THE STRESS SINGULARITY OF MODE-I CRACK PROPAGATING WITH TRANSONIC SPEED

The transient problem of a mode-I centered crack propagating in an unb ounded isotropic linear elastic body with the crack-tip speed larger t han the S-wave speed and less than the P-wave speed is studied. The me thod of self-similar potentials with the function-theoretic approach h as been successfully applied. Attention is focused on the stress singu larity and it is found that the asymptotic solution of the stress fiel d near the crack tips is of order -(1/2 + m), where m = 0 for the crac k-tip speed equal to the P-wave as well as S-wave speeds and m = 1/2 f or the crack-tip speed equal to root 2 of the S-wave speed. The possib ility of the mode-I crack propagating with the transonic speed is also discussed from the physical point of view, even though the problem ca n be solved mathematically.