The role of crystalline anisotropy in mechanical property extractions through Berkovich indentation
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S.A. Rodrı´guez Surface Phenomena Laboratory, Department of Mechanical Engineering. University of Sa˜o Paulo, 05508-90 Sao Paulo, Brazil (Received 31 July 2008; accepted 8 December 2008)
This work uses crystal plasticity finite element simulations to elucidate the role of elastoplastic anisotropy in instrumented indentation P–hs curve measurements in face-centered cubic (fcc) crystals. It is shown that although the experimental fluctuations in the loading stage of the P–hs curves can be attributed to anisotropy, the variability in the unloading stage of the experiments is much greater than that resulting from anisotropy alone. Moreover, it is found that the conventional procedure used to evaluate the contact variables ruling the unloading P–hs curve introduces an uncertainty that approximates to the more fundamental influence of anisotropy. In view of these results, a robust procedure is proposed that uses contact area measurements in addition to the P–hs curves to extract homogenized J2-plasticity-equivalent mechanical properties from single crystals. I. INTRODUCTION
An important line of work in the analysis of indentation experiments concerns the development of methodologies to extract the uniaxial stress-strain curve of the indented material. Because micro- and nanoindentation tests are routinely used at small (microstructural) length scales, these methodologies offer the potential to evaluate the mechanical properties of individual grains and microstructural units of material. Conventionally, mechanical property extractions have been performed by recourse to hardness measurements and assessments of the amount of material pileup and sinking-in developing at the contact boundary. In more recent years, the comprehension of in situ measurements of applied load (P)-penetration depth (hs) curves obtained through advanced instrumented indentation techniques has been the focus of systematic analyses. These investigations have resorted to elastic solutions for the unloading stage of the experiment along with presumptions about the amount of material pileup and sinking-in to find hardness p and Young’s modulus E (e.g., Refs. 1 and 2). Alternatively, extensive finite element simulations for polycrystalline aggregates performed through the J2-flow plasticity theory (assuming isotropic elasticity and isotropic hardening with the Von Mises yield surface), in conjunction with dimensional analyses and contact mechanics formulations, have been used to gain a profound understanding of the a)
Address all correspondence to this author. e-mail: [email protected] DOI: 10.1557/JMR.2009.0140 J. Mater. Res., Vol. 24, No. 3, Mar 2009
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relationships between relevant contact variables and mechanical properties (e.g., Refs. 3–16). These works have led to the development of self-consistent methodologies, where the entire P–hs curve is used to extract yield strength sys and hardening coefficient n in addition to hardness p and Young’s modulus E. The experimental fluctuations in the
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