Longitudinal fracture analysis of continuously inhomogeneous beam in torsion with stress relaxation

摘要

The present paper deals with longitudinal fracture analysis of a continuously inhomogeneous beam with stress relaxation. The beam is loaded in torsion. The stress relaxation behavior is treated by using two linear viscoelastic models under constant applied shear strain. The cross-section of the beam is a circle of linearly varying radius along the beam length. The longitudinal crack is a circular cylindrical surface. The beam is continuously inhomogeneous in both radial and length directions. The shear modulii and the coefficients of viscosity are distributed exponentially along the radius and along the length of the beam. The longitudinal fracture behavior is analyzed in terms of the strain energy release rate. A solution to the strain energy release rate is obtained by differentiating the strain energy. The solution is verified by considering the balance of the energy. The influence of the varying radius of the cross-section on the longitudinal fracture is studied. The effects of the varying shear modulii and coefficients of viscosity in radial and length directions of the beam on the longitudinal fracture behavior are evaluated. The change of the strain energy release rate with the time is analyzed.