Abstract

The behaviour of a sphere indentation with a prescribed load cycle is well understood through the use of Radok’s principle to study increasing load and Ting’s explanation of the behaviour under decreasing load: a straightforward account is given in Johnson’s Contact Mechanics. The theory will be reviewed, and Ting’s surprising explanation that, despite the intrinsic visco-elastic memory effect, all the loading-unloading behaviour which occurred before the current configuration should be ignored will (hopefully!) be clarified. Detailed results for the standard linear solid will be given, both for a sphere and for a conical indenter. What happens with a prescribed displacement cycle has not been studied before; and turns out to be more difficult. For with a load cycle, the essential relationship between the time during loading and the time during unloading such that the contact radii are equal can be found without worrying about the displacements: they may be found later. But with a displacement cycle, despite the superficial duality between stress strain, we cannot simply interchange the two hereditary integrals ; or their force/area equivalents: we have to worry about displacement and force together. Embarrassingly, only a step-by-step solution has been found. Results will be described both for a flat-ended indenter…which simply separates from the indented material…and for a sphere.

ps. and not a Laplace transform in sight!