Stress intensity factors of a crack lying in a viscoelastic layer embedded in two different media under an anti-plane concentrated load

A general solution to the problem of a crack lying in a viscoelastic layer sandwiched between two different media under an anti-plane concentrated load is presented. The fundamental elastic solution is obtained as a rapidly convergent series in terms of complex potentials via successive iterations of Möbius’ transformation in order to satisfy continuity conditions on two different interfaces. Based on the correspondence principle, the Laplace-transformed viscoelastic solution is then directly determined from the corresponding elastic solution. Therefore, the time-dependent mode-III stress intensity factor (SIF) of the crack tip can be solved numerically in a straightforward manner. Furthermore, the viscoelastic moduli of polyurethane at various temperatures are regressed from a uni-axial test with a constant load while a standard solid model is applied to formulate the viscoelastic constitutive equation. Finally, the effects of working temperature, boundary conditions and the geometric relation on the SIF are also discussed.