Longitudinal fracture of inhomogeneous beams with material non-linearity: An analytical investigation

Abstract

This paper describes an analytical approach for analysing of longitudinal fracture in beam structures which exhibit smooth material inhomogeneity along the height and length. A solution to the strain energy release rate is derived for a general loading scheme assuming non-linear mechanical behaviour of the material. The Ramberg-Osgood stress-strain relation is used to model the material non-linearity. It is assumed that the three material properties which are involved in the Ramberg-Osgood stress-strain relation vary continuously along the height and length of the beam (exponential laws are applied for describing the distribution of these properties along the height and length of the beam). The solution derived is valid for a longitudinal crack located arbitrary along the beam height. It is shown that the approach developed can be applied for evaluating the effects of material inhomogeneity along the height and length of the beam, non-linear mechanical behaviour of the material, crack location along the beam height and the crack length on the longitudinal fracture.