Crack Propagation Arrest by the Joule Heating in Micro/Nano-Sized Structures

Abstract

The concept of crack arrest design is proposed to enhance the safety of structures reducing the probability of crack propagation. The goal of crack arrest methods is to create compression stresses at the crack tip vicinity to stop the crack propagation. The thermal field at the crack tip vicinity can create such compression stresses. If a cracked electrically conductive structure is subjected to an electric load, a high temperature is induced by the Joule heating effect in regions subjected to higher electric current densities. A reliable computational method based on gradient theory is developed in the present paper. Due to a high concentration of electro-thermal-mechanical fields at the crack tip vicinity, the size effects are considered for both mechanical equation and the thermal transport. The strain gradients are included into the constitutive equations for the double stress tensor and electric displacements. Due to occurrence of higher order derivatives in governing equations of gradient theories it is needed to develop the collocation mixed FEM. The collocation mixed FEM is applied to our multiphysical problem with size effects for mechanical and thermal fields, where the C° continuous approximations are applied independently to displacements and strains and also to temperature and temperature gradients.