The Dynamic Energy Release Rate for a Steadily Propagating Antiplane Shear Crack in a Linearly Viscoelastic Body

The steady-state propagation of a semi-infinite, antiplane shear crack is reconsidered for a general, infinite, homogeneous and isotropic linearly viscoelastic body. As with an earlier study, the inertial term in the equation of motion is retained and the shear modulus is only assumed to be positive, continuous, decreasing, and convex. A Barenblatt type failure zone is introduced in order to cancel the singular stress, and a numerically convenient expression for the dynamic Energy Release Rate (ERR) is derived for a rather general class of crack face loadings. The ERR is shown to have a complicated dependence on crack speed and material properties with significant qualitative differences between viscoelastic and elastic material. The results are illustrated with numerical calculations for both power-law material and a standard linear solid.