A mode III Dugdale crack interacting with a non-elliptical inhomogeneity with internal uniform stresses. (July 2019) - Wang, Xu; Schiavone, Peter
Highlights: Uniform stresses inside a non-elliptical inhomogeneity interacting with a Dugdale crack. Cohesive zones affect shape of the inhomogeneity. Size of cohesive zones change with remote loading. Numerical examples to illustrate results. Abstract: Using conformal mapping techniques and the theory of Cauchy singular integral equations, we prove that the internal stresses inside a non-elliptical inhomogeneity can remain uniform despite the presence of a nearby finite mode III Dugdale crack in the surrounding matrix which is subjected to a uniform remote loading. Our numerical results indicate that: (i) the existence of the two plastic zones in the vicinity of the "crack tips" significantly influences the non-elliptical shape of the inhomogeneity; (ii) the changes in the two plastic zone length ratios are quite different as the remote loading increases; (iii) at a critical remote loading, one plastic zone vanishes while the other plastic zone occupies practically the entire crack length.