Analytical and numerical methods were presented which permitted the prediction of the kinking angle of a semi-infinite crack in the vicinity of a thermally and elastically mismatched circular inclusion. In order to obtain this angle, the maximum circumferential stress criterion was evaluated. In order to achieve this, the mixed-mode stress intensity factors at the crack tip had to be known as functions of the thermal and elastic mismatch as well as of the geometry. They followed from the solution of a system of singular integral equations for the dislocation densities which were used to model the crack. For an arbitrary elastic mismatch and for an arbitrarily oriented crack, only a numerical solution could be obtained. However, if the crack tip and the inclusion were sufficiently well separated and if the elastic mismatch was not too large, the integral equations could be solved analytically. Closed-form solutions for the stress intensity factors and the kinking angle could therefore be obtained in this case.

On the Interaction between Cracks and Inclusions. W.H.Muller: Zeitschrift für Angewandte Mathematik und Mechanik, 1995, 75[S1], S235-6