Two New Non-AFR Criteria for Depicting Strength Differential Effect (SDE) in Anisotropic Sheet Metals

Journal of Solid Mechanics

مقاله 5، دوره 10، شماره 1، خرداد 2018، صفحه 67-85   

نوع مقاله: Research Paper

نویسندگان

F Moayyedian^{* 1}؛ M Kadkhodayan²

¹Department of Mechanical Engineering, Eqbal Lahoori Institute of Higher Education, Mashhad, Iran

²Department of Mechanical Engineering, Ferdowsi University of Mashhad, Mashhad, Iran

چکیده

The issue of pressure sensitivity of anisotropic sheet metals is investigated with introducing two new non-AFR criteria which are called here linear and non-Linear pressure sensitive criteria. The yield and plastic potential functions of these criteria are calibrated with directional tensile/compressive yield stresses and directional tensile Lankford coefficients, respectively. To determine unknown coefficients of yield and plastic potential functions of these criteria two error functions are presented which are minimized by Downhill Simplex Method. Three anisotropic materials are considered as case studies such as Al 2008-T4 (BCC), Al 2090-T3 (FCC) and AZ31 (HCP). It is shown that the non-Linear pressure sensitive criterion is more accurate than the linear one and other existed criteria compared to experimental results in calculating the directional mechanical properties of anisotropic sheet metals.

کلیدواژه‌ها

Linear pressure sensitive criterion؛ Non-linear pressure sensitive criterion؛ Asymmetric anisotropic sheet metals؛ Non-AFR؛ Tensile/compressive yield stresses؛ Lankford coefficients

مراجع

[1] Spitzig W.A., Richmond O., 1984, The effect of pressure on the flow stress of metals, Acta Metallurgic 32)3(: 457-463.
[2] Liu C., Huang Y., Stout M.G., 1997, On the asymmetric yield surface of plastically orthotropic materials: a phenomenological study, Acta Metallurgica 45(6): 2397-2406.
[3] Barlat F., Brem J.C., Yoon J.W., Chung K., Dick R.E., Lege D.J., Pourboghrat F., Choi S.H., Chu E., 2003, Plane stress yield function for aluminum alloy sheets-part 1: theory, International Journal of Plasticity 19: 1297-1319.
[4] Stoughton T.B., Yoon J.W., 2004,A pressure-sensitive yield criterion under a non-associated flow rule for sheet metal forming, International Journal of Plasticity 20: 705-731.
[5] Hu W., Wang Z.R., 2009,Construction of a constitutive model in calculations of pressure-dependent material, Computational Material Sciences 46: 893-901.
[6] Hu W., 2005, An orthotropic criterion in a 3-D general stress state, International Journal of Plasticity 21: 1771-1796.
[7] Aretz H., 2009, A non-quadratic plane stress yield function for orthotropic sheet metals, Journal of Materials Processing Technology 36: 246-251.
[8] Lee M.G., Wagoner R.H., Lee J.K., Chung K., H.Y. Kim, 2008,Constitutive modeling for anisotropic/asymmetric hardening behavior of magnesium alloy sheets, International Journal of Plasticity 24: 545-582.
[9] Stoughton T.B., Yoon J.W., 2009,Anisotropic hardening and non-associated flow in proportional loading of sheet metals, International Journal of Plasticity 25: 1777-1817.
[10] Hu W., Wang Z.R., 2005, Multiple-factor dependence of the yielding behavior to isotropic ductile materials, Computational Materials Science 32: 31-46.
[11] Huh H., Lou Y., Bae G., Lee C., 2010, Accuracy analysis of anisotropic yield functions based on the root-mean square error, AIP Conference Proceeding of the NUMIFORM, Pohang, Republic of Korea.
[12] Moayyedian F., Kadkhodayan M., 2013,A general solution for implicit time stepping scheme in rate-dependant plasticity, International Journal of Engineering 26(6): 641-652.
[13] Lou Y., Huh H., Yoon J.W., 2013,Consideration of strength differential effect in sheet metals with symmetric yield functions, International Journal of Mechanical Sciences 66: 214-223.
[14] SafaeiM., Lee M.G., Zang S.L., WaeleW.D., 2014, An evolutionary anisotropic model for sheet metals based on non-associated flow rule approach, Computational Materials Science 81:15-29.
[15] Yoon J.W., Lou Y., Yoon J., Glazoff M.V., 2014, Asymmetric yield function based on the stress invariants for pressure sensitive metals, International Journal of Plasticity 56: 184-202.
[16] Safaei M., Yoon J.W., Waele W.D., 2014, Study on the definition of equivalent plastic strain under non-associated flow rule for finite element formulation, International Journal of Plasticity 58: 219-238.
[17] Moayyedian F., Kadkhodayan M., 2014,A study on combination of von Mises and Tresca yield loci in non-associated viscoplasticity, International Journal of Engineering 27: 537-545.
[18] Oya T., Yanagimoto J., Ito K., Uemura G., Mori N., 2014, Material model based on non-associated flow rule with higher-order yield function for anisotropic metals, Procedia Engineering 81: 1210-1215.
[19] Moayyedian F., Kadkhodayan M., 2015,Combination of modified Yld2000-2d and Yld2000-2d in anisotropic pressure dependent sheet metals, Latin American Journal of Solids and Structures 12(1): 92-114.
[20] Moayyedian F., Kadkhodayan M., 2015, Modified Burzynski criterion with non-associated flow rule for anisotropic asymmetric metals in plane stress problems, Applied Mathematics and Mechanics 36(3): 303-318.
[21] Ghaei A., Taherizadeh A., 2015, A two-surface hardening plasticity model based on non-associated flow rule for anisotropic metals subjected to cyclic loading, International Journal of Mechanical Sciences 92: 24-34.