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Effect of back pressure on impact and compression-after-impact characteristics of composites
Composite Structures 93 (2011) 944–951
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Effect of back pressure on impact and compression-after-impact characteristics of composites Mandar D. Kulkarni, Rahul Goel, N.K. Naik * Aerospace Engineering Department, Indian Institute of Technology Bombay, Powai, Mumbai 400 076, India
a r t i c l e
i n f o
Article history: Available online 30 June 2010 Keywords: Composite Low velocity impact Back pressure Compression-after-impact
a b s t r a c t Low velocity impact and compression-after-impact characteristics of a typical plain weave E-glass/epoxy composite are studied experimentally. Atmospheric pressure was maintained on the top surface and different pressures were applied on the rear side during impact experiments. Pressure on the rear side of the impacted plate is referred to as back pressure in further discussion. Effect of back pressure on the impact behavior is studied. It is observed that the variation in peak contact force and maximum central deflection are governed by two opposing phenomena. The parameters influencing the opposing phenomena are: induced curvature because of back pressure, effective pre-stressing and effective thickness. The incident impact energy was the same in all the experiments. Post-impact compressive strength was also investigated. Ó 2010 Elsevier Ltd. All rights reserved.
1. Introduction Composites offer a number of distinct advantages over conventional engineering materials. The advantages include higher specific strength and stiffness, superior corrosion resistance and enhanced dimensional stability. Composites are increasingly employed for a variety of high performance applications. Pressurized containers such as pressure vessels and aerospace surfaces are some of the typical applications. Composite vessels can be fragile and easily damaged by being dropped, rough handling, or impacts of dropped tools, runway debris and bird hits. These loading conditions represent low velocity impacts. The effect of impact induced damage on composites is of prime concern. In low velocity impact, the dynamic structural response of the target is of utmost importance as the contact duration is long enough for the entire structure to respond to the impact and, in consequence, more energy is absorbed elastically. The major changes that occur due to damage are reduction in flexural rigidity, compressive strength and load bearing capability. Poor post-impact compressive strength is the greatest weakness of composite laminates [1]. This is mainly due to local instability resulting from matrix cracking, delamination and fiber breakage causing large reduction in compressive strength. Hence, for the effective use of composite materials, both the impact and compression-after-impact (CAI) characteristics should be fully understood. Impact behavior of composites depends upon geometry, boundary conditions and mechanical properties of the plate as well as on * Corresponding author. Tel.: +91 22 2576 7114; fax: +91 22 2572 2602. E-mail address: [email protected] (N.K. Naik). 0263-8223/$ - see front matter Ó 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.compstruct.2010.06.027
projectile parameters such as shape, size, mass and velocity. Prestressing of the plate, pressure on the rear side of the impacted plate and bulging of the plate also influence the impact behavior of composites. Pressure on the rear side of the impacted plate is referred to as back pressure in further discussion. Back pressure on a plate like structure could lead to bulging of the plate outwards. The extent of bulging would depend upon the magnitude of back pressure. The effect of bulging is referred to as curvature effect in further discussion. Also back pressure could provide additional resistance for impact. In a way, it is equivalent to increase in thickness of the plate. Further, back pressure would induce in-plane tensile stresses in the plate. The induced tensile stresses are, in a way, similar to pre-stressing of the plate. Hence, the effect of back pressure on impact characteristics is a combination of the effect of pre-stressing, thickness and curvature of the plate. There are typical studies on the effect of pre-stressing of the target [2–6]. Sankar and Sun [2] conducted low velocity impact tests in the velocity range of 10–40 m/s on graphite/epoxy laminates. They found that tensile pre-stresses tend to increase the magnitude of contact force. They also noted that a higher pre-stress results in lesser energy transfer from the projectile to the plate. Robb et al. [3,4] investigated pre-stressing in E-glass/epoxy laminated plates with an average thickness of 3.8 mm. They employed pre-stress in tension and compression in the range of 2000–6000 microstrain. They concluded that in tension–tension and compression–compression type of biaxial pre-stressing, there was no effect on damage area but the peak contact force increased with prestressing. They also found that the notch sensitivity of the laminates was more under tension–tension biaxial pre-stressing and less under uniaxial compression. Nettles and Hodge [5] studied
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Nomenclature aam ad Ea Em Es EII F Flc Fm h
deceleration/acceleration of projectile obtained from accelerometer data deceleration/acceleration derived from curve fit of load cell data energy absorbed by the plate maximum plate energy plate strain energy incident impact energy contact force–curve fit obtained from load cell data contact force obtained from load cell peak contact force thickness of plate
impact response of carbon/epoxy laminates under impact energy of 3.4–6 J. They observed that tensile pre-stresses tend to increase the magnitude of contact force. Whittingham et al. [6] investigated carbon/epoxy laminates of 1.66 mm thickness. They also reported that the peak contact force increased as the pre-stress increased in case of biaxial tension for impact tests carried out at 10 J, whereas no significant trend was observed with 6 J. From these studies it can be concluded that the contact force increases with pre-stressing. There are typical studies on the effect of plate thickness on low velocity impact behavior [7–13]. Butcher [7] observed that increasing thickness of unidirectional (UD) carbon composites led to an increase in the critical stress. Miller et al. [8], Winkel and Adams [9] and Belingardi and Vadori [10] observed a linear relationship between contact force and thickness for different graphite/epoxy laminates. Caprino et al. [11] observed that, for carbon/epoxy laminates, the maximum contact force and penetration energy increased with increasing thickness, both following a power law with exponent close to 1.5. Kim and Kang [12] carried out studies on plain weave glass/epoxy laminates. They observed that, as the thickness increases, absorbed impact energy by deflection decreases whereas that by local indentation increases. In our earlier study [13], using a typical plain weave fabric Eglass/epoxy composite, it was observed that higher plate thickness leads to higher contact force. Also it was observed that, with increasing specimen thickness, the absorbed impact energy by the plate deflection decreases and that by local indentation or crack formation on the upper surface increases. The maximum plate deflection and duration of impact increase with decrease in specimen thickness. It was observed that the post-impact compressive strength decreases as the specimen thickness decreases. It was also observed that the damage area increased as the specimen thickness decreased from 8 mm to 5 mm. There are studies on the effect of various parameters on low velocity impact behavior of composites [14,15]. There are typical studies on the effect of curvature [16–24]. Marshall and Rhodes [16] explained the snap-buckling instability in the transverse loading response of many convex configurations such as arches and shells. They observed that the central deflection increases initially, then decreases and then again increases with the increase in load. The first region when the central deflection increases with the increase in load is the first equilibrium region. The later region when the central deflection again increases with the increase in load is the second equilibrium region. During quasi-static loading of such a structure, the response follows a path from first equilibrium region to second equilibrium region through an intermediate instability region. Wardle and Lagace [17] carried out experimental studies on the transverse impact behavior of graphite/epoxy laminates. They used specimens having thickness
H M PB t T V V0 Vrm Xc X nc d dm
height from which impactor is dropped mass of impactor gauge back pressure time duration of impact velocity of plate incident impact velocity of projectile maximum rebound velocity undamaged compressive strength of plate post-impact compressive strength of plate deflection of plate maximum deflection of plate
in the range of 0.8–2.4 mm. They used an impactor of mass 1.6 kg, and velocity in the range of 1–4 m/s. This is equivalent to impact energy in the range of 0.8–12.8 J. They observed that the trend of peak force with the curvature depends on which equilibrium path the peak force occurs. If the peak force occurs on the first equilibrium path, the peak force increases as the curvature increases, while if the peak force occurs on the second equilibrium path, the peak force decreases as the curvature increases. The transition region between the two equilibrium paths is due to snap through instability. Ambur et al. [18] analytically studied the low velocity impact with energy of 0.68 J (0.5 ft lb) on curved thin graphite/epoxy laminates and validated it with experimental results. In general, they observed that the contact force increases with increase in curvature. However, for the eight ply thick laminates, they found that the contact force decreases with increase in curvature. They attributed this to the softening mechanism that occurs with lower thickness laminates. This trend was because of limit point instability. Limit point instability occurs when the load increases until the panel deflects through some critical amount after which the load relaxes until the panel resists the motion in its inverted state. Kistler and Waas [19–21] carried out experimental, numerical as well as analytical studies on the effect of curvature on impact response of laminated panels. They analyzed quasi-isotropic graphite/epoxy laminates. Specimens were 8, 16 and 24 ply thick with average thickness of 1, 2 and 3 mm, respectively. They used impact energy in the range of 0.68–4.07 J. The nonlinear analytical model, nonlinear FEM model as well as experiments showed that, as curvature increases, the peak impact force decreases, and central deflection increases for eight ply thick specimen. They attributed this trend to limit point instability. The effect of curvature on impact force and central deflection was not significant for 16 and 24 ply thick specimens. Kim and Young [22] experimentally investigated carbon/epoxy eight ply thick (1 mm) laminates impacted with energy in the range of 2–6 J. They also observed that the peak contact force decreases with increase in curvature. Bases on the studies presented in Refs. [17–22], it can be inferred that contact force decreases with increase in curvature. But there are some contradictory studies too. Her and Liang [23] numerically studied graphite/epoxy spherical shell laminates with thickness of 2.54 mm. The impact parameters were: mass of impactor = 8.5 g, impactor velocity = 30 m/s. This is equivalent to incident impact energy of 3.83 J. They concluded that, for specimens with different radii of curvature, magnitude of contact force is virtually the same. Zhao et al. [24] investigated graphite/epoxy laminates of 2.5 mm thickness and impacted by energy of around 3.5 J. They observed that the maximum contact force increases and maximum central deflection decreases as the curvature increases. Though there is some disagreement among different stud-
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ies, in general, it can be concluded that increase in the pre-stress or plate thickness tends to increase the peak contact force, whereas increase in curvature tends to decrease the peak contact force. There are limited studies on the effect of back pressure on impact characteristics of composites. A typical study is on finding the burst pressure of impacted composite overwrapped pressure vessels [25]. This study considered the effect of impact on the burst pressure of the cylinders, which is a measure of the residual strength of the composite after impact. Details regarding effect of impact parameters are not presented. In addition to pre-stressing, thickness and curvature effects, studies are also available on the effect of weaving angle [26] and stitching of laminates [27] on the behavior of composites under low velocity impact. The aim of the present work is to study the effect of back pressure on low velocity impact behavior of polymer matrix composites. Studies are carried out on a typical plain weave E-glass/ epoxy composite. Compression-after-impact characteristics are also presented based on CAI test [13,28].
2. Experimental setup An instrumented drop weight impact test apparatus was used for conducting impact tests (Fig. 1). Accelerometer and load cell were used to record acceleration and contact force, respectively. The data was recorded using piezo-electric charge type accelerometer and bonded strain gauge load cell fitted on the impactor. The
compression load cell was integral with the impactor. The accelerometer was mounted on the impactor. The output of the instruments was recorded using a data acquisition card. The signals were amplified to match the entire range of the data acquisition card. Impact testing was conducted on the specimens clamped on all the four sides. Back pressure was applied using a pressure chamber placed below the specimen. The upper surface of the chamber, which was in direct contact with the specimen, was open and air pressure was directly applied on the rear side of the impacted surface of the specimen. The pressure in the chamber was varied from 0 MPa to 0.9 MPa gauge pressure. A pressure gauge attached to the chamber was used to record the back pressure on the specimen just before impact. Post-impact compression testing on impacted specimens was carried out using CAI test fixture as per NASA 1142 standard [28]. Compression-after-impact test fixture with an impacted specimen mounted is shown in Fig. 2. The specimens were clamped along the top and bottom edges during CAI tests. Anti-buckling guides were used to provide simple support along the lateral edges to prevent overall buckling of the specimen. The side supports were snug fit so that transverse deformation due to Poisson’s effect was not constrained. A gap of 5 mm between the supports and the end plate was provided to allow for the compression of the specimen. The CAI testing was carried out by loading the specimen on a Universal Testing Machine with a capacity of 200 kN. The loading axis was carefully aligned with the plate axis. The loading was along the warp direction and the loading rate was 0.5 mm/min.
Impactor free fall guides
Accelerometer Impactor release lever Load cell Impactor tup
Rebound catch mechanism Specimen
Specimen clamps
Back pressure chamber Compressor inlet
Press ure gauge Fig. 1. Photograph of drop weight impact test apparatus with back pressure chamber.
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Fig. 2. Compression-after-impact test fixture with an impacted specimen.
Compressive strength of the undamaged plain weave fabric Eglass/epoxy laminate was experimentally determined. Lockheed test fixture was used for the experimental studies. The loading was along the warp direction and the loading rate was 0.5 mm/ min. 2.1. Planning for experiments Studies were carried out on a typical plain weave E-glass/epoxy composite. Specifications of tow/strand, fabric, resin and composite are given in Appendix A. Plate thickness was 5.0 mm. The different back pressures PB considered for the study were 0, 0.3, 0.5, 0.7 and 0.9 MPa. Laminates of dimension 330 mm 330 mm were fabricated, using matched die moulding technique. Specimens of dimension 150 mm 150 mm were prepared from these laminates. All the experiments were carried out at room temperature. At least four specimens were tested for each back pressure case. The impact studies were carried out at the same incident impact energy, EII = 21.42 J, with impactor mass M = 4.71 kg, incident impact velocity V0 = 3.02 m/s and specimen thickness h = 5.0 mm. The unsupported area of the specimens during impact loading was 127 mm 127 mm. Stainless steel, cylindrical projectile with a tup of spherical tip of diameter 12 mm was used. 2.2. Data analysis
may not be uniform. This can be attributed to the geometry of the reinforcement and the local behavior of the plate during loading. Another possible reason for not getting smooth variation of contact force as a function of time is the frictional forces acting between the falling impactor and the guide. Considering the overall behavior of the plate, contact force variation is smoothened for further consideration. Curve fit for contact force data presented is indicated by F. Data obtained was smoothened by a fourth degree polynomial curve fit. Based on contact force obtained by curve fit (F), acceleration behavior is derived and presented as indicated by ad. The data obtained using accelerometer is also presented in Fig. 3 and is indicated as aam. It can be observed that ad and aam match well. Similar studies were also carried out starting with accelerometer data. The contact force data derived from accelerometer readings and that obtained from load cell also matched well. Further studies presented are based on load cell data. It was also observed that, in the range of parameters studied, there was contact between the impactor and the plate during the impact event. The different impact parameters from load cell data were derived as shown in Appendix B. Visual inspection of the impacted specimens was carried out by observing damage patterns on the upper and lower surfaces of the specimens. The damage patterns were photographed by placing the specimen against a source of light. Damage patterns after CAI test were also observed from impacted side, rear side and edges.
The data obtained during the impact experiments using accelerometer and load cell was analyzed. Fig. 3 presents contact force behavior obtained from load cell as indicated by Flc. This is for the case PB = 0.7 MPa. The contact force variation as a function of time is not a smooth curve. Damage progression during loading
3. Low velocity impact studies
Fig. 3. Deceleration/acceleration and contact force as a function of time, PB = 0.7 MPa, h = 5 mm, V0 = 3.02 m/s, M = 4.71 kg, EII = 21.42 J.
Fig. 4. Contact force, velocity, displacement and energy as a function of time, PB = 0.7 MPa, h = 5 mm, V0 = 3.02 m/s, M = 4.71 kg, EII = 21.42 J.
Velocity V, central deflection d and energy E of the plate are calculated as described in Appendix B using the contact force F ob-
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Table 1 Characteristic impact parameters: specimen dimensions: 127 mm 127 mm, thickness: 5 mm, clamped, plain weave E-glass/epoxy, incident impact energy: EII = 21.42 J. Back pressure, PB (MPa)
Peak contact force, Fm (kN)
Maximum acceleration, am (m/s2)
Maximum deflection, dm (mm)
Maximum rebound velocity, Vrm (m/s)
Impact duration, T (ms)
Maximum plate energy, Em (J)
0 0.3 0.5 0.7 0.9
4.84 4.77 4.40 4.59 4.50
1030 (110, 100) 1010 (90, 80) 950 (160, 80) 970 (120, 60) 950 (70, 20)
7.46 7.54 8.18 7.59 7.57
1.76 2.03 1.83 1.79 1.78
7.61 7.88 8.00 7.41 7.39
21.35 21.41 21.39 21.37 21.40
(0.53,0.45) (0.41, 0.39) (0.75, 0.38) (0.54, 0.29) (0.30, 0.12)
(0.42, 0.39) (0.74, 1.12) (0.83, 1.17) (1.1, 0.79) (0.65, 0.65)
(0.42, (0.19, (0.15, (0.37, (0.09,
0.52) 0.29) 0.12) 0.53) 0.08)
(0.19, (0.73, (0.68, (0.93, (0.41,
0.35) 0.83) 1.02) 0.43) 0.54)
(0.13, (0.02, (0.10, (0.09, (0.07,
0.20) 0.06) 0.14) 0.21) 0.07)
Table 2 Characteristic impact energies: specimen dimensions: 127 mm 127 mm, thickness: 5 mm, clamped, plain weave E-glass/epoxy, incident impact energy: EII = 21.42 J. Back pressure, PB (MPa)
Maximum plate energy, Em (J)
Energy absorbed, Ea (J)
Plate strain energy, Es = (Em Ea) (J)
0 0.3 0.5 0.7 0.9
21.35 21.41 21.39 21.37 21.40
13.78 11.58 12.52 13.57 11.97
7.57 9.83 8.87 7.80 9.43
(0.13, (0.02, (0.10, (0.09, (0.07,
0.20) 0.06) 0.14) 0.21) 0.07)
(2.75, (2.70, (1.06, (4.16, (2.64,
3.55) 1.77) 1.42) 3.12) 6.70)
(3.57, (1.80, (1.43, (3.18, (6.78,
2.62) 2.78) 1.03) 4.07) 3.33)
tained by curve fitting the load cell data. Representative plot of the variation of these impact parameters with time is shown in Fig. 4 for PB = 0.7 MPa. Energy E increases from 0 at t = 0 to a maximum value at around T/2 and then decreases to the final value Ea. Here, T is the impact duration. The maximum energy transferred from the projectile to the plate Em was slightly less than the incident impact energy EII. This is due to frictional losses during the loading phase. Em has two components, viz., the plate strain energy Es and the energy absorbed Ea. Es is responsible for the rebound of the impactor. Ea is partly lost in creating the damage and the rest in increasing the kinetic energy of the plate. It was observed that the plate has not come back to its original position at the end of the impact event. It was seen that the maximum values of E and d occur at the same time, and V is zero at that instant. It was observed that the instant of maximum contact force appears earlier than the occurrence of the maximum central deflection. This generates a phase whereby the contact force decreases while the central deflection increases. This is because of damage induced on the surface of the composite plate which then reduces the contact force while the central deflection is increasing. Tables 1 and 2 and Figs. 5–7, show values of impact parameters: Fm, dm, Vrm, T, Em, Ea and Es for different values of PB. The bracketed values in the tables are the scatter bands.
Photographs of damage pattern on the impacted and rear side for each case of back pressure are shown in Fig. 8. The corresponding values of damage dimension are shown in Table 3. The damage
Fig. 5. Peak contact force and maximum central deflection as a function of back pressure, h = 5 mm, V0 = 3.02 m/s, M = 4.71 kg, EII = 21.42 J.
Fig. 7. Energy as a function of back pressure, h = 5 mm, V0 = 3.02 m/s, M = 4.71 kg, EII = 21.42 J.
Fig. 6. Maximum rebound velocity and contact duration as a function of back pressure, h = 5 mm, V0 = 3.02 m/s, M = 4.71 kg, EII = 21.42 J.
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Impacted side
(a)
Rear side Warp
75 mm Fill
75 mm
(b)
Fig. 9. Damage tolerance as a function of back pressure, h = 5 mm, V0 = 3.02 m/s, M = 4.71 kg, EII = 21.42 J.
(c)
CAI testing was along the warp direction. The results of CAI testing are presented in Table 3. Here, the ratio X nc /Xc is the damage tolerance. The corresponding graph of damage tolerance versus PB is shown in Fig. 9. It is observed that the damage tolerance attains a minima for PB = 0.5 MPa. The damage patterns of the specimens under in-plane compressive loading of the CAI test were observed. The photographs of impacted side, rear side and edges are shown in Fig. 10. For all the different back pressure cases, catastrophic shear failure was observed at the location of impact. The shear failure was along 45° with respect to loading direction.
(d)
(e)
5. Results and discussion
Fig. 8. Damage patterns in woven fabric composites with back pressure subjected to low velocity impact, EII = 21.42 J: (a) PB = 0 MPa; (b) PB = 0.3 MPa; (c) PB = 0.5 MPa; (d) PB = 0.7 MPa; (e) PB = 0.9 MPa.
consists of fiber breakage, delamination and matrix cracking. Fiber breakage can be seen in the inner region of the damage and matrix crack can be seen in the surrounding region. The damage dimensions presented cover fiber breakage, delamination and matrix cracking. 4. Compression-after-impact studies CAI tests were performed for all the specimens using the CAI test fixture as per NASA 1142 standard [28]. The loading during
Variation of Fm with PB, as shown in Fig. 5, indicates that there is no significant variation of Fm as a function of PB. There are two effects at play when the composite plate is subjected to back pressure. Firstly, due to back pressure, the plate bulges and the top surface on which impact takes place is not plate-like but shell-like. It was observed that the bulging was almost linearly increasing with the increase in back pressure. For the case of PB = 0.9 MPa, 9 mm of upward bulging was observed. This is equivalent bulge to radius of 317 mm. As the bulging increases the curvature increases. The shell curvature effect during impact cannot be ignored. Secondly, back pressure imparts a certain pre-stress on the plate. Also, with back pressure, the resistance offered would increase. This is equivalent to considering increase in thickness of the specimen. The range of peak contact force in the present study is 4.3– 4.9 kN, and range of peak central deflection of the specimen is 7.4–8.2 mm with the incident impact energy of 21.42 J. Comparing this with the results given by Wardle and Lagace [17], it can be
Table 3 Damage tolerance characteristics: specimen dimensions: 127 mm 127 mm, thickness: 5 mm, clamped, plain weave E-glass/epoxy, incident impact energy: EII = 21.42 J, undamaged compressive strength (loading along warp): Xc = 175.0 (10, 11) MPa. PB (MPa)
Damage dimensions (mm): visual observations Top
0 0.3 0.5 0.7 0.9
X nc (MPa)
X nc /Xc (%)
142.3 116.7 112.2 124.4 130.9
81.3 66.6 64.1 71.0 74.8
Bottom
Along warp
Along fill
12.3 20.0 20.0 15.0 13.5
13.7 25.5 20.5 14.5 12.5
(0.3, (2.0, (1.4, (2.3, (3.5,
0.7) 2.2) 2.0) 2.0) 3.7)
(1.3, (1.5, (2.5, (1.7, (2.5,
Along 45° 1.7) 1.7) 2.7) 1.5) 2.9)
10.7 22.5 20.5 12.5 11.5
(1.3, (2.4, (2.5, (1.6, (1.5,
1.7) 2.5) 2.4) 1.5) 1.8)
Along warp
Along fill
15.0 26.5 26.0 24.5 19.5
15.0 28.0 27.0 24.5 17.0
(1.8, (0.4, (2.0, (3.9, (2.8,
2.0) 0.5) 1.5) 3.5) 2.3)
(1.7, (4.0, (1.5, (3.8, (8.0,
Along 45° 2.1) 4.2) 1.9) 3.5) 8.8)
PB – back pressure, X nc – post-impact compressive strength along warp, X nc /Xc – percentage damage tolerance.
15.0 29.5 25.5 24.5 17.5
(2.2, (1.5, (2.5, (4.9, (0.5,
1.6) 1.6) 2.4) 4.5) 0.8)
(4.0, 5.0) (15.5, 15.8) (5.7, 5.5) (7.3, 7.9) (13.0, 13.8)
(2.3, (6.0, (4.1, (4.8, (7.4,
2.4) 6.1) 5.2) 4.2) 7.7)
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Top view
Bottom view
Side view
(a) 147mm
Warp
Fill
67mm
5mm
123 mm
(b)
(c)
(d)
(e)
Fig. 10. Damage patterns in impacted woven fabric composites with back pressure under in-plane compressive loading, EII = 21.42 J: (a) PB = 0 MPa; (b) PB = 0.3 MPa; (c) PB = 0.5 MPa; (d) PB = 0.7 MPa; (e) PB = 0.9 MPa.
concluded that the impact conditions of the present study would lie on the second equilibrium path. Hence, as observed by Wardle and Lagace [17], increase in curvature would lead to decrease in contact force. In some other studies, on the effect of curvature [18–22], researchers have used 1 mm thick, eight-ply laminate, which is impacted by very low impact energies, not more than 6 J. They also concluded that, as the curvature increases, the contact force decreases. Kistler and Waas [19–21], explicitly observed that deflection increases as curvature increases, for 1 mm thick specimens. Thus it can be argued that 5 mm thick specimens with incident impact energy of 21.42 J, as used in the present study, would also follow the similar trend of decreasing contact force and increasing deflection with the increase in curvature. It is reasonable to state that the curvature caused by back pressure might decrease the peak contact force and increase the maximum central deflection. The effect of increasing pre-stressing and thickness is well studied in literatures [2–13]. It is observed that pre-stressing and increase in thickness lead to increase in contact force and decrease in central deflection, i.e., both effectively increase the resistance of the specimen. Other than bulging, the effects of back pressure are: effective pre-stressing and effective increase in thickness of the specimen. Hence, as observed in Refs. [2–13], the effect of pre-stressing and thickness should lead to an increase in contact force and decrease in central deflection. From Fig. 5 it can be observed that, in the present study, the contact force is nearly constant in the range of back pressures con-
sidered. It can be noted that two opposing phenomena take place. As the back pressure increases the curvature increases leading to decrease in contact force. On the other hand, as the back pressure increases the effective pre-stressing and the effective thickness of the plate increase leading to increase in contact force. The variation of contact force is the net effect of the two opposing phenomena explained above. Fig. 5 also presents variation of maximum central deflection as a function of back pressure. In this case also the variation of maximum central deflection is the net effect of two opposing phenomena as explained above. In the present case, the variation of maximum central deflection is not significant in the range of back pressures considered. Even though the variation of maximum central deflection is not much, it can be seen from Fig. 5 that the deflection is the maximum with PB = 0.5 MPa. Higher deflection means more bending stresses. Preliminary results of this study are presented in Ref. [29]. Variation of maximum rebound velocity and impact duration with back pressure is presented in Fig. 6. It can be seen that the variation of these parameters with back pressure is not significant. Variation of energy with back pressure is presented in Fig. 7. About 55–65% of the total plate energy is absorbed by the plate during impact (Table 2). Damage shape and size are presented in Fig. 8 and Table 3. It can be observed that the damage dimensions are more for the case of PB = 0.3 MPa and 0.5 MPa. The damage consists of fiber breakage, delamination and matrix cracking. Fiber breakage can be seen in the inner region of the damage and matrix cracking can be seen in the surrounding region. The damage dimensions presented cover fiber breakage, delamination and matrix cracking. The intensity of the damage within the damaged area is different at different locations. Hence, damage area cannot effectively represent the extent of damage during impact loading. Damage tolerance is the correct indication of the extent of damage during impact loading. It is also seen that the damage tolerance for PB = 0.5 MPa is the lowest (Fig. 9 and Table 3). This means that the overall damage is more for this particular case of back pressure. Fig. 10 presents damage patterns for post-impact compression tests. The compressive failure takes place at the location of impact. It was generally observed that the failure was catastrophic. The shear failure was along 45° with respect to loading direction.
6. Conclusions Studies are carried out on impact and post-impact characteristics of a typical plain weave E-glass/epoxy composite for different back pressures. Two opposing phenomena take place during impact loading on plate like structures with back pressure. As the back pressure increases the curvature increases leading to decrease in contact force and increase in central deflection. On the other hand, as the back pressure increases, the effective pre-stressing and the effective thickness of the plate increase leading to increase in contact force and decrease in central deflection. The variation of contact force and central deflection is the net effect of the two opposing phenomena. For the range of parameters considered, the specific observations are: (1) The maximum contact force is nearly constant with different back pressures considered. (2) The maximum central deflection is nearly constant with different back pressures considered. (3) The post-impact compressive shear failure was along 45° with respect to loading direction. (4) The damage tolerance was the least with PB = 0.5 MPa.
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Appendix A Specifications of tow/strand, fabric, resin and composite. Property
E-glass/epoxy
Reinforcement Filament diameter (lm) Filament density (gm/cc) Filaments per tow/ strand Tow/strand tex (gm/km) Type of weave No. of counts (per cm) Crimp (%) Fabric thickness (mm) Fabric aerial weight (gm/m2) Fiber volume fraction Void content (%) Matrix Process used
E-glass 20 2.62 182
a
150 Plain weave 12.1a 0.9a 0.28 388 0.51 0.75 Epoxy LY556 with hardener HY951 Matched die moulding
Along both warp and fill.
Appendix B From the load cell data, the acceleration is obtained using the expression,
ad ðtÞ ¼ FðtÞ=M The impactor velocity is computed as,
VðtÞ ¼ V 0 V0 ¼
Z
ad ðtÞdt
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 9:8 H
where, H = 0.464 m (kept the same for all experiments) On further integration, the displacement of the impactor is computed as,
dðtÞ ¼
Z
VðtÞdt
Central deflection of the plate is the same as the displacement of the impactor. The energy exchanged at time t, due to work done by contact force during the loading and unloading is computed as,
EðtÞ ¼
Z
FðtÞDðtÞdt
where, DðtÞ ¼ ddðtÞ=dt References [1] Richardson MOW, Wisheart MJ. Review of low velocity impact properties of composite materials. Composites Part A 1996;27(12):1123–31. [2] Sankar BV, Sun CT. Low velocity impact damage in graphite–epoxy laminates subjected to tensile initial stress. AIAA J 1986;24(3):470–1.
951
[3] Robb MD, Arnold WS, Marshall IH. The damage tolerance of GRP laminates under biaxial pre-stress. Compos Struct 1995;32(1):141–9. [4] Robb MD, Arnold WS, Marshall IH. Failure envelopes for notched CSM laminates under biaxial loading. Composites 1995;26(11):739–47. [5] Nettles AT, Hodge AJ. The impact response of carbon epoxy laminates. NASA STI report series: NASA TM-206317; 1997. [6] Whittingham B, Marshall IH, Mitrevski T, Jones R. The response of composite structures with pre-stress subject to low velocity impact damage. Compos Struct 2004;66(1):685–98. [7] Butcher BR. The impact resistance of unidirectional CFRP under tensile stress. Fibre Sci Technol 1979;12(4):295–326. [8] Miller AG, Hertzberg PE, Rantala VW. Toughness testing of composites materials. SAMPE Quart 1981:36–42. [9] Winkel JD, Adams DF. Instrumented drop weight impact testing of cross-ply and fabric composites. Composites 1985;16(4):268–78. [10] Belingardi G, Vadori R. Influence of the laminate thickness in low velocity impact behavior of carbon–epoxy composite material plate. Compos Struct 2003;61(1):27–38. [11] Caprino G, Lopresto V, Scarpani C, Briotti G. Influence of material thickness on the response of carbon–epoxy panels to low velocity impact. Compos Sci Technol 1999;59(15):2279–86. [12] Kim JK, Kang KW. An analysis of impact force in plain-weave glass–epoxy composite plates subjected to transverse impact. Compos Sci Technol 2001;61(1):135–43. [13] Naik NK, Joglekar MN, Arya H, Borade SV, Ramakrishna KN. Impact and compression after impact characteristics of plain weave fabric composites: effect of plate thickness. Adv Compos Mater 2004;12(4):261–80. [14] Naik NK, Ramasimha R, Arya H, Prabhu SV, Shama Rao N. Impact response and damage tolerance characteristics of glass–carbon/epoxy hybrid composite plates. Composites Part B 2001;32B:565–74. [15] Naik NK, Borade SV, Arya H, Sailendra M, Prabhu SV. Experimental studies on impact behaviour of woven fabric composites: effect of impact parameters. J Reinf Plast Compos 2002;21:1347–62. [16] Marshall IH, Rhodes J. Snap-buckling of thin shells of rectangular planform. Stability problems in engineering structures and components. Appl Sci 1979:249–64. [17] Wardle BL, Lagace AL. Behavior of composite shells under transverse impact and quasi-static loading. AIAA J 1998;36(6):1065–73. [18] Ambur DR, Starnes JR, Stoumbos TJ, Kapania RK. Influence of large-deflection effects on the impact response of flat and curved composite plates. In: 36th AIAA/ASME/ASCE/AHS/ASC structures, structural dynamics and materials conference; 1995. [19] Kistler LS, Waas AM. On the response of curved laminated panels subjected to transverse impact loads. Int J Solids Struct 1999;36(9):1311–27. [20] Kistler LS, Waas AM. Experiment and analysis on the response of curved laminated composite panels subjected to low velocity impact. Int J Impact Eng 1998;21(9):711–36. [21] Kistler LS, Waas AM. Impact response of cylindrically curved laminates including a large deformation scaling study. Int J Impact Eng 1998;21(1):61–75. [22] Kim YN, Yang IY. Impact response and damage of composite shell with various curvatures. Key Eng Mater 2004;270–273:1911–6. [23] Her SC, Liang YC. The finite element analysis of composite laminates and shell structures subjected to low velocity impact. Compos Struct 2004;66(1– 4):277–85. [24] Zhao GP, Cho C, Kwon OY. Simulation and experimental investigation of impact damage in composite shell. Key Eng Mater 2005;297–300:1339–43. [25] Beeson HD, Davis DD, Ross WL, Tapphorn RM. Composite over wrapped pressure vessels: database extension task 3.0 and impact damage effects control task 8.0. NTRS, NASA TP – 210769; 2002. [26] Atasa C, Liu D. Impact response of woven composites with small weaving angles. Int J Impact Eng 2008;35:80–97. [27] Aymerich F, Priolo P. Characterization of fracture modes in stitched and unstitched cross-ply laminates subjected to low velocity impact and compression after impact loading. Int J Impact Eng 2008;35(7):591–608. [28] NASA-aircraft industry standard specification for graphite fiber toughened thermoset resin composite materials. NASA Reference Publication 1142; 1985. [29] Kulkarni MD, Goel R, Naik NK. Effect of back pressure on impact behavior of composites. In: Bhattacharyya SK, et al. editors. Proceedings of ICTACEM-2007 (on CD), IIT Kharagpur, paper number: 72.
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Composite Structures journal homepage: www.elsevier.com/locate/compstruct
Effect of back pressure on impact and compression-after-impact characteristics of composites Mandar D. Kulkarni, Rahul Goel, N.K. Naik * Aerospace Engineering Department, Indian Institute of Technology Bombay, Powai, Mumbai 400 076, India
a r t i c l e
i n f o
Article history: Available online 30 June 2010 Keywords: Composite Low velocity impact Back pressure Compression-after-impact
a b s t r a c t Low velocity impact and compression-after-impact characteristics of a typical plain weave E-glass/epoxy composite are studied experimentally. Atmospheric pressure was maintained on the top surface and different pressures were applied on the rear side during impact experiments. Pressure on the rear side of the impacted plate is referred to as back pressure in further discussion. Effect of back pressure on the impact behavior is studied. It is observed that the variation in peak contact force and maximum central deflection are governed by two opposing phenomena. The parameters influencing the opposing phenomena are: induced curvature because of back pressure, effective pre-stressing and effective thickness. The incident impact energy was the same in all the experiments. Post-impact compressive strength was also investigated. Ó 2010 Elsevier Ltd. All rights reserved.
1. Introduction Composites offer a number of distinct advantages over conventional engineering materials. The advantages include higher specific strength and stiffness, superior corrosion resistance and enhanced dimensional stability. Composites are increasingly employed for a variety of high performance applications. Pressurized containers such as pressure vessels and aerospace surfaces are some of the typical applications. Composite vessels can be fragile and easily damaged by being dropped, rough handling, or impacts of dropped tools, runway debris and bird hits. These loading conditions represent low velocity impacts. The effect of impact induced damage on composites is of prime concern. In low velocity impact, the dynamic structural response of the target is of utmost importance as the contact duration is long enough for the entire structure to respond to the impact and, in consequence, more energy is absorbed elastically. The major changes that occur due to damage are reduction in flexural rigidity, compressive strength and load bearing capability. Poor post-impact compressive strength is the greatest weakness of composite laminates [1]. This is mainly due to local instability resulting from matrix cracking, delamination and fiber breakage causing large reduction in compressive strength. Hence, for the effective use of composite materials, both the impact and compression-after-impact (CAI) characteristics should be fully understood. Impact behavior of composites depends upon geometry, boundary conditions and mechanical properties of the plate as well as on * Corresponding author. Tel.: +91 22 2576 7114; fax: +91 22 2572 2602. E-mail address: [email protected] (N.K. Naik). 0263-8223/$ - see front matter Ó 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.compstruct.2010.06.027
projectile parameters such as shape, size, mass and velocity. Prestressing of the plate, pressure on the rear side of the impacted plate and bulging of the plate also influence the impact behavior of composites. Pressure on the rear side of the impacted plate is referred to as back pressure in further discussion. Back pressure on a plate like structure could lead to bulging of the plate outwards. The extent of bulging would depend upon the magnitude of back pressure. The effect of bulging is referred to as curvature effect in further discussion. Also back pressure could provide additional resistance for impact. In a way, it is equivalent to increase in thickness of the plate. Further, back pressure would induce in-plane tensile stresses in the plate. The induced tensile stresses are, in a way, similar to pre-stressing of the plate. Hence, the effect of back pressure on impact characteristics is a combination of the effect of pre-stressing, thickness and curvature of the plate. There are typical studies on the effect of pre-stressing of the target [2–6]. Sankar and Sun [2] conducted low velocity impact tests in the velocity range of 10–40 m/s on graphite/epoxy laminates. They found that tensile pre-stresses tend to increase the magnitude of contact force. They also noted that a higher pre-stress results in lesser energy transfer from the projectile to the plate. Robb et al. [3,4] investigated pre-stressing in E-glass/epoxy laminated plates with an average thickness of 3.8 mm. They employed pre-stress in tension and compression in the range of 2000–6000 microstrain. They concluded that in tension–tension and compression–compression type of biaxial pre-stressing, there was no effect on damage area but the peak contact force increased with prestressing. They also found that the notch sensitivity of the laminates was more under tension–tension biaxial pre-stressing and less under uniaxial compression. Nettles and Hodge [5] studied
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Nomenclature aam ad Ea Em Es EII F Flc Fm h
deceleration/acceleration of projectile obtained from accelerometer data deceleration/acceleration derived from curve fit of load cell data energy absorbed by the plate maximum plate energy plate strain energy incident impact energy contact force–curve fit obtained from load cell data contact force obtained from load cell peak contact force thickness of plate
impact response of carbon/epoxy laminates under impact energy of 3.4–6 J. They observed that tensile pre-stresses tend to increase the magnitude of contact force. Whittingham et al. [6] investigated carbon/epoxy laminates of 1.66 mm thickness. They also reported that the peak contact force increased as the pre-stress increased in case of biaxial tension for impact tests carried out at 10 J, whereas no significant trend was observed with 6 J. From these studies it can be concluded that the contact force increases with pre-stressing. There are typical studies on the effect of plate thickness on low velocity impact behavior [7–13]. Butcher [7] observed that increasing thickness of unidirectional (UD) carbon composites led to an increase in the critical stress. Miller et al. [8], Winkel and Adams [9] and Belingardi and Vadori [10] observed a linear relationship between contact force and thickness for different graphite/epoxy laminates. Caprino et al. [11] observed that, for carbon/epoxy laminates, the maximum contact force and penetration energy increased with increasing thickness, both following a power law with exponent close to 1.5. Kim and Kang [12] carried out studies on plain weave glass/epoxy laminates. They observed that, as the thickness increases, absorbed impact energy by deflection decreases whereas that by local indentation increases. In our earlier study [13], using a typical plain weave fabric Eglass/epoxy composite, it was observed that higher plate thickness leads to higher contact force. Also it was observed that, with increasing specimen thickness, the absorbed impact energy by the plate deflection decreases and that by local indentation or crack formation on the upper surface increases. The maximum plate deflection and duration of impact increase with decrease in specimen thickness. It was observed that the post-impact compressive strength decreases as the specimen thickness decreases. It was also observed that the damage area increased as the specimen thickness decreased from 8 mm to 5 mm. There are studies on the effect of various parameters on low velocity impact behavior of composites [14,15]. There are typical studies on the effect of curvature [16–24]. Marshall and Rhodes [16] explained the snap-buckling instability in the transverse loading response of many convex configurations such as arches and shells. They observed that the central deflection increases initially, then decreases and then again increases with the increase in load. The first region when the central deflection increases with the increase in load is the first equilibrium region. The later region when the central deflection again increases with the increase in load is the second equilibrium region. During quasi-static loading of such a structure, the response follows a path from first equilibrium region to second equilibrium region through an intermediate instability region. Wardle and Lagace [17] carried out experimental studies on the transverse impact behavior of graphite/epoxy laminates. They used specimens having thickness
H M PB t T V V0 Vrm Xc X nc d dm
height from which impactor is dropped mass of impactor gauge back pressure time duration of impact velocity of plate incident impact velocity of projectile maximum rebound velocity undamaged compressive strength of plate post-impact compressive strength of plate deflection of plate maximum deflection of plate
in the range of 0.8–2.4 mm. They used an impactor of mass 1.6 kg, and velocity in the range of 1–4 m/s. This is equivalent to impact energy in the range of 0.8–12.8 J. They observed that the trend of peak force with the curvature depends on which equilibrium path the peak force occurs. If the peak force occurs on the first equilibrium path, the peak force increases as the curvature increases, while if the peak force occurs on the second equilibrium path, the peak force decreases as the curvature increases. The transition region between the two equilibrium paths is due to snap through instability. Ambur et al. [18] analytically studied the low velocity impact with energy of 0.68 J (0.5 ft lb) on curved thin graphite/epoxy laminates and validated it with experimental results. In general, they observed that the contact force increases with increase in curvature. However, for the eight ply thick laminates, they found that the contact force decreases with increase in curvature. They attributed this to the softening mechanism that occurs with lower thickness laminates. This trend was because of limit point instability. Limit point instability occurs when the load increases until the panel deflects through some critical amount after which the load relaxes until the panel resists the motion in its inverted state. Kistler and Waas [19–21] carried out experimental, numerical as well as analytical studies on the effect of curvature on impact response of laminated panels. They analyzed quasi-isotropic graphite/epoxy laminates. Specimens were 8, 16 and 24 ply thick with average thickness of 1, 2 and 3 mm, respectively. They used impact energy in the range of 0.68–4.07 J. The nonlinear analytical model, nonlinear FEM model as well as experiments showed that, as curvature increases, the peak impact force decreases, and central deflection increases for eight ply thick specimen. They attributed this trend to limit point instability. The effect of curvature on impact force and central deflection was not significant for 16 and 24 ply thick specimens. Kim and Young [22] experimentally investigated carbon/epoxy eight ply thick (1 mm) laminates impacted with energy in the range of 2–6 J. They also observed that the peak contact force decreases with increase in curvature. Bases on the studies presented in Refs. [17–22], it can be inferred that contact force decreases with increase in curvature. But there are some contradictory studies too. Her and Liang [23] numerically studied graphite/epoxy spherical shell laminates with thickness of 2.54 mm. The impact parameters were: mass of impactor = 8.5 g, impactor velocity = 30 m/s. This is equivalent to incident impact energy of 3.83 J. They concluded that, for specimens with different radii of curvature, magnitude of contact force is virtually the same. Zhao et al. [24] investigated graphite/epoxy laminates of 2.5 mm thickness and impacted by energy of around 3.5 J. They observed that the maximum contact force increases and maximum central deflection decreases as the curvature increases. Though there is some disagreement among different stud-
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ies, in general, it can be concluded that increase in the pre-stress or plate thickness tends to increase the peak contact force, whereas increase in curvature tends to decrease the peak contact force. There are limited studies on the effect of back pressure on impact characteristics of composites. A typical study is on finding the burst pressure of impacted composite overwrapped pressure vessels [25]. This study considered the effect of impact on the burst pressure of the cylinders, which is a measure of the residual strength of the composite after impact. Details regarding effect of impact parameters are not presented. In addition to pre-stressing, thickness and curvature effects, studies are also available on the effect of weaving angle [26] and stitching of laminates [27] on the behavior of composites under low velocity impact. The aim of the present work is to study the effect of back pressure on low velocity impact behavior of polymer matrix composites. Studies are carried out on a typical plain weave E-glass/ epoxy composite. Compression-after-impact characteristics are also presented based on CAI test [13,28].
2. Experimental setup An instrumented drop weight impact test apparatus was used for conducting impact tests (Fig. 1). Accelerometer and load cell were used to record acceleration and contact force, respectively. The data was recorded using piezo-electric charge type accelerometer and bonded strain gauge load cell fitted on the impactor. The
compression load cell was integral with the impactor. The accelerometer was mounted on the impactor. The output of the instruments was recorded using a data acquisition card. The signals were amplified to match the entire range of the data acquisition card. Impact testing was conducted on the specimens clamped on all the four sides. Back pressure was applied using a pressure chamber placed below the specimen. The upper surface of the chamber, which was in direct contact with the specimen, was open and air pressure was directly applied on the rear side of the impacted surface of the specimen. The pressure in the chamber was varied from 0 MPa to 0.9 MPa gauge pressure. A pressure gauge attached to the chamber was used to record the back pressure on the specimen just before impact. Post-impact compression testing on impacted specimens was carried out using CAI test fixture as per NASA 1142 standard [28]. Compression-after-impact test fixture with an impacted specimen mounted is shown in Fig. 2. The specimens were clamped along the top and bottom edges during CAI tests. Anti-buckling guides were used to provide simple support along the lateral edges to prevent overall buckling of the specimen. The side supports were snug fit so that transverse deformation due to Poisson’s effect was not constrained. A gap of 5 mm between the supports and the end plate was provided to allow for the compression of the specimen. The CAI testing was carried out by loading the specimen on a Universal Testing Machine with a capacity of 200 kN. The loading axis was carefully aligned with the plate axis. The loading was along the warp direction and the loading rate was 0.5 mm/min.
Impactor free fall guides
Accelerometer Impactor release lever Load cell Impactor tup
Rebound catch mechanism Specimen
Specimen clamps
Back pressure chamber Compressor inlet
Press ure gauge Fig. 1. Photograph of drop weight impact test apparatus with back pressure chamber.
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Fig. 2. Compression-after-impact test fixture with an impacted specimen.
Compressive strength of the undamaged plain weave fabric Eglass/epoxy laminate was experimentally determined. Lockheed test fixture was used for the experimental studies. The loading was along the warp direction and the loading rate was 0.5 mm/ min. 2.1. Planning for experiments Studies were carried out on a typical plain weave E-glass/epoxy composite. Specifications of tow/strand, fabric, resin and composite are given in Appendix A. Plate thickness was 5.0 mm. The different back pressures PB considered for the study were 0, 0.3, 0.5, 0.7 and 0.9 MPa. Laminates of dimension 330 mm 330 mm were fabricated, using matched die moulding technique. Specimens of dimension 150 mm 150 mm were prepared from these laminates. All the experiments were carried out at room temperature. At least four specimens were tested for each back pressure case. The impact studies were carried out at the same incident impact energy, EII = 21.42 J, with impactor mass M = 4.71 kg, incident impact velocity V0 = 3.02 m/s and specimen thickness h = 5.0 mm. The unsupported area of the specimens during impact loading was 127 mm 127 mm. Stainless steel, cylindrical projectile with a tup of spherical tip of diameter 12 mm was used. 2.2. Data analysis
may not be uniform. This can be attributed to the geometry of the reinforcement and the local behavior of the plate during loading. Another possible reason for not getting smooth variation of contact force as a function of time is the frictional forces acting between the falling impactor and the guide. Considering the overall behavior of the plate, contact force variation is smoothened for further consideration. Curve fit for contact force data presented is indicated by F. Data obtained was smoothened by a fourth degree polynomial curve fit. Based on contact force obtained by curve fit (F), acceleration behavior is derived and presented as indicated by ad. The data obtained using accelerometer is also presented in Fig. 3 and is indicated as aam. It can be observed that ad and aam match well. Similar studies were also carried out starting with accelerometer data. The contact force data derived from accelerometer readings and that obtained from load cell also matched well. Further studies presented are based on load cell data. It was also observed that, in the range of parameters studied, there was contact between the impactor and the plate during the impact event. The different impact parameters from load cell data were derived as shown in Appendix B. Visual inspection of the impacted specimens was carried out by observing damage patterns on the upper and lower surfaces of the specimens. The damage patterns were photographed by placing the specimen against a source of light. Damage patterns after CAI test were also observed from impacted side, rear side and edges.
The data obtained during the impact experiments using accelerometer and load cell was analyzed. Fig. 3 presents contact force behavior obtained from load cell as indicated by Flc. This is for the case PB = 0.7 MPa. The contact force variation as a function of time is not a smooth curve. Damage progression during loading
3. Low velocity impact studies
Fig. 3. Deceleration/acceleration and contact force as a function of time, PB = 0.7 MPa, h = 5 mm, V0 = 3.02 m/s, M = 4.71 kg, EII = 21.42 J.
Fig. 4. Contact force, velocity, displacement and energy as a function of time, PB = 0.7 MPa, h = 5 mm, V0 = 3.02 m/s, M = 4.71 kg, EII = 21.42 J.
Velocity V, central deflection d and energy E of the plate are calculated as described in Appendix B using the contact force F ob-
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Table 1 Characteristic impact parameters: specimen dimensions: 127 mm 127 mm, thickness: 5 mm, clamped, plain weave E-glass/epoxy, incident impact energy: EII = 21.42 J. Back pressure, PB (MPa)
Peak contact force, Fm (kN)
Maximum acceleration, am (m/s2)
Maximum deflection, dm (mm)
Maximum rebound velocity, Vrm (m/s)
Impact duration, T (ms)
Maximum plate energy, Em (J)
0 0.3 0.5 0.7 0.9
4.84 4.77 4.40 4.59 4.50
1030 (110, 100) 1010 (90, 80) 950 (160, 80) 970 (120, 60) 950 (70, 20)
7.46 7.54 8.18 7.59 7.57
1.76 2.03 1.83 1.79 1.78
7.61 7.88 8.00 7.41 7.39
21.35 21.41 21.39 21.37 21.40
(0.53,0.45) (0.41, 0.39) (0.75, 0.38) (0.54, 0.29) (0.30, 0.12)
(0.42, 0.39) (0.74, 1.12) (0.83, 1.17) (1.1, 0.79) (0.65, 0.65)
(0.42, (0.19, (0.15, (0.37, (0.09,
0.52) 0.29) 0.12) 0.53) 0.08)
(0.19, (0.73, (0.68, (0.93, (0.41,
0.35) 0.83) 1.02) 0.43) 0.54)
(0.13, (0.02, (0.10, (0.09, (0.07,
0.20) 0.06) 0.14) 0.21) 0.07)
Table 2 Characteristic impact energies: specimen dimensions: 127 mm 127 mm, thickness: 5 mm, clamped, plain weave E-glass/epoxy, incident impact energy: EII = 21.42 J. Back pressure, PB (MPa)
Maximum plate energy, Em (J)
Energy absorbed, Ea (J)
Plate strain energy, Es = (Em Ea) (J)
0 0.3 0.5 0.7 0.9
21.35 21.41 21.39 21.37 21.40
13.78 11.58 12.52 13.57 11.97
7.57 9.83 8.87 7.80 9.43
(0.13, (0.02, (0.10, (0.09, (0.07,
0.20) 0.06) 0.14) 0.21) 0.07)
(2.75, (2.70, (1.06, (4.16, (2.64,
3.55) 1.77) 1.42) 3.12) 6.70)
(3.57, (1.80, (1.43, (3.18, (6.78,
2.62) 2.78) 1.03) 4.07) 3.33)
tained by curve fitting the load cell data. Representative plot of the variation of these impact parameters with time is shown in Fig. 4 for PB = 0.7 MPa. Energy E increases from 0 at t = 0 to a maximum value at around T/2 and then decreases to the final value Ea. Here, T is the impact duration. The maximum energy transferred from the projectile to the plate Em was slightly less than the incident impact energy EII. This is due to frictional losses during the loading phase. Em has two components, viz., the plate strain energy Es and the energy absorbed Ea. Es is responsible for the rebound of the impactor. Ea is partly lost in creating the damage and the rest in increasing the kinetic energy of the plate. It was observed that the plate has not come back to its original position at the end of the impact event. It was seen that the maximum values of E and d occur at the same time, and V is zero at that instant. It was observed that the instant of maximum contact force appears earlier than the occurrence of the maximum central deflection. This generates a phase whereby the contact force decreases while the central deflection increases. This is because of damage induced on the surface of the composite plate which then reduces the contact force while the central deflection is increasing. Tables 1 and 2 and Figs. 5–7, show values of impact parameters: Fm, dm, Vrm, T, Em, Ea and Es for different values of PB. The bracketed values in the tables are the scatter bands.
Photographs of damage pattern on the impacted and rear side for each case of back pressure are shown in Fig. 8. The corresponding values of damage dimension are shown in Table 3. The damage
Fig. 5. Peak contact force and maximum central deflection as a function of back pressure, h = 5 mm, V0 = 3.02 m/s, M = 4.71 kg, EII = 21.42 J.
Fig. 7. Energy as a function of back pressure, h = 5 mm, V0 = 3.02 m/s, M = 4.71 kg, EII = 21.42 J.
Fig. 6. Maximum rebound velocity and contact duration as a function of back pressure, h = 5 mm, V0 = 3.02 m/s, M = 4.71 kg, EII = 21.42 J.
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Impacted side
(a)
Rear side Warp
75 mm Fill
75 mm
(b)
Fig. 9. Damage tolerance as a function of back pressure, h = 5 mm, V0 = 3.02 m/s, M = 4.71 kg, EII = 21.42 J.
(c)
CAI testing was along the warp direction. The results of CAI testing are presented in Table 3. Here, the ratio X nc /Xc is the damage tolerance. The corresponding graph of damage tolerance versus PB is shown in Fig. 9. It is observed that the damage tolerance attains a minima for PB = 0.5 MPa. The damage patterns of the specimens under in-plane compressive loading of the CAI test were observed. The photographs of impacted side, rear side and edges are shown in Fig. 10. For all the different back pressure cases, catastrophic shear failure was observed at the location of impact. The shear failure was along 45° with respect to loading direction.
(d)
(e)
5. Results and discussion
Fig. 8. Damage patterns in woven fabric composites with back pressure subjected to low velocity impact, EII = 21.42 J: (a) PB = 0 MPa; (b) PB = 0.3 MPa; (c) PB = 0.5 MPa; (d) PB = 0.7 MPa; (e) PB = 0.9 MPa.
consists of fiber breakage, delamination and matrix cracking. Fiber breakage can be seen in the inner region of the damage and matrix crack can be seen in the surrounding region. The damage dimensions presented cover fiber breakage, delamination and matrix cracking. 4. Compression-after-impact studies CAI tests were performed for all the specimens using the CAI test fixture as per NASA 1142 standard [28]. The loading during
Variation of Fm with PB, as shown in Fig. 5, indicates that there is no significant variation of Fm as a function of PB. There are two effects at play when the composite plate is subjected to back pressure. Firstly, due to back pressure, the plate bulges and the top surface on which impact takes place is not plate-like but shell-like. It was observed that the bulging was almost linearly increasing with the increase in back pressure. For the case of PB = 0.9 MPa, 9 mm of upward bulging was observed. This is equivalent bulge to radius of 317 mm. As the bulging increases the curvature increases. The shell curvature effect during impact cannot be ignored. Secondly, back pressure imparts a certain pre-stress on the plate. Also, with back pressure, the resistance offered would increase. This is equivalent to considering increase in thickness of the specimen. The range of peak contact force in the present study is 4.3– 4.9 kN, and range of peak central deflection of the specimen is 7.4–8.2 mm with the incident impact energy of 21.42 J. Comparing this with the results given by Wardle and Lagace [17], it can be
Table 3 Damage tolerance characteristics: specimen dimensions: 127 mm 127 mm, thickness: 5 mm, clamped, plain weave E-glass/epoxy, incident impact energy: EII = 21.42 J, undamaged compressive strength (loading along warp): Xc = 175.0 (10, 11) MPa. PB (MPa)
Damage dimensions (mm): visual observations Top
0 0.3 0.5 0.7 0.9
X nc (MPa)
X nc /Xc (%)
142.3 116.7 112.2 124.4 130.9
81.3 66.6 64.1 71.0 74.8
Bottom
Along warp
Along fill
12.3 20.0 20.0 15.0 13.5
13.7 25.5 20.5 14.5 12.5
(0.3, (2.0, (1.4, (2.3, (3.5,
0.7) 2.2) 2.0) 2.0) 3.7)
(1.3, (1.5, (2.5, (1.7, (2.5,
Along 45° 1.7) 1.7) 2.7) 1.5) 2.9)
10.7 22.5 20.5 12.5 11.5
(1.3, (2.4, (2.5, (1.6, (1.5,
1.7) 2.5) 2.4) 1.5) 1.8)
Along warp
Along fill
15.0 26.5 26.0 24.5 19.5
15.0 28.0 27.0 24.5 17.0
(1.8, (0.4, (2.0, (3.9, (2.8,
2.0) 0.5) 1.5) 3.5) 2.3)
(1.7, (4.0, (1.5, (3.8, (8.0,
Along 45° 2.1) 4.2) 1.9) 3.5) 8.8)
PB – back pressure, X nc – post-impact compressive strength along warp, X nc /Xc – percentage damage tolerance.
15.0 29.5 25.5 24.5 17.5
(2.2, (1.5, (2.5, (4.9, (0.5,
1.6) 1.6) 2.4) 4.5) 0.8)
(4.0, 5.0) (15.5, 15.8) (5.7, 5.5) (7.3, 7.9) (13.0, 13.8)
(2.3, (6.0, (4.1, (4.8, (7.4,
2.4) 6.1) 5.2) 4.2) 7.7)
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M.D. Kulkarni et al. / Composite Structures 93 (2011) 944–951
Top view
Bottom view
Side view
(a) 147mm
Warp
Fill
67mm
5mm
123 mm
(b)
(c)
(d)
(e)
Fig. 10. Damage patterns in impacted woven fabric composites with back pressure under in-plane compressive loading, EII = 21.42 J: (a) PB = 0 MPa; (b) PB = 0.3 MPa; (c) PB = 0.5 MPa; (d) PB = 0.7 MPa; (e) PB = 0.9 MPa.
concluded that the impact conditions of the present study would lie on the second equilibrium path. Hence, as observed by Wardle and Lagace [17], increase in curvature would lead to decrease in contact force. In some other studies, on the effect of curvature [18–22], researchers have used 1 mm thick, eight-ply laminate, which is impacted by very low impact energies, not more than 6 J. They also concluded that, as the curvature increases, the contact force decreases. Kistler and Waas [19–21], explicitly observed that deflection increases as curvature increases, for 1 mm thick specimens. Thus it can be argued that 5 mm thick specimens with incident impact energy of 21.42 J, as used in the present study, would also follow the similar trend of decreasing contact force and increasing deflection with the increase in curvature. It is reasonable to state that the curvature caused by back pressure might decrease the peak contact force and increase the maximum central deflection. The effect of increasing pre-stressing and thickness is well studied in literatures [2–13]. It is observed that pre-stressing and increase in thickness lead to increase in contact force and decrease in central deflection, i.e., both effectively increase the resistance of the specimen. Other than bulging, the effects of back pressure are: effective pre-stressing and effective increase in thickness of the specimen. Hence, as observed in Refs. [2–13], the effect of pre-stressing and thickness should lead to an increase in contact force and decrease in central deflection. From Fig. 5 it can be observed that, in the present study, the contact force is nearly constant in the range of back pressures con-
sidered. It can be noted that two opposing phenomena take place. As the back pressure increases the curvature increases leading to decrease in contact force. On the other hand, as the back pressure increases the effective pre-stressing and the effective thickness of the plate increase leading to increase in contact force. The variation of contact force is the net effect of the two opposing phenomena explained above. Fig. 5 also presents variation of maximum central deflection as a function of back pressure. In this case also the variation of maximum central deflection is the net effect of two opposing phenomena as explained above. In the present case, the variation of maximum central deflection is not significant in the range of back pressures considered. Even though the variation of maximum central deflection is not much, it can be seen from Fig. 5 that the deflection is the maximum with PB = 0.5 MPa. Higher deflection means more bending stresses. Preliminary results of this study are presented in Ref. [29]. Variation of maximum rebound velocity and impact duration with back pressure is presented in Fig. 6. It can be seen that the variation of these parameters with back pressure is not significant. Variation of energy with back pressure is presented in Fig. 7. About 55–65% of the total plate energy is absorbed by the plate during impact (Table 2). Damage shape and size are presented in Fig. 8 and Table 3. It can be observed that the damage dimensions are more for the case of PB = 0.3 MPa and 0.5 MPa. The damage consists of fiber breakage, delamination and matrix cracking. Fiber breakage can be seen in the inner region of the damage and matrix cracking can be seen in the surrounding region. The damage dimensions presented cover fiber breakage, delamination and matrix cracking. The intensity of the damage within the damaged area is different at different locations. Hence, damage area cannot effectively represent the extent of damage during impact loading. Damage tolerance is the correct indication of the extent of damage during impact loading. It is also seen that the damage tolerance for PB = 0.5 MPa is the lowest (Fig. 9 and Table 3). This means that the overall damage is more for this particular case of back pressure. Fig. 10 presents damage patterns for post-impact compression tests. The compressive failure takes place at the location of impact. It was generally observed that the failure was catastrophic. The shear failure was along 45° with respect to loading direction.
6. Conclusions Studies are carried out on impact and post-impact characteristics of a typical plain weave E-glass/epoxy composite for different back pressures. Two opposing phenomena take place during impact loading on plate like structures with back pressure. As the back pressure increases the curvature increases leading to decrease in contact force and increase in central deflection. On the other hand, as the back pressure increases, the effective pre-stressing and the effective thickness of the plate increase leading to increase in contact force and decrease in central deflection. The variation of contact force and central deflection is the net effect of the two opposing phenomena. For the range of parameters considered, the specific observations are: (1) The maximum contact force is nearly constant with different back pressures considered. (2) The maximum central deflection is nearly constant with different back pressures considered. (3) The post-impact compressive shear failure was along 45° with respect to loading direction. (4) The damage tolerance was the least with PB = 0.5 MPa.
M.D. Kulkarni et al. / Composite Structures 93 (2011) 944–951
Appendix A Specifications of tow/strand, fabric, resin and composite. Property
E-glass/epoxy
Reinforcement Filament diameter (lm) Filament density (gm/cc) Filaments per tow/ strand Tow/strand tex (gm/km) Type of weave No. of counts (per cm) Crimp (%) Fabric thickness (mm) Fabric aerial weight (gm/m2) Fiber volume fraction Void content (%) Matrix Process used
E-glass 20 2.62 182
a
150 Plain weave 12.1a 0.9a 0.28 388 0.51 0.75 Epoxy LY556 with hardener HY951 Matched die moulding
Along both warp and fill.
Appendix B From the load cell data, the acceleration is obtained using the expression,
ad ðtÞ ¼ FðtÞ=M The impactor velocity is computed as,
VðtÞ ¼ V 0 V0 ¼
Z
ad ðtÞdt
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 9:8 H
where, H = 0.464 m (kept the same for all experiments) On further integration, the displacement of the impactor is computed as,
dðtÞ ¼
Z
VðtÞdt
Central deflection of the plate is the same as the displacement of the impactor. The energy exchanged at time t, due to work done by contact force during the loading and unloading is computed as,
EðtÞ ¼
Z
FðtÞDðtÞdt
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