Orthotropic Behaviour of Magnesium AZ31 Sheet during Strain Localization

Abstract:

It is known that metallic materials are characterized by anisotropy of their mechanical properties, with this being attributed to the conditions during the manufacturing process. For sheet metals, this anisotropy occurs symmetrically to the three orthogonal axes of the rolling, transverse and normal direction. This characteristic is referred to as orthotropic behaviour and manifests itself, for example, in earing during cupping tests. Therefore, orthotropic yield criteria are highly relevant for the numerical simulation of sheet metal forming processes. The Lankford coefficient, also known as the r-value, is a good experimental measure for characterizing orthotropic ductile behaviour of sheets, and can easily aid in parameter identification for yield criteria such as the Hill approaches. In the present investigations, Lankford coefficients were determined as a function of local strain in uniaxial tensile tests through high-resolution digital image correlation. The sample direction was varied between 0°, 45° and 90° to the rolling direction and the test temperature varied from RT to 350 °C at three different strain rates (0.01-1 s^-1). By means of a novel backward analysis, the measuring range for the Lankford coefficients was positioned exactly in the necking area. An increase in temperatures showed a decrease in the initial Lankford coefficient. The results showed non-constant Lankford coefficients and commence the course of a natural exponential function depending on the local strain. Regardless of strain rate, the results revealed that the Lankford coefficients (r-values) at 150 °C, 250 °C and 350 °C approaches a steady-state of r = 1.14 with strains greater than 50 %.

• Periodical: Materials Science Forum (Volume 1016)
• Pages: 541-552
• DOI: https://doi.org/10.4028/www.scientific.net/MSF.1016.541
• Online since: January 2021
• Authors: Thorsten Henseler*, Madlen Ullmann, Ulrich Prahl
• Keywords: Anisotropy, AZ31, Hill, Lankford, Localization, Magnesium, Orthotropic, Sheet, Yield Loci

References

[1] H. Altenbach, Werkstoffmechanik: Einführung mit 14 Tabellen, Dt. Verl. für Grundstoff-industrie, Wiley-VCH (2001) Leipzig, Stuttgart.

[2] Kelley E.W., Hosford W.F., Deformation characteristics of textured magnesium, Transactions of The Metallurgical Society of the American Institute of Mining (1968) 654–661.

[3] T. Hama, H. Takuda, Crystal plasticity finite-element simulation of work-hardening behavior in a magnesium alloy sheet under biaxial tension, Computational Materials Science 51 (2012) 156–164.

DOI: 10.1016/j.commatsci.2011.07.026

[4] N. Chandola, R.A. Lebensohn, O. Cazacu, B. Revil-Baudard, R.K. Mishra, F. Barlat, Combined effects of anisotropy and tension–compression asymmetry on the torsional response of AZ31 Mg, International Journal of Solids and Structures 58 (2015) 190–200.

DOI: 10.1016/j.ijsolstr.2015.01.001

[5] A.S. Khan, A. Pandey, T. Gnäupel-Herold, R.K. Mishra, Mechanical response and texture evolution of AZ31 alloy at large strains for different strain rates and temperatures, International Journal of Plasticity 27 (2011) 688–706.

DOI: 10.1016/j.ijplas.2010.08.009

[6] M.N. Mekonen, D. Steglich, J. Bohlen, D. Letzig, J. Mosler, Mechanical characterization and constitutive modeling of Mg alloy sheets, Materials Science and Engineering A 540 (2012) 174–186.

DOI: 10.1016/j.msea.2012.01.122

[7] M.N. Mekonen, D. Steglich, J. Bohlen, L. Stutz, D. Letzig, J. Mosler, Experimental and numerical investigation of Mg alloy sheet formability, Materials Science and Engineering A 586 (2013) 204–214.

DOI: 10.1016/j.msea.2013.07.088

[8] D. Banabic, H.-J. Bunge, K. Pöhlandt, A.E. Tekkaya, Formability of Metallic Materials: Plastic Anisotropy, Formability Testing, Forming Limits, Springer, Berlin, Heidelberg, (2000).

DOI: 10.1007/978-3-662-04013-3

[9] M.N. Mekonen, J. Bohlen, D. Steglich, D. Letzig, Mechanical characterisation of Mg alloys and model parameter identification for sheet forming simulations, International Journal of Material Forming 2 (2009) 53–56.

DOI: 10.1007/s12289-009-0437-5

[10] Y. Chino, H. Iwasaki, M. Mabuchi, Stretch formability of AZ31 Mg alloy sheets at different testing temperatures, Materials Science and Engineering A 466 (2007) 90–95.

DOI: 10.1016/j.msea.2007.02.027

[11] H. Wang, B. Raeisinia, P.D. Wu, S.R. Agnew, C.N. Tomé, Evaluation of self-consistent polycrystal plasticity models for magnesium alloy AZ31B sheet, International Journal of Solids and Structures 47 (2010) 2905–2917.

DOI: 10.1016/j.ijsolstr.2010.06.016

[12] R. Kawalla, M. Oswald, C. Schmidt, M. Ullmann, H.-P. Vogt, N.D. Cuong, Development of a strip-rolling technology for Mg alloys based on the twin-roll-casting process, The Minerals, Metals & Materials Society (2008) 177–182.

DOI: 10.1016/j.matpr.2015.05.013

[13] R. Kawalla, M. Ullmann, M. Oswald, C. Schmidt, Properties of strips and sheets of magnesium alloy produced by casting-rolling technology, International Conference on Magnesium Alloys their Applications 7 (2006).

DOI: 10.4028/www.scientific.net/msf.690.21

[14] T. Henseler, M. Ullmann, R. Kawalla, F. Berge, Influence of the Sheet Manufacturing Process on the Forming Limit Behaviour of Twin-Roll Cast, Rolled and Heat-Treated AZ31, Key Engineering Materials 746 (2017) 154–160.

DOI: 10.4028/www.scientific.net/kem.746.154

[15] M. Ullmann, F. Berge, K. Neh, R. Kawalla, Development of a rolling technology for twin-roll cast magnesium strip, Metalurgija 4 (2015) 711–714.

DOI: 10.1016/j.matpr.2015.05.013

[16] M. Graf, T. Henseler, M. Ullmann, R. Kawalla, U. Prahl, B. Awiszus, Study on determination of flow behaviour of 6060-aluminium and AZ31-magnesium thin sheet by means of stacked compression test, IOP Conf. Ser.: Mater. Sci. Eng. 480 (2019) 12023.

DOI: 10.1088/1757-899x/480/1/012023

[17] R. Kawalla, M. Ullmann, T. Henseler, U. Prahl, Magnesium Twin-Roll Casting Technology for Flat and Long Products - State of the Art and Future, Materials Science Forum 941 (2018) 1431–1436.

DOI: 10.4028/www.scientific.net/msf.941.1431

[18] E. Doege, B.A. Behrens, Handbuch Umformtechnik: Grundlagen, Technologien, Maschinen, second. Aufl., Springer-Verlag, Heidelberg, Dordrecht, London, New York, (2010).

DOI: 10.1007/978-3-642-04249-2

[19] K. Siegert, Blechumformung, Springer-Verlag, Berlin, Heidelberg, (2015).

[20] T. Naka, T. Uemori, R. Hino, M. Kohzu, K. Higashi, F. Yoshida, Effects of strain rate, temperature and sheet thickness on yield locus of AZ31 magnesium alloy sheet, Journal of Materials Processing Technology 201 (2008) 395–400.

DOI: 10.1016/j.jmatprotec.2007.11.189

[21] L. Wang, Q. Qiao, Y. Liu, X. Song, Formability of AZ31 Mg alloy sheets within medium temperatures, Journal of Magnesium and Alloys 1 (2013) 312–317.

DOI: 10.1016/j.jma.2014.01.001

[22] G. Gottstein, T. Al-Samman, Texture Development in Pure Mg and Mg Alloy AZ31, Materials Science Forum 495-497 (2005) 623–632.

DOI: 10.4028/www.scientific.net/msf.495-497.623

[23] T. Mayama, M. Noda, R. Chiba, M. Kuroda, Crystal plasticity analysis of texture development in magnesium alloy during extrusion, International Journal of Plasticity 27 (2011) 1916–(1935).

DOI: 10.1016/j.ijplas.2011.02.007

[24] T. Hama, Y. Tanaka, M. Uratani, H. Takuda, Deformation behavior upon two-step loading in a magnesium alloy sheet, International Journal of Plasticity (2016).

DOI: 10.1016/j.ijplas.2016.03.009

[25] S.-H. Choi, D.H. Kim, H.W. Lee, B.S. Seong, K. Piao, R. Wagoner, Evolution of the deformation texture and yield locus shape in an AZ31 Mg alloy sheet under uniaxial loading, Materials Science and Engineering A 526 (2009) 38–49.

DOI: 10.1016/j.msea.2009.06.060

[26] D. Banabic, W. Hußnätter, Modeling the material behavior of magnesium alloy AZ31 using different yield criteria, The International Journal of Advanced Manufacturing Technology 44 (2009) 969–976.

DOI: 10.1007/s00170-008-1900-z

[27] J. Blaber, B. Adair, A. Antoniou, Ncorr: Open-Source 2D Digital Image Correlation Matlab Software, Experimental Mechanics (2015).

DOI: 10.1007/s11340-015-0009-1