Viscoelastic inhomogeneous beams under step loading: a longitudinal fracture analysis

Abstract

The present paper describes a longitudinal fracture analysis of an inhomogeneous vscoelastic cantilever beam under step loading. The beam exhibits continuous material inhomogeneity along its thickness, width and length. The creep behaviour is treated by using a linear viscoelastic model. The beam is loaded by a bending moment applied in steps at the free end of the lower crack arm. The time-dependent longitudinal fracture behaviour is studied in terms of the strain energy release rare. For this purpose, a methodology for deriving the time-dependent strain energy release rate with taking into account the creep behaviour under step loading is developed by using the compliance of the beam. A time-dependent solution to the strain energy release rate under step loading is derived also by considering the strain energy cumulated in the beam structure for verification. The change of the strain energy release rate with the time due to creep under step loading is investigated by applying the methodology developed. The effects of the location and length of the crack and the continuous material inhomogeneity on the time-dependent strain energy release rate are analyzed.