Physica A 392 (2013) 5574–5580
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Impact fragmentation of polyurethane and polypropylene cylinder Hiroaki Kishimura ∗ , Daisuke Noguchi, Worrayut Preechasupanya, Hitoshi Matsumoto Department of Materials Science and Engineering, National Defense Academy, Yokosuka, Kanagawa 239-8686, Japan
highlights • The fragment mass distribution of a polymer cylinder depends on the projectile velocity. • The fragment mass distribution of a polymer cylinder depends on type of the polymer material. • For polyurethane, the fragments mass from a lower-velocity impact distributes in the lognormal form.
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Article history: Received 4 March 2013 Received in revised form 1 July 2013 Available online 25 July 2013 Keywords: Fragmentation Impact Polyurethane Polypropylene
abstract The impact fragmentation of a bulk polyurethane elastomer (PU) and polypropylene (PP) cylinder have been investigated using a Cu plate projectile launched by a propellant gun at a velocity of 0.53–1.4 km/s. A projectile drills into a PU sample and forms a cavity in the sample. A small number of tiny fragments are formed. When the projectile smashes in at 1.4 km/s, the PU cylinder bursts and PU fragments form. On the other hand, a brittle fracture occurs on the PP cylinder. The mass of fragments from the PU sample generated at a lower impact velocity is distributed in the lognormal form, whereas the mass of fragments from the PU sample generated by a 1.4 km/s impact follows a power-law distribution. The fragment mass distribution of the PP sample generated at a lower impact velocity obeys the powerlaw form, whereas that generated at a higher impact velocity follows the lognormal form. © 2013 Elsevier B.V. All rights reserved.
1. Introduction There has been a great deal of interest in the impact strength and fracture of polymer materials because of the increasing use of polymers in applications such as bumpers and shock absorbers. Characterization of the response over a wide range of stress, including hypervelocity impact, is needed for accurate design using these materials. Although polymers are often used as an ingredient of composite materials, the characterization of individual polymers is important for understanding the impact response of composite materials. Polyurethane elastomers (PUs) are multiphase systems composed of hard and soft segments [1,2]. Because of their wide range of properties, PUs can be used in many applications including shock absorbers. Static and dynamic loading tests have been conducted on PUs and the strain-rate dependence of the mechanical response has been revealed [1–8]. Furthermore, Hugoniot data for bulk PUs and polyurethane foam have been reported [3,5,6]. However, studies on the hypervelocity impact responses and fracture of bulk PUs have been limited. Dynamic fracture and fragmentation occur under a wide range of conditions, for example, impact velocities, materials, and configurations [9–27]. The fracture of materials is a familiar phenomenon, many scientists and engineers have been
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Fig. 1. A schematic diagram of experimental setup.
fascinated by the fragmentation process, and much effort has been made to understand fragmentation. Fragment mass distributions have been studied in several experiments [10,13,14,16–21,24–28] and numerical simulation techniques [19,22,23,29–31]. Results have shown that cumulative fragment mass distributions exhibit a power-law dependence, in which the exponent depends on the dimensionality of the fractured object regardless of the means of fragmentation and the fragmented material [16–20,22–25,28,30,31]. Oddershede et al. reported the dependence of the exponent on the dimensionality of the fragmented body [24]. Katsuragi et al. observed that the binomial multiplicative model is suitable for explaining two-dimensional (2D) brittle fragmentation, for which the fragment mass distribution follows a lognormal distribution [16,17]. Ishii and Matsushita experimentally found that the fragment mass distribution follows a lognormal form and a power-law form for lower and higher impact energies, respectively [25]. However, neither fragmentation nor fracture has been studied for bulk PU. In this study, the fragmentation and fracture of a bulk PU cylinder under several experimental conditions are reported. In addition to a PU target, impact experiments on bulk polypropylene (PP) cylinders were conducted for comparison. 2. Experimental The polymer targets were manufactured from commercial materials. The bulk PU used was a TR100-90 Ti-Prene cylinder (Tigers Polymer Co., Ltd.) with a diameter of 70 mm and a length of 100 mm. The PP cylinders were manufactured by Kyoei Sangyo Co., Ltd. The cylinder sample was mounted inside a steel vacuum chamber connected to a launcher tube. The upper half of the cylinder sample was held using a steel holder, which was set inside the vacuum chamber. The impacted projectile consisted of three parts: a polyethylene and polycarbonate sabot, a nose made of copper, and a magnet used for velocity measurement [32]. A copper plate with a diameter of 30 mm was used for the projectile nose. The sabot and nose moved without separating. The mass of the projectile was 39.0 ± 0.3 g. All shots were performed on a 30-mm-bore, 3-mlong, single-stage powder gun [33–35]. A schematic diagram is shown in Fig. 1. Peak shock pressures were calculated by the impedance matching method [3–7,34–37]. The experimental conditions are shown in Table 1. After fragmentation, we collected the fragments and measured the mass of each fragment with an electric balance. The surface texture of the recovered PU fragments and remaining samples (the rim of a crater and a piece of a fragment) were observed by scanning electron microscopy (SEM; S-4500, Hitachi Co., Ltd.). 3. Results and discussion The impact behaviors of PU and PP cylinders were markedly different. Fig. 2 shows typical recovered samples for each material. Each shot on a PP target resulted in brittle deformation and fracture. Although the entire PP target broke into fragments in every impact experiment, the number of fragments in the impact experiment without a holder was much larger than that in the experiment with the steel holder. In contrast to the PP target experiments, except for at an impact velocity of 1.4 km/s, a projectile drilled into a PU sample and formed a cavity in the sample, and the projectile was captured
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H. Kishimura et al. / Physica A 392 (2013) 5574–5580 Table 1 Experimental conditions for shock loading. Shot
Target material
Projectile velocity (km/s)
Peak pressure (GPa)
1 2 3 4 5 6 7 8 9 10
Polyurethane Polyurethane Polyurethane Polyurethane Polypropylene Polypropylene Polypropylene Polypropylene Polypropylene Polypropylene
1.1 1.1 1.3 1.4 1.1 1.2 0.8 0.98 0.53 0.65
4.6 4.9 6.1 6.9 3.4 3.9 2.5 3.2 1.5 1.9
Fig. 2. Photographs of recovered samples and fragments. For shot 4, the formation of a ring-shaped fragment is schematically explained.
inside the sample. A small number of tiny fragments were formed. No fracture was observed on the outer surface of the recovered PU sample. These results indicate the high shock-absorption capacity of PU. The PU target experiment with an impact velocity of 1.4 km/s resulted in similar brittle behavior. First, the projectile impacted on the sample and formed a hole with a sharp edge, then the projectile proceeded into the sample, before being captured by the sample. Unlike the experiments carried out at a lower impact velocity, the sample burst, inducing the formation of fragments. As a result, the burst occurs after the projectile penetrates enough, and then the shape of the fragment originating from the impact side of the target becomes a ring. Meanwhile, no fracture was observed on the steel holder. Note that fragments derived from the projectile were not picked for all experiments. The shapes of the fragments from the fractured PU samples depend on the experimental conditions. The fragments obtained from the burst PU sample have sharp edges with radial cracks. The fragments formed during drilling by the projectile are fine and have nonuniform shapes. The PP fragments have nonuniform shapes with sharp edges. Fig. 3 shows a log–log plot of the cumulative fragment mass distribution, N (m), for the PU (Fig. 3(a)) and PP (Fig. 3(b) and (c)) samples. The distributions for both samples depend on the experimental conditions. The mass of fragments obtained from the PU target experiment with an impact velocity of 1.4 km/s, which resulted in the sample bursting, shows a clear power-law dependence. On the other hand, the fragment mass distributions for the other PU samples, whose fragments were formed by the drilling of the target, produce a curve on the log–log plot. The fragment distribution from the PP target
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Table 2 Impact-fragment experimental results and fitting parameters. Shot
Target material
Peak pressure (GPa)
Total number of fragments
σ
¯ m
2 3 4 5 6 7 8 9 10
Polyurethane Polyurethane Polyurethane Polypropylene Polypropylene Polypropylene Polypropylene Polypropylene Polypropylene
4.9 6.1 6.9 3.4 3.9 2.5 3.2 1.5 1.9
45 244 463 371 414 201 4891 131 170
1.19 ± 0.01 1.97 ± 0.01
0.0174 ± 0.0001 0.00225 ± 0.00005
2.79 ± 0.003 2.62 ± 0.01
0.0288 ± 0.0002 0.0220 ± 0.0001
2.43 ± 0.01
0.00372 ± 0.0001
a
τ
1.6379 ± 0.0190
1.4775 ± 0.0077 1.4346 ± 0.0165 1.4788 ± 0.0110
b
c
Fig. 3. Cumulative mass distribution of fragments produced by a Cu projectile impact on (a) PU target and (b), (c) PP target. The solid line and dashed line represent fitting curves using an integrated lognormal distribution function. The fitting parameters are given in Table 2.
experiment differs with the impact velocity. For a lower impact velocity, one can see a power-law dependence. For an impact velocity higher than 1 km/s, the distribution is similar to that for the PU experiment except for an impact velocity of 1.4 km/s. The texture of a PU fragment recovered from the plate impact experiment with an impact velocity of 1.4 km/s was examined by SEM. The fragment, as described above, had a sharp edge with radial cracks. Fig. 4 displays a magnified image of the surface of the fragment. As shown in Fig. 4(a), a wide, linear, partly jagged channel was formed and part of the channel was covered. The small holes in the top right of Fig. 4(a) are the entrances of other channels. The edge of the channel is sharp and a number of small cracks grow from the edge (Fig. 4(b)). The lip of the channel cover is a concave curve and tiny cracks appear around the bottom of the curve. Fig. 4(c) shows that the tiny cracks on the surface of the PU sample are connected to each other. This indicates that the channel is a fracture surface caused by the large tensile stress generated by the bursting of the sample. The fragment mass distributions obtained from our experiments can be divided into two groups: those with a power-law dependence, N (m) ∼ m−(τ −1) , and other distributions. The latter distributions can be explained by the binomial multiplicative model. The model predicts that the fragment mass distribution obeys a lognormal distribution [17]. This distribution has been observed in the numerical results for three-dimensional (3D) viscoelastic crystal fragmentation upon repeated loading [23] and one-dimensional (1D) glass rod fragmentation caused by dropping at a low energy [25]. The integrated lognormal form can be written as N (m) = NT
∞ m
2
¯ exp − ln m′ /m
2π σ
2
1/2
m′
/2σ 2
dm′ ,
(1)
¯ and σ are fitting parameters. The solid line in Fig. 3 is the fit of the integrated lognormal form of the cumulative where NT , m, fragment mass distribution to our experimental data. The fitting parameters are given in Table 2.
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Fig. 4. SEM images of recovered PU fragment formed by impact at 1.4 km/s.
For the case of PP fragmentation, which exhibits a brittle fracture, it is clearly shown that the masses of fragments formed by the lower-velocity impact have a power-law distribution, whereas those of fragments formed by the higher-velocity impact have a lognormal distribution. This result contradicts the result from the 1D glass rod dropping experiment [25], from which a power-law distribution of fragments was obtained by a higher-energy impact. This discrepancy may originate from the dimensions of the samples. However, it is interesting that the exponent of − (τ − 1) in the power-law dependence
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for the fragmentation of the PP sample caused by the lower velocity impact indicates a 2D fracture rather than 3D fragmentation [19,24]. On the other hand, Timár et al. reported that fragmentation of spherical PP particles reveal a powerlaw mass distribution of fragments with an exponent close to 1.2, which is much lower than our results [28]. They suggested that the difference in mechanism for crack initiation and growth is attributed to the difference in the exponent. In a brittle solid, dependence of strength of a material on strain rate is expected. The fracture mechanism depends on the material strength governed by the strain rate [38]. The expected strain rate in the PP particle impact is much lower than strain rate realized in our plate impact experiment. In addition to strain-rate dependent mechanism, deformation mode during fragmentation can determine an exponent for a power-law mass distribution of fragments [28]. They reported that the fragments formed by the shear dominated cracking together with the healing mechanism of compressed crack surfaces obey a power-law mass distribution of fragments with an exponent of 1.25, whereas the mass distribution of the tension dominated breakup of heterogeneous brittle materials obeys a power-law behavior with an exponent of 1.9. For our plate impact experiment, although fully comminuted materials due to passage of the shock wave followed by shear fracture is expected to be formed [38], fracture induced by tensile stress can also be expected [34,39,40]. During the impact, there is a spherical shock wave propagating in the sample ahead of the projectile. The spherical shock wave induces compression and shear deformation. As the shock wave reaches the free surface of the sample and/or the edges of the sample, it is reflected as a rarefaction wave turning back to the sample. A shock wave also propagates in the projectile, and reflects back as a rarefaction wave when the shock wave arrives at a free surface of the projectile. The interaction of stress waves causes tensile stress and the sample breakup occurs in the case of a strong enough tension. However, a returning rarefaction wave will not occur for the spherical PP particle impact because thickness of a hard wall, which is a target, may be considered as infinite [28]. Meanwhile, a weak rarefaction wave with small amplitude will generate at the rear end of a target when a weakened shock wave arrives. The target will suffer weak tensile loading. Thus, a number of larger fragments tend to survive for the experiments carried out at a lower impact velocity. In addition, fragmentation by repetitive loadings might be possible for a strong shock wave because the shock wave will travel with the sample and interact with stress waves over and over again. Consequently, the cumulative fragment mass distribution for lower velocity impact obeys the power-law distribution, whereas the integrated lognormal form of the cumulative fragment mass distribution is observed for fragmentation by a higher velocity impact. Note that some of fragments can be caused by collision with the vacuum chamber. Collision with external boundaries may change the mass distribution from a power law [23]. However, we believe that the effect of the collision with the vacuum chamber on the fragment mass distribution is minor because the target holder prevents fragments from flying and collision. In the case of PU fragmentation, in contrast to the results for PP, the masses of fragments from the PU sample formed at the lower impact velocity have a lognormal distribution, whereas those from the PU sample formed by the 1.4 km/s impact have a power-law dependence. Considering that the tensile fracture for the 1.4 km/s impact on the PU sample is revealed by the SEM image, the fragment formation mechanism is clearly different for the fragments formed by lower- and highervelocity impacts on the PU sample. The exponent of − (τ − 1) in the power-law dependence agrees with previous reports and indicates that the fragmentation is 3D [19,23–25] and tensile dominated phenomena. 4. Conclusion The impact response and fragmentation of polyurethane elastomer and polypropylene cylinders have been investigated using a Cu plate projectile launched by a propellant gun at a velocity of 0.53–1.4 km/s. When the projectile impacted at 1.4 km/s, the PU cylinder burst and generated PU fragments, which underwent tensile deformation. On the other hand, a brittle fracture occurred on the PP cylinder. 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