A transient crack problem for an infinite strip under antiplane shear

Abstract

The problem of a semi-infinite crack suddenly arising in a loaded strip of finite width and then propagating with a constant velocity is considered. The analysis is carried out within the realm of the classical theory of elasticity and a state of antiplane shear is assumed. By using integral transform methods the problem is reduced to an equation of the Wiener—Hopf type, which can be solved by a standard technique involving the infinite product theory. In order to determine the stress state in the vicinity of the crack tip, i.e. the stress intensity factor, asymptotic expansions are employed. The time-dependence of this quantity is calculated numerically and exposed in diagrams. The influence of various parameters is discussed and it is shown that the stress intensity factor oscillates with a decreasing amplitude and tends to a steady-state value.