The present work aims to study the constitutive models’ influence on the reverse deep drawing simulation of cylindrical cups. Several constitutive laws were considered to predict the combined effects of anisotropy as well as the changes in strain path direction of the stainless steel. To this end, a number of models were used, worth mentioning among which are the isotropic with nonlinear kinematic hardening laws, along with the isotropic von Mises and anisotropic Hill’48 yield criteria. For the models’ parameters identification, uniaxial tensile and shear tests at several orientations to the rolling direction as well as reversed shear tests were carried out. Then, a subsequent comparison between experimental data and numerical simulations of reverse deep drawing tests were performed, using the finite element code Abaqus/Explicit. On the basis of the major reached results, it has been found that for the first stage, whatever the yield criteria used and for all the hardening models, the numerical punch-force evolution correlates well with the experimental one. For the second stage, the punch-force evolution was found to be remarkably more influenced by the yield criteria than by the kinematic laws. The major strain distribution greatly depends on the yield criteria. Meanwhile, it was slightly linked to the work hardening.
HussainiSMSinghSKGuptaAK. Experimental and numerical investigation of formability for austenitic stainless steel 316 at elevated temperatures. J Mater Res Technol2014; 3: 17–24.
2.
LaurentHGrèzeRManachPYet al.Influence of constitutive model in springback prediction using the split-ring test. Int J Mech Sci2009; 51: 233–245.
3.
MinDKJeonBHKimHJet al.A study on process improvements of multi-stage deep-drawing by the finite-element method. J Mater Process Technol1995; 54: 230–238.
4.
ThuillierSManachPYMenezesLF. Occurrence of strain path changes in a two-stage deep drawing process. J Mater Process Technol2010; 210: 226–232.
5.
ThuillierSManachPYMenezesLFet al.Experimental and numerical study of reverse re-drawing of anisotropic sheet metals. J Mater Process Technol2002; 125: 764–771.
6.
GantarGPepelnjakTKuzmanK. Optimization of sheet metal forming processes by the use of numerical simulations. J Mater Process Technol2002; 130: 54–59.
7.
GangadharJReddyKSKGoudRRet al.Finite element simulation of direct redrawing process of EDD steel at elevated temperatures. Mater Today: Proc2015; 2: 1968–1977.
8.
NetoDMOliveiraMCAlvesJLet al.Influence of the plastic anisotropy modelling in the reverse deep drawing process simulation. Mater Des2014; 60: 368–379.
9.
HaddadiHBelhabibS. Improving the characterization of a hardening law using digital image correlation over an enhanced heterogeneous tensile test. Int J Mech Sci2012; 62: 47–56.
10.
AbedrabboNPourboghratFCarsleyJ. Forming of AA5182-O and AA5754-O at elevated temperatures using coupled thermo-mechanical finite element models. Int J Plast2007; 23: 841–875.
11.
LiKPGengLWagonerRHSimulation of springback with the draw/ bend test. In: MeechJ (ed.). Proceedings of IPMM’99. The second international conference on intelligent processing and manufacturing of materials, Piscataway, NJ: IEEE, 1999, pp. 91–104.
12.
Jiang S, Garnett M and Liu S-D. Springback of sheet metal subjected to multiple bending-unbending cycles (No. 2000-01-1112), SAE Technical Paper, 2000.
13.
Geng LM. Application of plastic anisotropy and non-isotropic hardening to springback prediction. PhD Thesis, The Ohio State University, USA, 2000.
14.
Geng LM and Wagoner RH. Springback analysis with a modified hardening model (No. 2000-01-0768), SAE Technical Paper, 2000.
15.
PragerW. A new method of analyzing stresses and strains in work-hardening plastic solids. ASME J Appl Mech Trans1956; 78: 493–493.
16.
ZieglerH. A modification of Prager’s hardening rule. Q Appl Math1959; 17: 55–65.
17.
Armstrong PJ and Frederick CO. A mathematical representation of the multiaxial Bauschinger effect. Technical report, 1966.
18.
LemaitreJChabocheJL. Mechanics of solid materials, Cambridge: Cambridge University Press, 1994.
19.
OhnoNWangJD. Kinematic hardening rules with critical state of dynamic recovery part I: formulation and basic features for ratchetting behavior. Int J Plast1993; 9: 375–390.
20.
OhnoNWangJD. Nonlinear hardening rules with critical state of dynamic recovery Part II: Application to experiments of ratchetting behavior. Int J Plast1993; 9: 391–391.
21.
SoutoNAndrade-CamposAThuillierS. Material parameter identification within an integrated methodology considering anisotropy, hardening and rupture. J Mater Process Technol2015; 220: 157–172.
22.
SafaeiMZangSLeeMet al.Evaluation of anisotropic constitutive models: Mixed anisotropic hardening and non-associated flow rule approach. Int J Mech Sci2013; 73: 53–68.
23.
BanabicD. Sheet metal forming processes: Constitutive modeling and numerical simulation, New York: Springer Science & Business Media, 2010.
24.
HillR. A theory of the yielding and plastic flow of anisotropic metals. Proc Roy Soc Lond A: Math Phys Eng Sci1948; 193: 281–297.
25.
KuwabaraTvan BaelAIizukaE. Measurement and analysis of yield locus and work hardening characteristics of steel sheets with different r-values. Acta Mater2002; 50: 3717–3729.
26.
HuW. A novel quadratic yield model to describe the feature of multi-yield-surface of rolled sheet metals. Int J Plast2007; 23: 2004–2028.
27.
AhmadiSEivaniARAkbarzadehA. Experimental and analytical studies on the prediction of forming limit diagrams. Comput Mater Sci2009; 44: 1252–1257.
28.
BagherzadehSMirniaMJDarianiBM. Numerical and experimental investigations of hydro-mechanical deep drawing process of laminated aluminum/steel sheets. J Manuf Processes2015; 18: 131–140.
29.
HussainiSMKrishnaGGuptaAKet al.Development of experimental and theoretical forming limit diagrams for warm forming of austenitic stainless steel 316. J Manuf Processes2015; 18: 151–158.
30.
XiaoHBruhnsOTMeyersA. On objective corotational rates and their defining spin tensors. Int J Solids Struct1998; 35: 4001–4014.
31.
Anon. Models for metals subjected to cyclic loading. In: ABAQUS theory manual, Providence, RI: Hibbitt, Karlsson and Sorensen, 1998, pp. 4.3.5.1–4.3.5.4.
32.
ChabocheJLRousselierG. On the plastic and viscoplastic constitutive equations—Part I: Rules developed with internal variable concept. J Press Vess Technol1983; 105: 153–158.
33.
ChabocheJL. Time-independent constitutive theories for cyclic plasticity. Int J Plast1986; 2: 149–188.
34.
ThuillierSManachPY. Comparison of the work-hardening of metallic sheets using tensile and shear strain paths. Int J Plast2009; 25: 733–751.
35.
ZangSLThuillierSLe PortAet al.Prediction of anisotropy and hardening for metallic sheets in tension, simple shear and biaxial tension. Int J Mech Sci2011; 53: 338–347.
36.
ManachPYCoutyN. Elastoviscohysteresis constitutive law in convected coordinate frames: Application to finite deformation shear tests. Comput Mech2002; 28: 17–25.
Bochud N, Alves JL, Oliviera MC, et al. Constitutive parameters identification of advanced yield criteria from a reduced base of experimental results. In: Proceedings of the 7th international conference and workshop on numerical simulation of 3D sheet metal forming processes (Numisheet), Interlaken, Switzerland, 1–5 September 2008, pp.79–84.
39.
LaurentHGrèzeROliveiraMCet al.Numerical study of springback using the split-ring test for an AA5754 aluminum alloy. Finite Elem Anal Des2010; 46: 751–759.
