Holistic Approach on the Research of Yielding, Creep and Fatigue Crack Growth Rate of Metals Based on Simplified Model of Dislocation Group Dynamics

Abstract

The simplified model of numerical analyses of discrete dislocation motion and emission from a stressed source was applied to predict the yield stress, dislocation creep, and fatigue crack growth rate of metals dominated by dislocation motion. The results obtained by these numerical analyses enabled us to link various dynamical effects on the yield stress, dislocation creep, and fatigue crack growth rate with the experimental results of macroscopic phenomena, as well as to link them with theoretical results obtained by the concept of static, continuously distributed infinitesimal dislocations for the equilibrium state under low strain or stress rate conditions. This will be useful to holistic research approaches with concern for time and space scales, that is, in a time scale ranging from results under high strain rate condition to those under static or low strain rate condition, and in a space scale ranging from meso-scale to macro-scale mechanics. The originality of results obtained by these analyses were found by deriving the analytical formulations of number of dislocation emitted from a stressed source and a local dynamic stress intensity factor at the pile-up site of dislocations as a function of applied stress or stress rate and temperature material constants. This enabled us to develop the predictive law of yield stress, creep deformation rate, and fatigue crack growth rate of metals dominated by dislocation motion. Especially, yielding phenomena such as the stress rate and grain size dependence of yield stress and the delayed time of yielding were clarified as a holistic phenomenon composed of sequential processes of dislocation release from a solute atom, dislocation group moving, and stress concentration by pile-up at the grain boundary.