Crack deflection by an interface – asymptotics of the residual thermal stresses

The He and Hutchinson (1989) criterion allows to predict a matrix crack deflection by an interface under mechanical loadings. It has been improved by the same authors and Evans (1994) to take into account the residual thermal stresses. This criterion is revisited here from an asymptotic point of view. A first-order (local) and second-order (non-local) forms of this criterion are proposed for mechanical loadings. Next, the same approach is carried out for a pure thermal loading, i.e. for a cooling process for instance. It is shown that residual thermal stresses do not intervene at the leading order but play a role at the second one. When combined loadings are considered, the first-order criterion is still unchanged but the second-order one becomes quite illusory since it makes an explicit reference to the critical mechanical loading triggering the deflection. Nevertheless, some trends on the deflection promotion or inhibition are derived for a notched bimaterial under four-point bend loading. In the light of these results, criticisms to the He et al. (1994) expressions are brought.