Asymptotic crack-tip fields in an anisotropic plate subjected to bending, twisting moments and transverse shear loads

Abstract

Asymptotic crack-tip fields, including the effect of transverse shear deformation, in an anisotropic plate under bending, twisting moments and transverse shear loads are presented. By utilizing the Hellinger–Reissner variational principle, the equilibrium equations and generalized strain/stress relations for anisotropic Reissner plate theory are obtained. Assuming the displacement and stress resultant are in a separation-of-variable form, it is found that, for the first two order terms of the asymptotic solution, the equations governing crack-tip fields of anisotropic plate bending are analogous to those governing plane stress and anti-plane deformation of anisotropic elasticity. Thus the Stroh formalism can be used to characterize the crack-tip fields of the anisotropic plate up to the second-order term and the energy release rate can be expressed in a very compact form in terms of stress intensity factors and the Barnett–Lothe tensor L. The first three order terms of the crack-tip displacement and stress fields including the “T-stresses” in bending and transverse shear are presented. The displacement and stress fields near crack tips in isotropic plates up to the second order are also provided. The energy release rate expression for orthotropic and isotropic plates is also derived. The solutions of anisotropic plates by a combination of in-plane and bending loads is also investigated. The expression of the path-independent integral, J, in terms of the generalized stress and strain is derived which is useful to calculate the value of stress intensity factors. Finally, on the basis of the asymptotic solutions, methods of determining stress intensity factors and T-stresses are proposed.