Boundary element analysis of the stress field at the singularity lines in three-dimensional bonded joints under thermal loading

Abstract

The stress distribution near a point on the stress singularity line of dissimilar materials in three-dimensional joints under thermal loading are investigated using BEM based on Rongved’s fundamental solutions. Stress distributions for the material combinations in the singularity region, in the no singularity region, and in the boundary between them on the Dundurs composite plane are investigated. The influences of thermal expansion coefficients, loading conditions and dimensions on the stress distribution in three-dimensional joints composed of two blocks are examined. The stress intensity factors in threedimensional joints under a uniform change in temperature are proportional to the temperature variation, 1T, and depend on the difference in the thermal expansion coefficients. Furthermore, the level of the stress distributions around the stress singularity lines also increases significantly as the length of one side in the parallel cross section to the interface decreases. Stress singularities at the interface in the bonded joints of dissimilar materials are induced by mechanical loading or thermal loading. Thermal stresses are caused by differences in elastic properties and thermal expansion coefficients in dissimilar materials joints. The stress singularities exist not only at the vertex in three-dimensional joints of dissimilar materials but also along the intersection of the interface with its free surfaces. The cross line has been referred to as the stress singularity line. Li et al. [1992] reported the results of stress analysis for dissimilar materials using three-dimensional BEM based on Kelvin’s fundamental solutions. In the analysis, the interface must be divided using very fine meshes along the stress singularity lines, and hugely memory- and time-consuming procedures are required for accurate analysis. Then, Koguchi [1997] investigated the stress singularity in three-dimensional bonded joints using three-dimensional BEM based on Rongved’s fundamental solutions. Rongved’s fundamental solutions [Rongved 1955] satisfy boundary conditions at the interface. Therefore, the number of nodes and elements necessary for accurate analysis decreases, because the BEM based on Rongved’s fundamental solutions does not require the interface area of dissimilar materials joints to be divided into elements. Koguchi et al. [2003] also used the fundamental solution for two-phase transversely isotropic materials to investigate the stress singularity fields in three-dimensional bonded joints using three-dimensional BEM. Furthermore, Prukvilailert and Koguchi [2005] reported on stress singularity analysis around a point on the stress singularity line in three-dimensional bonded joints using three-dimensional BEM based on Rongved’s fundamental solutions. However, this previous research focused only on the stress