A Study of Indentation Creep Using the Finite Element Method

Indentation is a useful technique for studying the mechanical properties of a material. Measurable mechanical properties from indentation include time-dependent as well as time independent properties. Among these mechanical properties, time-dependent permanent deformation (creep) is of interest in this study. The purpose of this study is to explore the behavior of creep deformation of a solid under indentation. The main scientific research tool will be the finite element method.

Existing works by others provide limited solutions that allow us to correlate uniaxial creep to indentation creep. In this study, the task is taken a step further to enhance and modify previous solutions to more realistic indentation situations. Indentations with spherical and conical indenter geometries are considered. Practical data obtained from indentation creep are usually in the form of displacement (h) – time (t) or load (P) – displacement (h). Results in this study are derived to describe this behavior and obtain fundamental creep parameters from it.

Elasticity may not be ignored in the majority of indentation situations. Therefore, the effect of finite elastic deformation is considered in this study with the intention of characterizing elastic transient phenomena. From the results, certain criteria in terms of an experimentally measurable parameter will be suggested in order to avoid misinterpreting indentation data influenced by the initial elasticity.

The effect of finite strain – finite deformation in indentation is investigated. Creep solutions provided by others usually assume infinitesimal strain – infinitesimal deformation. As a result, only blunt cones approaching the geometry of a flat punch indenter have been considered for the most part in previous works. In this study, the problem of finite strain – finite deformation is addressed for conical indentation. Various half-included cone angles of the indenter are considered to account for finite strain – finite deformation problems.

The power law relation is the most common general description of creep deformation when strain rate and steady-state stress are involved. However, power law breakdown, due to large strain rates and stresses may occur during the initial parts of indentation, especially for conical indenters. Modeling of power law breakdown in indentation creep is presented and corresponding relations between uniaxial to indentation creep behavior are proposed in this study.