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

Abstract

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