Crack tip asymptotic fields in anisotropic planes: Importance of higher order terms

This paper introduces the series expansion of the crack tip asymptotic fields in an anisotropic plane. Using stress-based definitions of the fracture loading modes, we present the series solutions of stresses, strains and displacements associated with the modes I and II in a cracked anisotropic plane. Special care is given to the first non-singular terms of the stress field, deriving expressions of the T-stress and the crack rigid body rotation. We then present the elasticity solution of an infinite anisotropic plane containing an inclined central crack subjected to uniaxial or biaxial loading. Under such conditions, exact analytical solutions are obtained for all coefficients of the crack tip series expansion. Our results show that the T-term is the only stress parameter that depends on the elastic constants of the anisotropic material. Finally, we evaluate the dependency of the T-stress on the material properties, and show that how significantly the higher order terms, particularly the T-stress, can contribute to the stresses near the crack tip. (C) 2020 Elsevier Inc. All rights reserved.

Automated summary

This paper introduces the series expansion of crack tip asymptotic fields in an anisotropic plane. The study focuses on stress, strain, and displacement solutions for modes I and II, as well as the characteristics of crack rigid body rotation and T-stress. Additionally, the elasticity solution for an inclined central crack on an infinite anisotropic plane under uniaxial or biaxial loading is presented, with emphasis on the dependency of the T-stress on material properties.