PSI - Issue 28

Koji Uenishi et al. / Procedia Structural Integrity 28 (2020) 2072–2077 Uenishi et al./ Structural Integrity Procedia 00 (2020) 000 – 000

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1. Introduction In order to enhance the integrity of structures consisting of brittle solid materials, it is essential to investigate mechanical destabilization due to fracture evolution in such brittle solids. Although the mechanical behaviour of a single crack, or a source of further fracture under certain loading and environmental conditions, has been extensively studied and summarised in textbooks, etc., e.g. by Anderson (2017), in reality, multiple cracks may exist, expand and interact intermittently with one another in quasi-static and/or dynamic ways. However, the collective or global nature of such multiple cracks, as well as its relation with every individual or local crack behaviour, has not been fully understood yet. Therefore, here, by utilising the experimental technique of dynamic photoelasticity in conjunction with a high-speed digital video camera, we observe fracture development in an initially linear elastic rectangular polycarbonate specimen where sets of small-scale cracks are arranged by a digitally controlled laser cutter and external uniaxial tensile strain with a prescribed constant (displacement) rate is exerted by a tensile testing machine (Fig. 1a). We scrutinise local fracture evolution around each individual crack, and at the same time, we acquire global stress strain relation and dependence of the physical characteristics such as tensile strength on the applied strain rate. 2. Experimental observations First, we prepare transparent birefringent (photoelastic) polycarbonate specimens with small-scale parallel cracks that are widely distributed in a staggered way and perpendicular to the direction of uniaxial elongation (Fig. 1b). The laser cutter enables us to arbitrarily and precisely set a vast variety of crack distributions in the specimens with different values of initial crack density, and for every specimen and for each different strain rate exerted by the uniaxial tensile testing machine, we can readily obtain the global stress-strain relation. Figure 2 depicts the connection between the nominal stress and the nominal strain experimentally obtained at three different prescribed constant strain rates for the specimen illustrated in Fig. 1b. As theoretically predicted by Gomez et al. (2020) and preliminarily experimentally reported in Uenishi et al. (2018, 2019), the stress-strain relation in Fig. 2 is dependent on the uniaxial strain rate, and, for instance, at least for relatively smaller strain rates ranging from 1.3  10 − 4 /s to 1.3  10 − 2 /s, the global tensile strength increases with the strain rate. Also, for each of the three different values of the external strain rate, there exists a clear and abrupt stress drop like in the case of specimens without initial cracks. With the knowledge of these collective properties at hand, now we pay more attention to the local, subsidiary fracture possibly generated by the main or primary fracture. The point here is that for every strain rate applied, the stress drop occurs so abruptly that we cannot precisely grasp the transition from quasi-static to dynamic stage of fracture development from the global diagram like Fig. 2. In order to clarify the physical phenomena that can occur before, during and just after the global stress drop, as mentioned above, we try to trace the dynamic evolution of the primary fracture and the fracture-induced waves, as well as the emergence and propagation of the secondary and further fractures with the high-speed digital video camera. Figure 3 shows the archetypal dynamic development of the fracture and isochromatic fringe patterns or contours of the maximum in-plane shear stress  max established in a specimen during the global process of a stress drop. Here, the exerted displacement rate is 100 mm/min, equivalent to a strain rate of 1.3  10 − 2 /s for the experimental setup of Fig. 1a (initial effective specimen length 125 mm), and the snapshots are taken at a frame rate of 50,000 frames per second. Owing to the action of the external loading, the primary fracture starts propagating just after time t = 0  s and extends from left to right, and at time 40  s, branching of the primary fracture occurs. Then, around t = 80  s, the specimen is completely split into two by the primary fracture, which corresponds to the end point of the abrupt stress drop (zero nominal stress) in the global stress-strain curve, Fig. 2. At this stage, the initiation of the secondary fracture is also visible. It is noteworthy that the secondary fracture, initiated at positions away from the terminal point of the primary fracture, propagates into the opposite direction, from right to left. Around time 140  s, the propagation of the secondary fracture is arrested. Surprisingly, this arrested secondary fracture resumes its propagation in 200  s around t = 340  s, although no additional external load can exist. The reactivation of the propagation of the secondary fracture is clearly recognisable at and after time 360  s. Thus, although invisible in the global relation in Fig. 2, the dynamic fracture evolution can be categorised into three stages, as indicated at the right-bottom corner of Fig. 3: (1) The first stage is propagation of the primary