Mode-I crack-tip stress fields for inhomogeneous orthotropic medium

Abstract

Asymptotic analysis coupled with Westergaard stress function approach is used to develop quasi-static stress fields for a crack oriented along one of the principal axes of inhomogeneous orthotropic medium. In the formulation, four independent engineering constants, E 11, E 22, G 12, ν 12 are replaced by an effective stiffness E = E 11 E 22 , a stiffness ratio δ = ( E 11/ E 22), an effective Poisson’s ratio ν = ν 12 ν 21 , and a shear parameter k = ( E/2 G 12) − ν. It is assumed that the effective stiffness varies exponentially along one of the principal axes of orthotropy. The first two terms in the expansion of stress field are derived to explicitly bring out the influence of non-homogeneity on the structure of the stress field. Using the derived stress field equations, the isochromatic fringe contours are developed to understand the variation of stress field around the crack-tip as a function of both orthotropic stiffness ratio and non-homogeneous coefficient.