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=τ
0, 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
Lτ
02/μ
T≥2.0, where
L, τ
0, 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
Lτ
02/μ
T≥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.
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