Abstract
Stress singularity often occurs at singular points of structures, e.g. cracks, open wedges or corners of joined materials, etc. The flaw in a homogeneous medium and interface crack in bi-material systems are typical cases for stress singularity problems. Recently, many researches focus on multi-material systems. Several issues about stress singularities are discussed:(1) practical implementation of a powerful algorithm to calculate singularities in multi-material systems;(2) proper definition of the stress intensity factor (SIF) to characterize the stress fields, especially for stress oscillation, i.e., mode mixing;(3) physical interpretation of singular modes for multi-material systems.These issues are still not resolved yet.In this dissertation, the stress singularity of multi-material systems was re-analyzed by the complex variables techniques. Once a reference material is chosen, general Dunders parameters can be defined in the derivation of the characteristic equation, which can be simplified as the operation of a "Power Matrix". Hence, a powerful algorithm "General Transfer Matrix Method" (GTMM) to calculate the singularities for multi-material systems without limit on the number of materials can be achieved practically. The so-called "over-specified" condition was also clarified in the derivation and overcome by a newly defined SIF, which is a function of angle q. This general stress intensity factor (GSIF) distinguishes the mixed parts from the expression of stress components. The loading modes can be interpreted by the angular distribution of the SIF through numerical analysis and validated by photoelastic techniques.