Stress Singularities in Viscoelastic Media and Related Problems

Abstract

Stress singularities at sharp notch and crack tips in viscoelastic media are considered for both homogeneous and inhomogeneous media (particularly bimaterials). In Lecture 1 various invariants for elastic media are briefly reviewed and extended to the viscoelastic case. Some useful asymptotic results for both Laplace and Mellin transforms are also briefly reviewed. In Lecture 2 near crack tip behaviour is derived and a problem of a crack in an inhomogeneous viscoelastic strip treated by means of one of the invariants derived in Lecture 1. Dual variational principles are also derived for use in this problem. In Lecture 3 the problem of a crack meeting a viscoelastic bimaterial interface is considered and it is shown how the nature of the stress singularity evolves with time depending on the relaxation moduli of the bimaterial components. A partial interpretation of these results is given in terms of the force on a dislocation interacting with the biomaterial interface. In Lecture 4 the time evolution of the singular stress field at a wedge or notch tip in plane strain is discussed. Finally in Lecture 5 we consider the problem of interpreting a crack extent and location from measurements on the inside of a hole from which the crack is initiated.