The Meyer hardness: A measure for plasticity?
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The Meyer hardness: A measure for plasticity? M. Sakai Department of Materials Science, Toyohashi University of Technology, Tempaku-cho, Toyohashi 441-8580, Japan (Received 20 March 1999; accepted 15 June 1999)
The physical insight into the Meyer hardness is given on the basis of the experimental results for indentation load P versus indentation depth h relations and of a simple model for elastoplastic contact deformation. The quadratic relationships of P ⳱ k1h2 for loading and P ⳱ k2(h − hr)2 for unloading with the residual depth of impression hr are essential in the elastoplastic indentation processes and mechanisms. The indentation-induced residual strain energy stored in unloaded impression is properly taken into account. The Meyer hardness is an elastic and plastic parameter that depends not only on the plasticity but also on the elasticity of material indented and significantly depends on the geometry of indenter used. The Meyer hardness is given in terms of the energy consumed to create a residual indentation impression, leading to the concepts of “work of indentation” and “ductility index.”
I. INTRODUCTION
The Meyer hardness HM is the mean pressure defined by the ratio of indentation load P to the “projected” residual area Apro of indentation impression, i.e., HM ⳱ P/Apro.1,2 The use of the “curved” area Acur (i.e., the contacted area) of impression in the Brinell hardness is not a satisfactory physical concept, because the Brinell hardness, P/Acur, does not yield the mean pressure over the surface of indentation impression due to the compensation of the horizontal component of indentation load by the axial symmetry of the indenter used.1,2 The Meyer hardness is literally the resistance to penetration and has been related to the plastic flow stress Y (yield stress), Young’s modulus E, ultimate strength u, wear resistance, resistance to scratching, etc.1,2 The Meyer hardness HM has been expressed as CY using the constraint factor C, implying an intimate relation to the “plasticity” of materials.1,2 This constraint factor C for ideally plastic materials is about 3, although this value significantly depends on the geometry of indenter and the ratio of Y:E.1,2 For most types of pyramidal indentation, there is a significant elastic recovery of the indentation impression, when the indenter is removed, although the main recovery in dimensions occurs in the depth rather than in the in-surface projected area of impression.3,4 The elastic recovery in the depth of most brittle ceramic materials is about half of the maximum depth hmax that was formed in the fully loaded state at Pmax, whereas the elastic recovery in the cordial dimension (the in-surface diagonal length) of impression is a few percent or less of the dimension at Pmax.5–13 This experimental observation for the elastic recovery during unloading implies that the 3630
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J. Mater. Res., Vol. 14, No. 9, Sep 1999 Downloaded: 13 Mar 2015
Meyer hardness may also be strongly affected
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