Z.S. Ma
,
Y.C. Zhou
,
S.G. Long
,
C.S. Lu
材料科学技术（英文）
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/H0)2=1+(h*H/h), the relationship between elastic modulus E and indentation depth h can be expressed as (E/E0)4=1+(h*E/h) . By combining these two formulas, we find that there is a relationship between yield stress σy and indentation depth h: σy=σy0?(1+(h*E/h))r(n)?(1+(h*E/h))[0.25-0.54f(n)], where σy0 is the yield strength associated with the strain-hardening exponent n, the true hardness H0 and the true elastic modulus E0. f(n)= (2(1-n))-1 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.
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