Some analytical and numerical expressions for evaluation of the critical J-integral in plates with blunt V-notches under Mode I loading

The main aim of this article is to propose some analytical and numerical expressions for evaluation of the critical value of the J-integral (J(cr)) in plates weakened by blunt V-notches under Mode I loading for brittle or quasi-brittle materials. The critical J-integral is a material property in cracks. In notches, however, the specimen geometry also affects this parameter. In analytical expression, the relationship between J-integral and strain-energy density has been applied in order to evaluate the J(cr). The strain-energy density distribution over the semicircular arc of the notch (i.e. the parameter delta proposed in some previous articles) has also been used to derive a numerical equation for evaluation of the J(cr). The results have shown that the normalized J(cr) (J(cr)/J(IC)), that is, the ratio of the critical J-integral in notches to one in cracks, is a function of R-C/rho ratio, notch angle (2 alpha), and Poisson's ratio. The loading condition (bending or tensile loading), the ratio of the specimen width to the notch depth (w/a), and the notch acuity (a/rho) have negligible effect on the normalized J(cr), for constant values of other parameters. Good agreement was found in critical fracture load evaluated by means of the J(cr) criterion (using the proposed equations) with experimental data taken from the literature for blunt V-notches under Mode I loading.