The asymptotic near-tip solution for mode-III crack in steady growth in power hardening media

It is shown that, for mode-III crack in steady growth in power hardening media the near-tip singularity is not of the power function type but is logarithmic. By consideration of the inner boundary layer in the neighborhood of the unloading boundary, the asymptotic near-tip solutions for stress and strain fields are obtained, which satisfy all the necessary relations of elastic-plastic continuum mechanics, including the condition of continuity of the plastic parts of strain-rates across the unloading boundary.