On the Constraint Factor and Tabor Coefficient Pertinent to Spherical Indentation

Abstract

Measuring the uniaxial stress–strain response from indentation testing has been of great interest to the materials community ever since the seminal work on spherical indentation by David Tabor. In this regard, spherical indentation is the primary choice due to the ability to access a wide range of strains in a single test. While indentation testing is fairly simple to perform, the conversion factors required to calculate the uniaxial flow stress from hardness, which is commonly referred to as constraint factor and uniaxial strain from indentation contact radius and ball radius, which is called the Tabor coefficient, are not necessarily constant and most of the prior work involves assumptions about one of these conversion factors to calculate the other. In this work, we present a finite element analysis-based approach to independently determine the constraint factor and Tabor coefficient in the fully plastic indentation regime which is a pre-requisite for this analysis. The criteria to determine whether fully plastic indentation regime is satisfied has also been presented. The proposed approach has been validated by comparing the uniaxial stress–strain response from spherical indentation tests on OFHC copper and the data obtained by conventional uniaxial testing. Excellent agreement has been found between the two approaches which can be readily applied for measuring the uniaxial stress–strain response of coatings which is otherwise difficult to determine.