The Role of Elasticity in Hardness Testing

Abstract

The presently accepted theory for indentation hardness ignores the elastic stress field, and considers the material indented to behave in a rigid‐plastic manner. This postulation provides a useful first approximation, but fails to explain several of the important characteristics of the process. A newly developed approach to plasticity makes it possible to include elastic effects, which play a major role when the indenter is blunt. After being reviewed, the new theory is applied to explain several of the phenomenae associated with practical hardness testing. In the indentation hardness test, a blunt indenter that approximates a flat punch is forced into a plane surface. The size of the impression that remains after the indenter is removed is a measure of the hardness of the indented body. Hardness is usually expressed in units of pressure (mg/mm 2 or psi), obtained by dividing the maximum applied load (P) by the area of the indentation measured either over the surface of the indenter (Brinell hardness) or in the plane of the surface indented (Meyer hardness). In both the Brinell and Meyer tests, the indenter is a sphere, Fig. 1(a), and: HB ¼ Brinell hardness ¼ 2P pD 2 ð1 � ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 �ð 2a=DÞ 2 q Þ ð1Þ