J Mater Sci Technol ›› 2012, Vol. 28 ›› Issue (7): 626-635.

• Thin Film and Coatings • Previous Articles     Next Articles

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

Z.S. Ma1,2), Y.C. Zhou1,2), S.G. Long1,2), C.S. Lu3)   

  1. 1) Key Laboratory of Low Dimensional Materials & Application Technology of Ministry of Education, Xiangtan University, Xiangtan 411105, China
    2) Faculty of Materials, Optoelectronics and Physics, Xiangtan University, Xiangtan 411105, China
    3) Department of Mechanical Engineering, Curtin University of Technology, Perth, WA 6845, Australia
  • Received:2011-12-05 Revised:2012-02-08 Online:2012-07-28 Published:2012-07-26
  • Contact: Y.C. Zhou
  • Supported by:

    the National Natural Science Foundation of China (Grant Nos. 11102176, 11002122, 11172258, and 10828205), the Natural Science Foundation of Hunan Province for Innovation Group (Grant No. 09JJ7004), and the Key Special Program for Science and Technology of Hunan Province (Grant No. 2009FJ1002).  the Australian Research Council (Grant No. DP0985450).

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/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: σyy0?(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.