Elastic recovery in the unloading process of pyramidal microindentation

It is confirmed on the basis of extensive test results for various ceramic and metallic materials that the indentation load P versus penetration depth h curves (P–h curves) both in loading and unloading processes are well approximated with the quadratic formulas of P = k₁h² and P = k₂(h – h_r)², respectively, and unloading parameter k2 is quantitatively related to the elastic modulus E′ of the material indented, where h_r is the residual penetration depth after a complete unload. The unloading/reloading indentation processes for a locally deformed conical/pyramidal impression are well represented by the equivalent mechanical process of a conical/pyramidal indenter with the effective face angle of β_eff = (β – β_r) on a flat elastic half-space, in terms of the inclined face angles β and β_r of the indenter used and of the residual impression formed, respectively. With utilization of the unloading parameter k₂ and the relative residual depth of penetration ξ_r, a novel method is proposed for estimating E′. Theoretical considerations for a nonquadratic P–h unloading behavior are also made.