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 δ 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/ρ ratio, notch angle (2α), 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/ρ) 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.