Exact Analysis of Dynamic Sliding Indentation at any Constant Speed on an Orthotropic or Transversely Isotropic Half-Space

A plane-strain study of steady sliding by a smooth rigid indentor at any constant speed on a class of orthotropic or transversely isotropic half-spaces is performed. Exact solutions for the full displacement fields are constructed, and applied to the case of the generic parabolic indentor. The closed-form results obtained confirm previous observations that physically acceptable solutions arise for sliding speeds below the Rayleigh speed, for a single critical transonic speed, and for all supersonic speeds. Continuity of contact zone traction is lost for the latter two cases. Calculations for five representative materials indicate that contact zone width achieves minimum values at high, but not critical, subsonic sliding speeds. A key feature of the analysis is the factorization that gives, despite anisotropy, solution expressions that are rather simple in form. In particular, a compact function of the Rayleigh-type emerges that leads to a simple exact formula for the Rayleigh speed itself.