A non-local methodology for geometrically necessary dislocations and application to crack tips

Abstract

A non-local method for the establishment of geometrically necessary dislocation (GND) based on a non-local domain integral has been developed and incorporated into crystal plasticity finite element (CPFE) formulations. The proposed non-local GND method has been validated through a four-point bending case, where the mesh sensitivity of the traditional GND method has been substantially diminished by virtue of the applied non-local domain integral. A comprehensive parametric study has been conducted to investigate the non-local domain effect on the GND calculation. The application of the non-local GND method has resembled the experimental observation of the GND density distribution near a crack tip, and improved the stress field compared to the local method. The improvement on the accuracy of predicting a microstructural driving force at crack tips reveals the necessity of applying the non-local GND method in predicting material fatigue life.