Lengthwise Fracture Analysis of Inhomogeneous Viscoelastic Cantilever Beam Subjected to Sinusoidal Strains

Abstract

This paper describes an analysis of lengthwise fracture in a viscoelastic inhomogeneous cantilever beam configuration under strain that is a sinusoidal function of time. The mechanical behaviour of the beam is treated by a viscoelastic model having two linear springs and a linear dashpot. The beam is continuously inhomogeneous along its thickness. Therefore, the modulii of elasticity of the springs and the coefficient of viscosity of the dashpot vary smoothly along the thickness of the beam. The compliance method is applied to derive a solution of the strain energy release rate for the lengthwise crack in the beam structure. The J-integral is used for verification. The stress-strain-time dependence of the viscoelastic model is applied for describing the behavior of the beam when obtaining solutions of the strain energy release rate and the J-integral. Solutions are derived for both positive and negative angle of rotation of the lower crack arm free end (when the angle is positive, the upper crack arm is free of stresses, while at negative angle both crack arms are loaded). The effects of various factors including the sign of the angle of rotation on the strain energy release rate are analyzed.