Some new practical equations for rapid calculation of J-integral in plates weakened by U-notches under bending

The paper deals with calculations of the J-integral for a plate weakened by U-notches under Model bending loading in the case of a material obeying a linear elastic law. The main aim of the study is to suggest some new equations suitable for calculations of the J-integral under bending loading. Although some closed-form solutions exist in the literature based on elliptic integrals, some expressions, simple to be implemented, are useful as a rapid engineering tool. The semi-circular arc of the notch, which is traction-free, is assumed as the integration path and the J-integral is given as a function of the strain-energy density. For a numerical investigation of the strain-energy density distribution on the notch edge, the equation W(0) = W-max cos (delta)(0) has been assumed, where the exponent delta has been determined from finite element analyses. The influence on delta of the notch acuity of the specimen width to the notch depth ratio w/a has been investigated by means of several parametric finite element analyses. In particular, the following values of the notch acuity (a/rho) and notch depth ratio (w/a) have been analyzed: 4 <= a/rho <= 200 and 2 <= w/a <= 100. (C) 2009 Elsevier Ltd. All rights reserved.