Forming Limits of Sheet Metal

  • D. Banabic
Part of the Engineering Materials book series (ENG.MAT.)


Besides the flow curve and plastic anisotropy, the formability of a material includes the capability to undergo plastic deformation to a given shape without defects. The defects have to be considered separately for the fundamental sheet metal forming procedures of deep-drawing and stretching. The difference between these types of stamping procedures is based on the mechanics of the forming process.


Sheet Metal Deep Drawing Drawing Ratio Strain Path Form Limit Diagram 
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


mean cup diameter


ultimate strain


formability index


non-homogeneity coefficient


deep-drawability index


stress ratio


drawing ratio


1st principal (true, natural) strain


2nd principal (true, natural) strain


principal strain in sheet thickness direction


maximum principal stress


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References to Chapter 5

  1. 5.1
    Eary, D. F.: Techniques of press working sheet metals. London, Prentice Hall 1974.Google Scholar
  2. 5.2
    Marciniak, Z.: Limits of sheet metal formability (in Polish). Warsaw, WNT 1971.Google Scholar
  3. 5.3
    Marciniak, Z.: Aspects of material formability. Hamilton, McMaster University 1974.Google Scholar
  4. 5.4
    Marciniak, Z.: Sheet metal forming limits. In: Koistinen, D. P.; Wang, N. M. (eds): Mechanics of sheet metal forming, New York/London, Plenum Press 1978, 215–235.CrossRefGoogle Scholar
  5. 5.5
    Marciniak, Z.: Assessment of material formability. In: Advanced Technology of Plasticity, Proc. 2nd ICTP, Tokyo 1984, 685–694.Google Scholar
  6. 5.
    Marciniak, Z.: Priv. Comm.Google Scholar
  7. 5.7
    Marciniak, Z.; Kolodziejski, J.: Theory of plastic processes. Pt II: Sheet metal forming (in Polish), Warsaw, WBW 1983.Google Scholar
  8. 5.8
    Kumpulainen, J.: Factors limiting the formability of sheet metals. Thesis, Helsiki Univ. of Technology 1984.Google Scholar
  9. 5.9
    Cockroft, M. G.; Latham, D. J: Ductility and the workability of metals, J. Inst. Met. 96 (1968), 33–39.Google Scholar
  10. 5.10
    Pearce, R.: 4000 Years of sheet metal forming. In: Newby, J. R.; Niemeier, B. A. (eds): Formability of metallic materials 2000 AD, Chicago, ASTM 1982, 3–18.CrossRefGoogle Scholar
  11. 5.11
    Lange, K.: Sheet metal working (in German), Werkstattstech. 72 (1982), 237–246.Google Scholar
  12. 5.12
    Pearce, R.: Sheet metal testing–from the 19th century until now, In: Proc. Biennial Congr. IDDRG, Warwick, 1978, 355–362.Google Scholar
  13. 5.13
    Considere, A.: Application of iron and steel in constructions (in French), Annales des Ponts et Chaussees 9 (1985), 574–575.Google Scholar
  14. 5.14
    Erichsen, A. M.: A new test for thin sheets (in German), Stahl und Eisen 34 (1914), 879–882.Google Scholar
  15. 5.15
    Ragupathi, R. S.: Sheet metal properties and testing methods. In: Lange, K.(ed): Handbook of metal forming, Dearborn, Michigan, SME 1985.Google Scholar
  16. 5.16
    Pomey, G.: Formability of thin sheet (in French). (Vol. 1–3 ), Collection I.R.S.I.D. - O. T. U. A., Paris 1976.Google Scholar
  17. 5.17
    Pomey, 0.; Parniere, P.: Formability of thin sheet (in French), Techniques de l’ingenieur (1980), Nr. 1, M 695, 1–16, M 696, 1–19.Google Scholar
  18. 5.18
    Siebel, E.; Beisswanger H.: Deep-drawing (in German). München, Hanser 1955.Google Scholar
  19. 5.19
    Pöhlandt, K.: Materials testing for the metal forming industry. Berlin, Springer-Verlag 1989.CrossRefGoogle Scholar
  20. 5.20
    Averkiev. A. I.: Formability methods for metal sheets (in Russian), Masinostroenie, Moscow, 1985.Google Scholar
  21. 5.21
    Taylor, B.: Sheet formability testing. In: Newby, J. R. (ed): Metals Handbook, Vol 8: Mechanical testing, 9`h edn, Metals Park, Ohio, ASM 1985, 547–570.Google Scholar
  22. 5.22
    Gosh, A. K.; Hecker, S. S.; Keeler, S. P.: Sheet metal forming and testing. In: Newby, J. R. (ed): Metals Handbook, Vol. 8: Mechanical testing, 9`h edn, Metals Park Ohio, ASM 1985, 135–139.Google Scholar
  23. 5.23
    Narashimban, K.; Nendekar, V. M.: Formability testing of sheet metals, Trans. Indian Inst. Met. 49 (1996), 659–676.Google Scholar
  24. 5.24
    Kokkonen, V.; Hygren, G.: Investigation into the accuracy of the Erichsen cupping test, Sheet Metal Industries 36 (1959), 167–178.Google Scholar
  25. 5.25
    Kaftanoglu, B.; Alexander, J. M.: An investigation of the Erichsen test, J. Inst. Metals 90 (1961–1962), 457–470.Google Scholar
  26. 5.26
    Yokai, M.; Alexander, J. M.: A further investigation of the Erichsen test, Sheet Metal Industries 44 (1967), 466–475.Google Scholar
  27. 5.27
    Olsen, T. Y.: Machines for ductility testing, Proc. Amer. Soc. Mater. 20 (1920), 398–403.Google Scholar
  28. 5.28
    Hecker, S. S.: A cup test for assessing stretchability, Met. Eng. Quart. 2 (1974), 30–36.Google Scholar
  29. 5.29
    Ghosh, A. K.: The effect of lateral drawing-in on stretch formability, Met. Eng. Quart 3 (1975), 53–64.Google Scholar
  30. 5.30
    Jovignot, C.: Method and testing device for the study of fracture of sheet metals (in French), Revue de Metallurgie 27 (1930), 287–291.Google Scholar
  31. 5.31
    Siebel, E.; Pomp, A.: A new test for thin sheets (in German), Mitt. KWI 11 (1929), 287–291.Google Scholar
  32. 5.32
    Güth, H.: A new stretching test (in German), Metallwirtschaft 20 (1941), 55–58.Google Scholar
  33. 5.33
    Sachs, G.: A new testing device for deep-drawing (in German), Metallwirtschaft 9 (1930), 213–218.Google Scholar
  34. 5.34
    Loxley, E. M.; Swift, H. W.: The wedge drawing test, Engineering 159 (1945), 38–40, 77–80, 136–138.Google Scholar
  35. 5.35
    Guyot, J.: Deep-drawability of thin sheets (in French), Paris, Dunod 1962.Google Scholar
  36. 5.36
    Blume, I.: Assessment of the deep-drawability of sheets (in German), Metallbörse 12 (1922), 1945–1946.Google Scholar
  37. 5.37
    Chow, C. L.; Yu, L. G.: Demeri, M. Y.: A unified damage approach for predicting forming limit diagrans, Trans. ASME, J. Eng. Mater. Technol. 119 (1997), 346–353.CrossRefGoogle Scholar
  38. 5.38
    Hiroi, T.; Nishimura, H.: The influence of surface defects on the forming-limit diagram of steel sheet, J. Mater. Process. Technol. 72 (1997), 102–109.CrossRefGoogle Scholar
  39. 5.39
    Bressan, J. D.: The influence of material defects on the forming ability of sheet metal, J. Mater. Process. Technol. 72 (1997), 11–14.CrossRefGoogle Scholar
  40. 5.40
    Bleck, W.; et al.: A comparative study of the forming limit diagram models for steel sheets, J. Mater. Process. Technol. 83 (1998), 223–228.CrossRefGoogle Scholar
  41. 5.41
    Chung, S. Y.; Swift, H. W.: Cup-drawing from a flat blank, Proc. Inst. Mech. Eng. (1951) 199–223.Google Scholar
  42. 5.42
    Swift, H. W.: The mechanism of a simple drawing operation, Engineering (1954), 431–435.Google Scholar
  43. 5.43
    Swift, H. W.: The mechanism of a simple deep-drawing operation, Sheet Metal Ind. 31 (1954), 817–828.Google Scholar
  44. 5.44
    Willis, J.: Deep-drawing: A review of the practical aspects of professor H. W. Swift’s reseraches. London, Butterworths Scientific Pub. 1954.Google Scholar
  45. 5.45
    Beisswänger, H.; Gunther, H.: On the deep-drawability testing of sheet metal (in German), Werkstatt Betr. 99 (1966), 693–701.Google Scholar
  46. 5.46
    Siebel, E.; Beisswänger, H.: Deep-drawing (in German), München, Carl Hanser Verlag 1955.Google Scholar
  47. 5.47
    Fukui, S.: Researches on the deep-drawing process, Scientific Papers of the I. P. C. R. 34 (1939), 1422–1527.Google Scholar
  48. 5.48
    Yoshida, K.: Classification and systematization of sheet metal press-forming process, Scientific Papers of the I. P. C. R. 53 (1959), 1262–187.Google Scholar
  49. 5.49
    Yoshida, K.; Hayashi, Y.: Developments in research into sheet-metal forming process in Japan, Sheet Metal Industries 55 (1978), 14–17; 56 (1979), 261–270.Google Scholar
  50. 5.50
    Banabic, D.; Dorr, R. I.: Modelling of sheet metal forming (in Romanian), Cluj-Napoca, Transsilvania Press 1995.Google Scholar
  51. 5.51
    Sachs, G.: Sheet metal testing with the Erichsen device (in German), Metallwirtschaft 13 (1934), 78–91.Google Scholar
  52. 5.52
    Petrasch, W.: A deep-drawing test by impact (in German), Mitt. Forsch.-ges. Blechbearbeitung (1951), 209–211.Google Scholar
  53. 5.53
    Eisenkolb, F.: Research on the assessment of the formability of thin sheets (in German), Stahl und Eisen 52 (1932), 357–364.Google Scholar
  54. 5.54
    Engelhardt, W.: Development and first evaluation of a new method for testing deep-drawability (in German). Thesis, TU Dresden 1961.Google Scholar
  55. 5.
    ASTM E 290–97a: Standard test method for bend testing of material for ductility.Google Scholar
  56. 5.56
    Demeri, M. Y.: The stretch-bend forming of sheet metal, J. Appl. Metalwork. 2 (1981), 3–10.CrossRefGoogle Scholar
  57. 5.57
    Narayanaswamy, O. S.; Demeri, M. Y.: Analysis of the angular stretch-bend test, Novel techniques in metal deformation testing, Warrendale, PA, The Metallurgical Society of AIME (1983), 99–112.Google Scholar
  58. 5.58
    Drewes, E. J.; et al.: Proc. IDDRG Meeting Group I, Düsseldorf 1971.Google Scholar
  59. 5.59
    Miles, M. P.; Siles, J. L.; Wagoner, R. H.: Narasimhan, K.: A better formability test, Met. Trans. 24A (1993), 1143–1151.Google Scholar
  60. 5.60
    Lankford, W. I.; Snyder, S. C.; Bauscher, J. A.: New criteria for predicting the press performance of deep-drawing sheet, Trans. ASM 42 (1950), 1196–1232.Google Scholar
  61. 5.61
    Sowerby, R.; Johnson, W.: A review of texture and anisotropy in relation to metal forming, Mat. Sci. Eng. 20 (1975), 101–111.Google Scholar
  62. 5.62
    Mellor, P. B.; Parmar, A.: Plasticity analysis of sheet metal forming. Mechanics of sheet metal forming. Material behavior and deformation analysis. New York/London, Plenum Press 1978, 53–57.Google Scholar
  63. 5.63
    Mellor, P. B.: Experimental studies of plastic anisotropy in sheet metal. In: Hopkins, G. (ed): Mechanics of materials, Oxford, Pergamon Press 1982, 383–415.Google Scholar
  64. 5.64
    Chatfield, D. A.; Keeler, S. P.: Technology for using sheet steel designing for formability, Metal Progress (1971), 60–63.Google Scholar
  65. 5.65
    Lee D.; Majlessi, S. A.; Vogel, J. H.: Process modelling and simulation for sheet forming. In: Newby, J. (ed): Metals Handbook 8`h edn, Vol 14, Metals Park, OH, ASM 1989.Google Scholar
  66. 5.66
    Banabic, D.; Dorr R. I.: Formability of thin sheet metals (in Romanian). Bucarest, O. I. D. I. C. M. 1992.Google Scholar
  67. 5.67
    Whiteley, R. L.: The importance of directionality in deep-drawing quality sheet steel, Trans. ASM 52 (1960), 154–157.Google Scholar
  68. 5.68
    Hill, R.: The mathematical theory of plasticity. Oxford, Clarendon Press 1950.Google Scholar
  69. 5.69
    Hosford, W. F.; Backofen, W. A.: Strength and plasticity of textured metals, in Fundamentals of deformation processing, Syracuse University Press 1964, 259–292.Google Scholar
  70. 5.
    Warwick, J. 0.; Alexander, J. M.: Prediction of the limit drawing ratio from the stress-strain curve, J. Inst. Met. 91 (1962/63), 1–10.Google Scholar
  71. 5.71
    Fukui, S.; Yoshida, K.; Abe, K.: Correlation among experimental values obtained in various formability tests, Sci. Papers Inst. Phys. Chem. Res. 54 (1960), 199–205.Google Scholar
  72. 5.72
    Keeler, S. P.: Plastic instability and fracture in sheet stretched over rigid punches, Thesis, Massachusetts Institute of Technology, Boston, MA 1961.Google Scholar
  73. 5.73
    Gensamer, M.: Strenght and ductility, Trans. ASM 36 (1946), 30–60.Google Scholar
  74. 5.74
    Keeler, S. P.; Backofen, W. A.: Plastic instability and fracture in sheets stretched over rigid punches, Trans. ASM 56 (1963), 25–48.Google Scholar
  75. 5.75
    Goodwin, G. M.: Application of strain analysis to sheet metal forming problems in the press shop, Society of Automotive Engineers (1968), No. 680093, 380–387.Google Scholar
  76. 5.76
    Havranek, B.: The effect of mechanical properties on wrinkling in conical shells, J. Mech. Technol. 1 (1977), 115–29.CrossRefGoogle Scholar
  77. 5.77
    Arrieux, R.: Contribution to the determination of forming limit curves of titanium and aluminum. Proposal of an intrinsic criterion (in French), Thesis, INSA, Lyon 1981.Google Scholar
  78. 5.78
    Brozzo, P.; De Luca, B.; Rendina, R.: A new method for the prediction of the formability limits of metal sheets. In: 7h Biennual Congr.of the IDDRG, Amsterdam 1972.Google Scholar
  79. 5.79
    Hasek, V.; On the strain and stress states in drawing of large unregular sheet metal components (in German). Berichte aus dem Institut für Umformtechnik, Universität Stuttgart, Nr. 25, Essen, Girardet 1973.Google Scholar
  80. 5.80
    Nakazima, K.; Kikuma, T.; Hasuka, K.: Study on the formability of steel sheets, Yawata Tech. Rep. No. 284 (1971), 678–680.Google Scholar
  81. 5.81
    Hasek, V.: Research and theoretical description concerning the influences on the FLDs (in German), Blech Rohre Profile 25 (1978), 213–220, 285–292, 493–399, 617–627.Google Scholar
  82. 5.82
    Doege, E.; Kruskja, J.-U.; Schroeder, M.; Stock, G.: Description of cold workability of thin steel sheet by parameters determined by friction-less methods (in German), Blech Rohre Profile 40 (1993), 457–467.Google Scholar
  83. 5.83
    Grumbach, M.; Sanz, G.: Influence of various parameters on forming limit curves (in French), Rev. de Metallurgie 61 (1972), 273–290.Google Scholar
  84. 5.84
    Parniere, P.; Sanz, G.: Formability of thin sheet (in French). In: Baudelet, B. (ed): Forming of metals and alloys (in French), Paris, Editions CNRS 1976, 305–330.Google Scholar
  85. 5.85
    Kikuma, T.; Nakazima, K.: Aspects of deforming conditions and mechanical properties in the stretch forming limits of sheet metals, Trans. ISIJ 11 (1971), 827–830.Google Scholar
  86. 5.86
    Yoshida, K.; Hayashi, Y.: Developments in research into sheet metal forming pro- cesses in Japan, Sheet Metal Ind. 55 (1978), 714–720; 56 (1979), 261–267.Google Scholar
  87. 5.87
    Rault, D.: Description of deep-drawing (in French), in Baudelet, B. (ed): Forming of metals and alloys (in French), Paris, Editions CNRS 1976, 297–303.Google Scholar
  88. 5.88
    Banabic, D.: Research on thin sheet formability (in Romanian), Thesis, Technical University of Cluj-Napoca, Romania 1993.Google Scholar

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© Springer-Verlag Berlin Heidelberg 2000

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  • D. Banabic

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