Error estimation of the physical and mechanical characteristics measurements by indentation

The active application in the practice of testing the indentation methods, in particular to measure the physical and mechanical properties of metals, polymers, biological technologies demands to development techniques for the measurement error estimation. At the same time existing traditional measurement error evaluation system, based on the using of the reference blocks, is not always suitable for use in testing and research laboratories. The aim of this work was development the technique for estimating the indirect measurements error of materials physical and mechanical characteristics that can be applied in practice and based on the existing standards. Checking of the proposed approach using the experimental values of the hardness and elastic modulus obtained during static indentation for various metals.

It is shown that since the initial information about the material is an indentation curve representing the dependence of the load versus penetration depth of the indenter into the material tested, then it is better to confirm the metrological characteristics of the indentation measuring devices using the applied force and achieved displacement, but to estimate the accuracy of determining the properties through the error of indirect measurements. The equations for calculating the hardness and modulus of elasticity are derived. It allows to determine the component value most influencing the error magnitude. The calculation of error on the base of the value of boundary of a random and non-exclusive systematic error was carrying out.

The advantage of the developed technique is the fact that the measurement of the physical and mechanical characteristics is based on the experimental data and does not require the creation of the additional metrological assurance. The proposed approach seems appropriate to extend for the determination of the measurement error of other characteristics: the yield point, the strain hardening exponent, creep, relaxation, determined by the indentation methods.

1. Argatov I. Indentation Testing of Biological Material. Springer, 2018, 376 p. doi: 10.1007/978-3-319-78533-2

2. Herrmann К. Hardness Testing: Principles and Applications, ASM International Publ., 2011, 225 p.

3. Abetkovskaia S.O., Chizhik S.A., Rudnitsky V.A., Kren A.P. Evaluation of viscoelastic properties of materials by nanoindentation. Journal of Friction and Wear, 2010, vol. 31, issue 3, рр. 180–183. doi: 10.3103/S106836661

4. Fischer-Cripps Anthony C. Nanoindentation. Springer Science and Business Media, 2004, 264 p. doi: 10.1007/978-1-4757-5943-3

5. Kren A.P., Protasenya T.A. Determination of the physic and mechanical characteristics of isotropic pyrolytic graphite by dynamic indentation method. Russian Journal of Nondestructive Testing, 2014, vol. 50, no. 7, pp. 419– 425. doi: 10.1134/S1061830914070079

6. Oliver W.C., Pharr G.M. An improved technique for determining hardness and elastic modulus using load and displacement sensing indentation experiments. Journal of materials research, 1992, vol. 7, issue 6, pp. 1564–1583. doi: 10.1557/JMR.1992.1564

7. N'Jock M.Y., Roudet F., Idriss M., Bartier O., Chicot D. Work-of-indentation coupled to contact stiffness for calculating elastic modulus by instrumented indentation. Mechanics of Materials, 2016, vol. 94, pp. 170–179. doi: 10.1016/j.mechmat.2015.12.003

8. Koster W., Franz H. Poisson's ratio for metals and alloys. Metallurgical reviews, 1961, vol. 6, pp. 1–56. doi: 10.1179/mtlr.1961.6.1.1

9. Lee H.M., Lee W.J. Poisson's ratio of pure metals and their non-metallic compounds. Scripta Metallurgica et Materialia, 1991, vol. 25, issue 4, pp. 965–968. doi: 10.1016/0956-716X(91)90258-3