Inhomogeneous beams with different behaviour in tension and compression:a longitudinal crack study

An approach for investigating the strain energy release rate for longitudinal cracks in nonlinear elastic inhomogeneous beams is derived. The Ramberg–Osgood stress-strain relation is applied to describe the unsymmetrical mechanical behaviour of the material with respect to tension and compression. It is assumed that the beams have continuous material inhomogeneity in the height direction. Cracks can be located arbitrarily along the beam height. The approach is applied to investigate a longitudinal crack in a cantilever beam. The $J$-integral is used for verification of the solution.