Contact Deformation Regimes Around Sharp Indentations and the Concept of the Characteristic Strain
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Finite element simulations are performed to analyze the contact deformation regimes induced by a sharp indenter in elastic – power-law plastic solids. As the yield strength (ys) and strain hardening coefficient (n) decrease or, alternatively, as Young’s modulus (E) increases, the contact regime evolves from (i) an elastic–plastic transition, to (ii) a fully plastic contact response, and to (iii) a fully plastic regime where piling-up of material at the contact area prevails. In accordance with preliminary analyses by Johnson, it is found that Tabor’s equation, where hardness (H) ⳱ 2.7r, applies within the fully plastic regime of elastic – power-law plastic materials. The results confirm the concept of the uniqueness of the characteristic strain, ⑀r ⳱ 0.1, that is associated with the uniaxial stress, r. A contact deformation map is constructed to provide bounds for the elastic–plastic transition and the fully plastic contact regimes for a wide range of values of ys, n, and E. Finally, the development of piling-up and sinking-in at the contact area is correlated with uniaxial mechanical properties. The present correlation holds exclusively within the fully plastic contact regime and provides a tool to estimate ys and n from indentation experiments. I. INTRODUCTION
The development of indentation methodologies for the micromechanical characterization of materials requires a precise understanding of the correlation between uniaxial mechanical properties and hardness. One of such fundamental correlations was found by Tabor1 for pyramidal (Vickers) indenters. Considering indentation experiments conducted in specimens of pure copper and a mild steel which were previously subjected to different amounts of strain hardening, Tabor proposed that hardness is, to a great extent, proportional to the uniaxial stress at a plastic strain of 0.08. Namely, H ⳱ Cr ,
(1)
where H is the Vickers hardness of the material (as evaluated by the ratio between maximum applied load and projected contact area), C ⳱ 3.3, and r is the uniaxial stress corresponding to a characteristic uniaxial strain (⑀r) of 0.08. Over the years, Eq. (1) was simplified leading to the conception that hardness is proportional to the yield strength. Obviously, this simplification is inaccurate for materials exhibiting considerable strain hardening, as in the case of the metals that were originally studied by Tabor.
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J. Mater. Res., Vol. 17, No. 5, May 2002 Downloaded: 04 Sep 2014
A theoretical foundation for Tabor’s hardness equation was provided by Hill et al.2 and Lockett3 for wedge indentation and cone indentation, respectively, of rigid– perfectly plastic solids. In these slip-line analyses, yield strength was found to be proportional to hardness. More recently, Yu and Blanchard4 derived explicit solutions for the proportionality constant C in terms of the apex angle of the conical indenter. In light of the above slipline formulations, it become
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