Three-dimensional crack analyses under thermal stress field by XFEM using only the Heaviside step function

Abstract

A three-dimensional crack analysis method based on XFEM using only the Heaviside step function was applied to heat transfer and subsequent thermal stress analyses of cracked structures. The proposed method employs tip elements to discretize the weak form governing equations using the approximation function with discontinuity. Two kinds of XFEM analysis software, which perform steady-state or transient heat transfer analysis and thermal stress analysis to evaluate J-integrals and stress intensity factors, were developed. As the XFEM model for the stress analysis is consistent with the heat transfer analysis model, nodal temperature data can be directly imported for stress analysis as thermal load data. The developed codes were verified by solving some benchmark crack problems, including both mechanical and thermal loading cases, and comparing the results with those of conventional methods and a reference. It was shown that the developed codes provide appropriate results for practical thermal stress analysis of cracked structures considering temperature-dependent material properties.

Keywords

• xfem
• heat transfer analysis
• stress analysis
• thermal stress
• stress intensity factor
• domain integral method
• j-integral
• m-integral