The strengthening effect caused by an elastic contrast—part I: the bimaterial case

摘要

The final aim of the two parts of this study is to quantify the gain in strength of a layered heterogeneous structure caused by the elastic contrast between the layers, especially if no crack deflection is observed at the interface. In part I, the analysis focus on an example, the 3 point-bending of a bimaterial made of a compliant and a stiff layer; whereas part II is dedicated to the 3-point bending of a homogeneous beam embedding a thin stiff film. Baptized "step-over" and "jump-through", two original mechanisms of crack crossing the interface are proposed herein. They rely on a coupled criterion involving both energy requirement and stress condition. It is established from asymptotic expansions and the theory of singularities. This criterion is able to respond to the paradox posed by the traditional tools of brittle fracture mechanics which might carelessly conclude to a quasi infinite strength enhancement. The subtitle of this first part might be: can a crack pass through an interface?