Dynamic Analysis of Non-Symmetric Cracks Extension

Abstract

ABSTRACTThis paper applies the method of self-similar potentials to analyze the dynamic behaviors of the problems of mode-I, mode-II, and mode-III cracks propagating along the x-axis with constant speed, while the constant speeds of both crack tips are not the same, called nonsymmetric crack expansion. It is assumed that an unbound homogeneous isotropic elastic material is at rest for time t < 0. However, for time t ≥ 0, a central crack starts to extend from zero length along the x-axis. On the crack surfaces of x ≥ 0, there exists uniform distributed load such that the rightmost crack tip propagates with speed ms, while the leftmost crack tip with speed s, where m > 1 and is constant. First, the complete solutions of the mode-I, mode-II, and mode-III problems are obtained. After the complete solutions are found, attention is focused on the crack surface displacements and dynamic stress intensity factors. The results of this study show that the DSIF is equal to the static SIF when the crack-tip speed is zero, and DSIF is zero as the crack-tip speed approaches the Rayleigh-wave speed. Moreover, for the special case m = 1 which indicates that the velocities of both crack tips are the same, the DSIFs of this three modes in this study is the same as those of Ref. [15].