A multi‐scale approach to condense the cyclic elastic‐plastic behaviour of the crack tip region into an extended constitutive model

Abstract

ABSTRACTThe general idea of this paper is to model the mixed‐mode cyclic elastic‐plastic behaviour of the crack tip region at the global scale. It should be helpful, for instance, for predicting the effect of mixed mode overloads in fatigue. It is aimed at establishing a model reasonably precise (compared with elastic‐plastic finite element (FE) computations) but condensed into a set of partial derivative equations so as to avoid huge elastic‐plastic FE computations in the future. For this purpose, the kinematics of the crack tip region is characterized by a set of condensed variables. This is classical in linear elastic fracture mechanics (LEFM), the displacement field is approached by the product of spatial reference fields ( and ) and nominal stress intensity factors (K∞I and K∞II). Therefore, in LEFM, two condensed variables only, K∞I and K∞II, fully define the kinematics in the crack tip region. So as to generalize this approach to mixed mode cyclic elastic‐plastic conditions, we define first the intensity factors ( and ) of the elastic spatial reference fields ( and ) and we introduce two additional spatial reference fields ( and ) and their intensity factors ( and ) to account for plastic deformation within the crack tip region. Such an approximation is shown to be reasonably precise using FE computations. Therefore, the velocity field in the crack tip region is fully defined by only four condensed variables ( and ). Using the multi‐scale approach proposed herein, evolutions of ρI and ρII for various mixed‐mode loading conditions defined by K∞I and K∞II were generated using the finite‐element method (FEM). Then, it was shown that we can model these evolutions at the global scale through a yield locus, a flow rule and a kinematics hardening rule. It is also suggested how this model could be employed for predicting the effects of mixed mode plasticity on fatigue crack growth.