The ability of a theoretical model to accurately predict localization and failure strains, which characterize the formability of materials, has been a controversial subject as researchers have tried various analytical methods over the years to predict forming limit diagrams. In this work, we analyze various aspects of finite element modeling in which large deformation plasticity is coupled with continuum damage evolution. In the context of the Bammann-Chiesa-Johnson (BCJ) internal state variable model, we examine different finite element codes (DYNA3D, PRONTO3D, and JAC3D), sheet thicknesses (1.0 cm and 0.1 cm), types of instabilities (geometric perturbation and various initial void volume fraction mismatches), element types [solid continuum, Hughes and Liu (1980), and Belytschko and Tsay (1983)], mesh refinement, and two-stage nonproportional straining conditions. By varying these parameters in finite element calculations for determining forming limits, we ascertain not only the forming limit diagrams in a short time but an understanding of parametric effects that have been issues of concern for the auto, steel, and aircraft industries.
Get full access to this article
View all access options for this article.
References
1.
Asaro, R.J. (1979) "Geometrical Effects in the Inhomogeneous Deformation of Ductile Single Crystals,"Acta Met., Vol. 27, pp. 445.
2.
Bammann, D.J. (1984) "An Internal Variable Model of Viscoplasticity,"Aifantis E.C. and Davison, L. (eds.), Media with Microstructures and Wave Propagation, Int. J. Engineering Science, Vol. 8-10, Pergamon Press, p. 1041.
3.
Bammann, D.J. and Johnson, G.C. (1984) "Development of a Strain Rate Sensitive Plasticity Model," in Engineering Mechanics in Civil Engineering, eds. Boresi, A.P. and Chong, K.P., p. 454.
4.
Bammann, D.J. (1985) "An Internal Variable Model of Elastic-Viscoplasticity," in The Mechanics of Dislocations, eds. Aifantis, E.C. and Hirth, J.P., The American Society of Metals, p. 203.
5.
Bammann, D.J. and Johnson, G.C. (1987a) "On the Kinematics of Finite-Deformation Plasticity,"Acta Mechanica, Vol. 70, pp. 1-13.
6.
Bammann, D.J. and Aifantis, E.C. (1987b) "A Model for Finite-Deformation Plasticity,"Acta Mechanica, Vol. 69, pp. 97-117.
7.
Bammann, D.J. (1988) "Modelling the Large Strain-High Temperature Response of Metals," in Modelling and Control of Casting and Welding Processes IV ed. Giamei, A.F. and Abbaschian, G.J.TMS Publications, Warrendale, PA.
8.
Bammann, D.J. (1990a) "Modelling Temperature and Strain Rate Dependent Large Deformations of Metals,"Applied Mechanics Reviews, Vol. 43, No. 5, Part 2.
9.
Bammann, D.J.Chiesa, M.L. , McDonald, A., Kawahara, W.A., Dike, J.J. and Revelli, V.D. (1990b) "Prediction of Ductile Failure in Metal Structures," in Failure Criteria and Analysis in Dynamic Response, ASME AMD-Vol. 107.
10.
Bammann, D.J.Chiesa, M.L. , Horstemeyer, M.F. and Weingarten, L.I. (1993) "Failure in Ductile Materials Using Finite Element Methods," eds. Jones, N. and Weirzbicki, T., Structural Crashworthiness and Failure, Elsevier Applied Science.
11.
Bammann, D.J.Chiesa, M.L. and Johnson, G.C. (1995) "A State Variable Model for Temperature and Strain Rate Dependent Metals," eds. A.M. Rajendran and R.C. Batra, Constitutive Laws: Experiments and Numerical Implementation.
12.
Belytschko, T. and Tsay, C.S. (1983) Int. J. Numerical Methods in Engineering, Vol. 19, p. 405.
13.
Belytschko, T. , Moran, B. and Kulkarni, M. (1991) "On the Crucial Role of Imperfections in Quasi-Static Viscoplastic Solutions,"J. Applied Mechanics, 58(3), pp. 658-665.
14.
Belytschko, T. , Chiang, H.Y and Plaskacz, E.J. (1992) "Two Dimensional Shear Band Computations and the Effects of Imperfections,"Proc. of Third International Congress of Computational Plasticity, eds. D. R. J. Owen, E. Onate and E. Hinton, pp. 509-519.
15.
Biffle, J.H. (1990) "JAC3D A Three-Dimensional Finite Element Computer Program for Nonlinear Quasi-Static Response of Solids with the Conjugate Gradient Method," Sandia National Laboratories SAND87-1305.
16.
Chow, C.L. , Yu, L.G. and Demeri, M.Y (1997). "A Unified Damage Approach for Predicting Forming Limit Diagrams,"J. Engineering Materials and Techn., Trans. ASME, Vol. 119, pp. 346-353.
17.
Chu, C.C. (1984) "A Three-Dimensional Model of Anisotropic Hardening in Metals and Its Application to the Analysis of Sheet Metal Formability,"J. Mech. Phys. Solids, Vol. 32, No. 3, pp. 197-212.
18.
Cocks, A.C.F. and Ashby, M.G. (1980) "Intergranular Fracture during Power-Law Creep under Multiaxial Stresses,"Metal Science, Aug.-Sept., pp. 395-402.
19.
Dike, J.J. and Weingarten, L.I. (1991) "Failure in Steel Plates Subjected to Focused Blasts: Analysis! Experiment Comparisons," Sandia National Laboratories SAND91-8222.
20.
Gurson, A.L. (1977) J. Eng. Mat. Tech.., Vol. 99, pp. 2-15.
21.
Hallquist, J.O. (1988) "DYNA3D User's Manual (Nonlinear Dynamic Analysis of Structures in Three Dimensions)," Lawrence Livermore Laboratory National Laboratory Report, UCID-19592, Rev. 4.
22.
Hecker, S.S. (1977) "Experimental Studies of Sheet Stretchability,"Forming: Analysis, Modeling, and Experimentations, American Society of Metals, p. 150.
23.
Hill, R. (1952) J. Mech. Phys. Solids, Vol. 1, p. 19.
24.
Hill, R. (1958) "A General Theory of Uniqueness and Stability in Elastic-Plastic Solids,"J. Mech. Phys. Solids, Vol. 6, pp. 236-249.
25.
Horstemeyer, M.F. (1992) "Damage of HY100 Steel Plates from Oblique Constrained Blast Waves," AMD-Vol. 137, Advances in Local Fracture/Damage Models for the Analysis of Engineering Problems, eds., J. H. Giovanola and A. J. Rosakis, Book no. H00741.
26.
Horstemeyer, M.F. and Revelli, V. (1997) "Stress History Dependent Localization and Failure Using Continuum Damage Mechanics Concepts,"Applications of Continuum Damage Mechanics to Fatigue and Fracture, ASTM STP 1315, eds. D.L. McDowell, American Society for Testing and Materials, pp. 216-237.
27.
Hosford, W.H. and Caddell, R.M. (1983) Metal Forming: Mechanics and Metallurgy, Prentice-Hall, Inc.
28.
Hughes, T.R. and Liu, W.K. (1980) "Nonlinear Finite Element Analysis in Structural Mechanics,"US/Europe Workshop on Nonlinear Finite Element Analysis in Structural Mechanics, Ruhr, Germany.
29.
Johnson, G.C. and Bammann, D.J. (1984) "A Discussion of Stress Rates in Finite Deformation Problems,"Int. J. Solids Structures, Vol. 20, pp. 737-757.
30.
Kan, Y.R. , Johnson, H.R. and Dini, J.W. (1982) "Analysis and Experimental Evaluation of Liner Materials," SAND82-8004.
31.
Keeler, S.P. (1961) "Plastic Instability and Fracture in Sheets Stretched Over Rigid Punches," Sc.D. Thesis, Massachusetts Institute of Technology.
32.
Lange, K. (1985) Handbook of Metal Forming, McGraw-Hill Book Company.
33.
Lee, K.L. , Brandon, S.L., Horstemeyer, M.F. and Korellis, J.S. (1993) "An Experimental/Analytical Evaluation of Biaxial Sheet Failure," SAND93-8226.
34.
Marciniak, A. and Kuczynski, K. (1967) Int. J. Mech. Sci., Vol. 9, p. 609.
35.
Matsuoka, M. and Suko, C. (1967) The Sumito Search, No. 1, p. 71.
36.
Mróz, Z. (1967) J. Mech. Phys. Solids, Vol. 15, p. 163.
37.
Needleman, A. and Triantafyllidis, N. (1978) J. Eng. Mat. Tech., Vol. 110, p. 164.
38.
Needleman, A. and Tveergard, V. (1983) Mechanical Behavior of Materials-IV, eds. J. Carlsson and N. G. Ohlson, 1, Pergamon Press, NY, pp. 51-65.
39.
Needleman, A. (1988) "Material Rate Dependence and Mesh Sensitivity in Localization Problems,"Comp. Meth. Applied Mechanics in Engineering, Vol. 67, p. 69.
40.
Rebelo, N. , Nagtegaal, J.C.Taylor, L.M. and Passmann, R. (1992) "Industrial Application of Implicit and Explicit Finite Element Methods to Forming Processes," CED-Vol. 5/AMD-Vol. 156, Numerical Methods of Simulation of Industrial Metal Forming Processes, ASME, pp. 67-76.
41.
Sluys, L.J. , BoIck, J. and de Borst, R. (1992) "Wave Propagation and Localization in Viscoplastic Media,"Proc. of Third International Congress of Computational Plasticity, eds. D.R.J. Owen, E. Onate and E. Hinton, pp. 539-550.
42.
Storen, S. and Rice, J.R. (1975) "Localized Necking in Thin Sheets,"Mech. Phys. Solids, Vol. 23, p. 421.
43.
Swift, H.W. (1952) J. Mech. Phys. Solids, Vol. 1, p. 1.
44.
Taylor, L.M. and Flanagan, D.P. (1989) "PRONT03D—A Three-Dimensional Transient Solid Dynamics Program," Sandia National Laboratories SAND87-1912.
45.
Whirley, R.G. , Englemann, B.E. and Logan, R.W. (1992) "Some Aspects of Sheet Forming Simulation Using Explicit Finite Element Techniques," CED-Vol. 5/AMD-Vol. 156, Numerical Methods for Simulation of Industrial Metal Forming Processes, ASME, pp. 77-83.
