Elastic recovery in the unloading process of pyramidal microindentation

Abstract

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 – hr)2, respectively, and unloading parameter k2 is quantitatively related to the elastic modulus E′ of the material indented, where hr 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 βeff = (β – βr) on a flat elastic half-space, in terms of the inclined face angles β and βr 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 ξr, a novel method is proposed for estimating E′. Theoretical considerations for a nonquadratic P–h unloading behavior are also made.