Indentation of a Power Law Creeping Solid
Abstract
The aim of this paper is to establish a rigorous theoretical basis for interpreting the results of hardness tests on creeping specimens. We investigate the deformation of a creeping halfspace with uniaxial stressstrain behaviour dot{ɛ}=dot{ɛ}_{0}(σ /σ _{0})^{m}, which is indented by a rigid punch. Both axisymmetric and plane indenters are considered. The shape of the punch is described by a general expression which includes most indenter profiles of practical importance. Two methods are used to solve the problem. The main results are found using a transformation method suggested by R. Hill. It is shown that the creep indentation problem may be reduced to a form which is independent of the geometry of the punch, and depends only on the material properties through m. The reduced problem consists of a nonlinear elastic halfspace, which is indented to a unit depth by a rigid flat punch of unit radius (in the axisymmetric case), or unit semiwidth (in the plane case). Exact solutions are given for m = 1 and m = ∞ . For m between these two limits, the reduced problem has been solved using the finite element method. The results enable the load on the indenter and the contact radius to be calculated in terms of the indentation depth and rate of penetration. The stress, strain and displacement fields in the halfspace may also be deduced. The accuracy of the solution is demonstrated by comparing the results with fullfield finite element calculations. The predictions of the theory are shown to be consistent with experimental observations of hardness tests on creeping materials reported in the literature.
 Publication:

Proceedings of the Royal Society of London Series A
 Pub Date:
 April 1993
 DOI:
 10.1098/rspa.1993.0050
 Bibcode:
 1993RSPSA.441...97B