Advances in anisotropy of plastic behaviour and formability of sheet metals
Source abstract
Abstract
This paper reviews the most recent models for description of the anisotropic plastic behavior and formability of sheet metals. After a brief review of classic isotropic yield functions, recent advanced anisotropic criteria for polycrystalline materials of various crystal structures and their applications to cup drawing are presented. Next, the discussion focuses on novel formulations of anisotropic hardening. A brief review of the experimental methods used for characterizing and modeling the anisotropic plastic behavior of metallic sheets and tubes under biaxial loading is presented. The experimental methods and theoretical models used for measuring and predicting the limit strains, development of new tests for determining the Forming Limit Curves (FLC), as well as on studying the influence of various material or process parameters on the limit strains are presented.
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Research context
OpenAlex topics: Metal Forming Simulation Techniques · Metallurgy and Material Forming · High-Velocity Impact and Material Behavior
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References (100+)
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1. Morestin F, Boivin M (1996) On the necessity of taking into account the variation in the young modulus with plastic strain in elastic-plastic software. Nucl Eng Des 162:107–11610.1016/0029-5493(95)01123-4 ↗
2. Wagoner RH, Lim H, Lee M-G (2013) Advanced issue in springback. Int J Plast 45:3–2010.1016/j.ijplas.2012.08.006 ↗
3. Sun L, Wagoner RH (2011) Complex unloading behavior: nature of the deformation and its consistent constitutive representation. Int J Plast 27:1126–114410.1016/j.ijplas.2010.12.003 ↗
4. Yoshida F, Amaishi T (2020) Model for description of nonlinear unloading-reloading stress-strain response with special reference to plastic-strain dependent chord modulus. Int J Plast 130:10270810.1016/j.ijplas.2020.102708 ↗
5. Chaboche JL (1986) Time-independent constitutive theories for cyclic plasticity. Int J Plast 2:149–18810.1016/0749-6419(86)90010-0 ↗
6. Yoshida F, Uemori T (2002) A model of large-strain cyclic plasticity describing the Bauschinger effect and workhardening stagnation. Int J Plast 18:661–68610.1016/S0749-6419(01)00050-X ↗
7. Yoshida F, Uemori T (2003) A model of large-strain cyclic plasticity and its application to springback simulation. Int J Mech Sci 45:1687–170210.1016/j.ijmecsci.2003.10.013 ↗
8. Barlat F (1987) Crystallographic texture, anisotropic yield surfaces and forming limits of sheet metals. Mater Sci Eng 91:55–7210.1016/0025-5416(87)90283-7 ↗
9. Maeda T, Noma N, Kuwabara T, Barlat F, Korkolis YP (2018) Measurement of the strength differential effect of DP980 steel sheet and experimental validation using pure bending test. J Mater Process Technol 256:247–25310.1016/j.jmatprotec.2018.02.009 ↗
10. Steglich D, Tian X, Bohlen J, Kuwabara T (2014) Mechanical testing of thin sheet magnesium alloys in biaxial tension and uniaxial compression. Exp Mech 54:1247–125810.1007/s11340-014-9892-0 ↗
11. Aretz H, Keller S (2011) On the non-balanced biaxial stress state in bulge-testing. Proc. 10th Int Conf Technol plasticity, steel research international, Special Edition: 738–743
12. Kuwabara T, Van Bael A, Iizuka E (2002) Measurement and analysis of yield locus and work hardening characteristics of steel sheets with different r-values. Acta Mater 50:3717–372910.1016/S1359-6454(02)00184-2 ↗
13. Nagano C, Kuwabara T, Shimada Y (2018) Kawamura R, (2018) measurement of differential hardening under biaxial stress of pure titanium sheet. IOP Conf Ser Mater Sci Eng 418:01209010.1088/1757-899X/418/1/012090 ↗
14. Hippke H, Hirsiger S, Berisha B, Hora P (2020) Optimized and validated prediction of plastic yielding supported by cruciform experiments and crystal plasticity. Int J Mater Form. https://doi.org/10.1007/s12289-020-01569-610.1007/s12289-020-01569-6 ↗
15. Suh YS, Saunders FI, Wagoner RH (1996) Anisotropic yield functions with plastic-strain- induced anisotropy. Int J Plast 12:417–43810.1016/S0749-6419(96)00014-9 ↗
16. Kuwabara T, Mori T, Asano M, Hakoyama T, Barlat F (2017) Material modeling of 6016-O and 6016-T4 aluminum alloy sheets and application to hole expansion forming simulation. Int J Plast 93:164–18610.1016/j.ijplas.2016.10.002 ↗
17. ISO 16808 (2014) Metallic materials −Sheet and strip − Determination of biaxial stress-strain curve by means of bulge test with optical measuring systems
18. ISO 16842 (2014) Metallic materials −Sheet and strip −Biaxial tensile testing method using a cruciform test piece
19. Rusinek A, Klepaczko JR (2001) Shear testing of a sheet steel at wide range of strain rates and a constitutive relation with strain-rate and temperature dependence of the flow stress. Int J Plast 17:87–11510.1016/S0749-6419(00)00020-6 ↗
20. Bouvier S, Haddadi H, Levee P, Teodosiu C (2006) Simple shear tests: experimental techniques and characterization of the plastic anisotropy of rolled sheets at large strains. J Mater Process Technol 172:96–10310.1016/j.jmatprotec.2005.09.003 ↗
21. Rauch EF (2009) Plastic behavior of metals at large strains: experimental studies involving simple shear. J Eng Mater Technol 131:01110710.1115/1.3030942 ↗
22. An YG, Vegter H, Elliott L (2004) A novel and simple method for the measurement of plane strain work hardening. J Mater Process Technol 155–156:1616–162210.1016/j.jmatprotec.2004.04.344 ↗
23. Hu JJ, Chen GW, Liu YC, Hsu SS (2014) Influence of specimen geometry on the estimation of the planar biaxial mechanical properties of cruciform specimens. Exp Mech 54:615–63110.1007/s11340-013-9826-2 ↗
24. Nasdala L, Husni AH (2020) Determination of yield surfaces in accordance with ISO 16842 using an optimized cruciform test specimen. Exp Mech. https://doi.org/10.1007/s11340-020-00601-910.1007/s11340-020-00601-9 ↗
25. Pierron F, Grédiac M (2012) The virtual fields method: extracting constitutive mechanical parameters from full-field deformation measurements. Springer, New-York10.1007/978-1-4614-1824-5 ↗
26. Rossi M, Pierron F (2012) Identification of plastic constitutive parameters at large deformations from three dimensional displacement fields. Comput Mech 49:53–7110.1007/s00466-011-0627-0 ↗
27. Coppieters S, Kuwabara T (2014) Identification of post-necking hardening phenomena in ductile sheet metal. Exp Mech 54:1355–137110.1007/s11340-014-9900-4 ↗
28. Marek A, Davis FM, Rossi M, Pierron F (2019) Extension of the sensitivity-based virtual fields to large deformation anisotropic plasticity. Int J Mater Form 12:457–47610.1007/s12289-018-1428-1 ↗
29. Gaber C, Jocham D, Weiss HA, Böttcher O, Volk W (2017) Evaluation of non-linear strain paths using generalized forming limit concept and a modification of the time dependent evaluation method. Int J Mat Form 10:345–35110.1007/s12289-016-1283-x ↗
30. Volk W, Hoffmann H, Suh J, Kim J (2012) Failure prediction for nonlinear strain paths in sheet metal forming. CIRP Ann Manuf Technol 61:259–26210.1016/j.cirp.2012.03.111 ↗
31. Stoughton TB, Yoon JW (2012) Path independent forming limits in strain and stress spaces. Int J Solids Struct 49:3616–362510.1016/j.ijsolstr.2012.08.004 ↗
32. Stoughton TB, Yoon JW (2014) Stress-based forming limit curves. In: Hashmi MSJ (ed) Comprehensive Materials Processing (vol 1), Elsevier, Amsterdam, pp. 71–8410.1016/B978-0-08-096532-1.00104-7 ↗
33. ISO 12004-1; 12004–2 (2008) Metallic materials-sheet and strip-Determination of the Forming Limit Curves. Part 1: Measurement and application of forming-limit diagrams in the press shop Part 2: Determination of forming-limit curves in the laboratory
34. Hotz W, Merklein M, Kuppert A, Friebe H, Klein M (2013) Time dependent FLC determination – comparison of different algorithms to detect the onset of unstable necking before fracture. Key Eng Mater 549:397–40410.4028/www.scientific.net/KEM.549.397 ↗
35. Merklein M, Biasutti M (2013) Development of a biaxial tensile machine for characterization of sheet metals. J Mater Process Technol 213:939–94610.1016/j.jmatprotec.2012.12.005 ↗
36. Volk W, Hora P (2011) New algorithm for a robust user-independent evaluation of beginning instability for the experimental FLC determination. Int J Mat Form 4:339–34610.1007/s12289-010-1012-9 ↗
37. Martínez-Donaire A, Garcia-Lomas F, Vallellano C (2014) New approaches to detect the onset of localised necking in sheets under through-thickness strain gradients. Mat Des 57:135–14510.1016/j.matdes.2014.01.012 ↗
38. Wang K, Carsley JE, He B, Li J, Zhang L (2014) Measuring forming limit strains with digital image correlation analysis. J Mater Process Technol 214:1120–113010.1016/j.jmatprotec.2014.01.001 ↗
39. Dicecco S, Butcher C, Worswick M, Boettcher E, Chu F, Shi C (2016) Determination of forming limit diagrams of AA6013-T6 aluminum alloy sheet using a time and position dependent localized necking criterion. Mater Sci Eng 159:012009
40. Vysochinskiy D, Coudert T, Hopperstad OS, Lademo OG, Reyes A (2016) Experimental detection of forming limit strains on samples with multiple local necks. J Mater Process Technol 227:216–22610.1016/j.jmatprotec.2015.08.019 ↗
41. Banabic D, Lazarescu L, Paraianu L, Ciobanu I, Nicodim I, Comsa DS (2013) Development of a new procedure for the experimental determination of the forming limit curves. CIRP Ann Manuf Technol 62:255–25810.1016/j.cirp.2013.03.051 ↗
42. Leotoing L, Guines D, Zidane I, Ragneau E (2013) Cruciform shape benefits for experimental and numerical evaluation of sheet metal formability. J Mater Process Technol 213:856–86310.1016/j.jmatprotec.2012.12.013 ↗
43. Chu X, Leotoing L, Guines D, Ragneau E (2014) Temperature and strain rate influence on AA5086 forming limit curves: experimental results and discussion on the validity of the M-K model. Int J Mech Sci 78:27–3410.1016/j.ijmecsci.2013.11.002 ↗
44. Gao H, El Fakir O, Wang L, Politis DJ, Li Z (2017) Forming limit prediction for hot stamping processes featuring non-isothermal and complex loading conditions. Int J Mech Sci 131–132:792–81010.1016/j.ijmecsci.2017.07.043 ↗
45. Wang N, Ilinich A, Chen M, Luckey G, D’Amours G (2019) A comparison study on forming limit prediction methods for hot stamping of 7075 aluminum sheet. Int J Mech Sci 151:444–46010.1016/j.ijmecsci.2018.12.002 ↗
46. Nagra JS, Brahme A, Mishra R, Lebensohn RA, Inal K (2018) An efficient full-field crystal plasticity-based M–K framework to study the effect of 3D microstructural features on the formability of polycrystalline materials. Model Simul Mater Sci Eng 26:07500210.1088/1361-651X/aadc20 ↗
47. Schwindt C, Schlosser F, Bertinetti MA, Stout M, Signorelli JW (2015) Experimental and viscoplastic self-consistent evaluation of forming limit diagrams for anisotropic sheet metals: an efficient and robust implementation of the M–K model. Int J Plast 73:62–9910.1016/j.ijplas.2015.01.005 ↗
48. Signorelli J W, Bertinetti MA (2012) Self-consistent homogenization methods for predicting forming limits of sheet metal in: metal forming—process, Tools, Design, InTech, London, pp. 175–210
49. Kami A, Mollaei Dariani B, Sadough Vanini A, Comsa DS, Banabic D (2014) Prediction of the forming limit curves using GTN damage model. Rom J Tech Sciences – App Mech 59:253–264
50. Assempour A, Nejadkhaki HK, Hashemi R (2010) Forming limit diagrams with the existence of through-thickness normal stress. Comput Mater Sci 48:504–54810.1016/j.commatsci.2010.02.013 ↗
51. Erfanian F, Hashemi R (2018) A comparative study of the extended forming limit diagrams considering strain path, through-thickness normal and shear stress. Int J Mech Sci 148:316–32610.1016/j.ijmecsci.2018.09.005 ↗
52. Hashemi R, Abrinia K (2014) Analysis of the extended stress-based forming limit curve considering the effects of strain path and through-thickness normal stress. Mat Des 54:670–67710.1016/j.matdes.2013.08.023 ↗
53. Ma B, Diao K, Wu X, Li X, Wan M, Cai Z (2016) The effect of the through-thickness normal stress on sheet formability. J Manuf Process 21:134–14010.1016/j.jmapro.2015.12.006 ↗
54. Zhang F, Chen J, Chen J, Zhu X (2014) Forming limit model evaluation for anisotropic sheet metals under through-thickness normal stress. Int J Mech Sci 89:40–4610.1016/j.ijmecsci.2014.08.016 ↗
55. Bagherzadeh S, Mirnia MJ, Mollaei DB (2015) Numerical and experimental investigations of hydro-mechanical deep drawing process of laminated aluminum/steel sheets. J Manuf Process 18:131–14010.1016/j.jmapro.2015.03.004 ↗
56. Gorji M, Berisha B, Manopulo N, Hora P (2016) Effect of through thickness strain distribution on shear fracture hazard and its mitigation by using multilayer aluminum sheets. J Mater Process Technol 232:19–3310.1016/j.jmatprotec.2016.01.014 ↗
57. Jalali Aghchai A, Shakeri M, Mollaei Dariani B (2013) Influences of material properties of components on formability of two-layer metallic sheets. Int J Adv Manuf Technol 66:809–82310.1007/s00170-012-4368-9 ↗
58. Kami A, Mollaei Dariani B, Comsa DS, Banabic D, Sadough Vanini A, Liewald M (2017) An experimental study on the formability of a vibration damping sandwich sheet (Bondal). Proc. Rom Acad 18A:281–290
59. Kim D, Kim H, Kim JH, Lee MG, Kim KJ, Barlat F, Lee Y, Chung K (2015) Modeling of forming limit for multilayer sheets based on strain-rate potentials. Int J Plast 75:63–9910.1016/j.ijplas.2015.05.016 ↗
60. Liu J, Liu W, Xue W (2013) Forming limit diagram prediction of AA5052/polyethylene/AA5052 sandwich sheets. Mater Des 46:112–12010.1016/j.matdes.2012.09.057 ↗
61. Parsa MH, Ettehad M, Matin PH, Al Ahkami SN (2010) Experimental and numerical determination of limiting drawing ratio of Al3105-polypropylene-Al3105 sandwich sheets. J Eng Mater Technol 132:3100410.1115/1.4001264 ↗
62. Hora P, Tong L, Berisha B (2013) Modified maximum force criterion, a model for the theoretical prediction of forming limit curves. Int J Mat Form 6:267–27910.1007/s12289-011-1084-1 ↗
63. Lian J, Shen F, Jia X, Ahn DC, Chae DC, Münstermann S, Bleck W (2018) An evolving non-associated Hill48 plasticity model accounting for anisotropic hardening and r-value evolution and its application to forming limit prediction. Int J Solids Struct 151: 20–4410.1016/j.ijsolstr.2017.04.007 ↗
64. Hu Q, Li X, Zhu X, Chen J (2018) Investigations on the effects of hardening law and yield criterion on the forming limit prediction with perturbation approach. Acta Mech Solids Sin (in press)
65. Yoshida K, Kuroda M (2012) Comparison of bifurcation and imperfection analyses of localized necking in rate-independent polycrystalline sheets. Int J Solids Struct 49:2073–208410.1016/j.ijsolstr.2012.04.010 ↗
66. Butcher C, Anderson D, Worswick M (2013) Predicting failure during sheared edge stretching using a damage-based model for the shear-affected zone. SAE Int J Mater Manf 6:304–31210.4271/2013-01-1166 ↗
67. Ilinich A, Smith L, Golovashchenko S (2011) Analysis of methods for determining sheared edge formability, SAE technical paper 2011-01-106210.4271/2011-01-1062 ↗
68. Karnop R, Sachs G (1928) Festigkeitseigenschaften von Kristallen einer veredelbaren Aluminiumlegierung. Z Phys 49:480–49710.1007/BF01333632 ↗
69. Polanyi M, Schmid E (1923) Ist die Gleitreibung vom Druck normal zu den Gleitflächen abhängig. Z Phys 16:336–33910.1007/BF01327405 ↗
70. Bridgman P (1952) W:studies in large plastic flow and fracture. McGraw-Hill, New York
71. Lode W (1926) Versuche über den Einflus der mittleren Hauptspannung auf das Fliessen der Metalle Eisen, Kupfer und Nickel. Z Phys 36:913–93910.1007/BF01400222 ↗
72. Drucker DC (1949) Relation of experiments to mathematical theories of plasticity. J Appl Mech 16:349–35710.1115/1.4010009 ↗
73. Hershey AV (1954) The plasticity of an isotropic aggregate of anisotropic face centred cubic crystals. J Appl Mech 21:241–24910.1115/1.4010900 ↗
74. Hosford WF (1972) A generalized isotropic yield criterion. J Appl Mech 39:607–60910.1115/1.3422732 ↗
75. Cazacu O, Chandola N, Revil-Baudard B (2018) Analytical expressions for the yield stress and Lankford coefficients of polycrystalline sheets based on a new single crystal model. Int J Mater Form 11:571–58110.1007/s12289-017-1366-3 ↗
76. Barlat F, Lege DJ, Brem JC (1991) A six-component yield function for anisotropic materials. Int J Plast 7:693–71210.1016/0749-6419(91)90052-Z ↗
77. Watson M, Dick R, Huang Y H, Lockley A, Cardoso R, Santos A (2016) Benchmark 1 – failure prediction after cup drawing, reverse redrawing and expansion: part D: responses, NUMISHEET 2016, 10th Int Conf workshop numerical simulation of 3D sheet metal forming processes, J of physics: Conf series Cardoso R, Adetosro OB (Eds.), Vol. 734. https://doi.org/10.1088/1742-6596/734/2/02200110.1088/1742-6596/734/2/022001 ↗
78. Cazacu O (2019) New mathematical results and explicit expressions in terms of the stress components of Barlat et al. (1991) orthotropic yield criterion. Int J Solids Struct 176–177:86–9510.1016/j.ijsolstr.2019.05.016 ↗
79. Cazacu O, Revil-Baudard B, Chandola N (2019) Plasticity-damage couplings:from single crystal to polycrystalline materials. Springer, Berlin Heidelberg10.1007/978-3-319-92922-4 ↗
80. Dillamore I, Roberts W (1964) Rolling textures in fcc and bcc metals. Acta Metall 12:281–29310.1016/0001-6160(64)90204-4 ↗
81. Hirsch J (2005) Texture and anisotropy in industrial applications of aluminium alloys. Arch Metall Mater 50:21–34
82. Bishop J, Hill R (1951) A theoretical derivation of the plastic properties of a polycrystalline face-centred metal. Philos Mag J Sci 42:1298–130710.1080/14786444108561385 ↗
83. Taylor GI (1938) Analysis of plastic strain in a cubic crystal. In: Stephen Timoshenko 60 th anniversary volume pp 218–224
84. Barlat F, Cazacu O, Życzowski M, Banabic D, Yoon JW (2004) Yield surface plasticity and anisotropy. In: Raabe D, Roters F, Barlat F, Chen LQ (eds) Continuum scale simulation of engineering materials–fundamentals– microstructures – process applications. Wiley VCH, Manheim, pp 145–17710.1002/3527603786.ch6 ↗
85. Cazacu O, Revil-Baudard B, Chandola N (2018) A yield criterion for cubic single crystals. Int J Solids Struct 151:9–1910.1016/j.ijsolstr.2017.04.006 ↗
86. Chandola N, Cazacu O, Revil-Baudard B (2017) New polycrystalline modeling as applied to textured steel sheets. Mech. Res Commun 84:98–101
87. Chandola N, Cazacu O, Revil-Baudard B (2017) Predictions of plastic anisotropy of textured polycrystalline sheets using a new single crystal model. C R Mecanique 346:756–76910.1016/j.crme.2018.05.004 ↗
88. Hill R (1948) A theory of the yielding and plastic flow of anisotropic metals. Proc Roy Soc A193:281–297
89. Hill R (1990) Constitutive modelling of orthotropic plasticity in sheet metals. J Mech Phys Solids 38:405–41710.1016/0022-5096(90)90006-P ↗
90. Barlat F, Lian J (1989) Plastic behavior and stretchability of sheet metals. Part I: Yield function for orthotropic sheets under plane stress conditions. Int J Plast 5:51–6610.1016/0749-6419(89)90019-3 ↗
91. Karafillis AP, Boyce MC (1993) A general anisotropic yield criterion using bounds and a transformation weighting tensor. J Mech Phys Solids 41:1859–188610.1016/0022-5096(93)90073-O ↗
92. Banabic D et al (2010) Sheet metal forming processes. Springer, Berlin Heidelberg10.1007/978-3-540-88113-1 ↗
93. Cazacu O (2019) New expressions and calibration strategies for Karafillis and Boyce (1993) yield criterion. Int J Solids Struct 185–186:410–422
94. Cazacu O, Barlat F (2001) Generalization of Drucker's yield criterion to orthotropy. Math Mech Solids 6:613–63010.1177/108128650100600603 ↗
95. Cazacu O, Barlat F (2003) Application of representation theory to describe yielding of anisotropic aluminum alloys. Int J Eng Sci 41:1367–138510.1016/S0020-7225(03)00037-5 ↗
96. Barros PD, Neto DM, Alves JL, Oliveira MC, Menezes LF (2015) DD3IMP, 3D fully implicit finite element solver: implementation of CB2001 yield criterion. Rom J Techn Sci App Mech 60(1–2):105–136
97. Neto DM, Oliveira MC, Dick RE, Barros PD, Alves JL, Menezes LF, Neto DM, Oliveira MC, Dick RE, Barros PD, Alves JL, Menezes LF (2017) Numerical and experimental analysis of wrinkling during the cup drawing of an AA5042 aluminium alloy. Int J Mater Form 10:125–13810.1007/s12289-015-1265-4 ↗
98. Cazacu O (2018) New yield criteria for isotropic and textured metallic materials. Int J Solids Struct 139:200–21010.1016/j.ijsolstr.2018.01.036 ↗
99. Revil-Baudard B (2020) Forming of materials with cubic crystal structure. Procedia Manuf 47:1300–130710.1016/j.promfg.2020.04.245 ↗
100. Barlat F, Brem JC, Yoon JW, Chung K, Dick RE, Lege DJ, Pourboghrat F, Choi S-H, Chu E (2003) Plane stress yield function for aluminum alloy sheet-part I: theory. Int J Plast 19:1297–131910.1016/S0749-6419(02)00019-0 ↗