The strengthening effect caused by an elastic contrast-part II: stratification by a thin stiff layer

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, two original mechanisms baptized step-over and jump-through were proposed in Part I. They addressed the ability of a crack to pass through an interface and were applied to a bimaterial structure; whereas part II is dedicated to a homogeneous beam embedding a thin stiff film. The asymptotic expansions differ significantly since the small parameter is now the layer thickness. Unlike the first part where it was difficult to evidence the gain in toughness due to the superposition of two effects: a simultaneous increase in stiffness and in toughness, here it is possible to characterize the strength enhancement in using a single parameter. A discussion of the possibility to repeat the effect by multiplying the thin films is presented at the end.