The scale factor effect on Young’s modulus of steel specimens determined by tensile tests

The modulus elasticity (or Young’s modulus) is considered to be a rather stable physical and mechanical characteristic of metallic materials being a weak function of the chemical composition and structure. However, the temperature and anisotropy can be referred as the main factors affecting the Young modulus. Scanty data on the scale factor effect on Young’s modulus are sometime even contradictory. We present the results of studying the impact of the scale factor on Young’s modulus of steel 45 determined by the tension of cylindrical tensile specimens with different initial diameters on an Instron 8801 machine with a movable traverse speed of 0.1 mm/min at room temperature. An extensometer and a digital image correlation (DIC) method were used to measure elastic deformations. Both methods showed fairly close results during tensile testing of specimens with equal diameters. DIC method made it possible to measure elastic deformations on small-size specimens on which it was impossible to fix the extensometer. A decrease in the Young modulus with an increase in the specimen diameter has been revealed. Graphical dependences of the Young modulus on the specimen diameter and cross-sectional area have been obtained. Possible reasons for the decrease in the Young modulus under the influence of the scale factor have been indicated. A decrease in the specific surface area and specific surface energy, an increase in the deformable volume, and a decrease in the strain rate at a constant movable traverse speed are among the main reasons. The decrease in Young’s modulus under the influence of the scale factor must be taken into account in strength calculations and in assessing the residual life of large-scale parts and structures with relatively large cross sections and wall thicknesses.

1. Husain A., La P., Hongzheng Y., Jie S. Influence of temperature on mechanical properties of nanocrystalline 316L stainless steel investigated via molecular dynamics simulations / Materials. 2020. Vol. 13. N 12. P. 2803. DOI: 10.3390/ma13122803

2. Wang W., Liu B., Kodur V. Effect of temperature on strength and elastic modulus of high-strength steel / Journal of Materials in Civil Engineering. 2013. Vol. 25. N 2. P. 174 – 182. DOI: 10.1061/(ASCE)MT.1943-5533.0000600

3. Tromans D. Elastic anisotropy of HCP metal crystals and polycrystals / Int. J. Recent Res. Appl. Stud. 2011. Vol. 6. N 4. P. 462 – 483.

4. Gol’dshtein R. V., Mokryakov V. V., Chentsov A. V., et al. Anisotropy of the effective elastic modulus of a steel plate with a lattice of circular holes / Russian Metallurgy (Metally). 2017. P. 838 – 841. DOI: 10.1134/S0036029517100068

5. Rozanski A., Rajczakowska M., Serwicki A. The influence of microstructure geometry on the scale effect in mechanical behaviour of heterogeneous materials / J. Composite Mater. 2017. Vol. 24. N 4. P. 557 – 571. DOI: 10.1515/secm-2015-0007

6. Petrova Y., Perez-Juste J., Zhang Z., et al. Crystal structure dependence of the elastic constants of gold nanorods / J. Mater. Chem. 2006. Vol. 16. P. 3957 – 3963. DOI: 10.1039/B607364F

7. Vogl L. M., Schweizer P., Richter G., Spiecker E. Effect of size and shape on the elastic modulus of metal nanowires / MRS Advances. 2021. Vol. 6. P. 665 – 673. DOI: 10.1557/s43580-021-00103–3

8. Sutton M. A., Orteu J. J., Schreier H. Image correlation for shape, motion and deformation measurements: basic concepts, theory and applications. — NY: Springer New York, 2009. — 322 p.

9. Griffith A. A. The phenomena of rupture and flow in solids / Proc. Roy. Soc. Lond. 1921. Vol. 221. P. 163. DOI: 10.1098/rsta.1921.0006

10. Aleksandrov A. P., Zhurkov S. N. Brittle fracture phenomenon. — Moscow: Gos. tekhn.-teor. izd., 1933. — 52 p. [in Russian].

11. Shevandin E. M., Manevich Sh. S. Scale effect in brittle fracture of steel / Zh. Tekhn. Fiz. 1946. Vol. XVI. P. 1223 – 1234 [in Russian].

12. Chechulin B. B. The scale factor and the statistical nature of the strength of solids. — Moscow: Metallurgizdat, 1963. — 120 p. [in Russian].

13. Matyunin V. M. Indentation in diagnostics of mechanical properties of materials. — Moscow: Izd. dom MÉI. 2015. — 288 p. [in Russian].

14. Atkinson M. J. Phenomenology of the size effect in hardness tests with a blunt pyramidal indenter / J. Mater. Sci. 1998. N 33. P. 2937 – 2947.

15. Fedosov S. A., Peshek L. Determination of mechanical properties of materials by microindentation. — Moscow: MGU im. M. V. Lomonosova, 2004. — 98 p. [in Russian].

16. Golovin Yu. I. Nanoindentation and its possibilities. — Moscow: Mashinostroenie, 2009. — 312 p. [in Russian].

17. Matyunin V. M., Marchenkov A. Yu., Kazantsev A. G., et al. Static, dynamic and cyclic strength of metal of large hydraulic unit studs / Zavod. Lab. Diagn. Mater. 2015. Vol. 81. N 9. P. 59 – 66 [in Russian].

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