Analysis of microhardness data using the normalized power law equation and energy balance model

Abstract

where, P is load, k1 and n are materials constants and d is indentation (diagonal/diameter) size. This power law equation is also referred to in literature as Meyer’s law [2–4, 6, 7]. It should be noted that Meyer’s equation was originally developed for a spherical indenter, where n is directly related to the strain hardening coefficient of the material [1, 8]. Onitsch [1, 9] extended this Meyer’s power law equation for nonspherical indenters and observed that in a macrohardness range n is 2.0, whereas in a microhardness range, n is less than 2, irrespective of the type of material. When n is equal to 2, the above power law equation is also quoted as Kick’s law in literature [2, 10]. It has been pointed out earlier by several workers that Meyer’s constant, k1 is having a strange dimension of force/(length)n, which is dependent on the value of n [3, 11, 12]. In order to resolve this problem, Li and Bradt [3] introduced the reference indentation size corresponding to load independent hardness, whereas, Sargent [11] suggested using 10 μm indentation size corresponding to the standard hardness as a reference. Gong etal. [4] have proposed a modified energy balance model after realising the limitations of the existing energy and force balance model [2, 3, 12–14] for analysing the problem of the ISE and for determining true hardness i.e., the load independent hardness. The corresponding equation can be expressed as