J-integral expressions for semi-elliptical cracks in round bars

A finite element analysis (FEA) using the J-integral crack tip parameter has been employed to study 3-D semi-elliptical crack growth in round bars for a strain hardening material subject to uniaxial fatigue loading in both linear-elastic and elastic–plastic low cycle fatigue (LCF) conditions. The bar and crack geometries as well as the loading conditions are based on experimental observations. Similar FEA can be found in the literature, but they are limited to linear elastic conditions where a J-integral analysis is not necessary. To extend the analysis to incorporate plasticity, material Ramberg–Osgood hardening constants are input into the models. A generalized form of the stress intensity correction factor for the elastic and plastic parts of ΔJ is obtained by manipulating the elastic and plastic solutions for the J-integral and utilizing the FEA solutions for estimating ΔJ under elastic and elastic–plastic conditions. The correction factor for the plastic part of ΔJ is derived to be dependent on the bar and crack geometry and also strongly dependent on the Ramberg–Osgood hardening exponent, which conflicts with previous results for 2-D and 3-D crack geometries.