A new basis for the application of the $$J$$ J -integral for cyclically loaded cracks in elastic–plastic materials

Fatigue crack propagation is by far the most important failure mechanism. Often cracks under low-cycle fatigue conditions and, especially, short fatigue cracks cannot be treated with the conventional stress intensity range $$\Delta K$$ -concept, since linear elastic fracture mechanics is not valid. For such cases, Dowling and Begley (ASTM STP 590:82–103, 1976) proposed to use the experimental cyclic $$J$$ -integral $$\Delta J^{\exp }$$ for the assessment of the fatigue crack growth rate. However, severe doubts exist concerning the application of $$\Delta J^{\exp }$$ . The reason is that, like the conventional $$J$$ -integral, $$\Delta J^{\exp }$$ presumes deformation theory of plasticity and, therefore, problems appear due to the strongly non-proportional loading conditions during cyclic loading. The theory of configurational forces enables the derivation of the $$J$$ -integral independent of the constitutive relations of the material. The $$J$$ -integral for incremental theory of plasticity, $$J^{\mathrm{ep}}$$ , has the physical meaning of a true driving force term and is potentially applicable for the description of cyclically loaded cracks, however, it is path dependent. The current paper aims to investigate the application of $$J^{\mathrm{ep}}$$ for the assessment of the crack driving force in cyclically loaded elastic–plastic materials. The properties of $$J^{\mathrm{ep}}$$ are worked out for a stationary crack in a compact tension specimen under cyclic Mode I loading and large-scale yielding conditions. Different load ratios, between pure tension- and tension–compression loading, are considered. The results provide a new basis for the application of the $$J$$ -integral concept for cyclic loading conditions in cases where linear elastic fracture mechanics is not applicable. It is shown that the application of the experimental cyclic $$J$$ -integral $$\Delta J^{\exp }$$ is physically appropriate, if certain conditions are observed.