A new practical equation for evaluation of strain-energy density distribution and <italic>J</italic>-integral in plates with blunt V-notches under bending loading: Fid-Bau Portal

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

Barati, Ehsan / Mohammadi, Abbas

Abstract

Highlights ► A new practical equation for evaluation of the J-integral has been proposed. ► This equation is suitable for blunt V-notches under bending loading. ► The SED distribution at the notch tip has been evaluated. ► Good agreement was found in numerical and theoretical values of the J-integral.

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 $30 ⩽ 2 α ⩽ 150$ ; 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.