Viscoelastic inhomogeneous beam subjected to mechanical loading and periodically varying temperature: a longitudinal fracture analysis

Abstract

This paper deals with analysis of longitudinal fracture of inhomogeneous beam structure that exhibits viscoelastic behaviour under mechanical loading and periodically varying temperature. The analysis is performed assuming that a longitudinal crack is located arbitrarily along the beam thickness. The mechanical loading representing a bending moment applied at the free end of the upper crack arm varies continuously with time. A solution of the strain energy release rate that takes into account the viscoelastic behaviour of the beam is derived. When deriving the solution, the viscoelastic behaviour and the varying temperature are treated by applying a time-dependent modulus that is obtained by using the constitutive law of a viscoelastic model having three components (a spring and two dashpots) under smoothly varying stress with time. The material properties of the viscoelastic model which are involved in the expression for the time-dependent modulus vary continuously along the length and thickness of the beam due to material inhomogeneity. The solution of the strain energy release rate is verified by analyzing the strain energy in the beam structure. The effects of the varying temperature, the loading conditions and the inhomogeneity on the strain energy release rate are investigated.