Inhomogeneous beams of circular cross-section under axial forces: a longitudinal fracture analysis

Abstract

This paper deals with longitudinal fracture analysis of inhomogeneous non-linear elastic beams with continuously varying radius of the cross-section along the beam length. The external loading consists of axial forces. Beams with a longitudinal crack presenting a circular cylindrical surface are considered. The beams exhibit continuous material inhomogeneity in radial direction. A general approach for analyzing the strain energy release rate is developed by considering the energy balance. The approach is used to analyze the longitudinal fracture of an inhomogeneous non-linear elastic cantilever beam configuration. The strain energy release rate in the cantilever beam is derived also by considering the complementary strain energy for verification. The influence of the continuously varying radius of the cross-section along the length of the cantilever beam on the strain energy release rate is evaluated. The effects of the material inhomogeneity, location of the crack in radial direction, crack length and the material non-linearity on the strain energy release rate are also evaluated.