In this work, numerical simulation of AA5083-O aluminum alloy sheets is carried out using Yld2000-2d yield criterion to predict thinning and variation of load with displacement in sheet metal forming. It has been found that the accuracy of predictions in numerical simulation depends on the coefficients and the stress exponent used in the yield criterion. Hydraulic bulge tests with circular and elliptical die cavities are performed to characterize the material in equi-biaxial and plane strain conditions. An improved stress exponent is determined by incorporating the material properties obtained in plane strain in the existing criterion. The improved stress exponent is validated by using it in the numerical simulations of cylindrical cup deep drawing and stretch forming at room temperature. The same exponent is also used in the numerical simulations carried out for the case of experiments conducted at 250°C. The predicted thinning and load-displacement variations from the numerical simulations are validated with the experimental measurements. A considerable improvement in the results predicted using the improved stress exponent is observed at both the temperatures.
HillR. A theory of the yielding and plastic flow of anisotropic metals. Proc R Soc A Math Phys Eng Sci1948; 193: 281–297.
2.
HillR. Theoretical plasticity of textured aggregates. Math Proc Camb Philos Soc1979; 85: 179–191.
3.
HillR. Constitutive modelling of orthotropic plasticity in sheet metals. J Mech Phys Solids1990; 38: 405–417.
4.
HillR. A user-friendly theory of orthotropic plasticity in sheet metals. Int J Mech Sci1993; 35: 19–25.
5.
BarlatFLianK. Plastic behavior and stretchability of sheet metals. Part I: A yield function for orthotropic sheets under plane stress conditions. Int J Plast1989; 5: 51–66.
6.
BarlatFLegeDJBremJC. A six-component yield function for anisotropic materials. Int J Plast1991; 7: 693–712.
7.
BarlatFBremJCYoonJW, et al. Plane stress yield function for aluminum alloy sheets—part 1: theory. Int J Plast2003; 19: 1297–1319.
8.
BarlatFAretzHYoonJW, et al. Linear transformation-based anisotropic yield functions. Int J Plast2005; 21: 1009–1039.
9.
CazacuOBarlatF. Generalization of Drucker’s yield criterion to orthotropy. Math Mech Solids2001; 6: 613–630.
10.
BanabicDKuwabaraTBalanT, et al. Non-quadratic yield criterion for orthotropic sheet metals under plane-stress conditions. Int J Mech Sci2003; 45: 797–811.
11.
KarafillisAPBoyceMC. A general anisotropic yield criterion using bounds and a transformation weighting tensor. J Mech Phys Solids1993; 41: 1859–1886.
12.
HersheyAV. The plasticity of an isotropic aggregate of anisotropic face-centered cubic crystals. J Appl Mech1954; 21: 241–249.
13.
BandyopadhyayKHariharanKLeeMG, et al. Robust multi objective optimization of anisotropic yield function coefficients. Mater Des2018; 156: 184–197.
14.
LoganRWHosfordWF. Upper-bound anisotropic yield locus calculations assuming 111-pencil glide. Int J Mech Sci1980; 22: 419–430.
15.
YoshidaKIshizakaTKurodaM, et al. The effects of texture on formability of aluminum alloy sheets. Acta Mater2007; 55: 4499–4506.
16.
YanagaDKuwabaraTUemaN, et al. Material modeling of 6000 series aluminum alloy sheets with different density cube textures and effect on the accuracy of finite element simulation. Int J Solids Struct2012; 49: 3488–3495.
17.
HakoyamaTKuwabaraTBarlatF. Effect of the determination method of the material parameters on the accuracy of forming limit analyses for 5000 series aluminum alloy. AIP Conf Proc2016; 020014_1020014_6.
18.
LzSELVArescuLComşaDSNicodimI, et al. Characterization of plastic behaviour of sheet metals by hydraulic bulge test. Trans Nonferrous Met Soc China2012; 22: s275–s279.
19.
LazarescuLNicodimIPComsaDS, et al. A procedure for the evaluation of flow stress of sheet metal by hydraulic bulge test using elliptical dies. Key Eng Mater2012; 504–506: 107–112.
20.
ReesDW. Plastic flow in the elliptical bulge test. Int J Mech Sci1995; 37: 373–389.
21.
LenzenMMerkleinM. Improvement of numerical modelling considering plane strain material characterization with an elliptic hydraulic bulge test. J Manuf Mater Process2018; 2: 6.
22.
SatishDRKumarDRMerkleinM. Effect of temperature and punch speed on forming limit strains of AA5182 alloy in warm forming and improvement in failure prediction in finite element analysis. J Strain Anal Eng Des2017; 52: 258–273.
23.
ShaoZBaiQLiN, et al. Experimental investigation of forming limit curves and deformation features in warm forming of an aluminium alloy. Proc IMechE, Part B: J Engineering Manufacture2018; 232: 465–474.
24.
RenLMZhangSHPalumboG, et al. Warm deep drawing of magnesium alloy sheets — formability and process conditions. Proc IMechE, Part B: J Engineering Manufacture2008; 222: 1347–1354.
25.
MerkleinMLechlerJ. Investigation of the thermo-mechanical properties of hot stamping steels. J Mater Process Technol2006; 177: 452–455.
26.
OuyangYLeeMSMoonJ, et al. The effect of the blank holding force on formability in hot deep drawing of boron steel considering heat transfer phenomena and friction coefficient by simulation and experimental investigation. Proc IMechE, Part B: J Engineering Manufacture2012; 226: 1506–1518.
27.
TakudaHMoriKMasudaI, et al. Finite element simulation of warm deep drawing of aluminium alloy sheet when accounting for heat conduction. J Mater Process Technol2002; 120: 412–418.
28.
NakaTHinoRYoshidaF. Deep drawability of 5083 Al-Mg alloy sheet at elevated temperature and its prediction. Key Eng Mater2000; 177: 485–490.
29.
NakaTTorikaiGHinoR, et al. The effects of temperature and forming speed on the forming limit diagram for type 5083 aluminum–magnesium alloy sheet. J Mater Process Technol2001; 113: 648–653.
30.
PanickerSSSinghHGPandaSK, et al. Characterization of tensile properties, limiting strains, and deep drawing behavior of AA5754-H22 sheet at elevated temperature. J Mater Eng Perform2015; 24: 4267–4282.
31.
Ghaffari TariDWorswickMJWinklerS. Experimental studies of deep drawing of AZ31B magnesium alloy sheet under various thermal conditions. J Mater Process Technol2013; 213: 1337–1347.
32.
MorchhaleAKotkundeNSinghSK, et al. Prediction of fracture limits of IN625 alloy by coupling ductile damage models and anisotropic yielding functions with the classical Marciniak and Kuczyński model. Proc IMechE, Part B: J Engineering Manufacture2022; 236(6–7): 894–907.
33.
AbedrabboNPourboghratFCarsleyJ. Forming of aluminum alloys at elevated temperatures – Part 2: Numerical modeling and experimental verification. Int J Plast2006; 22: 342–373.
34.
BagheriaslRGhavamKWorswickMJ. Formability improvement with independent die and punch temperature control. Int J Mater Forming2014; 7: 139–154.
35.
NetoDMMartinsJMCunhaPM, et al. Thermo-mechanical finite element analysis of the AA5086 alloy under warm forming conditions. Int J Solids Struct2018; 151: 99–117.
36.
TimoshenkoSWoinowsky-KriegerS. Theory of plates and shells. 2nd ed.New York: Mcgraw Hill Book Company, 1964.
37.
BagheriaslR. Formability of aluminum alloy sheet at elevated temperature. PhD Thesis, University of Waterloo, Canada, 2012.
38.
AffrontiEMerkleinM. Analysis of the bending effects and the biaxial pre-straining in sheet metal stretch forming processes for the determination of the forming limits. Int J Mech Sci2018; 138–139: 295–309.
39.
ChangYTangXZhaoK, et al. Investigation of the factors influencing the interfacial heat transfer coefficient in hot stamping. J Mater Process Technol2016; 228: 25–33.
40.
HockettJESherbyOD. Large strain deformation of polycrystalline metals at low homologous temperatures. J Mech Phys Solids1975; 23: 87–98.
41.
AbedrabboNPourboghratFCarsleyJ. Forming of aluminum alloys at elevated temperatures – Part 1: Material characterization. Int J Plast2006; 22: 314–341.
