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

摘要

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 delta has been determined from finite element analyses. In particular, the following values of the notch acuity alpha/rho and the opening angle 2a have been analyzed: 4 < = alpha/rho < = 400 and 0 < = 2a < = 3pi/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.