacking, Mat54, Lsdyna 1. Introduction The fibrous composites are being increasingly used in load b earing st ru ctu res due to nu mb er o f adv ant ages o ver conventional materials: high specific strength and stiffness, good fat igu e perfo rman ce and co rros ion res istan ce. A serious obstacle to more widespread use is their sensitivity to imp act and stat ic loads in t he th ickness d irect io n. As composites have demonstrated to be very venerable to out of plane impact , wh ich cause barely visib le impact damage (BVID) reportedly contributes up to 60% loss in structures’ co mp ress ive stren gth and majo r reason o f catastroph ic failu res . The en ergy absorbed du ring impact is main ly dissipated by a combination of matrix damage, fibre fracture and fibre-mat rix d e-bond ing , wh ich leads to s ign ificant reduct ions in the load carry ing capab ilit ies. In ballist ic impacts the damage is localized and clearly v is ib le by external inspection, while low velocity impact involves long contact time between impactor and target, which produces g lobal st ruct u re d efo rmat ion with und et ect ed in tern al damage at points far fro m th e contact reg ion . Fo r such reasons the lo w velocity imp act are o ften simu lated by s imp le stat ic ind ent at io n -flexu re tests , n eg lect ing t he in fluen ce o f dy namic effects. It is also sugg ested t he co mp lete model to take int o acco unt the fu ll dyn amic behavior of the laminates. Abrate and al have investigated the delamination of two laminated composite graphite/PEEK * Corresponding author: zramdane@netcourri er.com (R. Zenasni) Published online at https://www.eduzhai.net Copyright © 2013 Scientific & Academic Publishing. All Rights Reserved and graphite/BMI under lo w velocity impact. The range number of layers varies fro m 9 to 95 p lies. The obtained result shown a higher delamination threshold load and h igher damage resistance. The resulting damage is not normally visible on the specimen surface nor is easily detected and grows rapidly during normal service cycles, thus reducing the strength and operational life. The area has been under active research for a quite some time. So me of the relevant articles addressing this issue found in the literature are presented below. The strategy of reducing the stiffness of damaged plies to a certain fraction without considering the degree of damage was used by some investigators[2, 3]. Other researchers applied damage theory of continuum mechanics to address the internal damage. They init iated the stress-strain relation for the actual damaged by introducing a fourth-order damage operator to transform the co mpliance matrix according to the damage states. Based on this work, several investigations were conducted in the subjects such as tension of co mposite laminates with ho les and high velocity impact of composite laminates[4-7]. They adopted the simp le assumption that when damage occurs, the mechanical properties would reduce to certain levels. The impact induced de-lamination another important damage mode was combined because the level of impact energy to in itiate de-lamination is low and the post-impact compressive strength reduces dramat ically. New techniques used in to model the laminate as a stack of elements tied by contact interface conditions, allows the inter-laminar layers to model and predict strength reduction. Because of the complex nature, a simple and effective criterion for the BVID prediction and damage/delamination init iation is still lacking. The stability of simulat ion was another important issue to be 2 Djillali Beida M aamar et al.: Finite Element M odeling of Composite M aterials Subjected to the Low Velocity Impact Damage considered, when changes of material properties were taken into account. Cantwell and Morton proposed a pine tree damage pattern and a reversed pine tree damage pattern for the impact-induced matrix cracks in thick and thin thickness laminated composites, respectively. Freitas proposed a pine tree damage pattern with vertical matrix cracks on the bottom layer. Since 1980s, many researchers have analytically and experimentally investigated the low velocity impact behaviour of co mposite laminated structures. Most composite structures will be under some level of stress when impacted. For examp le, the upper skin of the main wing of the aircraft will be mainly under in -plane co mpressive load during flight and the lower one will be under in-plane tensile load. So, foreign objects like hail and debris in the runway shall give an impact to 638. Umar Farooq and Karl Gregory have studied a composite laminated structure under in-plane load. However, a few studies on the impact behaviour of the composite laminates under in-plane load have been published. In 1985, Chen and Sun have developed a finite element program to analyze the impact response of the composite laminate under biaxial in -plane load. Using the fin ite element program they solved for three cases of in -plane load, tension/tension load of 3 times of critical buckling load of the plate, co mpression/compression load of 75% of it, and no in itial in-p lane load. The impact condition is the case that the mass of the impactor is very small and the impact velocity is very high. They concluded that the initial tensile in-p lane load tends to intensify the contact force while reducing the contact time, and an opposite conclusion is obtained for an init ial co mpressive in-plane load. After their study, it is very rare to find another analytical result on the impact behaviour of the composite laminates under in-plane load. Introduction Wu and Chang have conducted a transient dynamic fin ite element analysis for studying the response of laminated composite plates subjected to transverse impact loading by a foreign object. They have calcu lated displacements, the transient stress and the strain distributions through the thickness of laminate during the impact event. Gaurav Nilakantan and al. have used the mu ltiscale modeling techniques to analyze the impact damage of woven fabric by the finite element. On the other hand, Manish Khandelwal and al have studied the delamination init iation in FRP under low velocity impact. The analysis was conducted using 3D fin ite element. The co mposite material studied were Graphite/epo xy and hybrid Glass-Graphite Epo xy . 2. Finite Element Modeling 2.1. Composite Laminates The studied composite material was a TM 800s/M21; it was made of a matrix epo xy reinforced with carbon fiber of stacking sequence[45/0/-45/ 90]s. The composite fiber volume fraction was 33%. All the composite specimens were of the same d imensions: 120x60x2.5 mm. The p ly thickness was 0.25mm. The specimens were centrally loaded. The table 1 presents the mechanical propert ies of the composite materia l and the impactors. The impactors dropped the plate at the center. The Fig.1, present the fiber orientation in the system axis. A ll the sides of the laminated plate were fixed. The material of the impactors was ordinary steel. The impact problem can be described as shown in Fig.1. An impactor of a mass m and shape drops on the center of the laminated plate with a velocity V. Table 1. Mechanical properties of the composite material and the impactor E11 GP a E22 E33 GP a GP a ν12 ν23 ν13 165 7.64 7.64 0.35 0.4 0.35 Xt Xc Yt Yc Zt Zc GP a GP a GP a GP a GP a GP a 2.2 1.2 0.045 0.28 0.045 0.7 G12 G23 G13 S12 S23 S13 GP a GP a GP a GP a GP a GP a 5.61 2.75 5.61 0.05 0.05 0.05 E ρ GP a Kg/m3 ν 207 7850 0.3 Figure 1. A basic model for impact damage American Journal of M aterials Science 2013, 3(1): 1-7 3 2.2. Numerical Modeling The Ls dyna model Mat 54 was employed to study the impact behavior of the plate and the model Mat_20 for the impactors. The plate and the impactor were meshed using four quadratic isoparametric shell e le ment. y 2 1 θ x Figure 2. Local and global axis Fig.3, show the distribution of the bending moments and the shear forces through the composite plate. Z N N M NY M Q ???????????????? NX M M X Y Q Q NX MY MX N X M M NX N Figure 3. Bending moments and shear forces Where: Nx, Ny,Nxy: In plane loads Mx,My,Mxy: Bending mo ments about x-y axis Qx,Qy: Shear fo rces The stresses were calculated by the equation (1). The coefficient of stiffness’s in out of plane, o f the laminated plate where calculated using the equation (1). τσσxxyy (k τ yz τ xz ) = Q11 QQ1123 0 0 Q12 Q22 Q23 0 0 Q13 Q23 Q33 0 0 0 0 0 Q44 Q45 0 (k 0 0 Q 45 Q55 ) γεεxxyy γ yz γ xz (k ) (1) Q11 = Q 11m4 + 2(Q12 +2Q33 )m2n2 + Q22n4 Q22 = Q11n4 + 2(Q12 + 2Q33)m2n2 + Q22m4 Q 33 = (Q11 + Q22 − 2Q12 )m 2 n 2 + Q33 (m 2 − n 2 ) 2 Q13 = Q11m3n − Q22mn3 − (Q12 + 2Q33)mn(m2 − n2) Q23 = Q11mn3 − Q22m3n + (Q12 + 2Q33)mn(m2 − n2) Q12 = (Q11 + Q22 − 4Q33)m2n2 + Q12(m4 + n4) Q 44 = Q44m2 + Q55n2 Q 45 = (Q55 − Q44 )mn Q55 = Q44n2 + Q55m2 Where: Q33 = G12 Q55 = G13 Q44 = G23 E1, E2: Elastic modulus in axis 1 and 2 G12, G13, G23: Shear modulus Where: Q11 = 1 − E1 ν12ν 21 Q12 = 1 ν12 E2 −ν12ν 21 Q22 = 1 E2 −ν12ν 21 In the case of the in plane stresses, eq.(1) become (2): τσσxxyy τ yz τ xz (k ) = Q11 Q012 0 0 Q12 Q22 0 0 0 00 00 Q33 0 0 Q44 00 0 0 0 0 Q55 (k ) γεεxxyy γ yz γ xz (k ) (2) 2.3. Effect of the Impactor Shapes Three impactors of the same materia l and different shapes were used in order to impact the laminated plate (cy linder, ball, truncated cone). The table 2, present the geometrical properties of the three impactors. The impact velocity used was 6m/s for all the impactors. The table 3, shown the number of elements and nodes used in order to mesh the impactors and the composite plate Table 2. Geomet rical propert ies of the impactors Impactors geometrical propert ies Ball: Diameter =12mm Cylinder: Diamet er=8mm, height = 18mm Truncated cone: Diameter1=5mm, Diamet er2 =1 4mm,h eight =19 .7 4mm Table 3. Elements and nodes used in numericalmodeling Laminated plate Ball Cylinder Truncated cone Element s 115200 96768 166375 579726 Nodes 115921 98617 172256 594648 Figure 4, present the displacement variations en function of the impact time for the three impactors. The displacement curves present the same pace, the maximu m central displacement was obtained by a truncated cone about of 0.5549 mm for an impact time about 0.2ms, the ball g ive a value of displacement about 0.5356 mm for impact time about 0.19ms, while the cylinder provide a value about 0.5242 mm for the impact t ime about 0.18ms. The impact forces were shown in figure 5 en function of the impact time. The cylinder and a truncated cone present more or less the same curve forms with a slight variation. The impact force obtained was about 0.0045KN for a time of impact of 0.22ms. In the case of a ball, the load curve show a maximu m and a minimu m values. The maximu m load was about 0.035 KN for the impact time of 0.23ms. 4 Djillali Beida M aamar et al.: Finite Element M odeling of Composite M aterials Subjected to the Low Velocity Impact Damage values of stresses about 0.11GPa for ply 45° and 0°), wh ile in ply 90° the stresses value was 0.020 GPa. The truncated cone, shown a value of stresses about 0.13GPa for layer 45° and 0.12 GPa fo r layer -45°. The impact energy curves were shown in figure 7, the maximu m energy value was about 0.1166 J for impact time of 0.18ms for the three impactors. Figure 4. Displacement en function of time Figure 5. Impact load en function of time Figure 7. Impact energy en function of time 2.4. Effect of the Inclined Laminated Plate The laminated plate was inclined by an angle with respect to the horizontal axis, see figure 8. Three d ifferent angles were chosen (30°, 45° and 60°). The impactors dropped the inclined plate at the center with a velocity of 6m/s. Imp act or α Figure 8. Inclined laminate Figure 6. Von Mises stresses In figure 6, we present the maximal Von Mises stresses in each ply of the composite for the three impactors. The ball provides the maximu m stresses about 0.247GPa in plies of orientations 45° and 0°. The cy linder present a minimu m The central displacement for the three angles was presented in figure 9. The inclination of 30° gives a maximu m displacement of 0.493mm for a time of the impact about 0.2ms for the ball impactor. In the case of the cylinder, the maximal displacement was 0.392mm, while for the truncated cone the displacement obtained 0.314mm fo r the time of the impact about 0.2ms. In the case of the inclination of 45°, the ball impactor provides a maximal displacement about 0.32mm for the time of the time o f impact of 0.22ms. The cylinder g ives a displacement about 0.16mm; at the end the displacement obtained by the truncated cone was 0.161mm. The inclination of 60° g ives a displacement about 0.164mm for the ball (time of the impact about 0.22ms) and a American Journal of M aterials Science 2013, 3(1): 1-7 5 maximal value of 0.202 mm for the cylinder. The minimal displacement was 0.06&mm for the truncated cone (time of the impact about 0.11ms). load about 0.013KN corresponding for the time of the impact 0.03ms. The truncated cone, gives a minimal impact load 0.0096KN, while for the cy linder, the load was more or less equal to the ball impactor. Figure 9. Displacement variations Figure 10, present the variation of the impact load en function of the time of the impact for the three plate inclinations. The inclination 30° gives a maximal impact load about 0.023KN fo r the t ime of the impact of 0.05ms in the case of the cylinder impactor. The minimal impact load was obtained by the ball impactor (0.014KN which correspond for the time of the impact about 0.012ms). In the case of the inclination of 45°, the ball provides a maximal Figure 10. Impact load en function of time The inclination 60° g ives a maximal displacement about 0.019KN corresponding for the time of the impact 0.15ms in the case of the cylinder. The t runcated cone provides a minimal load (0.0034KN wh ich correspond to 0.03ms). 6 Djillali Beida M aamar et al.: Finite Element M odeling of Composite M aterials Subjected to the Low Velocity Impact Damage of the cylinder (0.023GPa for the ply 90°). The inclination 60°, the maximal stress was about 0.099 GPa for the ply 0° which was provided by the ball impactor. The truncated cone gives a value of minima l stresses (0.023GPa at the ply 90°). Figure 11. Maximal Von Mises stresses The maximal Von M ises stresses were shown in figure 11 for the different inclinations, ply o rientations, and the impactors. In the inclination of 30°, the ball provides the maximal stresses at the ply 0° about 0.2GPa. The cylinder gives a value of Von Mises stresses about 0.15GPa for the ply of orientation 45°. The truncated cone provides a minimal value of 0.048GPa at the ply of orientation 90°. The inclination 45°, the ma ximal va lue of the stress was obtained by the ball impactor at the ply 45° which correspond for a value about 0.12GPa . We obtain a minima l stress in the case Figure 12. Impact energy en function of time Figure 12, present the variation of the impact energy for the three laminate inclinations. The inclination 30°, g ives a maximal impact energy about 0.084J corresponding for the time of the impact about 0.22ms in the case of the ball impactor, the minimal energy was obtained by a truncated cone (0.05J wh ich correspond for 0.16ms). For the inclination of 45°, the maximal energy was 0.052J which American Journal of M aterials Science 2013, 3(1): 1-7 7 correspond to 0.19ms in the case of the ball impactor. The cylinder p rovides a value of the impact energy about 0.032J for a time o f 0.17ms. At the end the truncated cone gives minimal impact energy about 0.021J. In the case of angle of 60°, the maximal energy value was obtained by the ball impactor (0.027J which correspond for 0.18ms). The truncated cone gives a value of the energy of 0.0061J for the time of the impact about 0.12ms. 3. Conclusions The impact damage mechanis m in a laminate constitutes a complex p rocess. It’s a co mb ination of matrix cracking, buckling, fiber breaking, delamination its usually all interact with each other. The paper presents the numerical modeling of a low velocity impact damage of a composite material using the package Lsdyna. Three shapes of impactor were used in the analysis (Ball, truncated cone and cylinder). All the impactors dropped the laminate plate at the center with a velocity of 6m/s. The co mposite material used was a carbon/epoxy of sequence stacking[45/0/-45/ 90]s. The impact displacements, loads, energy impact and the maximal Von Mises stresses were reported in graphs en function of the impact time. The inclination of the laminate was taken account, three angle inclinations were chosen (30°,45° and 60°). In the case of an angle of 30°, the maximal displacement was obtained by the ball impactor. ACKNOWLEDGMENTS I would like to thank the company Livermo re So ftware Technology Corporation for the LS DYNA full evaluation package.  Waedle, B. L.; ana Lagace, P.A.; “On the Use of Dent Depth as an Impact M etric for Thin Composite Structures, “Journal of Reinforced Plastics and Composites, Vol. 16, No. 12, pp. 1093-1110, 1997.  Kwon, Y.S, and Sankar, B. V.: “Indentation-Flexure and Low-Velocity Impact Damage in Graphite Epoxy Laminates, “Journal; of Composites Technology and Research, Vol. 15, No. 2, pp. 101-111.  Swanson, S.R.: “Limits of Quasi-Static Solutions in Impact of Composite Structures,” Composite Engineering, Vol. 2, No. 4, pp.261-267, 1992.  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