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ARTICLES YOU MAY BE INTERESTED INAbstract. The study is aimed at theoretical, experimental and computational determination of the coefficients in crack tip asymptotic expansions for a wide class of specimens under mixed-mode loading conditions. A multiparametric presentation of the stress filed near the crack tips for a wide class of specimens is given. Theoretical, experimental and computational results obtained in this research show that the isochromatic fringes in the vicinity of the crack tip require keeping the higher-order stress terms in the asymptotic expansion of the stress field around the crack tip, since the contribution from the higher-order stress terms is not negligible in the crack tip stress field. One can see that the higherorder terms of the asymptotic expansion are important when stress distribution is also to be known farther from the crack tip, and it is necessary to extend the domain of validity of the Williams solution. It is shown that, at large distances from the crack tips, the effect of the higher-order terms of the Williams series expansion becomes more considerable. A closed-form multiparametric presentation of the stress filed 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 influence of considering 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.

The present study is aimed at analytical determination of coefficients in crack tip expansion 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. The analytical dependence of the coefficients on the geometrical parameters and the applied loads for two finite cracks in an infinite plane medium is given. It is shown that the effect of the higher order terms of the Williams series expansion becomes more considerable at large distances from the crack tips. The knowledge of more terms of the stress asymptotic expansions allows us to approximate the stress field near the crack tips with high accuracy.

The paper is devoted to analytical determination of coefficients of the Williams asymptotic expansion of the stress field in the neighborhood of two collinear crack tips in an infinite plate under mixed mode loading. On the basis of the Kolosof-Muskhelishvili approach the complete asymptotic expansion of the stress field in the vicinity of the crack tips of two collinear cracks of equal lengths under mixed mode loading is derived. The analysis of the higher order terms in the asymptotic expansion series is performed. It is clear that it is necessary to take into account the higher order terms.