Longitudinal cracks in non-linear elastic inhomogeneous round bars subjected to tension

摘要

The present paper is focused on longitudinal fracture behavior of inhomogeneous round bars loaded in tension. The longitudinal cracks under consideration are cylindrical surfaces (the crack front is a circle). The fracture behavior is analyzed in terms of the strain energy release rate. A general solution procedure for the strain energy release rate is derived by applying the Ramberg-Osgood constitutive law for modeling the non-linear mechanical behavior of the inhomogeneous material. Bars whose modulus of elasticity varies continuously in radial direction are considered. The general solution procedure is applicable for cracks located arbitrary in radial direction. The procedure is used to analyze the longitudinal fracture behavior of a cantilever. The fracture in the cantilever is investigated also by considering the energy balance for verification of the solution to the strain energy release rate. Influences of material inhomogeneity, loading conditions and crack location in radial direction on the fracture behavior of the cantilever are investigated and discussed in detail.