Abstract
Following the way developed by KOSTROV (1966), we discuss the problem of longitudinal shear crack propagation. A formal solution for an arbitrarily given shear stress drop p(x, t along the crack was obtained previously (TAKEUCHI and KIKUCHI, 1970). In the present paper, making use of this solution, we worked out the case of p(x, t)=const=τ0, i. e., the constant shear stress drop. According to our numerical computations, the fracture velocity increases with the time to its final value VS, shear wave velocity in the medium, when Lτ02/μT≥2.0, where L, τ0, μ and T are initial length of the crack, shear stress drop, rigidity and surface energy, respectively. This condition may be compared with the Griflith condition Lτ02/μT≥2.55 in the corresponding statical problem. It is known by the analysis of seismic surface waves that in the Chilean earthquake in 1960, a fracture of total length of about 1000km propagated with nearly S-wave velocity. We can apply our results in the present paper to this earthquake and estimate the maximum value of T and the minimum value of L. The results, together with the similar results, are shown in Table 2 and 3.
