Decomposition of Eshelby’s energy momentum tensor and application to path and domain independent integrals for the crack extension force of a plane circular crack in Mode III loading

Vanishing divergence of Eshelby’s (energy momentum) tensor allows formulation of path or domain independent integral expressions of the crack extension force. In this work, a decomposition scheme of this tensor is presented, which results in zero divergence decomposed parts that allow formulation of expressions yielding the Mode I, II and III crack tip parameters J and K,with particular emphasis on Mode III, at present. By using the Mode III decomposed part of Eshelby’s tensor and the virtual crack extension method, a path and a domain independent integral, both new, for the crack extension force of a plane circular crack in axi-symmetric Mode III loading, are derived as examples of application.