A Comparison of the Dynamic Transient Anti-Plane Shear Crack Energy Release Rate for Standard Linear Solid and Power-Law-Type Viscoelastic Materials

The problem of a semi-infinite mode III crack that suddenly begins to propagate at a constant speed is considered for a general linear viscoelastic body. It is shown that the results of an earlier paper for the Laplace transforms of the stress and displacement with the Laplace transform variable s being real and positive are valid, with minor modification, for complex values of s such that Re(s)>0. Therefore, these Laplace transforms can be inverted by means of a Bromwich path integral. Under the assumption that a Barenblatt-type failure zone exists at the crack tip, the energy release rate (ERR) and the work done in the failure zone (WFZ) are calculated through numerical inversion of Laplace transforms. The ERR and WFZ for the standard linear solid and power law material models are contrasted and also compared with the elastic and quasi-static results. The graphs and table illustrate considerable differences in the ERR and WFZ for these different models. These differences may be important to predictions of stable versus unstable crack speeds based upon a critical ERR fracture criterion.