Anisotropy

Linguistics

Engineering

Philosophy

Stress field

Stress intensity factor

Crack closure

Materials science

Stress (linguistics)

Plane stress

Plane (geometry)

Economics

Rotation (mathematics)

Geology

Paleontology

Physics

Finite element method

Crack tip opening displacement

Mathematics

Optics

Elasticity (physics)

Asymptotic expansion

Mathematical analysis

Geometry

Series (stratigraphy)

Composite material

Structural engineering

Finance

Mechanics

Series expansion

Order (exchange)

Fracture mechanics

Applied Mathematical Modelling

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.

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