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Simulation of Metal Forming Processes

  • A. E. Tekkaya
Chapter
Part of the Engineering Materials book series (ENG.MAT.)

Abstract

The term process simulation describes all methods by which one or more of the process parameters of a real physical process or process family is or are predicted approximately before its or their actual happening, [7.1]. The aim of the determination of these parameters in case of metal forming processes is usually one or more of the following:
  • Checking the feasibility of the process design for producing a workpiece,

  • Evaluating the product properties for service use,

  • Increasing the insight about the real process in order to optimize the production sequence.

The simulation in production processes aims to manufacture products economically. Therefore, the application of process simulation must be always more economical than the application of the real process.

Keywords

Sheet Metal Flow Curve Equivalent Plastic Strain Versus Versus Versus Versus Bulk Metal 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

List of Special Symbols

A

Area

[B]

Shape function matrix for the rate of deformation components

D

Rate of deformation tensor

E

Young’s modulus of elasticity

E

Green Lagrangian finite strain tensor

f

Force vector

F

Deformation gradient tensor

G

Shear modulus of elasticity

G

Kirchhoff stress tensor

H

2nd Piola Kirchhoff stress tensor

I

Identity tensor

J

Jacobian determinant

L

Velocity gradient tensor

n

Normal unit vector

[N]

Shape function matrix for the velocities

S

Penalty factor

S

1st Piola Kirchhoff stress tensor

t

Time

T

Temperature

T

Cauchy (true) stress tensor

u

Displacement vector

v

Velocity vector

V

Volume

W

Work

W

Spin tensor

x

Position vector

Y

Yield stress

σf

Flow stress

δ

Virtual change

ε

Infinitesimal strain tensor

λ

Lagrangian function

μ

Coulomb coefficient of friction

ν

Poisson’s number

П

Plastic potential

ρ

Density

\(\bar \varepsilon \)

Equivalent plastic strain (Umformgrad)

Nabla operator

e

Element related

el

Elastic

n

Normal

pl

Plastic

0

Initial state related

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References to Chapter 7

  1. 7.1
    Roll, K.; Tekkaya, A. E.: Numerical methods of process simulation, in: Lange, K. (ed.): Metal Forming. Handbook for industry and science (in German). Vol. 4, Berlin, Springer-Verlag 1993, 330–435.Google Scholar
  2. 7.2
    Malvern, L. E.: Introduction to the mechanics of a continuous medium. Englewood Cliffs, N J, Prentice-Hall 1969.Google Scholar
  3. 7.3
    Eringen, A. C.: Mechanics of continua. New York, John Wiley & Sons 1967.Google Scholar
  4. 7.4
    Becker, E.; Bürger W.: Continuum mechanics (in German). Stuttgart, B. G. Teubner 1975.Google Scholar
  5. 7.5
    Prager, W.: Introduction into continuum mechnics (in German). Basel, Birkhäuser 1961.Google Scholar
  6. 7.6
    Truesdell, C. (ed.): Mechanics of solids, Vol III, Berlin, Springer-Verlag 1984.Google Scholar
  7. 7.7
    Haupt, P.: Continuum mechanics and theory of materials. Berlin, Springer-Verlag 2000.Google Scholar
  8. 7.8
    Betten, J.: Continuum mechanics.(in German). Berlin, Springer-Verlag 1993.Google Scholar
  9. 7.9
    Lubliner, J.: Plasticity theory. New York, Macmillan 1990.Google Scholar
  10. 7.10
    Wagoner, R. H.; Chenot, J.-L: Fundamentals of metal forming. New York, Wiley 1997.Google Scholar
  11. 7.11
    Simo, J. C.; Hughes, T. J. R.: Computational inelasticity. New York, Springer-Verlag 1998.Google Scholar
  12. 7.12
    Marsden, J. E.; Hughes, T. J. R.: Mathematical foundations of elasticity. Englewood Cliffs, N J, Prentice-Hall 1983.Google Scholar
  13. 7.13
    Hill, R.: The Mathematical theory of plasticity. Oxford, Clarendon Press 1950.Google Scholar
  14. 7.14
    Ismar, H.; Mahrenholtz, O.: Technical plastomechanics (in German). Braunschweig, Vieweg 1979.CrossRefGoogle Scholar
  15. 7.15
    Kachanov, L. M.: Fundamentals of the theory of plasticity. Moscow, MIR Publishers 1974.Google Scholar
  16. 7.16
    Roll, K.: Application of numerical approximations for the description of cold bulk metal forming processes (in German). Berichte aus dem Institut für Umformtechnik, Universität Stuttgart, Nr. 66. Berlin, Springer-Verlag 1982.Google Scholar
  17. 7.17
    Gerhardt, J.: Mechanical and thermal simulation of threedimensional metal forming processes (in German). Berichte aus dem Institut für Umformtechnik, Universität Stuttgart, Nr. 101. Berlin, Springer-Verlag 1988.Google Scholar
  18. 7.18
    Herbertz, R.: Suitability of a rigid-viscoplastic material law for solving metal forming problems using the finite-element method (in German). Thesis, RWTH Aachen 1982.Google Scholar
  19. 7.19
    Tekkaya, A. E.: Fully automatic simulation of bulk metal forming processes, 6th Int. Conf. on Numerical Methods in Industrial Forming Processes (NUMIFORM ‘88), Enschede/The Netherlands, 22–25 June 1998, 529–534.Google Scholar
  20. 7.20
    Tekkaya, A. E.; Sen, A.: Linear contact algorithm for rigid-plastic finite element simulation, steel research, 63 (1992) 12, 531–536.Google Scholar
  21. 7.21
    Herrmann, M.: Contribution to the calculation of sheet metal forming processes using the finite element method (in German). Berlin, Springer-Verlag 1991.Google Scholar
  22. 7.22
    Matzenmiller, A.: A rational concept of solution for geometrical and physical nonlinear structure calculations (in German). Thesis, Universität Stuttgart 1998.Google Scholar
  23. 7.23
    Tekkaya, A. E.: Determination if residual stresses in cold bulk metal forming (in German). Berichte aus dem Institut für Umformtechnik, Universität Stuttgart, Nr. 83, Berlin, Springer-Verlag, 1986.Google Scholar
  24. 7.24
    Nagtegaal, J. C.; Veldpaus, F. E.: On the implementation of finite strain plasticity equations in a numerical model. In: J. F. T. Pittman (ed): Numerical analysis of forming processes. New York,Wiley 1984, 351–371.Google Scholar
  25. 7.25
    Simo, J. C.; Taylor, R. L: Consistent tangent operators for the rate-independent elastoplasticity. Comp. Meth. Appl. Mech. Eng. 48 (1985), 101–118.CrossRefGoogle Scholar
  26. 7.26
    Nagtegaal, J. C.: On the implementation of inelastic constitutive equations with special reference to large deformation problems. Comp. Meth. Appl. Mech. Eng. 33 (1982), 469–484.CrossRefGoogle Scholar
  27. 7.27
    Keck, P.; Wilhelm, M.; Lange, K.: Application of the finite element method to the siMulation of sheet forming processes: Comparison of calculations and experiments, Int. J. for Numer. Methods in Engg., 30 (1990), 1415–1430.CrossRefGoogle Scholar
  28. 7.28
    Lubarda, V. A.: Elastic-plastic deformation at finite strain. Ph.D.-Thesis, Stanford University 1980.Google Scholar
  29. 7.29
    Wilkins, M. L.: Calculation of elastic-plastic flow. In: Methods of Computational Physics 3. New York, Academic Press 1964.Google Scholar
  30. 7.30
    Dong, X.; Wang, S. P.; Nakamachi, E.: Dynamic explicit finite element analysis. In: 1996 Nakamachi Lab. Report, Osaka Institute of Technology, Osaka 1996.Google Scholar
  31. 7.31
    Hughes, T. J. R.: Numerical implementation of constitutive models: Rate-independent deviatoric plasticity. In: Nemat-Mnasser, S.; Asaro, R- J. (eds): Proc. Theoretical foundation for large scale computing for nonlinear material behaviour. Dordrecht, The Netherlands, M. Nijhoff Publ. 1984.Google Scholar
  32. 7.47
    McMeeking, R. M.; Rice, J. R.: Finite-element formulations for problems of large elastic-plastic deformation, Int. J. Solids Structures 10 (1975), 601–616.CrossRefGoogle Scholar
  33. 7.32
    Meirovich, L.: Elements of vibration analysis. Tokyo, McGraw-Hill Kogakusha 1975.Google Scholar
  34. 7.33
    Rebelo, N.; Nagtegaal, J. C.; Taylor, L. M.: Comparison of implicit and explicit finite element methods in the simulation of forming processes. In: NUMIFORM ‘82. Rotterdam, Balkema 1992, 99–108.Google Scholar
  35. 7.
    Schweizerhof, K.; Hallquist, J. O.: Explicit integration schemes and contact formulations for thin sheet metal forming. In: FE-Simulation of 3D sheet metal forming processes in automotive industry. VDI-Ber. 894 (1991), 405–439.Google Scholar
  36. 7.35
    ABAQUS theory manual, Vers. 5.5. Hibbitt, Karlsson & Sorensen Inc. 1995.Google Scholar
  37. 7.36
    Tekkaya, A.E.: State-of-the-art of simulation in metal forming. 6th SheMet Conf., Enschede, The Netherlands, 6–8 April 1998. Vol. I, 53–66.Google Scholar
  38. 7.37
    Hallquist, J. O.; Wainscott, B.; Schweizerhof, K.: Improved simulation of thin-sheet metalforming using LS-DYNA3D on parallel computers. J. Mater. Process. Technol. 50 (1995), 144–157.CrossRefGoogle Scholar
  39. 7.38
    Tekkaya, A. E.: Status and developments in the simulation of forming processes. Wire 48 (1998), 31–36.Google Scholar
  40. 7.39
    Courant, R.: Variational methods for the solution of problems of equilibrium and vibrations, Trans. Amer. Math Soc. (1942), 1–23.Google Scholar
  41. 7.40
    Argyris, J. H.: Energy theorems and structural analysis. Pt. I. Aircraft Eng. 26 (1954), 383.Google Scholar
  42. 7.41
    Turner, M. J.; et al.: Stiffnesss and deflection analysis of complex structures. J. Aeronaut. Sci. 25 (1956), 805–823.Google Scholar
  43. 7.42
    Clough, R. W.: The finite element method in plane stress analysis. Proc. 2’“ A.S.C.E. Conf. on Electronic Comp., Pittsburgh, PA, Sep. 1960.Google Scholar
  44. 7.43
    Zienkiwicz, O. C.; Cheung, Y. K.: The finite element method in continuum and structural mechanics. New York, Mc Graw-Hill 1965.Google Scholar
  45. 7.44
    Zienkiwisz, O. C.; et al.: Solution of engineering problems, `initial stress’ finite element approach, Int. J. Num. Meth. Engg. 1 (1969), 75–100.CrossRefGoogle Scholar
  46. 7.45
    Lung, M.: A method for calculating the velocity and stress field of stationary rigid-plastic deformations using finite elements (in German). Dr.-Ing. Thesis, Technische Universität Hannover 1971.Google Scholar
  47. 7.46
    Lee, C. H.; Kobayashi, S.: New solution to rigid-plastic deformation problems using matrix methods, Trans. ASME, J. Eng. Ind. 95 (1973), 865–873.CrossRefGoogle Scholar
  48. 7.48
    Kudo, H.; Matsubara, S.: Joint examination project of validity of various numerical methods for the analysis of metal forming processes, Tutzingen 1978, 378–403.Google Scholar
  49. 7.49
    Woo, D. M.: On the complete solution of the deep-drawing problem, Int. J. Mech. Sci. 10 (1968), 83–94.CrossRefGoogle Scholar
  50. 7.50
    Tekkaya, A. E.; Complete numerical solution of the axisymmetrical deep-drawing problem, Ma Sc Thesis, Middle East Technical University, Ankara 1980.Google Scholar
  51. 7.51
    Roll, K.; priv. comm. Stuttgart 1990.Google Scholar
  52. 7.52
    Wang, N.-M.; Budiansky, B.: Analysis of sheet metal stamping by a finite-element method, Trans. ASME, J. Appl. Mech.. 45 (1978), 73–82.CrossRefGoogle Scholar
  53. 7.53
    Wifi, A. S.: An incremental complete solution of the stretch-forming and deep-drawing of a circular blank using a hemispherical punch, Int. J. Mech. Sci. 18 (1976), 23–31.CrossRefGoogle Scholar
  54. 7.54
    Gotoh, M.; Ishise, F.: A finite element analysis of rigid-plastic deformation of the flange in a deep-drawing process based on a fourth-degree yield function, Int. J. Mach. Sci. 20 (1978), 423–435.CrossRefGoogle Scholar
  55. 7.55
    Toh, C. H.; Kobayashi, S.: Finite element process modelling of sheet metal forming of general shapes“; In: Grundlagen der Umformtechnik I, 39–56. Berlin, Springer-Verlag, 1983.Google Scholar
  56. 7.56
    Tang, S. C.; Chu, E.; Samanta, S. K.: Finite element prediction of the deformed shape of an automotive body panel during preformed stage. In: NUMIFORM’82, Swansea, Pineridge Press, Swansea, 1982, 629–640.Google Scholar
  57. 7.57
    Belytschko, T.; Mullen, R.: Explicit integration of structural problems. In: Bergan, P.; et al. (eds): Finite Elements in Nonlinear Mechanics;; 1977, 672–720.Google Scholar
  58. 7.58
    Benson, D. J.; Hallquist, J. O.: A simple rigid body algorithm for structural dynamics programs, Int. J. Num. Meth. Eng., 22 (1986), 723–749.CrossRefGoogle Scholar
  59. 7.59
    Massoni, E.; et al.: A finite element modelling for deep drawing of thin sheet in automotive industry. In: K. Lange, K. (ed): Advanced Technology of Plasticity 1987. Vol. II. Berlin, Springer-Verlag 1987, 719–725.Google Scholar
  60. 7.60
    Wang, N.-M.; Wenner, M. L.: Elastic-viscoplastic analysis of simple stretch forming problems. In: Koistinen, D. P.; Wang, N.-M. (eds): Mechanics of Sheet Metal forming, 1978, 367–402.CrossRefGoogle Scholar
  61. 7.61
    Xing, H.-L.; Makinouchi, A.: 3-D thermal-elastic-plastic FEM in finite deformation and ist application to non-isothermal sheet forming. In: Owen, J.; et al. (eds): Computational Plasticity, Swansea, Pineridge Press 1997, 1445–1452.Google Scholar
  62. 7.62
    Wisselink, H.: Analysis of guillotining and slitting. Ph.-D. Thesis, University of Twente,The Ntetherlands 2000.Google Scholar
  63. 7.63
    v. d. Moesdijk, R.: Numerical modeling of shape aberrations due to blanking. Ph.-D. Thesis, University of Twente, The Nethertlands 1999.Google Scholar
  64. 7.64
    Goijaerts, A. D.: Prediction of ductile fracture in metal blanking. Ph.-D. Thesis, Technical University of Eindhoven, 1999.Google Scholar
  65. 7.65
    Lee, Y. K.; Yang, D. Y.: Automatic generation of meshes with surface element layers and core mesh for finite element simulation of metal forming processes. In: 6th Int. Conf. on Numerical Methods in Industrial Forming Processes (NUMIFORM ‘88), Enschede/The Netherlands, 22–25 June 1998, 121–128.Google Scholar
  66. 7.66
    Kopp, R.; Karhausen, K.; Schneider, R.: Application of FEM to prediction of micro-microstructure in hot forming of metals. Proc. 4th Int. Conf. on Technology of Plasticity, 1993, 1203–1211.Google Scholar
  67. 7.67
    Kavakli, S.; Tekkaya, A. E.: Automatic hexahedral mesh generation for the simulation of metal forming processes. In: Proc. 4th Int. Conf. on Computational Plasticity (COMPLAS-IV), Barcelona/Spain, 3–6 April 1995. Vol. I, 431–442.Google Scholar
  68. 7.68
    Schafstall, H., Femutec Ing.-Ges. mbh., Hamburg, priv. comm. 1997. 7.69 Räuchle, F., Universität Stuttgart, priv. comm. 1997.Google Scholar
  69. 7.70
    Roll, K.: Compararation of simulation systems - tasks for the future (in German). In: Proc. 4. Sächsiche Fachtagung Umformtechnik, Nov. 5–6, 1997, Chemnitz, 315–334.Google Scholar

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  • A. E. Tekkaya

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