Relation between Strain Energy Release Rates and Generalized Stress Intensity Factors for V-shaped Notches

A concise formula depicting the relation between strain energy release rates and generalized stress intensity factors for two-dimensional V-notches is presented. The distributions of stress components before the notch in an arbitrary direction are written in the same form as that of the bisector direction by introducing arbitrarily directional generalized stress intensity factors. The asymptotic displacement components due to notch propagation are obtained by means of the stress intensity factor of the crack emanating from the root of the V-notch, which is directly evaluated via generalized stress intensity factors of a perfect notch in the absence of the crack itself. Then, the stain energy release rate is derived through calculating the work that would be done by the forces applied to closing the notch again. Finally, effects arising from the geometric parameters of V-notches are discussed.