Some useful expressions and a proof of the validity of the volume free procedure for the SED method application
Pietro Foti, Filippo Berto
Abstract
This work provides some useful expressions for the application of the strain energy density method to component having sharp V-notches under mixed loading conditions. The strain energy density method is characterized by showing a low sensitivity to the mech refinement; however, both the conventional procedure for the application of this method and the volume free procedure result in unavoidable approximation of the theoretical control volume integration domain. The analytical expressions for the parameters e1, e2 and e3, useful to evaluate the averaged strain energy density value in the control volume starting from the notch stress intensity factors values have been obtained. The theoretical difference, obtained by approximating the control volume shape according to both the conventional and the volume free procedure, has been assessed and the mesh size, below whose value the approximation of the control volume shape results in negligible difference with respect to the SED value that should be obtained theoretically, has been found as a function of R0. It has been found that for the conventional procedure, a mesh size equal to or lower than R0/3 ensures having an absolute difference lower than 4% while as regards the volume free procedure a mesh size equal to or lower than R0/7 is required regardless of the mode mixity and the Poisson ratio.