New method for determining Young's modulus by non-ideally sharp indentation

Abstract

In a previously developed method for estimating Young's modulus E by depth-sensing indentation with spherical-tipped Berkovich indenter, the E value is deduced from several functional relationships (established by finite element analysis) relating nominal hardness/reduced elastic modulus ratio (H[sub n]/E[sub r]) and elastic work/total work ratio (Wₑ/W). These relationships are specified for different absolute bluntness/maximum displacement ratios (Δh/h[sub m]). This paper reports the generalization of the method by proposing a function to replace all the above mentioned H[sub n]/E[sub r]-Wₑ/W relationships. The function contains only a parameter V[sub r] ≡ V[sub ideal]/V[sub blunt] instead of Δh/h[sub m], where V[sub ideal] is defined as the indented volume bounded by the cross-sectional areas measured at the maximum displacement hm for an ideally sharp indenter, and V [sub blunt] is that of the real indenter. The use of V[sub r] to replace Δh/h[sub m] is for the purpose of extending the application of the method for non-spherical tipped Berkovich indenters. The effectiveness of the method for materials of prominent plasticity was demonstrated by performing tests on carbon steel and aluminum alloy using three Berkovich indenters with different tip shapes.