Relation between the reduced and unreduced hardness in nanomicroindentation tests

Hooke's law is generalized to the case of arbitrary elastic or plastic indentation epsilon=(2/root pi)(w(1)/root A), where epsilon=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)/w(1)=m(s); w(s) is the elastic deformation along the perimeter of the indent, and m(s)congruent to 0.78. It is shown that the correction Delta E-r to the elastic modulus E-r determined from the condition of linearity of the initial part of the unloading diagram, is Delta E-r=0.27(Delta P/P-m), where Delta P 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 phi at the tip of the indenter, the ratio HM/q grows by an exponential law. (C) 1999 American Institute of Physics. [S1063-7842(99)00907-1].