Nonlinear viscoelastic crack-tip fields

摘要

Stress and displacement fields near the tip of an opening-mode crack in a two-dimensional deformation field of a nonlinear viscoelastic material are investigated with the aid of HRR solution and the elasticity recovery correspondence principle recently proposed by Zhang. Nonlinear viscoelastic constitutive relations in the form of simplified single integral are adopted and the instantaneous stress-strain responses are assumed to be following a power law. Poisson's ratio is assumed constant. With these assumptions, the singularity behavior at the end of a tensile crack is the same as that of the HRR solution. If the remote external stress is prescribed, then the stress fields are the same as HRR solution and the displacement fields are those for HRR solution by taking Stieltjes convolutions. On the other hand, if the discontinuous displacements at a point of the crack surface are prescribed, the displacement fields are the same as that of HRR solution and the stress fields are those for HRR solution by taking Stieltjes convolutions.