Forming limit diagram is extensively used in the analysis of sheet metal forming to define the limit of deformation of materials without necking or fracture. This article contributes in construction of strain- and stress-based forming limit diagrams by theoretical analysis of several available instability criteria, including bifurcation analysis of diffuse and through-thickness neck formation, shear stress-based criteria onset of through-thickness necking, and so on, and comparative studies among different available theories are done with earlier published work on forming limit in different literatures. The scope of Tresca criterion in forming limit diagram is also investigated in this article. It is found that apart from stress-based forming limit diagram, conventional failure criterion equivalent failure strain versus triaxiality (η) plot is also strain path independent.
KeelerSPBackhofenWA. Plastic instability and fracture in sheet stretched over rigid punches. ASM Trans Q1964; 56: 25–48.
2.
GoodwinGM. Application of strain analysis to sheet metal forming in the press shop. SAE paper 680093, 1968.
3.
MarciniakZKuczynskiKPokoraT. Influence of the plastic properties of a material on the forming limit curve for sheet metal in tension. Int J Mech Sci1973; 15: 789–805.
4.
NakazimaKKikuumaTHasukaK. Study on the formability of steel sheets. Yawata technical report no. 264, 1968, pp.141–154.
5.
MarciniakZADuncanJ. Mechanics of sheet metal forming. London: Edward Arnold, 1992.
6.
StoughtonTB. General forming limit criterion for sheet metal forming. Int J Mech Sci2000; 42: 1–27.
7.
KleemolaHJPelkkikangasMT. Effect of predeformation and strain path on the forming limits of steel, copper, and brass. Sheet Metal Ind1977; 63: 591–599.
8.
ArrieuxRBedrinCBoivinM. Determination of an intrinsic forming limit stress diagram for isotropic metal sheets. In: Proceedings of the 12th Biennial Congress of the IDDRG, Santa Margherita Ligure, Italy, 1982, pp.61–71.
MarciniakZKuczynskiK. Limit strains in the processes of stretch forming sheet steel. J Mech Phys Solids1967; 1: 609–620.
13.
GhazanfariAAssempourA. Calibration of forming limit diagrams using a modified Marciniak–Kuczynski model and an empirical law. Mater Design2012; 34:185–191.
14.
BressanJDWilliamsJA. The use of a shear instability criterion to predict local necking in sheet metal deformation. Int J Mech Sci1983; 25: 155–168.
15.
TrescaH. Mémoire sur l’écoulement des corps solides soumis à de fortes pressions. CR Acad Sci Paris1864; 59: 754.
16.
UthaisangsukVPrahlUBleckW. Characterisation of formability behaviour of multiphase steels by micromechanical modeling. Int J Fracture2009; 157: 55–69.
17.
BrunetMMorestinF. Experimental and analytical necking studies of anisotropic sheet metals. J Mater Process Tech2001; 112(2–3): 214–226.
18.
NurcheshmehMGreenDE. Prediction of sheet forming limits with Marciniak and Kuczynski analysis using combined isotropic–nonlinear kinematic hardening. Int J Mech Sci2011; 53(2): 145–153.
19.
Aghaie-KhafriMMahmudiR. Predicting of plastic instability and forming limit diagrams. Int J Mech Sci2004; 46(9): 1289–1306.
20.
KeelerSPBrazierWG. Relationship between laboratory material properties and press shop formability. In: Proceedings of conference on microalloy 1977, vol. 75, pp.517–528.
21.
StoughtonTBZhuX. Review of theoretical models of the strain-based FLD and their relevance to the stress-based FLD. Int J Plasticity2004; 20(8–9): 1463–1486.
22.
AlsosHSHopperstadOSTörnqvistR. Analytical and numerical analysis of sheet metal instability using a stress based criterion. Int J Solids Struct2008; 45(7–8): 2042–2055.
23.
WierzbickiTBaoYLeeYW. Calibration and evaluation of seven fracture models. Int J Mech Sci2005; 47: 719–743.
24.
SimhaCHMGholipourJBardelcikA. Prediction of necking in tubular hydroforming using an extended stress-based FLC. J Eng Mater: T ASME2007; 129(1): 136–147.
25.
BaiYWierzbickiT. Application of extended Mohr–Coulomb criterion to ductile fracture. Int J Fracture2010; 161: 1–20.
26.
JohnsonGRCookWH. Fracture characteristics of three metals subjected to various strains, strain rates, temperatures and pressures. Eng Fract Mech1985; 21(1): 31–48.
27.
PaulSK. Real microstructure based micromechanical model to simulate microstructural level deformation behavior and failure initiation in DP 590 steel. Mater Design2013; 44: 397–406.
28.
PaulSKKumarA. Micromechanics based modeling to predict flow behavior and plastic strain localization of dual phase steels. Comp Mater Sci2012; 63: 66–74.
