Abstract
The author proposed the criterion of micro-crack nucleation, which was deduced theoretically from shock wave theory, and derived the micro-crack evolution equation (Kobayashi, 2012). In the previous paper (Kobayashi, 2017a, 2017b), the crack opening criterion was deduced from the proposed micro-crack evolution equation. The dynamics of crack-front propagation in heterogeneous media was theoretically studied and the crack-front stability conditions was discussed based on the fluctuation of crack fronts induced by small heterogeneities (asperities) in fracture energy; the existence of a propagating mode called crack front waves along the crack front with a velocity slightly less than the Rayleigh wave velocity was found (Ramanathan and Fishe, 1997; Morrissey and Rice, 1998, 2000). The crack front waves (CFW) propagating in soda-lime glass and PMMA were experimentally studied and similar in many aspects to the CFW theoretically predicted above (Sharon et al., 2001; Fineberg et al., 2003). In the present paper, the crack front solitary pulse wave radiated from crack propagated as shock wave is theoretically analyzed based on the proposed micro-crack evolution equation and is verified to be soliton. The long-period pulse waves suggested by the solitary pulse wave analyzed in the present paper were observed in the seismograms of the 2016 Kumamoto Earthquake and the 2018 Hokkaido Eastern Iburi Earthquake at the neighborhood of the seismic centers. The crack propagating in the inhomogeneous media, which is characterized by the crack center strain to be largest and the shock wave velocity at the crack center being smaller than the surrounding velocities, is stably propagating such as the guided wave due to self-focusing just like as the brittle fracture progress. It is suggested based on the proposed micro-crack evolution equation considering the effect of the plastic strain that the numerical simulations and discussions in this paper are available under the plastic deformation.
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