Incremental model for fatigue crack growth based on a displacement partitioning hypothesis of mode I elastic–plastic displacement fields

Abstract

ABSTRACTThe mode I displacement field in the near crack tip region is assumed to be depicted by its partition into an elastic field and a plastic field. Then, each part of the displacement field is also assumed to be the product of a reference field, a function of space coordinates only, and of an intensity factor, function of the loading conditions. This assumption, classical in fracture mechanics, enables one to work at the global scale since fracture criteria can be formulated as a function of the stress intensity factors only. In the present case, the intensity factor of the plastic part of the displacement field measures crack tip plastic flow rate at the global scale. On the basis of these hypotheses, the energy balance equation and the second law of thermodynamics are written at the global scale, i.e. the scale of the K‐dominance area. This enables one to establish a yield criterion and a plastic flow rule for the crack tip region. Then, assuming a relation between plastic flow in the crack tip region and fatigue crack growth allows an incremental model for fatigue crack growth to be built. A few examples are given to show the versatility of the model and its ability to reproduce memory effects associated with crack tip plasticity.