Quasi-static mode III fracture in a nonhomogeneous viscoelastic body

An analysis is presented of the quasi-static propagation of a semi-infinite mode III crack in an inhomogeneous isotropic viscoelastic body. A shear modulus is assumed of the form G(t,y)=μ(t)η(y) where |y| denotes the distance measured from the plane of the crack and μ(t) is a positive, nonincreasing, convex function of time. A closed form expression is derived for the energy release rate (ERR) when a Barenblatt type failure zone is incorporated into the crack model. Numerical and asymptotic results illustrate the combined effects of viscoelastic properties, material inhomogeneity, and the failure zone at the crack tip upon the ERR.