An energy-based method to extract plastic properties of metal materials from conical indentation tests
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ing Qian Department of Engineering Mechanics, Tsinghua University, Beijing 100084, People’s Republic of China
Jian Lua) Laboratoire des syste`mes me´canique et dinge´nierie simultane´e, FRE, CNRS 2719, Université de technologie de Troyes, Troyes 10010, France
Zhen Han Yao Department of Engineering Mechanics, Tsinghua University, Beijing 100084, People’s Republic of China (Received 1 November 2004; accepted 2 February 2005)
Based on dimensional analysis and finite element computations, an energy-based representative strain for conical indentation in elastoplastic materials has been proposed to establish an explicitly one-to-one relationship between the representative stress r, the indentation loading curvature C, and the ratio of reversible work We to total work Wt performed by the indenter, i.e., r/C ⳱ F0(We/Wt), where r is the flow stress corresponding to the representative strain. The relationship provides a very simple method to evaluate the representative stress r from the three directly measurable quantities We, Wt, and C. Numerical examples and further theoretical analysis reveal that a unique, stable solution can be obtained from the present method for a wide range of material properties, including both highly plastic materials (e.g., Ni for which E/y ⳱ 1070) and highly elastic materials (e.g., materials for which E/y ⳱ 25 and n ⳱ 0.5), using indenters with different tip apex angles. Based on the representative strains and stresses given by two indenters with different tip apex angles, e.g., (r,80, ⑀r,80) and (r,65, ⑀r,65), the plastic properties of materials, i.e., the yield strength y and strain hardening exponent n can be further determined. I. INTRODUCTION
Indentation tests have been applied to determine the hardness of materials1 since the early 1900s. During the past three decades, instrumented indentation tests have been developed and are widely used at present to characterize material properties, such as hardness and Young’s modulus,2,3 on a small scale. In recent years, interest has been mounting in the development of systematic methods to extract the local stress–strain relationship of materials from indentation tests. The present work is part of wider research on methods used to determine the plastic properties of elastoplastic materials using conical indentation tests. Recently, single indenter algorithms were presented to extract the mechanical properties of materials from the indentation loading and unloading curves produced by a sharp indenter.4,5 However, other investigations show6–8 that the stress–strain
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Address all correspondence to this author. e-mail: [email protected] DOI: 10.1557/JMR.2005.0147 1194
J. Mater. Res., Vol. 20, No. 5, May 2005
curve cannot be uniquely determined from the loading and unloading curve given by a prescribed indenter . To take this into account, further research has been conducted to infer the stress–strain relationship using additional experimental information. Tunvisut et al.9 and Mata and Alcala10,11 used the loading–unloading curves, together
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