Structural Engineering and Mechanics

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An advanced criterion based on non-AFR for anisotropic sheet metals

  • Moayyedian, Farzad (Department of Mechanical Engineering, Eqbal Lahoori Institute of Higher Education (ELIHE)) ;
  • Kadkhodayan, Mehran (Department of Mechanical Engineering, Ferdowsi University of Mashhad (FUM))
  • Received : 2015.09.17
  • Accepted : 2016.01.11
  • Published : 2016.03.25
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Abstract

In the current research an advanced criterion with non-associated flow rule (non-AFR) for depicting the behavior of anisotropic sheet metals is presented to consider the strength differential effects (SDEs) for these materials. Owing to the fact that Lou et al. (2013) yield function is dependent on structure of an anisotropic material (BCC, FCC and HCP), an advanced yield function with inspiring of Yoon et al. (2014) yield function is proposed which is dependent upon anisotropic structures. Furthermore, to compute Lankford coefficients, a new pressure sensitive plastic potential function which would be dependent to anisotropic structure is presented and coupled with the proposed yield function with employing a non-AFR in a novel criterion which is called here 'dvanced criterion'. Totally eighteen experimental data are required to calibrate the criterion contained of directional tensile and compressive yield stresses for the yield function and directional Lankford coefficients for the plastic potential function. To verify the criterion, three anisotropic sheet metals with different structures are taken as case studies such as Al 2008-T4 (a BCC material), Al 2090-T3 (a FCC material) and AZ31 (a HCP material).

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References

  1. Aretz, H. (2005), "A non-quadratic plane stress yield function for orthotropic sheet metals", J. Mater. Pr. Tech., 168(1), 1-9. https://doi.org/10.1016/j.jmatprotec.2004.10.008
  2. Barlat, F., Brem, J.C., Yoon, J.W., Chung, K., Dick, R.E., Lege, D.J., Pourboghrat, F., Choi, S.H. and Chu, E. (2003), "Plane stress yield function for aluminum alloy sheets-part 1: theory", Int. J. Plast., 19(9), 1297-1319. https://doi.org/10.1016/S0749-6419(02)00019-0
  3. Hu, W. (2005), "An orthotropic criterion in a 3-D general stress state", Int. J. Plast., 21(9), 1771-1796. https://doi.org/10.1016/j.ijplas.2004.11.004
  4. Huh, H., Lou, Y., Bae, G. and Lee, C. (2010), "Accuracy analysis of anisotropic yield functions based on the root-mean square error", AIP Conference Proceeding of the 10th NUMIFORM, 1252, 739-746.
  5. Hu, W. and Wang, Z.R. (2005), Multiple-factor dependence of the yielding behavior to isotropic ductile materials", Comput. Mater. Sci., 32(1), 31-46. https://doi.org/10.1016/j.commatsci.2004.06.002
  6. Hu, W. and Wang, Z.R. (2009), "Construction of a constitutive model in calculations of pressure-dependent material", Comput. Mater. Sci., 46(4), 893-901. https://doi.org/10.1016/j.commatsci.2009.04.038
  7. Lee, M.G., Wagoner, R.H., Lee, J.K., Chung, K. and Kim, H.Y. (2008), "Constitutive modeling for anisotropic/asymmetric hardening behavior of magnesium alloy sheets", Int. J. Plast., 24(4), 545-582. https://doi.org/10.1016/j.ijplas.2007.05.004
  8. Liu, C., Huang, Y. and Stout, M.G. (1997), "On the asymmetric yield surface of plastically orthotropic materials: a phenomenological study", Acta Metallurgica, 45(6), 2397-2406.
  9. Lou, Y., Huh, H. and Yoon, J.W. (2013), "Consideration of strength differential effect in sheet metals with symmetric yield functions", Int. J. Mech. Sci., 66, 214-223. https://doi.org/10.1016/j.ijmecsci.2012.11.010
  10. Moayyedian, F. and Kadkhodayan, M. (2015), "Combination of modified Yld2000-2d and Yld2000-2d in anisotropic pressure dependent sheet metals", Latin Am. J. Solid. Struct., 12(1), 92-114. https://doi.org/10.1590/1679-78251372
  11. Moayyedian, F. and Kadkhodayan, M. (2015), "Modified Burzynski criterion with non-associated flow rule for anisotropic asymmetric metals in plane stress problems", Appl. Math. Mech., English Edition, 36(3), 303-318. https://doi.org/10.1007/s10483-015-1913-6
  12. Safaei, M., Zang, S.L., Lee, M.G. and Waele, W.D. (2013), "Evaluation of anisotropic constitutive models: Mixed anisotropic hardening and non-associated flow rule approach", Int. J. Mech. Sci., 73, 53-68. https://doi.org/10.1016/j.ijmecsci.2013.04.003
  13. Safaei, M., Lee, M.G., Zang, S.L. and Waele, W.D. (2014), "An evolutionary anisotropic model for sheet metals based on non-associated flow rule approach", Comput. Mater. Sci., 81, 15-29. https://doi.org/10.1016/j.commatsci.2013.05.035
  14. Safaei, M., Yoon, J.W. and Waele, W.D. (2014), "Study on the definition of equivalent plastic strain under non-associated flow rule for finite element formulation", Int. J. Plast., 58, 219-238. https://doi.org/10.1016/j.ijplas.2013.09.010
  15. Spitzig, W.A. and Richmond, O. (1984), "The effect of pressure on the flow stress of metals", Acta Metallurgica, 32(3), 457-463. https://doi.org/10.1016/0001-6160(84)90119-6
  16. Stoughton, T.B. and Yoon, J.W. (2004), "A pressure-sensitive yield criterion under a non-associated flow rule for sheet metal forming", Int. J. Plast., 20(4-5), 705-731. https://doi.org/10.1016/S0749-6419(03)00079-2
  17. Stoughton T.B. and Yoon, J.W. (2009), "Anisotropic hardening and non-associated flow in proportional loading of sheet metals", Int. J. Plast., 25(9), 1777-1817. https://doi.org/10.1016/j.ijplas.2009.02.003
  18. Taherizadeh, A., Green, D.E. and Yoon, J.W. (2011), "Evaluation of advanced anisotropic models with mixed hardening Evaluation of advanced anisotropic models with mixed hardening for general associated and non-associated flow metal plasticity", Int. J. Plast., 27(11), 1781-1802. https://doi.org/10.1016/j.ijplas.2011.05.001
  19. Yoon, J.W., Lou, Y., Yoon, J. and Glazoff, M.V. (2014), "Asymmetric yield function based on the stress invariants for pressure sensitive metals", Int. J. Plast., 56, 184-202. https://doi.org/10.1016/j.ijplas.2013.11.008

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