An Inverse Approach for Extracting Elastic–plastic Properties of Thin Films from Small Scale Sharp Indentation

Abstract

An inverse method for extracting the elastic-plastic properties of metallic thin films from instrumented sharp indentation has been proposed in terms of dimensional analysis and finite element modeling. A wide range of materials with different elastic modulus, yield strength, and strain-hardening exponent were examined. Similar to the Nix-Gao model for the depth dependence of hardness H, ( H H 0 ) 2 = 1 + h H * h , the relationship between elastic modulus E and indentation depth h can be expressed as ( E E 0 ) 4 = 1 + h E * h . By combining these two formulas, we find that there is a relationship between yield stress σ y 0 and indentation depth h: σ y = σ y 0 ⋅ ( 1 + h H * h ) f ( n ) ⋅ ( 1 + h E * h ) [ 0.25 − 0.54 f ( n ) ] where σ y0 is the yield strength associated with the strain-hardening exponent n, the true hardness H0 and the true elastic modulus E0. f ( n ) = 1 2 ( 1 − n ) is constant, which is only related to n, and h H * and h E * are characteristic lengths for hardness and elastic modulus. The results obtained from inverse analysis show that the elastic-plastic properties of thin films can be uniquely extracted from the solution of this relationship when the indentation size effect has to be taken into account.