Evaluation of correlations between principal axes in uniaxial tensile tests of aluminum based on Mohr’s strain circle

–

Evaluation of correlations between principal axes in uniaxial tensile tests of aluminum based on Mohr’s strain circle

IIZUKA Takashi

Abstract. Anisotropic elasticity is expected to contribute significantly to material deformation and should be considered in nature. Therefore, in this study, the correlations between elastic and plastic strains are investigated, with emphasis on the principal axes. In an experiment, strains are measured in eight directions during tensile tests, and Mohr’s circles are derived for elastic and plastic strains. The planar anisotropy of elasticity and plasticity for some mechanical properties is confirmed, and the angle deviations between the principal axes of stress and strain are compared for elasticity and plasticity. In the case of aluminum, for both elasticity and plasticity, the planar anisotropy of its mechanical properties indicates four-fold symmetry, and the principal axes of elastic and plastic strains are identical, with some angle deviations from the principal axes of stress.

Keywords
Anisotropic Metals, Principal Axes, The Associated Flow Rule, Mohr’S Strain Circle

Published online 4/24/2024, 10 pages
Copyright © 2024 by the author(s)
Published under license by Materials Research Forum LLC., Millersville PA, USA

Citation: IIZUKA Takashi, Evaluation of correlations between principal axes in uniaxial tensile tests of aluminum based on Mohr’s strain circle, Materials Research Proceedings, Vol. 41, pp 1017-1026, 2024

DOI: https://doi.org/10.21741/9781644903131-112

The article was published as article 112 of the book Material Forming

Content from this work may be used under the terms of the Creative Commons Attribution 3.0 license. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.

References
[1] J.F.W. Bishop, R. Hill, A theory of the Plastic Distortion of a Polycrystalline Aggregate under Combined Stresses, Phil. Mag. 42 (1951) 414-427. https://doi.org/10.1080/14786445108561065
[2] W.F. Hosfold, A Generalized Isotropic Yield Criterion, J. Appl. Mech. 39 (1972) 607-609. https://doi.org/10.1115/1.3422732
Reference to a chapter in an edited book:
[3] R. Hill, A theory of the yielding and plastic flow of Anisotropic Metals, Proc. Royal Soc. London A193 (1948) 281-297. https://doi.org/10.1098/rspa.1948.0045
[4] F. Barlat, D.J. Lege, J.C. Brem: A Six-component Yield Function for Anisotropic Materials, Int. J. Plast. 7 (1991) 693-712. https://doi.org/10.1016/0749-6419(91)90052-Z
[5] F. Barlat, R.C. Becker, Y. Hayashida, Y. Maeda, M. Yanagawa, K. Chung, J.C. Brem, D.J. Lege, K. Marsui, S.J. Murtha, S. Hattori, Yielding Description for Solution Strengthened Aluminum Alloys, Int. J. Plast. 13 (1997) 385-401. https://doi.org/10.1016/S0749-6419(97)80005-8
[6] F. Barlat, Y. Maeda, K. Chung, M. Yanagawa, J.C. Brem, Y. Hayashida, D.J. Lege, K. Matsui, S.J. Murtha, S. Hattori, R.C. Becker, S. Makosey, Yield Function Development for Aluminum Alloy Sheets, J. Mech. Phys. Solids 45 (1997) 1727-1763. https://doi.org/10.1016/S0022-5096(97)00034-3
[7] F. Barlat, J.C. Brem, J.W. Yoon, K. Chung, R.E. Dick, D.J. Lege, F. Pourboghrat, S.-H. Choi, E. Chu, Plane Stress Yield Function for Aluminum Alloy Sheets -Part I:Theory, Int. J. Plast. 19 (2003) 1297-1319. https://doi.org/10.1016/S0749-6419(02)00019-0
[8] J.F.W. Bishop, R. Hill, A Theoretical Derivation of the Plastic Properties of a Polycrystalline Face-centred Metal, Phil. Mag. 42 (1951) 1298-1397. https://doi.org/10.1080/14786444108561385
[9] J.W. Hutchinson, Plastic Stress-strain Relations of F.C.C Polycrystalline Metals Hardening According to Taylor’s Rule, J. Mech. Phy. Solids 12 (1963) 11-24. https://doi.org/10.1016/0022-5096(64)90003-1
[10] R.W. Logan, W.F. Hosford, Upper-bound Anisotropic Yield Locus Calculations Assuming <111>-pencil Glide, Int. J. Mech. Sci. 22 (1980) 419-430. https://doi.org/10.1016/0020-7403(80)90011-9
[11] R.J. Asaro, Micromechanics of Crystals and Polycrystals, Adv. Appl. Mech. 23 (1983) 1-115. https://doi.org/10.1016/S0065-2156(08)70242-4