Skip to main content
SpringerLink
Log in

A lower bound damage-based finite element simulation of stretch flange forming of Al–Mg alloys

  • Research Article
  • Published:
International Journal of Fracture Aims and scope Submit manuscript

Abstract

Numerical simulation of stretch flange forming of Al–Mg sheet AA5182 was performed using the upper and lower bound constitutive models of Gurson–Tvergaard–Needleman (GTN) and Sun and Wang, respectively. Stress and strain-controlled nucleation rules are adopted for both models. The lower bound model of Sun and Wang has been extended to include the void coalescence criterion of Tvergaard and Needleman to form the so-called Sun–Tvergaard–Needleman (STN) model. Upper and lower bound formability predictions are combined to create a predictive formability band as actual formability lies between these limits. The resulting formability predictions are compared with experimental results and an appropriate void nucleation stress and strain suggested.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Chein WY, Pan J, Tang SC (2001) Modified anisotropic Gurson yield criterion for porous ductile sheet metals. J Eng Mater Technol 132:409–416

    Article  Google Scholar 

  • Chen ZT (2004) The role of heterogeneous particle distribution in the prediction of ductile fracture. Ph.D. Thesis, University of Waterloo, Canada

  • Chen ZT, Worswick MJ, Pilkey AK, Lloyd DJ (2005) Damage percolation during stretch flange forming of aluminum sheet. J Mech Phys Solids 53:2692–2717

    Article  ADS  Google Scholar 

  • Chen ZT, Worswick MJ, Lloyd DJ (2006) Damage-based finite element modeling of stretch flange forming of aluminum-magnesium alloy. Mater Sci Forum 519–521:815–820

    Google Scholar 

  • Chu CC, Needleman A (1980) Void nucleation effects in biaxially stretched sheets. J Eng Mater Technol 102:249–256

    Article  Google Scholar 

  • Cinotti N (2003) Stretch flange formability of aluminum alloy. Master Thesis, University of Waterloo, Canada

  • Francescato P, Pastor J, Riveill-Reydet B (2004) Ductile failure of cylindrically porous materials. Part I – plane stress problem and experimental results. Eur J Mech Solids 23:181–190

    Article  MATH  Google Scholar 

  • Gurson AL (1977) Continuum theory of ductile rupture by void nucleation and growth – Part I. Yield criteria and flow rules for porous ductile media. J Eng Mater Technol 99:2–15

    Google Scholar 

  • Leblond JB, Perrin G, Devaux J (1994) Bifurcation effects in ductile metals with damage delocalization. J Appl Mech 61:236–242

    MATH  Google Scholar 

  • Liao KC, Pan J, Tang SC (1997) Approximate yield criteria for anisotropic porous ductile sheet metals. Mech Mater 26:213–226

    Article  Google Scholar 

  • Lievers WB, Pilkey AK, Lloyd DJ (2003) The influence of iron content on the bendability of AA6111 sheet. Mater Sci Eng A 361:312–320

    Article  Google Scholar 

  • Lievers WB, Pilkey AK, Lloyd DJ (2004) Using incremental forming to calibrate a void nucleation model for automotive aluminum sheet alloys. Acta Mater 52: 3001–3007

    Article  Google Scholar 

  • Needleman A (1987) Continuum model for void nucleation by inclusion debonding. J Appl Mech 54:525–531

    Article  MATH  Google Scholar 

  • Pardoen T, Hutchinson JW (2000) An extended model for void growth and coalescence. J Mech Phys Solids 48:2567–2512

    Google Scholar 

  • Reusch F, Svendsen B, Klingbeil D (2003) Local and non-local Gurson-based ductile damage and failure modeling at large deformation. Eur J Mech Solids 22:779–792

    Article  MATH  Google Scholar 

  • Richmond O, Smelser RE (1985) Alcoa Technical Center Memorandum

  • Saje M, Pan J, Needleman A (1982) Void nucleation effects on shear localization in porous plastic solids. Int J Fract 19:163–182

    Article  Google Scholar 

  • Shabrov MN, Needleman A (2002) An analysis of inclusion morphology effects on void nucleation. Model Simul Mater Sci Eng 10:163–183

    Article  ADS  Google Scholar 

  • Shima S, Oyane M (1976) Plasticity theory for porous metals. Int J Mech Sci 18:285–291

    Article  Google Scholar 

  • Sun Y (1995a) Influence of void nucleation and growth on deformation localization in tensile sheet specimen. Eng Fract Mech 51:381–395

    Article  Google Scholar 

  • Sun Y (1995b) Constitutive equations for ductile materials containing large and small voids. Mech Mater 19:119–127

    Article  Google Scholar 

  • Sun Y, Wang D (1989) A lower bound approach to the yield loci of porous materials. Acta Mech Sin 5:237–243

    Article  Google Scholar 

  • Sun Y, Wang D (1995) Analysis of shear localization in porous materials based on a lower bound approach. Int J Fract 71:71–83

    Article  Google Scholar 

  • Thomason PF (1990) Ductile fracture of metals. Pergamon Press Inc., Oxford

    Google Scholar 

  • Tszeng TC (2000) Interfacial stresses and void nucleation in discontinuously reinforced composites. J Eng Mater Technol 122:86–92

    Article  Google Scholar 

  • Tvergaard V (1981) Influence of voids on shear band instabilities under plane strain conditions. Int J Fract 17:389–407

    Article  Google Scholar 

  • Tvergaard V (1982) Ductile fracture by cavity nucleation between larger voids. J Mech Phys Solids 30:265–286

    Article  MATH  ADS  Google Scholar 

  • Tvergaard V, Needleman A (1984) Analysis of the cup-cone fracture in a round tensile test bar. Acta Metall 32:157–169

    Article  Google Scholar 

  • Tvergaard V, Needleman A (1995) Effects of non-local in porous plastic solids. Int J Solids Struct 8:1063–1077

    Article  Google Scholar 

  • Wang DA, Pan J, Liu SD (2004) An anisotropic yield criterion for porous ductile sheet metals with planar anisotropy. Int J Damage Mech 13:7–33

    Article  Google Scholar 

  • Wen J, Huang Y, Hwang KC, Liu C, Li M (2005) The modified Gurson model accounting for the void size effect. Int J Plast 21:381–395

    Article  MATH  Google Scholar 

  • Worswick MJ, Pelletier P (1998) Numerical simulation of ductile fracture during high strain rate deformation. Eur Phys J Appl Phys 4:257–267

    Article  ADS  Google Scholar 

  • Yan XQ (1992) Effect of yield surface curvature on local necking in biaxially stretched sheets in porous materials. J Eng Mater Technol 114:196–200

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mechanical Engineering, University of New Brunswick, Fredericton, NB, E3B 5A3, Canada

    Cliff Butcher & Zengtao Chen

  2. Department of Mechanical and Mechatronics Engineering, University of Waterloo, Waterloo, ON, N2L 3G1, Canada

    Michael Worswick

Authors
  1. Cliff Butcher
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Zengtao Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Michael Worswick
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Cliff Butcher.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Butcher, C., Chen, Z. & Worswick, M. A lower bound damage-based finite element simulation of stretch flange forming of Al–Mg alloys. Int J Fract 142, 289–298 (2006). https://doi.org/10.1007/s10704-006-9044-3

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10704-006-9044-3

Keywords

Search

Navigation