- Email: [email protected]
epoxy composite laminate
Pergamon
Int. J. Impact Engng Vol. 15, No. 4, pp. 451--464, 1994 Elsevier Science Ltd Printed in Great Britain 0734-743X(94)E0016-O 0734-743X/94 ST.00+ 0.00
PREDICTING THE BALLISTIC LIMIT WOVEN GLASS/EPOXY COMPOSITE
FOR PLAIN LAMINATE
S. T. JENQ,H.-S. JING and CHARLESCHUNG Institute of Aeronautics and Astronautics, National Cheng Kung University, Tainan 701, Taiwan, Republic of China
(Received 21 September 1993; and in revised form 7 February 1994) Summary--This paper is concerned with predicting the ballistic limit of plain woven glass/epoxy composite laminates struck by a 14.9 gm bullet-like rigid projectile with a tip radius of 5 mm. The 4 mm thick square specimens were clamped along their 100 mm edges. A pneumatic gun was used to propel the bullet with incident velocities ranging from 140 to 200 m/sec. The ballistic limit was experimentally determined to be near 153 m/sec. A series of quasi-static punch tests was performed in order to investigate the progressive damage modes of the targets and to obtain the punch load-displacement relation. These quasi-static punch tests were conducted to characterize the penetration process. Similar to dynamic impact test results, the major damage modes for targets subjected to quasi-static punch loading were found to be governed by delamination and fiber breakage. After specimens were perforated, a steady friction force was observed from quasi-static punch tests. Test results also indicate that the rhombus-shaped delamination of impact damaged samples is greater than that of quasi-statically punched specimens. A partial hybrid stress finite element code was incorporated with the proposed static penetration model to simulate the dynamic impact process. An energy consideration was applied to predict the ballistic limit. The difference between the predicted ballistic limit and test findings was found to be approximately 24% if the target's static material properties were used in the code simulation. Due to the rate-sensitive nature of glass/epoxy composites, the effect of dynamic elastic properties on the predicted ballistic limit was further studied. Good agreement between the predicted ballistic limit and test results was found if the target's elastic moduli used in simulation were increased to two times the static values.
INTRODUCTION
Laminated composites have been widely adopted in many applications to resist foreign object impact loading. It is important to understand the dynamic behavior of composite structures and the associated damage mechanisms. The condition for perforation (or ballistic limit) is certainly the most important factor for designing a suitable protective structure. Although the impact damage characterization and the study of impact residual properties of composite laminates have been extensively reported [1-5] in the past two decades, only a limited amount of work is found to analytically model the penetration/perforation of composite laminates and to predict the ballistic limit of composite structures. A brief summary of the work related to the current study follows. Cantwell and Motron [6] examined the perforation process in a series of CFRP composites. Both the drop-weight tower tester and gas gun were used to conduct impact tests. Effects of varying target thickness and length of span on the energy required to perforate the composite targets were examined. According to this study, for low velocity impact loading conditions, the structural response of targets is important, and the areal dimensions of the target determine the perforation threshold energy. However, under high velocity impact loading, the perforation threshold appears to be independent of the areal geometry of the target. According to the dissipation of energy during the impact process, a simple perforation model was proposed. For target thicknesses up to and including 4 ram, a good relationship between the experimental trends and the model-predicted results was reported. For thicker specimens, this model is no longer applicable due to change in perforation mode. Zhu et al. I-7] investigated the impact response of woven Kevlar/polyester laminates of varying thickness to quasi-static and dynamic penetration by cylindro-conical projectiles. 451
452
S.T. JENQ et al.
Ballistic limits were determined for a series of targets with thicknesses ranging from 3.125 to 12.7 mm. It was concluded that local deformation and fiber failure constitute the major energy absorption mechanisms in impact perforation. Delamination, in both the static or dynamic cases, did not seem to dissipate a large amount of energy. An analytical representation of the normal impact and perforation of conically-tipped hard-steel cylinders was also developed by Zhu et al. [8]. This model utilizes the laminated plate theory to determine global target deflection. Dissipative mechanisms, including indentation of the striker tip, bulging at the surface, delamination, fiber failure, and friction are taken into account. The predicted ballistic limit agrees well with those of test results; for thinner targets (3.125 mm thick) the difference is 12%, with a difference of 1.3 % for thicker specimens (9.525 mm thick). Lee and Sun [9] developed a quasi-static model to simulate the penetration process of composite laminates struck by blunt-ended projectiles. A series of static punch tests was conducted to characterize the load-displacement relation during penetration for ([0/90/45/-45]s)2, Herculus AS4/3501-6 graphite/epoxy composites. The major damage modes were reported to be delamination and plugging. An axisymmetric finite element analysis was performed to simulate the quasi-static penetration process. An effective modulus scheme was adopted in the analysis. Comparisons of punch load-displacement curves have shown good agreement between modeling and testing. In addition, the ballistic limit of graphite/epoxy laminates struck by a blunt-ended impactor was determined from a series of impact tests by Lee and Sun [10]. The penetration model developed in reference (9) was incorporated into a dynamic finite element analysis as the penetration criteria. Comparison between the computed ballistic limit and test results shows good agreement. Sun and Potti [11] further utilized the static punch curve as a basis to calculate the energy required for penetration of composite laminates. A series of impact tests was performed to study 2, 4.1, 6.1, and 8.1 mm thick graphite-epoxy (Hercules AS4-3501/6) quasi-isotropic composite laminates. The projectiles were 14.6 mm in diameter, 24 mm in length, and made of hardened tool steel. They were fired against targets with incident velocities ranging from 20 to 150 m/sec. The researchers found that the overall damage pattern in the dynamic case was similar to that of the static case. The residual velocities predicted using static punch-through energy are overestimates of the experimental values for thick laminates, but this method provides an easy and inexpensive upper bound approximation. Recently, more attention has been focused on the development of using glass fiber reinforced plastics (GFRP) in many applications due to their cost effectiveness and high toughness at impact rates. Therefore, a series of impact tests was conducted in this work in order to study the perforation condition (or ballistic limit) of plain woven glass/epoxy laminated targets struck by a 14.9 gm bullet-like penetrator with a tip radius of 5 mm. Similar to the work reported by Lee and Sun [9, I0], quasi-static punch tests were conducted to examine the punch load-displacement relation and to characterize the penetration process. The static penetration model developed in this paper was incorporated into the partial hybrid stress finite element dynamic analysis [12, 13] as the penetration criteria. The energy balance consideration was adopted to predict the ballistic limit. Comparison between the predicted ballistic limit and that found from tests is to be reported. Due to the rate-sensitive nature of glass/epoxy composites [14-16], the effect of the variation of dynamic elastic moduli on the predicted ballistic limit is also studied. EXPERIMENTAL
SETUP AND TEST RESULTS
In this work, the wet layup method was utilized to fabricate (0°, 90°)1o laminated specimens made of plain woven E-glass fabrics (Taiwan Glass Co., Ltd TGFW-600) and epoxy resin system (Ciba-Geigy, Aradite LY564). During the layup process, the weft and warp fibers were carefully aligned so that each layer may preserve the same directions of reinforcement. The fiber volume ratio of the specimens was determined to range from 51.7
Predicting the ballistic limit for plain woven glass/epoxy laminate
453
]-ABLE 1. THE STATICMECHANICALPROPERTIESOF tHE LAMINATEDGLASS/EPOXYTARGETSUSEDIN CODE SIMULATION p* V* Ell E22 E33 G12
1 884 kg/m 3 51.7-52.4% 27.8 GPa 27.8 GPa 8.0 GPa 5.32 GPa
G23 GI3 vi2 v23 vl3
4.07 GPa 4.07 GPa 0.09 0.30 0.30
* Vf and p represent the fiber volume ratio and density, respectively. to upper grip of MTS
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to 52.4%. A list of the specimens' static mechanical properties used in the code simulation is given in Table 1. Both quasi-static punch tests and dynamic impact tests were performed. The rigid bullet-like penetrator with a tip radius of 5 mm was made from a 12.5 mm diameter hardened 4340 steel rod. During the tests, the 4 mm thick square specimens were clamped along their I00 mm edges. As proposed by Lee and Sun [9, 10], the purpose of performing the static punch tests is to characterize the progressive damage mechanism and to obtain the punch load-displacement curve in order to characterize the penetration process. When performing the quasi-static punch tests, the rigid fixture (shown in Fig. 1) was mounted on an MTS machine with a stroke-rate controlled at 0.125 mm/sec. An analog-to-digital converting interface and a personal compute were used to record the load-displacement relation from quasi-static punch tests by means of Labtech softward. Three typical load-displacement curves measured from quasi-static punch tests are plotted in Fig. 2. Test results reveal that these punch curves are reproducible and preserve a specific pattern. The basic pattern of these curves can be represented by the curve shown in Fig. 3, and five checkpoints (0, A, B, C and D) are marked in this figure for convenience. For a specimen loaded from point O to A, no major damage mode is observed. However, if the loading level approaches checkpoint A, the slopes of the load-displacement curves shown in Fig. 2 decrease slightly indicating that matrix cracks occur in the specimen. When the loading level reaches checkpoint A, delamination occurs and develops immediately in the specimen, resulting in an extreme decrease in loading corresponding to the loading
S . T . JENQ et al.
454 7.0
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path AB. This phenomenon is similar to that reported by Lee and Sun [9-1 when conducting quasi-static punch tests with a blunt-ended cylindrical projectile. As the punch further penetrates into the target, fibers under the area of contact start to break and are pushed in the direction of penetrator motion. This phenomenon occurs when a specimen is loaded along the loading path BC. At point C, the tip of the penetrator is about to exit from the distal surface of the target. A nearly constant friction between the penetrator and specimen is observed from the loading path CD. Note that if we compare the punch load-displacement curves shown in Fig. 2 and those reported by Lee and Sun I-9, 10-1, only one abrupt decreasing loading (path AB), representing the major delamination damage mode, is observed in this work. Furthermore, no obvious transition region for friction is observed because the plugging phenomenon is not observed in the present study. Six high speed impact tests were also conducted in order to examine the impact damage of composite specimens and to determine the ballistic limit of the laminated targets struck by a bullet-like impactor with rounded tip weighing 14.9 g. A pneumatic gun was used to fire the projectile against targets with incident velocities ranging from 140 to 200 m/sec. The ballistic limit was experimentally determined to be near 153 m/sec. The projectile
Predicting the ballistic limit for plain woven glass/epoxy laminate
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FIG. 4. A schematic drawing of the high speed impact test set-up. TABLE 2. A SUMMARYOF THE IMPACTTESTRESULTS Test no.
Incident velocity (Vs) (m/sec)
Exit velocity (VR)(m/sec)
Estimated ballistic limit (m/sec)
Note
D01 D02 D03 D04 D05 D06
141.5 145.2 153.9 164.5 169.8 190.1
43.7 60.6 103.1
158.6 159.6 159.7
pp* with rebound pp with rebound cpt cp cp cp
* Abbreviation 'pp' represents partial penetration. t Abbreviation "cp' represents complete penetration.
incident velocity was determined by means of a pair of photo-sensors, while the residual (terminal) velocity was detected by a set of short-screens displaced 5 cm apart. A schematic drawing of the dynamic impact test system is presented in Fig. 4. Note that the projectile was not deformed after impact tests. A summary of the projectile's incident and residual velocities for those tests conducted is given in Table 2. The major damage pattern found from the impacted specimens was similar to that from the quasi-static penetrated specimens. However, the area of the rhombus-shaped delamination for the high speed impacted specimens was determined to be about nine times (3 x 3) greater than that of the quasi-statically penetrated specimens, as shown in Fig. 5(a) and (b). The estimated ballistic limit shown in the fourth column of Table 2 is calculated based on the principle of conservation of energy for rigid penetrators, satisfying the simple relationship 1_ ,,2 i _ ,,2 t_ ,,2 for V~>VBL, (1) ]trip VBL _ -- -~rltp v s -- ]Irtp v r , where mp is the mass of the projectile and the estimated ballistic limit is represented by VBL.The striking velocity and residual velocity of the projectile are denoted by V~and Vr, respectively. Upon examining the estimated ballistic limit shown in Table 2, it is found that the data scattering is limited, and an averaged ballistic limit of 159.3 m/s is determined. COMPUTATION
M O D E L AND R E S U L T
The ballistic limit of a composite target was numerically computed in order to check against the test result. The computational procedure for predicting the ballistic limit consists of three phases: (1) determine the penetration criterion based on the quasi-static punch curves obtained from tests to characterize the major damage mechanisms (delamination
456
S, T. JENQ et al.
El
(top vlew)
(bottom view]
(elde vlew)
(side view)
FIG. 5. Photographs of the (a) quasi-static penetrated specimen and (b) impact damaged specimen struck by the projectile with an incident velocity of 153.9 m/sec.
and fiber failure) and locate the termination of these mechanisms; (2) develop a partial hybrid stress finite element code capable of taking into account the structural stiffness degradation in order to fit the quasi-static punch (load-displacement) curves; and (3) simulate the dynamic impact test conditions with the proposed static penetration model in order to determine the velocity of the impactor when the major damage mechanisms have terminated. Friction is not incorporated into the finite element analysis; however, an energy balance consideration is used to account for the frictional resistance in order to determine the projectile's residual velocity for complete perforation. The ballistic limit can then be subsequently calculated by using Eqn (1) for given incident and the corresponding computed residual velocities. The constitutive relation of a single layer in linear elasticity problems can be expressed by cr = C~,
(2)
where trT = [fix, O'y,trz, Zyz,
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Zxy];
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and
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If we separate the stresses and strains into two parts, a flexural part and a transverse shear
Predicting the ballistic limit for plain woven glass/epoxy laminate
457
part, then Eqn (2) can be expressed as af = Cf~f
(3a)
(7t = Ct£ t,
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~t=Stat,
(4b)
where the compliance matrices Sf and St are the direct inversion of Cf and Ct, respectively. A variationally consistent partial hybrid stress element (PHSE) can be formulated based upon the previously developed functional for analyzing the transient response of composites [12,] as I-I : f v [½(Odl)TCt(Ofu) + a T ( D t u ) -- ~tlr 1 Tt Sttr t -- ½pl'lTl'l,] dV -
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where the displacement and surface traction vectors are represented by u and i "T, respectively. The superscript 'T' in the above equation stands for the transpose of the vector or matrix in question, and (") represents for time derivative of (). Note that the special differential operators (Df and Dt) for the flexural and transverse shear parts are expressed as 0 Ox D f=
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and
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With the standard procedures of finite element method, the corresponding partial hybrid stress element can then be established. The three dimensional isoparametric twenty-node hexahedron element is adopted in finite element analysis. In each element, the displacement is interpolated by the nodal values. The final equation of motion can be written as Mii+Kq = Q,
(7)
where M, K and Q represent the consistent mass matrix, stiffness matrix, and consistent load vector, respectively, and the global vector of nodal displacements is denoted by q. Detailed discussion about the assumed stress field for partial hybrid stress finite element development is given in [13,]. Based on Eqn (7), the assembled global equation can be solved by the Runge-Kutta numerical scheme iteratively in time to compute the unknown nodal displacement vector for a prescribed loading and boundary conditions. A point mass is used to model the impactor because it is considered to be rigid. The Hertz contact law [17-], F = k ~ x 3/2
and
4 l,.Fl-v 2 1-]-1 k = 3-Rs'~'L Es + ~s_l=l ,
(8)
is used to model the contact force (F) exerted on the laminated target and penetrator with a specific incident velocity. Parameter 'ct' represents the indentation, and 'k' is a constant depending upon the projectile's tip radius (Rs), the elastic modulus (E s) and Poisson's ratio (Vs) of the penetrator, and the transverse elastic modulus (E33) of the G F R P target. The impact response of a simply supported 20 x 20 x 0.8 cm steel plate due to the central impact of a 2 cm diameter steel sphere at an initial velocity of 100 cm/sec was numerically simulated in order to check against the analytical result by Karas shown on page 140 of [18,]. Figures 6 and 7 show the time history of the target central displacement and contact force,
458
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respectively. The solid and dotted lines plotted in these figures represent, respectively, the current PHSE simulated result and that given by Karas. G o o d agreement is found. Before performing the transient analysis of a composite target impacted by a projectile, the partial hybrid stress finite element program was simplified to a static version capable of simulating the quasi-static punch test conditions. For the current problem, a 10 x 10 mesh in the x - y plane is employed for the quarter plate, as shown in Fig. 8. Due to the simple stacking sequence of the laminated specimens studied, only three elements are chosen through the thickness. The simulated static punch curve is presented in Fig. 9, and good correlation between the test findings and simulated results was reported. Initially, the specimen was loaded from checkpoint O to A as shown in Fig. 3. The effect of matrix cracks corresponding to the slight decrease in slope on loading path OA was not considered in the current simulation. When the loading level reaches checkpoint A, delamination occurs and develops to a certain extent immediately in the specimen, and resulting in an extreme decrease in loading corresponding to the loading path AB. This effect was modeled by degrading the apparent transverse shear moduli (G13 and G23) uniformly in the delamination zone shown in Fig. 10 since the delaminated interfaces could no longer carry the transverse
Predicting the ballistic limit for plain woven glass/epoxy laminate
459
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shear stress. The degraded apparent shear moduli (G* 2 and G*3) were determined numerically to be 2.44 GPa, which is about 60% of the corresponding values for an intact specimen. This delamination zone was proposed according to the delamination area found from the quasi-statically punched specimens. When a specimen was continuously loaded beyond checkpoint B, severe damage on the target was found around the region under contact. In this region, an extensive amount of glass fiber in the penetrated specimen was broken and pushed forward in the direction of punch movement. The elastic moduli are further degraded uniformly in the damaged region shown in Fig. 10. Notice that this result was determined numerically based on a semi-empirical exercise to fit the static punch loading path between checkpoints B and C. Figure 11 shows the relation between the percentage of modulus degradation [i.e.M.D. (%)] versus displacement corresponding to
S. T. JENQ et al.
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FIG. 10. A schematic drawing of the proposed major damage zone of target based on static punch test result.
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loading path BC. After checkpoint C, the projectile started to exit from the distal surface of target, and a near constant friction force was observed from the punch curves. In summary, the above static punch simulation can be divided into three stages: (1) pre-delamination, (2) delamination initiation and propagation, and (3) fiber breakage and pushing forward of fibers. A steady friction force is assumed when the tip of the penetrator starts to exit from the distal surface of target, and the load magnitude at checkpoint C is selected. The aforementioned procedures were proposed to serve as a guideline for the subsequent dynamic impact analysis. Although the delamination area found from the dynamic impact test is larger than that observed from the static punch test, it was reported that the delamination did not seem to dissipate a large amount of energy [7]. In addition, the major fiber failure mode and its associated damage area for targets impacted by a projectile are similar to that found from the quasi-statically penetrated specimens. Therefore, the proposed procedures seem feasible for simulating the dynamic penetration process
Predicting
the ballistic
limit
for plain
woven
glass/epoxy
461
laminate
25
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[lo], and the validity is to be justified by the agreement between experimental findings and the simulated results. Transient analysis of the impact system was numerically analyzed. Initially, the incident velocity of the projectile was specified and the target was assumed to be stress-free and stationary. Two simple displacement criteria were proposed to characterize the impact damage processes: (1) If the displacement of impactor is loaded to point A (i.e. S,=5.37 mm) shown in the static punch curve, the apparent transverse shear moduli (Cl3 and G,,) for the target’s damaged zone are degraded to the values determined from the fitted results of the static punch simulation. When the target is further loaded beyond checkpoint B, the elastic moduli are then degraded according to the fitted results obtained from the static punch simulation to account for the extensive damage mechanisms, including fiber breakage and pushing forward of fibers. (2) If the specimen is continuously loaded to a displacement level (i.e. Sc= 18 mm) corresponding to checkpoint C, the specimen is modelled to be on the verge of perforation and the finite element code simulation is then terminated. Figures 12 and 13 show the displacement and velocity responses of the projectile when the target was struck by the projectile traveling with an incident velocity of 170 m/set. The solid (or dotted) lines shown in these two figures represent the simulated responses with (or without) consideration of the degradation of the static elastic properties of the target due to impact damage. The figures reveal that the degraded shear modulus was initiated at 35 ps to account for the delamination damage, and that the dynamic analysis
S.T. JENQ
462
et
al.
was terminated at 125 #s according to the displacement criterion set by checkpoint C. The timing and the amount of degradation of the target were based upon the information obtained from the static punch simulated. The numerically computed final velocity of the projectile, corresponding to checkpoint C, was then used to calculate the residual velocity (V~)of projectile based on the energy balance consideration E r -_ _
(9)
! 2 -- F~(b + h), -~mpV r2 __ X2mpVe - -
where b represents the length of the projectile, h is the thickness of the target, and Vc and Fe are the projectile velocity and the steady friction force corresponding to checkpoint C and loading path CD, respectively. By substituting the projectile residual velocity (V~)from Eqn (9) into Eqn (1) for the specific incident velocity (V~), the predicted ballistic limit (VBL) can be calculated. A series of impact test simulations (runs s01 to s08) was performed for projectiles striking with velocities ranging from 115 to 250 m/sec. Note that the static elastic properties shown in Table 1 were used as the input data. The computed projectile residual velocity and the corresponding estimated ballistic limit for various incident velocities are listed in Table 3, and the mean value of the predicted ballistic limit for runs s01 to s08 was determined to be 116 m/sec. The difference between this averaged ballistic limit (116 m/sec) and the impact test determined ballistic limit (153 m/sec) is about 24%. This difference may be due to the following reasons: (1) the proposed static penetration model incorporated in the transient finite element analysis is unable to closely predict the dynamic impact response; or (2) the high strain-rate effect on the variation of the dynamic elastic properties of GFRP laminated target needs to be considered in the numerical simulations. The latter seems to be important in accounting for the difference mentioned, because GFRP has been determined to be a rate-sensitive material [14-16]. Based on the previously reported high strain-rate tensile test result [14] for woven-roving GFRP specimens cut with the tensile axis either parallel to one of the principal reinforcing directions (0° specimens) or lying in the plane of reinforcement and inclined at 45 ° to both the principal reinforcing directions (45 ° specimens), the dynamic Young's modulus at a strain-rate of 870 sec- 1 was determined to be approximately 2.3 times that of the quasi-static value for the 0 ° specimens and 1.62 times the static value for the 45 ° specimens at a strain rate of 1120 sec-x. In addition, reference (15) reported that the dynamic Young's modulus
TABLE 3.
A SUMMARY OF THE SIMULATED IMPACT TEST RESULTS
Run no.
Incident velocity (m/sec)
Simulated residual velocity I (m/sec)
Predicted ballistic limit 2 (m/sec)
sOl sO2 sO3 sO4 sO5 sO6 sO7 s08
115 130 150 170 180 190 200 250
34.1 64.4 96.2 125.1 137.2 148.9 162.1 217.9
109.8 112.9 115.0 115.1 116.5 117.9 I 18.0 122.6
the static elastic properties were used in the numerical simulations
dm01 dm02 dm03 dm04 dm05 dm06 dm07
150 160 170 180 190 200 250
31.6 61.6 79.0 97.4 112.1 128.3 192.8
146.6 147.7 150.5 151.4 153.4 153.4 159.1
the dynamic elastic properties were used in the numerical
Note
simulations
* The simulated residual velocities are computed based on Eqn (10). The predicted ballistic limit is calculated based on Eqn (1) for given striking velocity and residual velocity.
Predicting the ballistic limit for plain woven glass/epoxylaminate 3OO • I
test data simulatedre .sult w/o strain-rateeffect -------o----- simulatedresult . with strain-rateeffect /
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300
striking velocity (m/see) FIG. 14. A plot of the striking velocityversus terminal (or exit) velocity.
of 0 ° G F R P laminated specimens impacted along fiber direction at an averaged compressional strain rate of 2020 set-1 was approximately 1.92 times that of the static value and 1.43 times the static value for 0 ° G F R P laminates transversely impacted at a strain rate of 6596 sec- 1. Therefore, additional simulations (runs no. dm01 to dm07) were performed using the dynamic elastic modulus as input data to incorporate the high-strain effect of G F R P laminated targets due to impact. Note that judging from the previously reported high strain-rate test results described in the previous paragraph for G F R P specimens at impact rate of strain, the dynamic elastic modulus was chosen to be two times the static values. The corresponding simulated terminal velocity and estimated ballistic limit for targets struck by a projectile fired at incident velocities ranging from 150 to 250 m/see are presented in Table 3. A mean value of the predicted ballistic limit for runs dm01 to dm07 was calculated to be 151.7 m/see, which is in good agreement with the ballistic limit (153 m/see) determined from the series of impact tests. A plot of the projectile striking velocity versus the terminal velocity is shown in Fig. 14. Curves A and B correspond respectively to the simulated results for runs s01 to s08 and runs dm01 to din07 given in Table 3. The square dark points shown in Fig. 14 represent the impact test results given in Table 2. Figure 14 reveals that a discrepancy exists between the experimental trend and curve A when the static elastic properties are used in the code simulation. Nevertheless, the trend of the test results agrees well with curve B if the dynamic elastic moduli are used as input data in the finite element simulation. Therefore, it seems admissible to use curve B to predict the terminal velocity of the projectile for various striking velocities. The current dynamic finite element program incorporating the proposed simple static penetration model seems capable of closely predicting the ballistic limit of the glass/epoxy composite targets if the dynamic elastic moduli are used as the input data in code simulations. The purpose of this paper is to report a simple and effective method based on quasi-static punch test results in order to predict the ballistic limit of a 4 mm thick plain weave G F R P target struck by a round-nosed projectile numerically, without performing a series of expensive impact tests. Further studies to determine a more sophisticated strain- or stress-state based damage criteria for finite element analysis seems important to predict the ballistic limit with varying penetrator diameter and target thickness ratios.
464
S.T. JENQ et al. CONCLUSIONS
The p u r p o s e of this w o r k is to predict the ballistic limit for plain woven g l a s s / e p o x y l a m i n a t e d targets struck by a rigid, bullet-like projectile. A series of i m p a c t tests were c o n d u c t e d to d e t e r m i n e the ballistic limit of 4 m m thick c l a m p e d targets. Q u a s i - s t a t i c punch tests were p e r f o r m e d to investigate the progressive d a m a g e m o d e s of targets. The m a j o r d a m a g e m o d e s were d e t e r m i n e d to be d e l a m i n a t i o n a n d fiber breakage. T h e p u n c h l o a d - d i s p l a c e m e n t relation was o b t a i n e d from these tests a n d used as a basis to characterize the p e n e t r a t i o n process. Test results reveal that the characteristics of the p u n c h curves found in this s t u d y are quite different from those r e p o r t e d by Lee and Sun (1991) because a b l u n t - e n d e d p e n e t r a t o r was used in their work. A static version of the p a r t i a l h y b r i d stress finite element code c a p a b l e of t a k i n g into a c c o u n t the structural stiffness d e g r a d a t i o n due to i m p a c t - i n d u c e d d a m a g e was d e v e l o p e d to s i m u l a t e the quasi-static p u n c h test conditions. The static p u n c h s i m u l a t i o n can be d i v i d e d into three consecutive stages: (1) p r e - d e l a m i n a t i o n , (2) d e l a m i n a t i o n initiation a n d p r o p a g a t i o n , a n d (3) fiber b r e a k a g e a n d pushing f o r w a r d of fibers. A d y n a m i c version of the finite element p r o g r a m was i n c o r p o r a t e d with the p r o p o s e d p e n e t r a t i o n m o d e l to analyze the i m p a c t responses of target a n d projectile. The friction force o b s e r v e d form the static tests was not c o n s i d e r e d in the static p u n c h s i m u l a t i o n but was used in an energy b a l a n c e c o n s i d e r a t i o n to calculate the t e r m i n a l velocity of the p e n e t r a t o r . T h e ballistic limit can be p r e d i c t e d based on the principle of c o n s e r v a t i o n of energy for a rigid projectile for specific striking a n d t e r m i n a l velocities. G o o d a g r e e m e n t between the p r e d i c t e d ballistic limit a n d test results is o b t a i n e d if the d y n a m i c elastic p r o p e r t i e s of target are used as i n p u t d a t a in code simulations. H o w e v e r , a 24% difference is r e p o r t e d if the static elastic p r o p e r t i e s are used in the n u m e r i c a l analysis. It is c o n c l u d e d that the p r o p o s e d p e n e t r a t i o n m o d e l is a d e q u a t e for p r e d i c t i n g the ballistic limit of a g l a s s / e p o x y target struck by a bullet-like p e n e t r a t o r if the high s t r a i n - r a t e elastic p r o p e r t i e s of the target is considered. REFERENCES 1. J. A. ZUKASet al., Impact Dynamics. John Wiley, New York (1982). 2. S. P. JOSHIand C. T. SUN,Impact induced fracture in a laminated composite. J. Comp. Mats 19, 51-66 (1985). 3. N. CRISTESCU,L. E. MALVERNand R. L. SIERAKOWSKI,Failure mechanism in composite plate impacted by blunt-ended penetrators. Foreign Object Impact Damage to Composite, AS T M S T P 568, pp. 159-172 (1975). 4. G. E. HUSMAN,J. M. WHITNEYand J. C. HALPIN,Residual strength characterization of laminated composites subjected to impact loading. Foreign Object Impact Damage to Composite, A S T M S T P 568, pp. 92-I 13 0975). 5. S. T. JENQ, S. B. WANGand L. T. SHEU, A model for predicting the residual strength of GFRP laminates subject t o ballistic impact. J. Rein. Plastics Comp. l 1, 1127-1141 (1992). 6. W. J. CANTWELLand J. MORTON, Impact perforation of carbon fibre reinforced plastic, 38, 119-141 (1990). 7. G. ZHU, W. GOLDSMITH and C. K. H. DHARAN, Penetration of laminated Kevlar by projectiles--I. Experimental investigation. Int. J. Solids Structures 29(4), 399-420 (1992). 8. G. ZHU, W. GOLDSMITHand C. K. H. DHARAN,Penetration of laminated Kevlar by projectiles--II. Analytical model. Int. J. Solids Structures 29(4), 521--436 (1992). 9. S.-W. R. LEE and C. T. SUN, Modeling of penetration process for composite laminates subjected to a blunt-ended punch. Proceedings of the 23rd International S A M P E Technical Conference, Kiamesha Lake, New York, pp. 624-638 (1991). 10. S.-W. R. LEE and C. T. SUN, Ballistic limit of composite laminates by a quasi-static penetration model. Proceedings of the 24th International SAM P E Technical Conference, Toronto, Canada, pp. T497-T511 (1992). 11. C. T. SUN and S. V. POTTI, High velocity impact and penetration of composite laminates. Proceedings of the Ninth International Conference on Composite Materials (ICCM/IX), Vol. 5, pp. 261-268, Madrid, Spain (1993). 12. H.-S. JING and M.-L. LIAO,Partial hybrid stress element for transienranalysis of thick laminated composite plates. Int. d. Numer. Meth. Engng 29, 1787-1796 (1990). 13. H.-S. JING and M.-L. LIAO,Partial hybrid stress element for the analysis of thick laminated composite plates. Int. J. Numer. Meth. Engng 28, 2813-2827 (1989). 14. J. HARDINGand L. M. WELSH,A tensile testing technique for fiber-reinforced composites at impact rates of strain. J. Mater. Sci. 18, 1810--1826 (1983). 15. S. T. JENQ and S. L. SHEU, High strain rate compressional behavior of stitched and unstitched composite laminates with radial constraint. Comp. Struct. 25, 427-438 (1993). 16. K. KAWATAet al., Macro- and micro-mechanics of high-velocity brittleness and high-velocity ductility of solids. Proceedings of the I U T A M on M M M H V D F , Tokyo, Japan, pp. 91-112 (1985). 17. S. H. YANGand C. T. SUN, Indentation law for composite laminates. A S T M S T P 787, pp. 425-449 (1982). 18. W. GOLDSMITH,Impact. Edward Arnold, London (1960).
Int. J. Impact Engng Vol. 15, No. 4, pp. 451--464, 1994 Elsevier Science Ltd Printed in Great Britain 0734-743X(94)E0016-O 0734-743X/94 ST.00+ 0.00
PREDICTING THE BALLISTIC LIMIT WOVEN GLASS/EPOXY COMPOSITE
FOR PLAIN LAMINATE
S. T. JENQ,H.-S. JING and CHARLESCHUNG Institute of Aeronautics and Astronautics, National Cheng Kung University, Tainan 701, Taiwan, Republic of China
(Received 21 September 1993; and in revised form 7 February 1994) Summary--This paper is concerned with predicting the ballistic limit of plain woven glass/epoxy composite laminates struck by a 14.9 gm bullet-like rigid projectile with a tip radius of 5 mm. The 4 mm thick square specimens were clamped along their 100 mm edges. A pneumatic gun was used to propel the bullet with incident velocities ranging from 140 to 200 m/sec. The ballistic limit was experimentally determined to be near 153 m/sec. A series of quasi-static punch tests was performed in order to investigate the progressive damage modes of the targets and to obtain the punch load-displacement relation. These quasi-static punch tests were conducted to characterize the penetration process. Similar to dynamic impact test results, the major damage modes for targets subjected to quasi-static punch loading were found to be governed by delamination and fiber breakage. After specimens were perforated, a steady friction force was observed from quasi-static punch tests. Test results also indicate that the rhombus-shaped delamination of impact damaged samples is greater than that of quasi-statically punched specimens. A partial hybrid stress finite element code was incorporated with the proposed static penetration model to simulate the dynamic impact process. An energy consideration was applied to predict the ballistic limit. The difference between the predicted ballistic limit and test findings was found to be approximately 24% if the target's static material properties were used in the code simulation. Due to the rate-sensitive nature of glass/epoxy composites, the effect of dynamic elastic properties on the predicted ballistic limit was further studied. Good agreement between the predicted ballistic limit and test results was found if the target's elastic moduli used in simulation were increased to two times the static values.
INTRODUCTION
Laminated composites have been widely adopted in many applications to resist foreign object impact loading. It is important to understand the dynamic behavior of composite structures and the associated damage mechanisms. The condition for perforation (or ballistic limit) is certainly the most important factor for designing a suitable protective structure. Although the impact damage characterization and the study of impact residual properties of composite laminates have been extensively reported [1-5] in the past two decades, only a limited amount of work is found to analytically model the penetration/perforation of composite laminates and to predict the ballistic limit of composite structures. A brief summary of the work related to the current study follows. Cantwell and Motron [6] examined the perforation process in a series of CFRP composites. Both the drop-weight tower tester and gas gun were used to conduct impact tests. Effects of varying target thickness and length of span on the energy required to perforate the composite targets were examined. According to this study, for low velocity impact loading conditions, the structural response of targets is important, and the areal dimensions of the target determine the perforation threshold energy. However, under high velocity impact loading, the perforation threshold appears to be independent of the areal geometry of the target. According to the dissipation of energy during the impact process, a simple perforation model was proposed. For target thicknesses up to and including 4 ram, a good relationship between the experimental trends and the model-predicted results was reported. For thicker specimens, this model is no longer applicable due to change in perforation mode. Zhu et al. I-7] investigated the impact response of woven Kevlar/polyester laminates of varying thickness to quasi-static and dynamic penetration by cylindro-conical projectiles. 451
452
S.T. JENQ et al.
Ballistic limits were determined for a series of targets with thicknesses ranging from 3.125 to 12.7 mm. It was concluded that local deformation and fiber failure constitute the major energy absorption mechanisms in impact perforation. Delamination, in both the static or dynamic cases, did not seem to dissipate a large amount of energy. An analytical representation of the normal impact and perforation of conically-tipped hard-steel cylinders was also developed by Zhu et al. [8]. This model utilizes the laminated plate theory to determine global target deflection. Dissipative mechanisms, including indentation of the striker tip, bulging at the surface, delamination, fiber failure, and friction are taken into account. The predicted ballistic limit agrees well with those of test results; for thinner targets (3.125 mm thick) the difference is 12%, with a difference of 1.3 % for thicker specimens (9.525 mm thick). Lee and Sun [9] developed a quasi-static model to simulate the penetration process of composite laminates struck by blunt-ended projectiles. A series of static punch tests was conducted to characterize the load-displacement relation during penetration for ([0/90/45/-45]s)2, Herculus AS4/3501-6 graphite/epoxy composites. The major damage modes were reported to be delamination and plugging. An axisymmetric finite element analysis was performed to simulate the quasi-static penetration process. An effective modulus scheme was adopted in the analysis. Comparisons of punch load-displacement curves have shown good agreement between modeling and testing. In addition, the ballistic limit of graphite/epoxy laminates struck by a blunt-ended impactor was determined from a series of impact tests by Lee and Sun [10]. The penetration model developed in reference (9) was incorporated into a dynamic finite element analysis as the penetration criteria. Comparison between the computed ballistic limit and test results shows good agreement. Sun and Potti [11] further utilized the static punch curve as a basis to calculate the energy required for penetration of composite laminates. A series of impact tests was performed to study 2, 4.1, 6.1, and 8.1 mm thick graphite-epoxy (Hercules AS4-3501/6) quasi-isotropic composite laminates. The projectiles were 14.6 mm in diameter, 24 mm in length, and made of hardened tool steel. They were fired against targets with incident velocities ranging from 20 to 150 m/sec. The researchers found that the overall damage pattern in the dynamic case was similar to that of the static case. The residual velocities predicted using static punch-through energy are overestimates of the experimental values for thick laminates, but this method provides an easy and inexpensive upper bound approximation. Recently, more attention has been focused on the development of using glass fiber reinforced plastics (GFRP) in many applications due to their cost effectiveness and high toughness at impact rates. Therefore, a series of impact tests was conducted in this work in order to study the perforation condition (or ballistic limit) of plain woven glass/epoxy laminated targets struck by a 14.9 gm bullet-like penetrator with a tip radius of 5 mm. Similar to the work reported by Lee and Sun [9, I0], quasi-static punch tests were conducted to examine the punch load-displacement relation and to characterize the penetration process. The static penetration model developed in this paper was incorporated into the partial hybrid stress finite element dynamic analysis [12, 13] as the penetration criteria. The energy balance consideration was adopted to predict the ballistic limit. Comparison between the predicted ballistic limit and that found from tests is to be reported. Due to the rate-sensitive nature of glass/epoxy composites [14-16], the effect of the variation of dynamic elastic moduli on the predicted ballistic limit is also studied. EXPERIMENTAL
SETUP AND TEST RESULTS
In this work, the wet layup method was utilized to fabricate (0°, 90°)1o laminated specimens made of plain woven E-glass fabrics (Taiwan Glass Co., Ltd TGFW-600) and epoxy resin system (Ciba-Geigy, Aradite LY564). During the layup process, the weft and warp fibers were carefully aligned so that each layer may preserve the same directions of reinforcement. The fiber volume ratio of the specimens was determined to range from 51.7
Predicting the ballistic limit for plain woven glass/epoxy laminate
453
]-ABLE 1. THE STATICMECHANICALPROPERTIESOF tHE LAMINATEDGLASS/EPOXYTARGETSUSEDIN CODE SIMULATION p* V* Ell E22 E33 G12
1 884 kg/m 3 51.7-52.4% 27.8 GPa 27.8 GPa 8.0 GPa 5.32 GPa
G23 GI3 vi2 v23 vl3
4.07 GPa 4.07 GPa 0.09 0.30 0.30
* Vf and p represent the fiber volume ratio and density, respectively. to upper grip of MTS
penetrato~
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to 52.4%. A list of the specimens' static mechanical properties used in the code simulation is given in Table 1. Both quasi-static punch tests and dynamic impact tests were performed. The rigid bullet-like penetrator with a tip radius of 5 mm was made from a 12.5 mm diameter hardened 4340 steel rod. During the tests, the 4 mm thick square specimens were clamped along their I00 mm edges. As proposed by Lee and Sun [9, 10], the purpose of performing the static punch tests is to characterize the progressive damage mechanism and to obtain the punch load-displacement curve in order to characterize the penetration process. When performing the quasi-static punch tests, the rigid fixture (shown in Fig. 1) was mounted on an MTS machine with a stroke-rate controlled at 0.125 mm/sec. An analog-to-digital converting interface and a personal compute were used to record the load-displacement relation from quasi-static punch tests by means of Labtech softward. Three typical load-displacement curves measured from quasi-static punch tests are plotted in Fig. 2. Test results reveal that these punch curves are reproducible and preserve a specific pattern. The basic pattern of these curves can be represented by the curve shown in Fig. 3, and five checkpoints (0, A, B, C and D) are marked in this figure for convenience. For a specimen loaded from point O to A, no major damage mode is observed. However, if the loading level approaches checkpoint A, the slopes of the load-displacement curves shown in Fig. 2 decrease slightly indicating that matrix cracks occur in the specimen. When the loading level reaches checkpoint A, delamination occurs and develops immediately in the specimen, resulting in an extreme decrease in loading corresponding to the loading
S . T . JENQ et al.
454 7.0
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Basic pattern of the quasi-static punch curves.
path AB. This phenomenon is similar to that reported by Lee and Sun [9-1 when conducting quasi-static punch tests with a blunt-ended cylindrical projectile. As the punch further penetrates into the target, fibers under the area of contact start to break and are pushed in the direction of penetrator motion. This phenomenon occurs when a specimen is loaded along the loading path BC. At point C, the tip of the penetrator is about to exit from the distal surface of the target. A nearly constant friction between the penetrator and specimen is observed from the loading path CD. Note that if we compare the punch load-displacement curves shown in Fig. 2 and those reported by Lee and Sun I-9, 10-1, only one abrupt decreasing loading (path AB), representing the major delamination damage mode, is observed in this work. Furthermore, no obvious transition region for friction is observed because the plugging phenomenon is not observed in the present study. Six high speed impact tests were also conducted in order to examine the impact damage of composite specimens and to determine the ballistic limit of the laminated targets struck by a bullet-like impactor with rounded tip weighing 14.9 g. A pneumatic gun was used to fire the projectile against targets with incident velocities ranging from 140 to 200 m/sec. The ballistic limit was experimentally determined to be near 153 m/sec. The projectile
Predicting the ballistic limit for plain woven glass/epoxy laminate
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FIG. 4. A schematic drawing of the high speed impact test set-up. TABLE 2. A SUMMARYOF THE IMPACTTESTRESULTS Test no.
Incident velocity (Vs) (m/sec)
Exit velocity (VR)(m/sec)
Estimated ballistic limit (m/sec)
Note
D01 D02 D03 D04 D05 D06
141.5 145.2 153.9 164.5 169.8 190.1
43.7 60.6 103.1
158.6 159.6 159.7
pp* with rebound pp with rebound cpt cp cp cp
* Abbreviation 'pp' represents partial penetration. t Abbreviation "cp' represents complete penetration.
incident velocity was determined by means of a pair of photo-sensors, while the residual (terminal) velocity was detected by a set of short-screens displaced 5 cm apart. A schematic drawing of the dynamic impact test system is presented in Fig. 4. Note that the projectile was not deformed after impact tests. A summary of the projectile's incident and residual velocities for those tests conducted is given in Table 2. The major damage pattern found from the impacted specimens was similar to that from the quasi-static penetrated specimens. However, the area of the rhombus-shaped delamination for the high speed impacted specimens was determined to be about nine times (3 x 3) greater than that of the quasi-statically penetrated specimens, as shown in Fig. 5(a) and (b). The estimated ballistic limit shown in the fourth column of Table 2 is calculated based on the principle of conservation of energy for rigid penetrators, satisfying the simple relationship 1_ ,,2 i _ ,,2 t_ ,,2 for V~>VBL, (1) ]trip VBL _ -- -~rltp v s -- ]Irtp v r , where mp is the mass of the projectile and the estimated ballistic limit is represented by VBL.The striking velocity and residual velocity of the projectile are denoted by V~and Vr, respectively. Upon examining the estimated ballistic limit shown in Table 2, it is found that the data scattering is limited, and an averaged ballistic limit of 159.3 m/s is determined. COMPUTATION
M O D E L AND R E S U L T
The ballistic limit of a composite target was numerically computed in order to check against the test result. The computational procedure for predicting the ballistic limit consists of three phases: (1) determine the penetration criterion based on the quasi-static punch curves obtained from tests to characterize the major damage mechanisms (delamination
456
S, T. JENQ et al.
El
(top vlew)
(bottom view]
(elde vlew)
(side view)
FIG. 5. Photographs of the (a) quasi-static penetrated specimen and (b) impact damaged specimen struck by the projectile with an incident velocity of 153.9 m/sec.
and fiber failure) and locate the termination of these mechanisms; (2) develop a partial hybrid stress finite element code capable of taking into account the structural stiffness degradation in order to fit the quasi-static punch (load-displacement) curves; and (3) simulate the dynamic impact test conditions with the proposed static penetration model in order to determine the velocity of the impactor when the major damage mechanisms have terminated. Friction is not incorporated into the finite element analysis; however, an energy balance consideration is used to account for the frictional resistance in order to determine the projectile's residual velocity for complete perforation. The ballistic limit can then be subsequently calculated by using Eqn (1) for given incident and the corresponding computed residual velocities. The constitutive relation of a single layer in linear elasticity problems can be expressed by cr = C~,
(2)
where trT = [fix, O'y,trz, Zyz,
Zxz ,
Zxy];
ex = [e~, ey, e.., 7y_-,7=, 7xy]
and
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If we separate the stresses and strains into two parts, a flexural part and a transverse shear
Predicting the ballistic limit for plain woven glass/epoxy laminate
457
part, then Eqn (2) can be expressed as af = Cf~f
(3a)
(7t = Ct£ t,
(3b)
where subscripts f and t represent flexural and transverse shear, respectively. The matrices Cf and Ct can be extracted directly from Eqn (2). Inverting Eqns (3a) and (3b) yields ~f =Sfaf
(4a)
~t=Stat,
(4b)
where the compliance matrices Sf and St are the direct inversion of Cf and Ct, respectively. A variationally consistent partial hybrid stress element (PHSE) can be formulated based upon the previously developed functional for analyzing the transient response of composites [12,] as I-I : f v [½(Odl)TCt(Ofu) + a T ( D t u ) -- ~tlr 1 Tt Sttr t -- ½pl'lTl'l,] dV -
fS
l"Vu dS,
(5)
where the displacement and surface traction vectors are represented by u and i "T, respectively. The superscript 'T' in the above equation stands for the transpose of the vector or matrix in question, and (") represents for time derivative of (). Note that the special differential operators (Df and Dt) for the flexural and transverse shear parts are expressed as 0 Ox D f=
0
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0
0
and
Dr=
0 Oz 0
L
0
O Ox
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O
(6)
Oz Oy
Oz
With the standard procedures of finite element method, the corresponding partial hybrid stress element can then be established. The three dimensional isoparametric twenty-node hexahedron element is adopted in finite element analysis. In each element, the displacement is interpolated by the nodal values. The final equation of motion can be written as Mii+Kq = Q,
(7)
where M, K and Q represent the consistent mass matrix, stiffness matrix, and consistent load vector, respectively, and the global vector of nodal displacements is denoted by q. Detailed discussion about the assumed stress field for partial hybrid stress finite element development is given in [13,]. Based on Eqn (7), the assembled global equation can be solved by the Runge-Kutta numerical scheme iteratively in time to compute the unknown nodal displacement vector for a prescribed loading and boundary conditions. A point mass is used to model the impactor because it is considered to be rigid. The Hertz contact law [17-], F = k ~ x 3/2
and
4 l,.Fl-v 2 1-]-1 k = 3-Rs'~'L Es + ~s_l=l ,
(8)
is used to model the contact force (F) exerted on the laminated target and penetrator with a specific incident velocity. Parameter 'ct' represents the indentation, and 'k' is a constant depending upon the projectile's tip radius (Rs), the elastic modulus (E s) and Poisson's ratio (Vs) of the penetrator, and the transverse elastic modulus (E33) of the G F R P target. The impact response of a simply supported 20 x 20 x 0.8 cm steel plate due to the central impact of a 2 cm diameter steel sphere at an initial velocity of 100 cm/sec was numerically simulated in order to check against the analytical result by Karas shown on page 140 of [18,]. Figures 6 and 7 show the time history of the target central displacement and contact force,
458
S.T. JENQ et al. o to
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Time (/~sec)
FIG. 7. The numerical simulated time history of the contact force when the target is struck by a steel sphere traveling with an initial velocityof 100 cm/sec.
respectively. The solid and dotted lines plotted in these figures represent, respectively, the current PHSE simulated result and that given by Karas. G o o d agreement is found. Before performing the transient analysis of a composite target impacted by a projectile, the partial hybrid stress finite element program was simplified to a static version capable of simulating the quasi-static punch test conditions. For the current problem, a 10 x 10 mesh in the x - y plane is employed for the quarter plate, as shown in Fig. 8. Due to the simple stacking sequence of the laminated specimens studied, only three elements are chosen through the thickness. The simulated static punch curve is presented in Fig. 9, and good correlation between the test findings and simulated results was reported. Initially, the specimen was loaded from checkpoint O to A as shown in Fig. 3. The effect of matrix cracks corresponding to the slight decrease in slope on loading path OA was not considered in the current simulation. When the loading level reaches checkpoint A, delamination occurs and develops to a certain extent immediately in the specimen, and resulting in an extreme decrease in loading corresponding to the loading path AB. This effect was modeled by degrading the apparent transverse shear moduli (G13 and G23) uniformly in the delamination zone shown in Fig. 10 since the delaminated interfaces could no longer carry the transverse
Predicting the ballistic limit for plain woven glass/epoxy laminate
459
Y (mm)
agedzon} / .
.~1~ 0
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30
40
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X (mm)
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. . . .
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Displacement (mm) FIc. 9. A comparison of the numerically simulated and test-determined static punch curves.
shear stress. The degraded apparent shear moduli (G* 2 and G*3) were determined numerically to be 2.44 GPa, which is about 60% of the corresponding values for an intact specimen. This delamination zone was proposed according to the delamination area found from the quasi-statically punched specimens. When a specimen was continuously loaded beyond checkpoint B, severe damage on the target was found around the region under contact. In this region, an extensive amount of glass fiber in the penetrated specimen was broken and pushed forward in the direction of punch movement. The elastic moduli are further degraded uniformly in the damaged region shown in Fig. 10. Notice that this result was determined numerically based on a semi-empirical exercise to fit the static punch loading path between checkpoints B and C. Figure 11 shows the relation between the percentage of modulus degradation [i.e.M.D. (%)] versus displacement corresponding to
S. T. JENQ et al.
460
mm
Vi
Y
k,,,.,~
r:5 mm
target thickness []
clamped end .
major damage zone, containing delamination and broken fibers
FIG. 10. A schematic drawing of the proposed major damage zone of target based on static punch test result.
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loading path BC. After checkpoint C, the projectile started to exit from the distal surface of target, and a near constant friction force was observed from the punch curves. In summary, the above static punch simulation can be divided into three stages: (1) pre-delamination, (2) delamination initiation and propagation, and (3) fiber breakage and pushing forward of fibers. A steady friction force is assumed when the tip of the penetrator starts to exit from the distal surface of target, and the load magnitude at checkpoint C is selected. The aforementioned procedures were proposed to serve as a guideline for the subsequent dynamic impact analysis. Although the delamination area found from the dynamic impact test is larger than that observed from the static punch test, it was reported that the delamination did not seem to dissipate a large amount of energy [7]. In addition, the major fiber failure mode and its associated damage area for targets impacted by a projectile are similar to that found from the quasi-statically penetrated specimens. Therefore, the proposed procedures seem feasible for simulating the dynamic penetration process
Predicting
the ballistic
limit
for plain
woven
glass/epoxy
461
laminate
25
20
15
10
5
0 0
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Time FIG. 12. A plot or the displacement
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(sec.)
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versus
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[lo], and the validity is to be justified by the agreement between experimental findings and the simulated results. Transient analysis of the impact system was numerically analyzed. Initially, the incident velocity of the projectile was specified and the target was assumed to be stress-free and stationary. Two simple displacement criteria were proposed to characterize the impact damage processes: (1) If the displacement of impactor is loaded to point A (i.e. S,=5.37 mm) shown in the static punch curve, the apparent transverse shear moduli (Cl3 and G,,) for the target’s damaged zone are degraded to the values determined from the fitted results of the static punch simulation. When the target is further loaded beyond checkpoint B, the elastic moduli are then degraded according to the fitted results obtained from the static punch simulation to account for the extensive damage mechanisms, including fiber breakage and pushing forward of fibers. (2) If the specimen is continuously loaded to a displacement level (i.e. Sc= 18 mm) corresponding to checkpoint C, the specimen is modelled to be on the verge of perforation and the finite element code simulation is then terminated. Figures 12 and 13 show the displacement and velocity responses of the projectile when the target was struck by the projectile traveling with an incident velocity of 170 m/set. The solid (or dotted) lines shown in these two figures represent the simulated responses with (or without) consideration of the degradation of the static elastic properties of the target due to impact damage. The figures reveal that the degraded shear modulus was initiated at 35 ps to account for the delamination damage, and that the dynamic analysis
S.T. JENQ
462
et
al.
was terminated at 125 #s according to the displacement criterion set by checkpoint C. The timing and the amount of degradation of the target were based upon the information obtained from the static punch simulated. The numerically computed final velocity of the projectile, corresponding to checkpoint C, was then used to calculate the residual velocity (V~)of projectile based on the energy balance consideration E r -_ _
(9)
! 2 -- F~(b + h), -~mpV r2 __ X2mpVe - -
where b represents the length of the projectile, h is the thickness of the target, and Vc and Fe are the projectile velocity and the steady friction force corresponding to checkpoint C and loading path CD, respectively. By substituting the projectile residual velocity (V~)from Eqn (9) into Eqn (1) for the specific incident velocity (V~), the predicted ballistic limit (VBL) can be calculated. A series of impact test simulations (runs s01 to s08) was performed for projectiles striking with velocities ranging from 115 to 250 m/sec. Note that the static elastic properties shown in Table 1 were used as the input data. The computed projectile residual velocity and the corresponding estimated ballistic limit for various incident velocities are listed in Table 3, and the mean value of the predicted ballistic limit for runs s01 to s08 was determined to be 116 m/sec. The difference between this averaged ballistic limit (116 m/sec) and the impact test determined ballistic limit (153 m/sec) is about 24%. This difference may be due to the following reasons: (1) the proposed static penetration model incorporated in the transient finite element analysis is unable to closely predict the dynamic impact response; or (2) the high strain-rate effect on the variation of the dynamic elastic properties of GFRP laminated target needs to be considered in the numerical simulations. The latter seems to be important in accounting for the difference mentioned, because GFRP has been determined to be a rate-sensitive material [14-16]. Based on the previously reported high strain-rate tensile test result [14] for woven-roving GFRP specimens cut with the tensile axis either parallel to one of the principal reinforcing directions (0° specimens) or lying in the plane of reinforcement and inclined at 45 ° to both the principal reinforcing directions (45 ° specimens), the dynamic Young's modulus at a strain-rate of 870 sec- 1 was determined to be approximately 2.3 times that of the quasi-static value for the 0 ° specimens and 1.62 times the static value for the 45 ° specimens at a strain rate of 1120 sec-x. In addition, reference (15) reported that the dynamic Young's modulus
TABLE 3.
A SUMMARY OF THE SIMULATED IMPACT TEST RESULTS
Run no.
Incident velocity (m/sec)
Simulated residual velocity I (m/sec)
Predicted ballistic limit 2 (m/sec)
sOl sO2 sO3 sO4 sO5 sO6 sO7 s08
115 130 150 170 180 190 200 250
34.1 64.4 96.2 125.1 137.2 148.9 162.1 217.9
109.8 112.9 115.0 115.1 116.5 117.9 I 18.0 122.6
the static elastic properties were used in the numerical simulations
dm01 dm02 dm03 dm04 dm05 dm06 dm07
150 160 170 180 190 200 250
31.6 61.6 79.0 97.4 112.1 128.3 192.8
146.6 147.7 150.5 151.4 153.4 153.4 159.1
the dynamic elastic properties were used in the numerical
Note
simulations
* The simulated residual velocities are computed based on Eqn (10). The predicted ballistic limit is calculated based on Eqn (1) for given striking velocity and residual velocity.
Predicting the ballistic limit for plain woven glass/epoxylaminate 3OO • I
test data simulatedre .sult w/o strain-rateeffect -------o----- simulatedresult . with strain-rateeffect /
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of 0 ° G F R P laminated specimens impacted along fiber direction at an averaged compressional strain rate of 2020 set-1 was approximately 1.92 times that of the static value and 1.43 times the static value for 0 ° G F R P laminates transversely impacted at a strain rate of 6596 sec- 1. Therefore, additional simulations (runs no. dm01 to dm07) were performed using the dynamic elastic modulus as input data to incorporate the high-strain effect of G F R P laminated targets due to impact. Note that judging from the previously reported high strain-rate test results described in the previous paragraph for G F R P specimens at impact rate of strain, the dynamic elastic modulus was chosen to be two times the static values. The corresponding simulated terminal velocity and estimated ballistic limit for targets struck by a projectile fired at incident velocities ranging from 150 to 250 m/see are presented in Table 3. A mean value of the predicted ballistic limit for runs dm01 to dm07 was calculated to be 151.7 m/see, which is in good agreement with the ballistic limit (153 m/see) determined from the series of impact tests. A plot of the projectile striking velocity versus the terminal velocity is shown in Fig. 14. Curves A and B correspond respectively to the simulated results for runs s01 to s08 and runs dm01 to din07 given in Table 3. The square dark points shown in Fig. 14 represent the impact test results given in Table 2. Figure 14 reveals that a discrepancy exists between the experimental trend and curve A when the static elastic properties are used in the code simulation. Nevertheless, the trend of the test results agrees well with curve B if the dynamic elastic moduli are used as input data in the finite element simulation. Therefore, it seems admissible to use curve B to predict the terminal velocity of the projectile for various striking velocities. The current dynamic finite element program incorporating the proposed simple static penetration model seems capable of closely predicting the ballistic limit of the glass/epoxy composite targets if the dynamic elastic moduli are used as the input data in code simulations. The purpose of this paper is to report a simple and effective method based on quasi-static punch test results in order to predict the ballistic limit of a 4 mm thick plain weave G F R P target struck by a round-nosed projectile numerically, without performing a series of expensive impact tests. Further studies to determine a more sophisticated strain- or stress-state based damage criteria for finite element analysis seems important to predict the ballistic limit with varying penetrator diameter and target thickness ratios.
464
S.T. JENQ et al. CONCLUSIONS
The p u r p o s e of this w o r k is to predict the ballistic limit for plain woven g l a s s / e p o x y l a m i n a t e d targets struck by a rigid, bullet-like projectile. A series of i m p a c t tests were c o n d u c t e d to d e t e r m i n e the ballistic limit of 4 m m thick c l a m p e d targets. Q u a s i - s t a t i c punch tests were p e r f o r m e d to investigate the progressive d a m a g e m o d e s of targets. The m a j o r d a m a g e m o d e s were d e t e r m i n e d to be d e l a m i n a t i o n a n d fiber breakage. T h e p u n c h l o a d - d i s p l a c e m e n t relation was o b t a i n e d from these tests a n d used as a basis to characterize the p e n e t r a t i o n process. Test results reveal that the characteristics of the p u n c h curves found in this s t u d y are quite different from those r e p o r t e d by Lee and Sun (1991) because a b l u n t - e n d e d p e n e t r a t o r was used in their work. A static version of the p a r t i a l h y b r i d stress finite element code c a p a b l e of t a k i n g into a c c o u n t the structural stiffness d e g r a d a t i o n due to i m p a c t - i n d u c e d d a m a g e was d e v e l o p e d to s i m u l a t e the quasi-static p u n c h test conditions. The static p u n c h s i m u l a t i o n can be d i v i d e d into three consecutive stages: (1) p r e - d e l a m i n a t i o n , (2) d e l a m i n a t i o n initiation a n d p r o p a g a t i o n , a n d (3) fiber b r e a k a g e a n d pushing f o r w a r d of fibers. A d y n a m i c version of the finite element p r o g r a m was i n c o r p o r a t e d with the p r o p o s e d p e n e t r a t i o n m o d e l to analyze the i m p a c t responses of target a n d projectile. The friction force o b s e r v e d form the static tests was not c o n s i d e r e d in the static p u n c h s i m u l a t i o n but was used in an energy b a l a n c e c o n s i d e r a t i o n to calculate the t e r m i n a l velocity of the p e n e t r a t o r . T h e ballistic limit can be p r e d i c t e d based on the principle of c o n s e r v a t i o n of energy for a rigid projectile for specific striking a n d t e r m i n a l velocities. G o o d a g r e e m e n t between the p r e d i c t e d ballistic limit a n d test results is o b t a i n e d if the d y n a m i c elastic p r o p e r t i e s of target are used as i n p u t d a t a in code simulations. H o w e v e r , a 24% difference is r e p o r t e d if the static elastic p r o p e r t i e s are used in the n u m e r i c a l analysis. It is c o n c l u d e d that the p r o p o s e d p e n e t r a t i o n m o d e l is a d e q u a t e for p r e d i c t i n g the ballistic limit of a g l a s s / e p o x y target struck by a bullet-like p e n e t r a t o r if the high s t r a i n - r a t e elastic p r o p e r t i e s of the target is considered. REFERENCES 1. J. A. ZUKASet al., Impact Dynamics. John Wiley, New York (1982). 2. S. P. JOSHIand C. T. SUN,Impact induced fracture in a laminated composite. J. Comp. Mats 19, 51-66 (1985). 3. N. CRISTESCU,L. E. MALVERNand R. L. SIERAKOWSKI,Failure mechanism in composite plate impacted by blunt-ended penetrators. Foreign Object Impact Damage to Composite, AS T M S T P 568, pp. 159-172 (1975). 4. G. E. HUSMAN,J. M. WHITNEYand J. C. HALPIN,Residual strength characterization of laminated composites subjected to impact loading. Foreign Object Impact Damage to Composite, A S T M S T P 568, pp. 92-I 13 0975). 5. S. T. JENQ, S. B. WANGand L. T. SHEU, A model for predicting the residual strength of GFRP laminates subject t o ballistic impact. J. Rein. Plastics Comp. l 1, 1127-1141 (1992). 6. W. J. CANTWELLand J. MORTON, Impact perforation of carbon fibre reinforced plastic, 38, 119-141 (1990). 7. G. ZHU, W. GOLDSMITH and C. K. H. DHARAN, Penetration of laminated Kevlar by projectiles--I. Experimental investigation. Int. J. Solids Structures 29(4), 399-420 (1992). 8. G. ZHU, W. GOLDSMITHand C. K. H. DHARAN,Penetration of laminated Kevlar by projectiles--II. Analytical model. Int. J. Solids Structures 29(4), 521--436 (1992). 9. S.-W. R. LEE and C. T. SUN, Modeling of penetration process for composite laminates subjected to a blunt-ended punch. Proceedings of the 23rd International S A M P E Technical Conference, Kiamesha Lake, New York, pp. 624-638 (1991). 10. S.-W. R. LEE and C. T. SUN, Ballistic limit of composite laminates by a quasi-static penetration model. Proceedings of the 24th International SAM P E Technical Conference, Toronto, Canada, pp. T497-T511 (1992). 11. C. T. SUN and S. V. POTTI, High velocity impact and penetration of composite laminates. Proceedings of the Ninth International Conference on Composite Materials (ICCM/IX), Vol. 5, pp. 261-268, Madrid, Spain (1993). 12. H.-S. JING and M.-L. LIAO,Partial hybrid stress element for transienranalysis of thick laminated composite plates. Int. d. Numer. Meth. Engng 29, 1787-1796 (1990). 13. H.-S. JING and M.-L. LIAO,Partial hybrid stress element for the analysis of thick laminated composite plates. Int. J. Numer. Meth. Engng 28, 2813-2827 (1989). 14. J. HARDINGand L. M. WELSH,A tensile testing technique for fiber-reinforced composites at impact rates of strain. J. Mater. Sci. 18, 1810--1826 (1983). 15. S. T. JENQ and S. L. SHEU, High strain rate compressional behavior of stitched and unstitched composite laminates with radial constraint. Comp. Struct. 25, 427-438 (1993). 16. K. KAWATAet al., Macro- and micro-mechanics of high-velocity brittleness and high-velocity ductility of solids. Proceedings of the I U T A M on M M M H V D F , Tokyo, Japan, pp. 91-112 (1985). 17. S. H. YANGand C. T. SUN, Indentation law for composite laminates. A S T M S T P 787, pp. 425-449 (1982). 18. W. GOLDSMITH,Impact. Edward Arnold, London (1960).