Computational modelling of microstructurally sensitive fatigue crack nucleation using discrete dislocation plasticity

Abstract

Discrete Dislocation Plasticity (DDP) modelling is employed to investigate various mi- crostructural quantities that are believed to drive fatigue crack nucleation at the microscale. The exploration begins with the calculation of geometrically necessary dislocation (GND) density within the DDP framework and the study of its behaviour during cyclic loading. The observations from modelling are compared against reports from the literature and conclusions are drawn on the GND density calculations within DDP. A central quantity in this thesis is the dislocation configurational energy. This quantity is assigned to describe the elastically-stored energy associated with the interaction of disloca- tions and their structures. It is the energy which is over and above that from the summation of the dislocation line energies when considered isolated and non-interacting. The total geometrically necessary and statistically stored dislocation density mean free distance allows the configurational energy density to be determined, thus providing a length scale over which the configurational energy is stored. A higher length scale crystal plasticity stored energy density has recently been introduced which attempts to capture local dislocation configurational energy density as an indicator of fatigue crack nucleation and growth. The former is compared and assessed against the dislocation configurational energy density. The dislocation configurational energy and stored energy densities are determined in discrete dislocation and crystal plasticity modelling respectively and assessed with respect to experiments on single crystal nickel fatigue crack nucleation, reported in the literature. Direct comparisons between the three techniques are provided for two crystal orientation fatigue tests. These provide confirmation that both quantities correctly identify the sites of fatigue crack nucleation and that stored energy density is a reasonable approximation to the more rigorous dislocation configurational energy. GND density is shown to be important in locating crack nucleation sites because of its role in the local configurational energy density.