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A Methodology for Inverse Determination of Stress-strain Curves Based on Spherical Indentation

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Abstract

Instrumented indentation testing is widely used for the mechanical characterization of materials and phases. Among important mechanical parameters such as hardness and Young’s modulus the determination of yield stress and hardening behavior of metallic materials calculated from indentation results is a particular topical subject. This paper presents a methodology which allows for the reconstruction of the stress-strain curve from a single load-displacement curve measured by a spherical indenter. The method is based on the depth-dependent strain field induced by a spherical indenter. The loading part of the curve is discretised in single tuples of indentation depth and force. Since the mean strain induced by the spherical indenter is dependent on indentation depth, every depth can be assigned to a mean uniaxial strain value. The force is then used to calculate the associated uniaxial stress. The method was exemplarily applied to the carbon steel C45 in different heat treatment conditions. It could be shown that after a calibration procedure the stress-strain curves of the carbon steel can be calculated without the requirement of assuming a mathematical description of the curve (e.g. power-law material behavior). The method and its framework can easily be expanded and adjusted in order to be used as an easy and quick method for inverse determination of material parameters.

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Authors and Affiliations

  1. Chair of Materials Technology, Ruhr-Universität Bochum, 44780, Bochum, Germany

    F. Pöhl

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  1. F. Pöhl
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Correspondence to F. Pöhl.

Appendix: Equation

Appendix: Equation

$$\begin{array}{@{}rcl@{}} \sigma_{\mathrm{y},i} = f({\Theta}_{i}, C_{i}, E) \end{array} $$
(A.1)
$$\begin{array}{@{}rcl@{}} &=& \left( a_{1} + a_{2} \left( C_{i} \frac{210 \ \text{GPa}}{E}\right) + a_{3} \left( C_{i} \frac{210 \ \text{GPa}}{E} \right)^{2} \right.\\ &&+ a_{4} \left( C_{i} \frac{210 \ \text{GPa}}{E} \right)^{3}\\ &&+\left. a_{5} \left( C_{i} \frac{210 \ \text{GPa}}{E} \right)^{4} +a_{6} \left( C_{i} \frac{210 \ \text{GPa}}{E} \right)^{5} \right) E \end{array} $$
Table 6 Half-apex angle-dependent coefficients a1-a6 of equation (A.1)
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Pöhl, F. A Methodology for Inverse Determination of Stress-strain Curves Based on Spherical Indentation. Exp Tech 42, 343–353 (2018). https://doi.org/10.1007/s40799-018-0238-1

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  • DOI: https://doi.org/10.1007/s40799-018-0238-1

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