A continuum theory of twinning-transformation toughening

In this article, the twinning-induced toughening problem is addressed in the framework of plane strain. The fundamental solution for a pointwise twinning eigenstrain located in an infinite plane is derived first. With this solution, problems of twinned inclusions are formulated using the Green's function method, and the interaction problem is solved for a crack-tip with a twinning point source (strain nucleus). Based on this solution, a continuum formulation for twinning-induced toughening is also developed using the Green's function method. Finally, some examples are presented to demonstrate the validity and relevance of the fundamental formulations proposed in the paper. In comparison with the conventional approaches, this continuum framework of twinning-induced toughening provides a well-rounded understanding of the toughening mechanisms in crystalline materials. It enables the prediction and optimization of the material behaviour under various loading conditions.