A new practical equation for evaluation of strain-energy density distribution and J-integral in plates with blunt V-notches under bending loading

Abstract

The main aim of the present paper is providing a new practical equation for evaluation of the J-integral in plates with blunt V-notches under bending loading. Although some closed-form solutions exist in the literature, the present equation is useful as a rapid engineering purpose.The distribution of the strain-energy density (SED) over the semi-circular arc of the notch root has been evaluated by means of finite element analyses using ANSYS software. The effect of the notch acuity (a/ρ), the specimen width to the notch depth ratio (w/a), and the notch angle (2α) on the strain-energy density distribution have been studied. In these studies the parameters were chosen as 4⩽a/ρ⩽200, 2⩽w/a⩽100, and 30⩽2α⩽150; from which a total of 800models were analyzed. The J-integral has been evaluated using the strain-energy density distribution over the notch root. The semi-circular arc of the notch root, which is traction-free, has been used as integration path. The J-integral evaluated by means of proposed numerical relations was compared with that calculated by closed-form solutions, and good agreement was found.