J-integral evaluation for U- and V-blunt notches under Mode I loading and materials obeying a power hardening law

The paper deals with calculations of the J-integral for a plate weakened by U- and V-blunt notches under mode I loading in the case of a linear and nonlinear elastic material. The main aim of the study is to suggest simple equations suitable for rapid calculations of the J-integral. The semicircular arc of the notch, which is traction free, is assumed as integration path and the J-integral is given as a function of the strain energy over the notch edge. For a numerical investigation of the strain energy density distribution on the notch edge the equation W (theta) = W-max cos(delta) (theta) has been assumed, where 8 has been determined from finite element analyses. In particular, the following values of the notch acuity a/p and the opening angle 2 alpha have been analyzed: 4 <= a/p <= 400 and 0 <= 2 alpha <= 3 pi/4. Considering plates weakened by lateral and central notches under symmetric mode I loading, the approximate relationships for the strain energy density, which require the presence of a non zero notch radius for their application, and the J-integral are discussed firstly considering a linear elastic material and then a material obeying a power hardening law during the loading phase. The predicted results of the J-integral are consistent with those directly obtained from finite element analyses.