Determination of plastic properties of metals by instrumented indentation using a stochastic optimization algorithm
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P-O. Bouchard Mines ParisTech, CEMEF, Centre de Mise en Forme des Mate´riaux, UMR CNRS 7635, 06904 Sophia-Antipolis Cedex, France
R. Ghisleni and J. Michlera) Laboratory for Mechanics of Materials and Nanostructures, EMPA—Swiss Federal Laboratories for Materials Testing and Research, 3602 Thun, Switzerland (Received 31 July 2008; accepted 28 October 2008)
A novel optimization approach, capable of extracting the mechanical properties of an elasto-plastic material from indentation data, is proposed. Theoretical verification is performed on two simulated configurations. The first is based on the analysis of the load–displacement data and the topography of the residual imprint of a single conical indenter. The second is based on the load–displacement data obtained from two conical indenters with different semi-angles. In both cases, a semi-analytical approach [e.g., Dao et al., Acta Mater. 49, 3899 (2001) and Bucaille et al., Acta Mater. 51, 1663 (2003)] is used to estimate Young’s modulus, yield stress, and strain hardening coefficient from the load–displacement data. An inverse finite element model, based on a commercial solver and a newly developed optimization algorithm based on a robust stochastic methodology, uses these approximate values as starting values to identify parameters with high accuracy. Both configurations use multiple data sets to extract the elastic-plastic material properties; this allows the mechanical properties of materials to be determined in a robust way.
I. INTRODUCTION
In recent years, instrumented indentation has developed into an effective, non-destructive method for evaluating the mechanical properties of metallic materials at the nanoscale.1–3 The standard test for determining the mechanical properties is the tensile test; however, this requires more complex testing equipment and the preparation of tensile test samples. With indentation, the Young’s modulus is estimated by analyzing the slope of the unloading part of the load (L) and penetration depth (h) curve (hereafter called L – h curve) and the indenter contact area.4,5 The determination of the plastic properties from the loading part of the L – h curve of metals was first obtained in the form of empirical relationships, which directly correlated hardness with yield stress and tensile strength.5,6 The ideal conversion of the L – h data to the stress–strain data (hereafter called s – e curve) is more challenging since there is not a direct relationship between the L – h curve and the s – e curve.7,8 This problem became the goal of several scientists, who recently a)
Address all correspondence to this author. e-mail: [email protected] DOI: 10.1557/JMR.2009.0118
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J. Mater. Res., Vol. 24, No. 3, Mar 2008 Downloaded: 31 Aug 2014
advanced different models that estimate s – e curves from L – h curves.8–14 The investigation of new and improved models allowing the determination of the plastic properties of metals is still widely studied today.15–20 Reviews of the existing models have been publish
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