Finite element analysis for conical indentation unloading of elastoplastic materials with strain hardening Original Research Article

Finite element analysis is conducted for various elastoplastic solids with linear strain-hardening that are contacted by cone indenters having three different inclined face angles [β=10.0°, 19.7° (Vickers equivalent angle), and 30.0°]. The indentation load P vs. penetration depth h relationship during unloading is intensively examined. Although the P–h unloading relationship for a cone indentation is apparently non-quadratic [P=α(h−hr)m; m<2.0], it is emphasized from the geometrical similarity of cone indentation that the unloading process conforms to a quadratic relation [P=k2(h−hr)2; hr is the residual depth of impression after a complete unload] in its essential physical process. The unloading parameter k2 is, then, directly related to the elastic modulus E′ of the material on the basis of the concept of “effective face angle βeff” of indenter. The indentation unloading process is well described by the loading process of a conical indenter with the effective face angle of βeff(=β−βr) pressed into a flat elastic half-space, in which the inclined face angles of the indenter used and of the residual hardness impression formed are defined by β and βr, respectively. The non-quadratic term included in unloading P–h relation results from the locally distorted convex surface profile of the residual impression.