Multi-parameter description of the crack-tip stress field: Analytic determination of coefficients of crack-tip stress expansions in the vicinity of the crack tips of two finite cracks in an infinite plane medium

The study is aimed at analytical determination of coefficients in crack tip stress expansions for two collinear finite cracks of equal lengths in an infinite plane medium. The study is based on the solutions of the complex variable theory in plane elasticity theory. Multiparametric presentation of the stress field near the crack tips in the infinite plate with two collinear cracks of finite lengths is obtained and analyzed for a full range of mixed mode loading from pure tension to pure shear. The method of analytical determination of coefficients of the complete asymptotic expansion of the stress field near the crack tip is presented. The influence of consideration of various numbers of terms of the series expansion on the stress distribution is discussed, and the significance of the multi-parameter fracture mechanics approach is emphasized.