A scaling approach to model history effects in fatigue crack growth under mixed mode I + II + III loading conditions for a 316L stainless steel

Abstract

Plastic deformation introduces internal stresses in the crack tip region that modify crack growth (direction and kinetics). Therefore, fatigue crack propagation models for metallic materials have to care about history effects. A model was developed for mode I fatigue crack growth under variable amplitude loading conditions. The purpose of this work is to extend it to account for I+II+III mixed mode loadings and for a 316L steel which displays both isotropic and kinematic non-linear hardening. The approach aims at establishing a model reasonably precise (compared with elastic–plastic FE computations) but condensed into a set of partial derivative equations so as to avoid huge elastic–plastic FE computations. For this purpose, the kinematics of the crack tip region is characterized by a set of condensed variables: to identify the parameters of the model, a scaling approach is used to transpose local results obtained using elastic–plastic FE simulations of crack tip cyclic plastic deformation to the global scale. In LEFM, the displacement field is approached by the product of spatial reference fields u̲Ie,u̲IIe and u̲IIIe and nominal stress intensity factors KI∞,KII∞ and KIII∞. Three condensed variables only, KI∞,KII∞ and KIII∞, fully define the kinematics in the crack tip region. So as to generalize this approach to mixed mode cyclic elastic–plastic conditions, the velocity field at crack tip is approached using first the intensity factors K˜˙I,K˜˙II and K˜˙III of the elastic spatial reference fields u̲Ie,u̲IIe and u̲IIIe and three additional spatial reference fields u̲Ic,u̲IIc and u̲IIIc and their intensity factors ρ˙I,ρ˙II and ρ˙III to account for plastic deformation within the crack tip region. Such an approximation is shown to be reasonably precise using finite element computations. The velocity field in the crack tip region is fully defined using only six condensed variables (K˜˙I,K˜˙II,K˜˙III,ρ˙I,ρ˙II,ρ˙III). Using the scaling approach proposed herein, evolutions of ρI, ρII and ρIII for various nominal mixed mode loading conditions defined by KI∞,KII∞ and KIII∞ were generated using the finite element method. It was shown that we can model these evolutions scale through a yield locus, a flow rule and a kinematics hardening rule. Fatigue crack growth experiments were performed in mode I (with or without overloads) using potential drop and digital image correlation as a measurement of crack tip propagation. SEM fractographies were also performed to determine the fatigue crack growth rate at the local scale from striations. The 316L steel displays a very significant cyclic hardening effect, which is expected to contribute to history effects in fatigue crack growth. In mode I, the model yields satisfactory results. Experiments have to be performed to be compared with model predictions in mixed mode conditions.