The Dynamic, Steady-State Propagation of an Antiplane Shear Crack in a General Linearly Viscoelastic Layer

Abstract

In a previous paper, the dynamic, steady-state propagation of a semi-infinite antiplane shear crack was considered for an infinite, general linearly viscoelastic body. Under the assumptions that the shear modulus is a positive, nonincreasing continuous and convex function of time, convenient, closed-form expressions were derived for the stress intensity factor and for the entire stress distribution ahead of and in the plane of the advancing crack. The solution was shown to have a simple, universal dependence on the shear modulus and crack speed from which qualitative and quantitative information can readily be gleaned. Here, the corresponding problem for a general, linearly viscoelastic layer is solved. An infinite series representation for the stress intensity factor is derived, each term of which can be calculated recursively in closed form. As before, a simple universal dependence on crack speed and material properties is exhibited.