Dynamic steady-state mode III fracture in a nonhomogeneous viscoelastic body

The problem of a propagating semi-infinite mode III crack in an infinite inhomogeneous viscoelastic body is analyzed. Inertial effects are included in the equation of motion while the crack is assumed to propagate with a fixed speed. Material inhomogeneity is introduced into the problem by assuming a shear modulus of the form G(t, y)=μ(t) η(y) where |y| denotes the distance measured from the plane of the crak and μ(t) is a positive, nonincreasing, convex function of time. Expressions for the stress and displacement are derived from the solution to the corresponding Riemann-Hilbert problem. 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 results illustrate the combined effects of viscoelastic properties, material inhomogeneity, and the crack tip failure zone upon the ERR.