Calculation of the Generalized Stress Intensity Factors for a V-notched Anisotropic Body

Abstract

A robust method for calculating a generalized stress intensity factor for a V-notched anisotropic body under symmetric and/or anti-symmetric deformation is derived for plane stress or plane strain. The compact formulation for the generalized stress intensity factors is derived based on Stroh formalism. A path-independent line integral together with an auxiliary field solution, called the interaction M-integral, is utilized to solve for these generalized stress intensity factors. Through numeric evaluation of the interaction M-integral using a finite element solution, the generalized stress intensity factors can be found. These generalized stress intensity factors can be used to predict the failure conditions without the need for a detailed notch-tip field solution. Since the interaction M-integral is path-independent, the calculation can be carried out in the region away from the notch tip where a conventional finite element solution is sufficient to perform this analysis.

Numeric results for the generalized stress intensity factors are given for a thin rectangular plate with double edge notches. The specimen geometry used follows that in the ASTM standard D 5379/D 5379M-93 for shear property testing of fiber-reinforced composite materials. The method is first verified for three example problems. Then, the generalized stress intensity factors are given for a wide range of notch depths and angles for isotropic and anisotropic material property cases. Two in-plane fiber orientations of a unidirectional fiber-reinforced graphite/epoxy composite are considered. Two loading cases are given to produce symmetric and anti-symmetric deformation. The generalized stress intensity factor results given here for anti-symmetric deformation are unprecedented.