epoxy composite laminates

Composites Science and Technology 69 (2009) 725–735

Contents lists available at ScienceDirect

Composites Science and Technology journal homepage: www.elsevier.com/locate/compscitech

Multi-site impact response of S2-glass/epoxy composite laminates L.J. Deka, S.D. Bartus 1, U.K. Vaidya * Department of Material Science and Engineering, The University of Alabama at Birmingham, Birmingham, AL 35294-4461, United States

a r t i c l e

i n f o

Article history: Received 26 October 2007 Received in revised form 18 February 2008 Accepted 3 March 2008 Available online 16 March 2008 Keywords: High velocity impact Multi-site damage Finite element modeling Ballistic impact Composite laminate VARTM

a b s t r a c t High velocity transverse impact to laminated fiber reinforced composites is of interest in marine, military and civilian applications. Most studies in literature have addressed single point isolated impact events; while this work draws distinction in that we consider multi-site sequential and simultaneous impacts to composite structures. The overall objectives of this work were to investigate the response of laminated composites subjected to high velocity, multi-site impacts from a modeling and experimental viewpoint. Energy absorption, new surface creation, and failure mechanisms from sequential and simultaneous multi-site high velocity impacts are compared to assess additive and cumulative effects of these scenarios. Finite element modeling (LS-DYNA 3D) was used to gain insight into failure modes, energy absorption, and damage prediction. The modeling results correlated well with experimental data obtained from three layer laminates of vacuum assisted resin transfer molding (VARTM) processed S2-glass/SC15 epoxy. The impact damage has been characterized using optical nondestructive evaluation (NDE) techniques. Specimens subjected to sequential impact exhibited average of 10% greater energy absorption and 18% increase in damage than specimens impacted simultaneously. Ó 2008 Elsevier Ltd. All rights reserved.

1. Introduction Marine, military and civilian structures are frequently subjected to impact loading by secondary blast debris, primary blast debris (shrapnel), and multiple bullet impact. Under ballistic impact, the kinetic energy of the projectile is dissipated in the form of several mechanisms. The predominant energy absorption mechanisms of laminates under high velocity, small mass impact are: kinetic energy imparted to the specimen, namely cone formation on the distal side of the laminate and/or spall formation, and energy absorption as a result of shear plugging, tensile fiber failure of the primary yarns, fiber debonding, fiber pull-out, elastic deformation of the secondary yarns, matrix cracking (intralaminar), interlaminar delamination, and frictional energy absorbed during interaction of the penetrator and laminate [1–3]. Most studies reported in open literature only address single point impacts with little consideration given to the effect of multi-site projectile impact. When laminated composites are subjected to ballistic impact, the material response is determined by interactions of multiple stress waves generated at the laminate interfaces [4]. In the case of a simultaneous multiple projectile impact scenario, stress waves interact with one another or with newly formed delaminations from adjacent damage zones, causing constructive/destruction

* Corresponding author. Tel.: +1 205 934 9199; fax: +1 205 934 8485. E-mail address: [email protected] (U.K. Vaidya). 1 Present address: U.S. Army Research Laboratory, Aberdeen, Maryland, United States. 0266-3538/$ - see front matter Ó 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.compscitech.2008.03.002

interference and/or wave scattering [5]. This can change the peak stress witnessed by a target, specimen compliance, and damage mechanisms resulting in a change in the extent of damage and energy absorption when compared to a single projectile impact. Cantwell and Morton [6], Reid and Zhou [7], and Abrate [8,9] have provided extensive reviews on impact behavior of composite and laminated structures, however, none of the work cited discusses the effect of multi-site impact. Fragment cluster impact (FCI) is a common scenario arising from the fragmentation of a metallic case containing a high explosive (HE) charge (bursting munitions). The most damaging result is the ejection of high velocity projectiles from the charge. In FCI, the material response is thought to be governed by synergistic effects such as the propagation and interaction of stress/shock waves (additive effects) and dynamic cracks/damage (cumulative effects). The situation where multiple fragments impact a structure simultaneously within a local area has been studied recently [5–7,9–14]. Qian et al. [12] and Qian and Qu [13] investigated FCI of a thin metallic armor plate. The study by Qian et al. [12] focused on an analytical model to distinguish between cumulative and additive effects on specimens subjected to impact by an explosive fragment generator. Qian and Qu [13] used numerical simulation (LS-DYNA code) of FCI to reproduce the experimental results in Qian et al. [12]. The modeling results indicated that fragment cluster density and the fragment hit-time interval were the main parameters distinguishing cumulative and additive damage mechanisms. Riedel et al. [11] conducted a limited study of a carbon–epoxy aircraft wingbox subjected to blast and impact from a fragmenting HE

726

L.J. Deka et al. / Composites Science and Technology 69 (2009) 725–735

warhead. Commercial hydrocode AUTODYN was used to simulate the entire loading situation. The primary fragments of the warhead were accurately modeled with respect to fragment sizes, distribution angles and velocities but the extent of the delamination in the areas of high impact densities was underpredicted. A substantial amount of work has been done to model the failure mechanism of composites due to transverse impact loading [15–21]. But limited studies have been done on the progressive failure of composites under high strain rate loading. However, it is generally expected that composites fail in a progressive manner. Ladeveze et al. [22,23] used a damage mechanics approach to describe matrix cracking and fiber/matrix debonding by introducing damage variables associated with the material stiffness reduction in their plasticity model. Johnson et al. [24] reported a numerical method to predict composite damage using the framework outlined by Ladeveze et al. [22]. Matzenmiller et al. [25] developed a continuum damage mechanics (CDM) model for unidirectional composites. On the basis of CDM, Williams and Vaziri [26] wrote material subroutines for matrix/fiber failure in LS-DYNA. Yen [27] developed Material Model 161 and 162 (MAT 161/162) for LS-DYNA that captures the progressive failure mode of composite laminates (both unidirectional and plain weave laminates) during transverse impact. Because of the inherent ability to model progressive damage MAT 161/162 has been used successfully in predicting energy absorption and damage [27–31]. The objective of the current work is to understand the energy absorption and damage propagation of S2-glass/SC-15 composite laminates subjected to simultaneous and multi-site high velocity impact using explicit commercial software LS-DYNA. The results are then compared to the experimental work detailed in [32–36]. 2. Materials and processing All specimens were processed using vacuum assisted resin infusion/transfer molding (VARTM). VARTM is considered an affordable process because tooling costs; high temperature and pressure cycles, closed-molds, and post-machining operations incurred in traditional autoclave processing are eliminated. With VARTM, resin is infused into dry fabric preform assembled on single-sided tooling that is covered with an inexpensive vacuum bag film. Large structural parts with inserts or multiple layers can be produced rapidly. Other advantages of VARTM are low process volatile emissions, high fiber-to-resin ratios, and good repeatability. S2-glass/SC-15 epoxy resin was chosen for the composite system. This particular combination was used because it is a well established benchmark as an impact resistant material [20,21, 37–39]. The preform consisted of a 24 oz. yd.2 24K tow, plain woven S2-glass with 933 sizing. Applied Poleramic Inc. SC-15 rubber toughened epoxy resin was used as the matrix because of its low viscosity and high toughness relative to other epoxy systems. The lay up scheme was [0°/90°]3 with an average thickness of 2 mm ± 0.05 mm. Archimedes immersion density technique was used to determine the average fiber volume fraction, which was 40.1 ± 0.2%. Specimens of dimensions 20.3  20.3 cm2 were cut from the panels and then post cured at 82 °C for 5 h. 3. Experimental set-up A single-stage light-gas gun was designed and constructed inhouse for the impact experiments. The unique capability of this gun lies in its ability to launch up to three projectiles near-simultaneously or sequentially with controlled impact locations. The gas gun has three barrels, equally spaced 120° apart on a 20 mm radius (approximately), Fig. 1. The 25.4 mm ID barrels are breach loaded and connected to a single 63.5 mm diameter butterfly valve via a

B 38 mm 25.4 mm

A

C

Fig. 1. Illustration showing the dimensions, configuration, and firing order of the tri-fire gas gun barrels.

common 200 mm ID manifold. This insures that the sabot assisted projectiles will be subjected to the same firing pressure, while the mass and dimensional tolerances of the sabots are maintained to very high standards to insure the near-simultaneous impact condition. One or two of the barrels can be plugged allowing a two projectile or single projectile test condition, respectively. These plug(s) can be rotated such that the near-simultaneous and sequential impact series can be contrasted while maintaining constant impact locations. Pressure versus velocity studies were conducted prior to testing in order to obtain calibration curves for single, two, and three projectile test conditions. The projectiles used in the study were 7.94 mm diameter (ffi0.30 caliber), grade 25, alloyed steel ball bearings with a hardness of 63–67 Rockwell C, and a mass of 2.039 g. The projectile velocity through each barrel (single projectile) was found to be extremely consistent for a given pressure indicating that assumption of a near-simultaneous impact condition is likely valid. This will be verified in future work via high-speed photography since the only current means of measuring projectile velocity is using photoelectric chronographs (Model: Oehler 35 chronograph and Oehler Sky). The boundary conditions were fully clamped on four sides with 232.3 cm2 of exposed specimen and 180.6 cm2 of clamped area. This provided a large enough area to ensure that the delamination damage did not interact with the boundaries. Delamination damage was characterized using an optical nondestructive evaluation (NDE) technique. The S2-glass/epoxy specimens are translucent and when damaged, present very distinct delaminations. In order to characterize the delamination area, a light box was constructed. It consists of specimen supports, a reflective tunnel to provide for even illumination, a 25.4 mm scale and a 150 W halogen light source. Digital images were taken normal to the back lit specimen with the scale placed within view. The images were then post processed using Image-Pro Plus (Media Cybernetics Inc.). The same software was then used to trace out and measure the delaminated areas, in which case the number of delaminations is equal to the number of plies minus one. Once the delaminated area is traced out, the software calculates the encircled area based on the calibration with respect to the scale. The goal in the 0.30 caliber projectile impact study was to investigate the effect of number of impacts. In the assessment of the number of impacts, single, two and three projectile simultaneous and sequential impacts were carried out on the three layer laminates. The impact velocity was kept constant throughout all the impact events. 4. Modeling approach 4.1. Numerical tools and model development Hypermesh (Version 7) and finite element model builder (FEMB) computer code have been used for pre-processing in the

727

L.J. Deka et al. / Composites Science and Technology 69 (2009) 725–735

4.2. Material model The material model MAT 162, based on the Hashin’s failure criteria [40] with five failure modes: tensile and compressive fiber failure, fiber crushing, through thickness matrix failure and delamination, was assigned to model the plain weave composite laminate [41]. The CDM approach proposed by Matzenmiller et al. [25] has been incorporated into MAT 162. MAT 162 can simulate progressive damage of composite laminates by controlling strain softening after failure during high velocity impact. The CDM formulation takes into consideration the post failure mechanisms in a composite plate as characterized by a reduction in material stiffness. A set of damage variables, -i with i = 1, . . . , 6, are introduced to relate the damage growth to stiffness reduction (Ered, Gred) in the material [41] as given by: 1

-i ¼ 1  emi

m

ð1r j i Þ

Ered ¼ ð1  -i ÞE0 ;

ð1Þ Gred ¼ ð1  -i ÞG0

ð2Þ

Table 1 Material properties of a plain weave S2-glass/SC-15 epoxy laminates Density, q, kg mm3 Tensile modulus, EA, EB, EC, GPa Poisson’s ratio, m21, m31, m32 Shear modulus, GAB, GBC, GCA, GPa Inplane tensile strength, SAT, SBT, GPa Out of plane tensile strength, SCT, GPa Compressive strength, SAC, SBC, GPa Fiber crush, SFC, Gpa Fiber shear, SFC, GPa Matrix mode shear strength, SAB, SBC SCA, Gpa Residual compressive scale factor, SFFC Friction angle, PHIC Damage parameter, AM1, AM2, AM3, AM4 Strain rate parameter, C1 Delamination, S_DELM Eroding strain, E_LIMIT

1.85E06 27.1, 27.1, 12.0 0.11, 0.18, 0.18 2.9, 2.14, 2.14 0.604 0.058 0.291 0.85 0.3 0.075, 0.058, 0.058 0.3 10 0.6, 0.6, 0.5,0.2 0.1 5,7 1.2

where -i is the damage variable, mi the strain softening parameter and rj the damage threshold. The damage variable -i varies from 0 to 1.0 as rj varies from 1 to a, respectively. Material model 162 requires four strain softening input parameters; (m1 – fiber damage in x direction, m2 – fiber damage in y direction, m3 – fiber crush and punch shear damage and m4 – delamination damage). The calibration of the strain softening parameters for S2-glass/SC-15 epoxy composite laminate was conducted by Xiao et al. [30]using quasistatic punch shear test. The load versus displacement curve of an 11 layer S2-glass/SC-15 epoxy composite laminate is shown in Fig. 2 [30]. The curve is a combination of four different sections and each section is governed by a corresponding strain softening parameter, m. Xiao et al. [30] conducted quasi-static punch shear tests on 1, 2, 4, 6, 11, and 22 layer laminates and proposed different values for different strain softening parameters. They claimed that one could achieve the simulated load versus displacement curve similar to the experimental quasi-static punch shear test of S2glass/SC-15 epoxy composite laminate with the above mentioned ‘‘m” values irrespective of the laminate thickness. In the present study the strain softening parameters defined by Xiao et al. [30] were used. These parameters were as follows; fiber damage, m1/m2 = 2, fiber crush and shear damage, m3 = 0.50, delamination, m4 = 0.2. However, energy absorption was underpredicted using m1/m2 = 2. By iteration, a value of m1/m2 = 0.6 was found to provide the best correlation to predict energy absorption with respect to the experimental results. The values of the other strain softening parameters, m3 and m4 were maintained at 0.50 and 0.2, respectively, based on the assumption that m3 and m4 did not significantly affect the kinetic energy absorption (area under stress–strain curve). These parameters determine the slope of the prefailure/peak regime of the load–displacement curve shown in Fig. 2. Furthermore, the laminate thickness was very small ( 2 mm) and hence the fiber crushing effect was minimal. During high velocity impact, high strain rate and high pressure conditions are imparted in the impact area. Harding and his coworkers [42,43] reported in their study that woven glass and aramid composites exhibit significant rate sensitivity. The effect of strain rate on the ply strength is modeled by strain rate dependent functions expressed as [41]:   fe_ g ð3Þ fSrt g ¼ fS0 g 1 þ C 1 ln e_0 where C1 is the strain rate constant for strength properties, {S0} are the quasi-static reference strength values, {Srt} are the rate dependent strength values, e_ 0 is the quasi-static reference strain rate

m1/m2

Simulated curve Experimental curve

30

m3 Load (kN)

model development. LS-DYNA (Version 970) was used to analyze perforation mechanisms, failure modes, and damage evaluation during high velocity projectile impact projectile on the three layers, S2-glass–epoxy target plates. Both the projectile and the composite plates have been meshed in HypermeshTM with eight node brick elements with a single integration point. The three layer plain weave composite plate were modeled using three layers of brick elements with 16,000 elements per lamina. Each layer has one element through the thickness and represents one plain weave layer. The three spherical projectiles were made using 3150 brick elements per projectile. For simultaneous impact, the three projectiles were placed 0.04 mm away from the target in order to minimize the computational time, whereas in the sequential impact series, the projectiles were staggered 50 mm normal to the target in order to minimize stress wave interactions. Same relative impact positions were maintained. The same specimen dimensions (20.3  20.3 cm2) and boundary conditions (full symmetry approach and fully clamped) used in the experimental were maintained in the simulation. The material properties used in the simulation for the laminate are shown in Table 1 [30] and the projectile in Table 2.

20

m4 10

Progressive damage zone

Punch shear zone

Table 2 Material properties for .30 caliber tool steel spherical projectile Density, q, kg mm3 Young’s modulus, E, GPa Poisson’s ratio Yield strength, GPa

7.86.E06 210 0.28 1.08

1

3

5

7

Displacement (mm) Fig. 2. Load–displacement plot of the 11 layer composite plate under quasi-static loading with 25.4 mm diameter support span [30].

728

L.J. Deka et al. / Composites Science and Technology 69 (2009) 725–735

value, and e_ are the associated strain rate values. The value of C1 is chosen as 0.1 [27,43]. The spherical projectile was modeled using MAT 3 (MAT_PLASTIC_KINEMATIC) [41]. MAT 3 is a bi-linear elastic-plastic model that contains formulations combining isotropic and kinematic hardening. In the present analysis, the hardening parameter, b was considered zero (Kinematic hardening) since no deformation of the projectile was observed during impact experiments. More details on MAT 3 and MAT 162 can be found in [41]. 4.3. Contact type Contact definition is required when two parts come into contact with each other. LS-DYNA has three different contact types: kinematic constraint method, the penalty method and the distributed parameter method. Contact between the projectile and laminate was defined using CONTACT_ERODING_SINGLE_SURFACE [41]. Penetration was handled using eroding elements with strain based failure criterion. If an element underwent tensile failure and exceeded the axial tensile strain (E_LIMIT), then it was to be automatically eroded. In all the simulations, E_LIMIT has been activated using a value of 1.2 [30]. 5. Results and discussion Impact experiments on three layer S2-glass/SC-15 composite laminates were performed at 0.30 caliber threat above ballistic limit, i.e. complete perforation. Single projectile impact was conducted first as a baseline study to validate the numerical model. After single site impact, multi-site impacts were performed on the three layer laminates with an average impact energy of 46.75 J per projectile. Multi-site impact events were conducted in near-simultaneous and sequential. Both impact modes, near-simultaneous and sequential impacts were conducted at different impact locations on the three layer laminate with two and three .30 caliber steel projectiles. The results are discussed from a viewpoint of energy absorption and new surface creation due to delamination. Energy absorption provides an indication of ballistic efficiency, and is a function of areal density. New surface creation, such as delamination, is considered because it is the most detrimental damage mode in composites in terms of post-impact performance. 5.1. Single projectile impact results The single projectile impact study was conducted on three layer laminates in order to establish a benchmark for the multiple impact study. Table 3 shows the single projectile impact result for

three layer S2-glass/epoxy laminate above the ballistic limit of the laminates in consideration. The impact velocity was held constant at 223.1 m s1 (standard deviation = 19.1 m s1), which is above the ballistic limit. The average energy absorption was 43.9 J, Table 3. The average new surface creation was 73.7 cm2. Numerical predictions of energy absorption and delamination area with an impact velocity of 223.1 m s 1 were found to be 42.36 and 70.1 cm2 which are almost 95–96% of corresponding experimental results. Delamination is detrimental to post-impact performance is caused by interlaminar stresses (rz, syz, szx) which initiate matrix microcracks that span the fiber–matrix interface and propagate along the fiber. MAT 162 provides an insight into the physics of the delamination of the composite plate as given by Eq. (4):  2  2  2 hrz i syz szx þ þ 1 ð4Þ fdelamination ¼ Sd Syx Szx ZT where ZT, SYZ and SZX are the failure strength properties and rz, syz and szx are corresponding stress state. The delamination scale factor, Sd is introduced to match the predicted results to experimental values. The value of Sd is iterated based upon the laminate architecture and interface condition. A typical delamination damage during a single projectile impact with impact velocity 221.8 m s1 is shown in Fig. 3. By trial and error, a Sd value of 7 was found to result in close agreement with the experiments for the 3-layer S2-glass/ epoxy laminate subjected to single projectile impact. The kinetic energy absorption and reduction in velocity due to the projectile penetration at two different strain softening parameters for tensile fiber failure, m1/m2 = 2 and 0.6, is shown in Fig. 4. Xiao et al. [30] evaluated the strain softening parameters for plain weave S2-glass/SC-15 epoxy plates using m1/m2 values of 2. In the present case m1 /m2 = 2 resulted in under prediction of the kinetic energy absorption (Fig. 4) indicating that the material experienced elastic brittle damage during impact. By trial and error, a softening parameter, m1/m2 = 0.6, predicted energy absorption within 96.5% of the experimental data. Therefore, it was determined that the strain softening parameters for tensile fiber failure, m1 and m2 have significant effect on kinetic energy absorption. 5.2. Two projectile impact results 5.2.1. Two projectile impact results near ballistic limit The two projectile impact positions for simultaneous and sequential impact are shown in Fig. 5. The positions A and C in the figure correspond to the primary yarns. These positions were chosen to examine damage interaction along the primary yarns which is also because the highest stress wave speed is along the primary yarns. In the sequential impact model, the second projectile (position C) was staggered 50 mm away from the target to min-

Table 3 Three layer laminate, single projectile results above the ballistic limit Specimen

Test configuration

Incident velocity (m s1)

1

Center impact Center impact Center impact Center impact Center impact Center impact

215.1 224.6

2 3 4 5 6

Energy absorption (J)

Standard deviation (J)

New surface creation (cm2)

Standard deviation (cm2)

Predicted average energy absorption (J)

Predicted average new surface creation (cm2)

0

47.2

3.4

73.2

8.5

43.26

70.1

63.3

47.3

82.3

0

46.3

59.8

221.8

95.9

40.8

77.7

264.7

174.4

40.5

68.6

221.5

92.5

41.3

80.7

213

Residual velocity (m s1)

729

L.J. Deka et al. / Composites Science and Technology 69 (2009) 725–735

50

250

40

200

156.4 m s-1 30

150

(a) m1 /m2 = 2 93.76 m s-1 100

20

(b) m1 /m2 = 0.6 10

50

0

Projectile velocity (m s-1)

Kinetic energy (J)

Fig. 3. Delamination under single impact condition at velocity 221.8 m s1 (a) experimental (b) simulation.

0 0

20

40

60

80

Time (ms) Fig. 4. Simulation result showing kinetic energy and velocity lost by the projectile for three layer laminate at single projectile impact velocity of 221.8 m s1 at different strain softening parameters (a) m1/m2 = 2, underprediction (b) m1/m2 = 0.6, excellent prediction, (99%).

imize stress wave interaction generated from previous impact. Damage modes were investigated under two velocities namely 200 m s1 and 220 m s1. These velocities resulted in impact conditions near the ballistic limit, (below the threshold velocity for complete penetration) and above the ballistic limit, respectively. The experimental and simulation results for simultaneous and sequential two projectile impact for three layer laminates are given in Table 4. The impact velocity for the two projectile impact was 201.2 m s1 (standard deviation = 4.2 m s1) for sequential impact

a

and 201.9 m s1 (standard deviation = 1.9 m s1) for near-simultaneous impact (will be referred to as simultaneous impact throughout the document). This velocity was closer to the single projectile ballistic limit for the three layer laminate. For the two projectile sequential impact experiments, position A was the first to be impacted, followed by position C. The average impact energy per projectile was 41.3 J and 41.6 J for simultaneous and sequential two projectile impact, respectively. This corresponded to an average new surface creation of 107.9 cm2 and 140.29 cm2 for simultaneous and sequential impacts, respectively. Although the average impact energy for the simultaneous and sequential two projectile impacts was within 0.7% of one another, sequential impact resulted in a 23% increase in new surface creation. Simultaneous and sequential impact simulations were performed with impact velocities of 201.2 m s1 and 201.9 m s1, respectively to compare with the experimental data. Strain softening parameters (m1, m2, m3 and m4) and delamination parameter, Sd calibrated from single projectile impact were incorporated into two projectile impact simulations. Predicted impact energy absorbed per projectile was 38.76 J and 35.6 J for simultaneous and sequential two projectile impact, respectively, indicating that the strain softening parameters, m1/m2 = 0.6, m3 = 0.5 and m4 = 0.2 provide a good correlation between numerical and experimental data for single as well as the two projectile impact events. Predicted delamination for simultaneous and sequential two projectile impact was found be 127.50 cm2 and 145.2 cm2 at Sd = 7, respectively. These overpredictions corresponded to 17% and 3.5% of the experimental data, respectively. In order to obtain close

b

C

50 mm

A A

C Fig. 5. Impact positions (A, C) of the two projectiles: (a) simultaneous impact, (b) sequential impact.

730

L.J. Deka et al. / Composites Science and Technology 69 (2009) 725–735

Table 4 Three layer laminate, simultaneous and sequential two projectile impact results Incident velocity (m s-1)

Residual velocity (m s-1)

Energy absorption (J)

Standard deviation (J)

New surface creation (cm2)

Standard deviation (cm2)

Simultaneous impact 1 A, C 2 A, C 3 A, C 4 A, C 5 A,C

200.5a 203.3a 232.2b 230.2b 220.6b

0.0 0.0 101.1 113.5 105.9

82.0 84.2 89.1 81.8 76.4

1.5

13.9

6.4

98.1 117.7 138.9 109.5 107.3

Sequential impacta 1 A C 2 A C 3 A C 4 A C

193.2 198.7 203.9 203 207.5 199.9 201.1 202.1

0 0 0 0 0 0 0 0

38.1 40.3 42.4 42.0 NA 40.7 NA 41.6

0.8

NA

Specimen

a b

Test configuration

17.7

6.79

Predicted average energy absorption (J)

77.52a 76b

71.2

Predicted average new surface creation (cm2)

102.4a 106.5b

145.2

147.7 137.8 135.1

Near the ballistic limit. Above the ballistic limit.

correlations to the experimental delaminated area for simultaneous impact, the Sd factor had to be reduced iteratively to a value of 5. The experimental and corresponding prediction of delaminated region in two projectile simultaneous and sequential impact events using Sd = 5 are shown in Figs. 6 and 7, respectively.

5.2.2. Two projectile impact results above ballistic limit Two projectile simultaneous impact above ballistic limit were conducted at 227.7 m s1 (standard deviation = 6.2 m s1), Table 4. The average energy absorption was 82.4 J. This resulted in a new surface creation of 118.6 cm2. The simulation predicted 76 J

Fig. 6. Experimental delamination: (a) simultaneous impact at impact velocity of 203.3 m s1, (b) sequential impact at impact velocities of 203 m s1 (A) and 203.9 m s1(C).

Fig. 7. Predicated delamination: (a) simultaneous impact at impact velocity of 203.3 m s1, (b) sequential impact at impact velocities of 203.9 m s1 (A) and 203 m s1(C).

731

L.J. Deka et al. / Composites Science and Technology 69 (2009) 725–735

plots near and above ballistic limit for simultaneous and sequential impact is shown in Fig. 8. It was observed that during simultaneous impact, the residual kinetic energies of the projectiles at positions A and C were the same, while during sequential impact, the residual kinetic energy of the projectile at position C was higher than that of the first projectile, position A, resulting in a lower energy lost (7%) at position C, than at position A (Fig. 8), the first projectile to touch down.

120

Kinetic energy absorbed (J)

X 100

Sequential impact by A at 203.9 m s-1 Sequential impact by B at 203 m s-1 Simultaneous impact by A and C at 230.2 m s-1

80

60

40

C = 35. 67 J

Z

Y

A +C = 77.07 J

5.3. Three projectile impact results

20

A = 38.82 J 0 0

0.1

0.2

0.3

0.4

0.5

0.6

Time (ms) Fig. 8. Simulation results showing the kinetic energy dissipated due to projectile penetration at above ballistic limit, 230.2 m s1 during two projectile (A, C) simultaneous impact and near ballistic limit, 203.9 m s1(A) and 203 m s1 (C) during two projectile sequential impact event. X, Y and Z represent onset of projectile indentation.

(38.11 J per projectile) kinetic energy absorption at impact velocity of 227.7 m s1 and corresponding new surface creation of 106.5 cm2. These predictions match within 90% of the experimental data. The predicted projectile energy lost versus time history

5.3.1. Simultaneous three projectile impact results above ballistic limit The positions for simultaneous three projectile impacts are shown in Fig. 9. The results of simultaneous impact above ballistic limit for three layer laminates are given in Table 5. The incident velocity was 214.7 m s1 with a standard deviation of 12.2 m s1. Impact energy absorption and new surface creation was 121.2 J and 158.6 cm2, respectively. Since individual projectile velocities could not be measured experimentally, the average results of the three projectiles are compared. In the simultaneous impact simulation, strain softening parameters, mi (i = 1, . . . , 4) and delamination factor, Sd = 7 are kept same as in sequential impact. The average impact velocity, 214.7 m s1 (same as the experiment) was assigned to all the three projectile locations (A, B and C). At the onset of penetration, the three projectiles, moving with a velocity of

Fig. 9. (a) Simultaneous impact positions of the three projectiles and (b) residual velocity after penetration.

Table 5 Three layer laminate, simultaneous and sequential three projectile impact results above ballistic limit Incident velocity (m s1)

Residual velocity (m s1)

Energy absorption (J)

Standard deviation (J)

New surface creation (cm2)

Standard deviation (cm2)

Predicted average energy absorption (J)

Predicted average new surface creation (cm2)

Simultaneous impact 1 A, B, C 2 A, B, C 3 A, B, C 4 A, B, C 5 A, B, C

213.9 215.1 195.4 221.1 227.9

73.0 98.0 NR NR 101

127.3 112.2 NA NA 127.7

8

NA 169.4 164 157.3 147.3

10

109

162.15

Sequential impact 1 B C A 2 B C A 3 B C A 4 B C A 5 B C A

231.3 221.5 225.2 226.4 227.3 225.8 224.9 225.8 223.7 222.1 222.7 227 226.4 223.7 229.4

82.5 37.7 0 97.1 98 74.9 99.5 100.7 83.7 NR 82.8 0 79.7 NR 89.5

47.6 48.6 51.7 42.6 42.9 46.3 41.5 41.6 43.9 NA 43.6 52.5 45.8 NA 45.5

3.6

197

19.6

108

148.2

Specimen

Test configuration

172.9

184

185.1

199

732

L.J. Deka et al. / Composites Science and Technology 69 (2009) 725–735

214.7 m s1, transfer the same amount of momentum to the plate. However, during penetration the region between projectile locations A and C, Fig. 9a, was the first to sustain damage. This is attrib-

uted to stress wave interactions along the primary yarns (i.e. along the fiber axis). The residual velocity of the projectiles is also shown in Fig. 9b. During penetration, regions A and C sustained more

Fig. 10. Stress wave interaction in simultaneous three projectile impact: (a) stress state at 6.9 ls, (b) stress state at 13.9 ls, constructive interference between A and C. The numbers in the figure correspond to the stress level.

Fig. 11. Delamination damage in three projectile simultaneous impact at impact velocity, 215.1 m s1 (a) experimental, (b) delamiantion at Sd = 7, (c) delamination at Sd = 5.

a

b A

A

100 mm

C

127. 53 m s-1

C 126. 51 m s-1

50 mm

B B 116. 95 m s-1 Fig. 12. (a) Sequential impact position of the three projectile, (b) residual velocity after penetration.

L.J. Deka et al. / Composites Science and Technology 69 (2009) 725–735 35

.30 caliber simultaneous

Kinetic energy (J)

30

.30 caliber sequential

Start of penetration 25 20 15

Full penetration

10 5 0

0

0.1

0.2

0.3

0.5

0.4

0.6

Time (ms) Fig. 13. Modeling result showing the three layer laminate response to sequential and simultaneous impact (kinetic energy transfer) for .30 caliber three projectiles.

140

120

Residual velocity (m s-1)

11 % 51 %

100

135 % 80 y = -24.75x + 129.82 R2 = 0.9937

60

40 Sequential experimental

20 Sequential FEA

0 0

0.5

1

1.5

2

2.5

3

3.5

Number of impacts Fig. 14. .30 caliber sequential impact series comparing the experimental results to the FEA prediction.

733

damage (primary yarn regions), which reduces the laminate stiffness in those regions resulting in a decrease in energy absorption; in other words higher residual velocity. The stress wave propagation after 6.9 and 13.9 ls for the simultaneous impact simulation is shown in Fig. 10. The stress wave propagates preferentially along the 0°/90° fiber axis in the plain weave layers. The maximum stress developed along the primary yarns is marked as 1 in Fig. 10, indicates that the primary yarns are more damage prone. The stresses in the secondary yarns, marked as 2 in Fig. 10 are lower and less damage prone. The total absorbed energy prediction (summation of the three projectile energies) at impact velocity of 214.7 m s1 was found to be 108 J which is 90% of the corresponding experimental data. Typical delamination damage is illustrated in Fig. 11a. Using a value of Sd = 7 resulted in over prediction of delaminated area (red region) of 434.6 cm2 which extended to the boundary, Fig. 11b, whereas a valued of Sd = 5 predicted delamination of 148.2 cm2 which corresponds to 94% of the experimental results, Fig. 11c. 5.3.2. Sequential three projectile impact results above ballistic limit The results for sequential 0.30 caliber, three projectile impact are given in Table 5. The average impact velocity was 227.0 m s1 with a standard deviation of 4.0 m s1. The total energy absorption (summation of the three projectile energies) was 134.8 J and the new surface creation was 177.3 cm2. Note that the standard deviation for sequential energy absorption is calculated after the individual projectile energies were summed. The average energy absorption for the first, second and third impact was 42.4 J, 44.7 J and 47.7 J respectively. For specimens 1 and 4 (Table 5), the third projectile did not fully penetrate. As described previously, the three projectile simultaneous impact model had all three projectiles impacting at the same time while the projectiles were staggered 50 mm apart in the z-direction in the sequential impact simulation, Fig. 12a. The impact positions and order were kept constant; positions B (1st), C (2nd), and A (3rd), respectively. This projectile staggering was sufficient to allow the primary stress wave to pass the location of the next impact before the next projectile struck the target. Average impact velocity, 227.0 m s1 (similar to experimental) was assigned to all the three projectiles.

Fig. 15. Delamination progression in three projectile sequential impact series in specimen 2 (a) experimental (b) simulation at Sd = 5.

734

L.J. Deka et al. / Composites Science and Technology 69 (2009) 725–735

A point to note is that in the sequential model, the target plate never came to complete rest, e.g. zero kinetic energy, before the next projectile impacted. The plate kinetic energy as a function of time for sequential impact is shown in Fig. 13. Each of the three projectiles had nearly identical response during impact, so they were summed. The plate kinetic energy decreased about 46% before the second projectile struck, and 34% before the third impact. Increasing the time hit interval until the plate is completely at rest would be computationally costly. The residual velocities of the projectiles are shown in Fig. 12b. The model predicted total energy absorption of 109 J which is 81.5% of the corresponding experimental result. This 19.5% under prediction is explained in Fig. 14 which shows residual velocity data from the experimental results and the FEA prediction at impact velocity of 227.0 m s1 for a .30 caliber, three projectile sequential impact. The residual velocity results of 1st (B), 2nd (C) and 3rd (A) projectile sequential impact are linear with a slope of 24.8 m s1/impact (e.g. increasing energy absorption with increasing damage) with an R2 value of 0.9937. The residual velocity for the first impact was over predicted by 11%. This is attributed to a difference in incident velocities between what was used in single and sequential three projectile impact results. The model validation was based off data for a projectile with an incident velocity of 221.3 m s1 (preliminary single projectile impact velocity) and according to that the strain softening parameters were calibrated and same strain softening parameters (m1/m2 = 0.6, m3 = 0.5 and m4 = 0.2) were maintained throughout 160 Sequential three projectile impact

140

Kinetic energy at Sd = 5

Kinetic energy (J)

120

Kinetic energy at Sd = 7

st

1 impact regime

100 80

1st and 2nd impact regime

60

Simulteneous three projectile impact

40 20

1st, 2nd and 3rd impact regime

0 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Time (ms) Fig. 16. Simulation results showing little change in kinetic energy due to change in delamination factor, Sd from 5 to 7.

all the two and three projectile multi-site impact simulations. The subsequent residual velocity predictions, however, deviated considerably from the experimental results. The residual velocity in the simulation for the second sequential impact was over predicted by 51% and 135% for the third impact. The prediction was non-linear and indicated an increase in residual velocity with increasing number of impacts. There was an 8% increase in residual velocity prediction between impacts one and two and only a 1% increase between impacts two and three. So, the FEA residual velocity prediction did not follow the same trend seen in the experimental results. In fact, the trend was opposite as experimental residual velocity decreased with increasing number of impacts. This resulted higher energy absorption with increasing damage. By the third impact the model over predicted residual velocity by 135%. This can be explained by the CDM theory developed by Matzenmillar et al. [25]. As damage accumulates, as dictated by Eqs. (1) and (2) (Section 4.2), the material stiffness is reduced by the damage variable, -i . Since resistance to penetration is directly tied to the stiffness, reduction in stiffness will in turn decrease energy absorption of the plate. Delamination prediction at Sd = 5 matches closely (162.51 cm2, 92%) with corresponding experimental data at an average impact velocity of 227 m s1, since Sd = 7 overpredicted the delaminated region. Sequential delamination damage study was conducted on specimens 1 and 2, where the specimen was removed, imaged and replaced between each impact in order to gain an understanding of delamination progression. The average new surface creation for the first, second and third impacts was 54.7 cm2, 113.1 cm2 and 151.7 cm2, respectively. Delamination progression observed in experimental and the prediction is shown in Fig. 15, for a three projectile sequential impact series (specimen 2). In sequential impact Sd = 5 was used because Sd = 7 overpredicted the delaminated region. Sd = 5 resulted 64.48 cm2 (1.17%), 104.16 cm2 (93%) and 162.16 cm2 (94%) of delaminated region. The total delamination prediction was 93% of the corresponding experimental data. The impact of the Sd factor on kinetic energy dissipation from the projectile penetration during three projectile simultaneous and sequential impact is illustrated in Fig. 16. It is clearly seen that the change in kinetic energy due to decrease in delamination factor Sd from 7 to 5 for simultaneous impact condition at impact velocity of 214.7 m s1 is insignificant (0%). The change in kinetic energy is 2% in the case of sequential impact series at an impact velocity of 227.0 m s1. Fig. 17 shows the simulated delamination area with respect to the experimental data for single and multi-site impact events. Numerical results based on Sd factor 5 and 7 provided 200

Kinetic energy (J) and delamination (cm2)

Kinetic energy, experimental

200

Expt. result for single impact Sim. result for single impact

Delaminated area (cm2)

180

Expt. results for seq. impact

Sd = 5

Sim. results for seq. impact

160

Expt. results for simul. impact Sim. results for simul. impact

Sd = 5

Sd = 7

140 120

Sd = 5

100 80

Sd = 7

180

Kinetic energy, simulation Delamination, experimental

160

Delamination, simulation

140 120 100 80 60 40 20 0

60

0

1

2

3

4

Number of impact Fig. 17. Predicted delamination at Sd = 5 or 7 showing good approximation of the experimental results for single and multi-site impact.

Two Proj. Simul. Impact

Two Proj. Seq. Impact

Three Proj. Simul. Impact

Three Proj. Seq. Impact

Fig. 18. Kinetic energy and delamination comparison between experimental and simulation during two and three projectile impact on a three layer laminate.

L.J. Deka et al. / Composites Science and Technology 69 (2009) 725–735

excellent prediction of the experimental results. Optimization of Sd factor is iterative and was determined to play a vital role in predicting the size and shape of the delamination. Fig. 18 compares energy absorption and new surface creation (i.e. delamination) for sequential and simultaneous projectile impacts. Specimens subjected to sequential impact exhibited 10.1% greater energy absorption than specimens impacted simultaneously. Sequential impact resulted in a 23.0% and 14.2% increase in delamination damage over simultaneous impact for two and three projectile impacts, respectively. 6. Conclusions High velocity impact studies were conducted on S2-glass/epoxy laminates subjected to single and multi-site near sequential and simultaneous impact conditions. An increase in new surface creation was noted for specimens impacted sequentially in contrast to those impacted simultaneously. Sequential impact resulted in a 23.0% and 14.2% increase in delamination damage over simultaneous impact for two and three projectile impacts, respectively. The residual velocity of the projectile was influenced by the stress wave interactions, particularly along the primary yarns, and also by the amount of delamination damage developed. As projectiles impacted the damaged regions, the progressive decrease in contact stiffness reduced the ability of the laminate to absorb energy, which resulted in an increase in exit velocity. This was noted for both sequential and simultaneous impact scenarios. The delamination parameter Sd and the strain softening parameter mi in the modeling study were found to be most sensitive to obtaining close correlation with the experimental test results. Acknowledgement The authors gratefully acknowledge the support provided by Dr. Yapa Rajapakse, Office of Naval Research (ONR). Dr. Frederick JustAgosto and Dr. Basir Shafiq of University of Puerto Rico, Mayaguez are also gratefully acknowledged for their collaboration with UAB in the ONR research. References [1] Goldsmith W, Dharan CKH, Chang Hui. Quasi-static and ballistic perforation of carbon fiber laminates. Int J Impact Eng 1995;32(1):89–103. [2] Sun CT, Potti SV. A simple model to predict residual velocities of thick composite laminates subjected to high velocity impact. Int J Impact Eng 1996;18(3):339–53. [3] Morye SS, Hine PJ, Duckett RA, Carr DJ, Ward IM. Modeling of the energy absorption by polymer composites under ballistic impact. Compos Sci Technol 2000;60:2631–42. [4] Parga-Landa B, Vlegels S, Hernández-Olivares F, Clark SD. Analytical simulation of stress wave propagation in composite materials. Compos Struct 1999;45:125–9. [5] Ball RE. The fundamentals of aircraft combat survivability analysis and design. 2nd ed. Reston, VA: American Institute of Aeronautics and Astronautics, Inc.; 2003. [6] Cantwell WJ, Morton J. The impact resistance of composite materials—a review. Composites 1991;22(5):347–62. [7] Reid SR, Zhou G. Impact behavior of fiber-reinforced composite materials and structures. Cambridge, England: Woodhead Publishing Ltd; 2000. [8] Abrate S. Impact on composite structures. Cambridge, UK: Cambridge University Press; 1998. [9] Abrate S. Ballistic impact on composite structures. In: 18th annual ASC symposium. Gainesville FL; 2003. p. 223–31. [10] Rosset WS. Patterned armor performance and evaluation. Int J Impact Eng 2005;31:1223–34. [11] Riedel W, Thoma K, Kurtz A, Collins P, Greaves L. Vulnerability of composite aircraft comp onents to fragmenting warheads-experimental analysis, material modeling and numerical studies. In: 20th international symposium on ballistics, 23–27 September, Orlando, Florida; 2002.

735

[12] Qian L, Qu M, Feng G. Study on terminal effects of dense fragment cluster impact on armor plate. Part I: analytical model. Int J Impact Eng 2005;31:755–67. [13] Qian L, Qu M. Study on terminal effects of dense fragment cluster impact on armor plate. Part II: numerical simulations. Int J Impact Eng 2005;31:769–80. [14] Leppänen J. Experiments and numerical analyses of blast and fragment impacts on concrete. Int J Impact Eng 2005;31:43–86. [15] Abrate A. Impact on laminated composites: recent advances. Appl Mech Rev 1994;47:517–43. [16] Choi HY, Chang FK. Impact damage Threshold of laminated composite in failure criteria and analysis in dynamic response. AMD, 107, ASME applied mechanics division, November, Dallas, TX; 1990. p. 31–5. [17] Davies GAO, Zhang X. Impact damage prediction in carbon prediction composite structures. Int J Impact Eng 1999;16:147–9. [18] Richardson MOW, Wisheart MJ. Review of low velocity impact properties of composite materials. Composites 1996;27(A):1123–31. [19] Cantwell WJ, Morton J. Impact perforation of carbon fiber reinforced plastic. J Compos Sci Technol 1990;38:119–40. [20] Mahfuz H, Zhu Y, Haque A, Abutalib A, Vaidya U, Jeelani S, et al. Investigation of high-velocity impact on integral armor using finite element method. Int J Impact Eng 2000;24:203–17. [21] DeLuca E, Prifti J, Betheney W, Chou SC. Ballistic damage impact of S2 glass reinforced plastic structural armor. J Compos Sci Technol 1998;58:1453–61. [22] Ladeveze P, LeDantec E. Damage modelling of the elementary ply for laminated composite. Compos Sci Technol 1992;43:257–67. [23] Allix O, Ladeveze P. Interlaminer interface modeling for the prediction of delamination. Compos Struct 1992;22:235–42. [24] Johnson AF, Pickett AK, Rozycki P. Computational methods for predicting the impact damage in composite structures. J Compos Sci Technol 2001;61: 2183–92. [25] Matzenmillar A, Lubliner J, Taylor RL. A constitutive model for anisotropic damage in fiber composites. Mech Mater 1995;20:125–52. [26] Williams KV, Vaziri R. Application of a damage mechanics model for predicting the impact response of composite materials. Comput Struct 2001;79: 997–1011. [27] Yen Chian-Fong. Ballistic impact modeling of composite materials. In: Proceedings of the 7th international LS-DYNA users conference, Detroit, Michigan; 2002. p. 15–25. [28] Brown K, Brooks R, Warrior N. Numerical simulation of damage in thermoplastic composite materials. In: proceedings of the 5th european LSDYNA users conference, Birmingham, UK, May 25–26, 2005. [29] Chan S, Fawaz Z, Behdinan K, Amid R. Ballistic limit prediction using a numerical model with progressive damage capability. Compos Struct 2007;77:466–74. [30] Xiao JR, Gama BA, Gillespie JW. Progressive damage and delamination in plain weave S-2 glass/SC-15 composites under quasi-static punch shear loading. Compos Struct 2007;77:182–96. [31] Deka LJ, Bartus SD. Damage evolution and energy absorption of FRP plates subjected to ballistic impact using a numerical model. In: Proceedings of the 9th international LS-DYNA users conference, 2006, June 4–6, Dearborn, MI. [32] Bartus SD. Simultaneous and sequential multi-site impact response of composite laminates. The University of Alabama at Birmingham. PhD thesis. 2007. [33] Bartus SD, Vaidya UK. Near-simultaneous and sequential multi-site impact response of S-2 glass/epoxy laminates. In: International conference on composite materials 16, July 8–13, 2007, Kyoto, Japan. [34] Bartus SD, Vaidya UK. Impact on composite structures—a review. J Adv Mater 2007;39(3):3–21. [35] Bartus SD, Deka L, Vaidya UK, 2006. Simultaneous and Sequential Multi-Site Impact Response of S-2 Glass/Epoxy Composite Laminates. SAMPE, 30 April–4 May, Long Beach, CA. [36] Bartus SD, Vaidya UK, 2004. Fragment Cloud Impact Response of Carbon– Epoxy Plates. In: 45th AIAA/ASME/ASCE/AHS/ASC structures, structural dynamics, and materials conference, 19–22 April, Palm Springs, CA. [37] Fink BK. Performance metrics for composite integral armor. J Thermoplast Compos Mater 2000;13:417–31. [38] Gama BA, Bogetti TA, Fink BK, Yu CJ, Claar TD, Eifert HH, et al. Aluminum foam integral armor: a new dimension in armor design. Compos Struct 2001;52:381–95. [39] Vaidya UK, Abraham A, Bhide S. Affordable processing of thick section and integral multi-functional composites. Composites: Part A 2001;32:1133–42. [40] Hashin Z. Failure criteria for unidirectional fiber composites. J Appl Mech 1980;47:329–34. [41] LS-DYNA Theoretical Manual. Version 970, Livermore Software Tech. Corp., April 2003. [42] Harding J. The high speed punching of woven roving glass reinforced composites. Inst. Phys. Conf. Ser. No. 47: Chapter 3. The Institute of Physics, Bristol and New York. p. 318–30. [43] Walsh LM, Harding J. Effect of strain rate on the tensile failure of woven reinforced polyester resin composite. In: Proceedings of DYMAT 85, international conferance on mechanics and physical behaviour of materials under dynamic loading, Jour de Physique, Colloque C5. p. 532–654.