PSI - Issue 68

Koji Uenishi et al. / Procedia Structural Integrity 68 (2025) 554–558 Uenishi et al. / Structural Integrity Procedia 00 (2025) 000–000

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1. Introduction We have been investigating the multiscale fracture behavior of brittle materials (Gomez et al., 2020), in particular, local fracture behavior in a global crack system that may be related to, for example, a cluster of earthquakes and earthquake swarms induced by multiple local fractures in a global geological fault system. So far, through the laboratory two-dimensional fracture experiments utilizing the technique of dynamic photoelasticity in conjunction with high-speed cinematography, we have found that the local fracture behavior in polycarbonate specimens with sets of preexisting small-scale parallel cracks strongly depends on the external (quasi-) static / impact loading conditions as well as on the initial inclination angle and distribution pattern of the sets of parallel cracks. For instance, if a number of perforation lines consisting of small-scale cracks are preset in a brittle polycarbonate specimen by a digitally controlled laser cutter, fractures can easily jump to distant places and propagate back-and-forth inside the specimen and they do not always propagate along one of the perforation lines and break the specimen in an “unzipping” fashion (Uenishi and Nagasawa, 2023; Uenishi et al., 2024). However, the mechanical details behind this rather unexpected behavior of (un)fracture along, across or beyond perforation lines have not been thoroughly understood yet. Therefore, here, we study the fundamental characteristics of “unzipping” fracture related to perforation lines containing small-scale cracks. 2. Fracture propagating along a straight perforation line consisting of small-scale cracks In the study on fracture behavior of perforated materials (e.g. Tokiyoshi et al., 2001; Dastjerdi et al. 2011; Ma et al., 2015; Carlsson and Isaksson, 2019; Lin et al., 2023; Peng et al., 2023; Wang et al., 2023), instead of straight cracks, circular holes are usually aligned in a single or two straight line(s). Here, in order to comprehend basic two dimensional fracture behavior of multiple, truly straight small-scale cracks aligned in a single line, polycarbonate specimens with two geometrically different configurations are prepared by a digitally controlled laser cutter as shown in Figs. 1 and 2. In the relatively “dense” first experiment, in a transparent birefringent brittle specimen (140 mm ´ 45 mm ´ 2 mm), cracks of length 3 mm are placed at a spatial distance of 1 mm while in the relatively “coarse” second experiment, cracks of length 2 mm at a spatial distance of 8 mm are preset. Both specimens are subjected to tension at a constant strain rate of 1.67 ´ 10 - 1 /s using a tensile testing machine, and dynamic behavior and isochromatic fringe patterns inside the specimens are visualized photoelastically with a high-speed video camera at a frame rate of 400,000 frames per second (fps) (Fig. 1) or 200,000 fps (Fig. 2). The mass density, shear modulus and Poisson’s ratio of the polycarbonate are 1,200 kg/m 3 , 820 MPa and 0.37, and with these material properties, the longitudinal (P) and shear (S) wave speeds are calculated to be some 1,820 m/s and 830 m/s. Figure 1(a) shows the dynamic development of fracture along the perforation line with relatively densely distributed small-scale cracks indicated in Fig. 1(b). If there exists only one single perforation line consisting of densely distributed small-scale cracks in a specimen, as easily expected, dynamic fracture can propagate in an “unzipping” way along the perforation line, unidirectionally from right to left linking the edges of the cracks without diverting the direction of propagation and branching. However, the experimentally obtained photographs in Fig. 1(a) clearly show that the speed of fracture propagation fluctuates, repeatedly every 7.5 µ s, between two levels, a high supershear level (at a level above the relevant shear wave speed of the specimen; e.g. at time 12.5, 20, 27.5 µ s) and a low subsonic level (e.g. at 17.5, 25 µ s). The supershear fracture propagation can be simply identified by the Mach (shock) wavefronts indicated in red in Fig. 1(a) just before the fracture leaves the edge of a preexisting small-scale crack, and its speed is calculated from the experimental photographs to be about 1,200 m/s. That is, the Mach number with respect to the S wave speed is M S = 1,200 m/s / 830 m/s = 1.45 (Mach number with respect to the P wave speed M P = 1,200 m/s / 1,820 m/s = 0.66). On the other hand, the subsonic fracture speed just before the fracture approaches the edge of the next crack in the perforation line is evaluated to be some 200 m/s, with the Mach number M S = 0.24 ( M P = 0.11). Thus, during propagation, the Mach number M S fluctuates approximately between 0.24 and 1.45. However, the apparent average speed of fracture propagation is evaluated to be (3 + 1) mm / 7.5 µ s = 530 m/s, which is in a subsonic range and well below the shear wave speed, with the Mach number M S = 0.64 ( M P = 0.29), and the supershear fracture may not be recognized if only global fracture behavior is observed at larger time intervals. In Fig. 2, when the perforation line contain coarsely distributed small-scale cracks, the speed of fracture propagation seems to fluctuate even within supershear levels, and as seen in the central section at time 40 and 45 µ s,