Thermal and thermo-mechanical influence on crack propagation using an extended mesh free method

Abstract

In this paper, the eXtended Element Free Galerkin method (XEFG) is used to model the crack growth in elastic materials. The effect of thermo-mechanical loading on the crack growth is investigated. The partition of unity principle is introduced to enhance the accuracy and to better simulate the crack growth. In order to get the direction of the crack growth, first the Stress Intensity Factors (SIF) are calculated using the interaction energy integral, then the crack is assumed to propagate in the direction of the maximum principal stress. The different steps of the mesh free method implementation from the governing equations to the discretized system of linear equations are recalled. The method is validated by calculating the stress intensity factors for static cracks and to comparing them those found in the literature. Further, the capability of the mesh free method for predicting crack growth under thermo-mechanical loading is demonstrated by comparing the obtained paths with others results from the literature. The implemented method presents a good efficiency and accuracy with relatively sparse node distributions.