Relation between the reduced and unreduced hardness in nanomicroindentation tests

Hooke’s law is generalized to the case of arbitrary elastic or plastic indentation , where ɛ=q/E _r is the elastic strain, q is the average pressure over the contact area, E _r is the reduced elastic (Young’s) modulus, A is the projected area of the contact, w ₁ is the deformation in elastic indentation by a flat punch. On this basis a relation is obtained between the reduced hardness H and unreduced hardness H _h, which depends on the ratio w _s/w₁=m _s; w _s is the elastic deformation along the perimeter of the indent, and m _s≅0.78. It is shown that the correction ΔE _r to the elastic modulus E _r determined from the condition of linearity of the initial part of the unloading diagram, is ΔE _r=0.27(ΔP/P _m), where ΔP is the value used in the calculation of E _r for the length of the linear part of the diagram, reckoned from the maximum load P _m. It is shown that for metallic construction materials of medium hardness one has q=HM, where HM is the Meyer hardness. With increasing HM and increasing angle ϕ at the tip of the indenter, the ratio HM/q grows by an exponential law. Zh. Tekh. Fiz. 69, 42–48 (July 1999)