0
TECHNICAL PAPERS

Modified Anisotropic Gurson Yield Criterion for Porous Ductile Sheet Metals

[+] Author and Article Information
W. Y. Chien, J. Pan

Mechanical Engineering, The University of Michigan, Ann Arbor, MI 48109

S. C. Tang

Ford Research Laboratory, Ford Motor Company, Dearborn, MI 48121

J. Eng. Mater. Technol 123(4), 409-416 (Jul 25, 2000) (8 pages) doi:10.1115/1.1395023 History: Received July 25, 2000
Copyright © 2001 by ASME
Your Session has timed out. Please sign back in to continue.

References

Gurson,  A. L., 1977, “Continuum theory of ductile rupture by void growth: part I—yield criteria and flow rules for porous ductile media,” ASME J. Eng. Mater. Technol., 99, p. 2.
Yamamoto,  H., 1978, “Conditions for shear localization in the ductile fracture of void-containing materials,” Int. J. Fract., 14, p. 347.
Needleman,  A., and Triantafyllidis,  N., 1978, “Void growth and local necking in biaxial stretched sheets,” ASME J. Eng. Mater. Technol., 100, p. 164.
Saje,  M., Pan,  J., and Needleman,  A., 1982, “Void nucleation effects on shear localization in porous plastic solids,” Int. J. Fract., 19, p. 163.
Tvergaard,  V., 1981, “Influence of voids on shear band instabilities under plane strain conditions,” Int. J. Fract., 17, p. 389.
Tvergaard,  V., 1982, “On localization in ductile materials containing spherical voids,” Int. J. Fract., 18, p. 237.
Pan,  J., Saje,  M., and Needleman,  A., 1983, “Localization of deformation in rate sensitive porous plastic solids,” Int. J. Fract., 21, p. 261.
Tvergaard,  V., and Needleman,  A., 1984, “Analysis of the cup-cone fracture in a round tensile bar,” Acta Metall., 32, p. 157.
Hill,  R., 1948, “A theory of the yielding and plastic flow of anisotropic metals,” Proc. R. Soc. London, Ser. A, A193, p. 281.
Hill,  R., 1979, “Theoretical plasticity of textured aggregates,” Math. Proc. Cambridge Philos. Soc., 85, p. 179.
Gotoh,  M., 1977, “A theory of plastic anisotropy based on a yield function of fourth order (plane stress state),” Int. J. Mech. Sci., 19, p. 505.
Budianski, B., 1984, “Anisotropic plasticity of plane-isotropic sheets,” Dvorak, G. J. and Shield, R. T. eds., Mechanics of Material Behavior, Elsevier, Amsterdam, p. 15.
Logan,  R. W., and Hosford,  W. F., 1980, “Upper-bound anisotropic yield locus calculations assuming 〈111〉 pencil glide,” Int. J. Mech. Sci., 22, p. 419.
Bassani,  J. L., 1977, “Yield characterization of metals with transversely isotropic plastic properties,” Int. J. Mech. Sci., 19, p. 651.
Barlat,  F., Lege,  D. J., and Brem,  J. C., 1991, “A six-component yield function for anisotropic materials,” Int. J. Plast., 7, p. 693.
Barlat,  F., Maeda,  Y., Chung,  K., Yanagawa,  M., Brem,  J. C., Hayashida,  Y., Lege,  D. J., Matsui,  K., Murtha,  S. J., Hattori,  S., Becker,  R. C., and Makosey,  S., 1997, “Yield function development for aluminum alloy sheets,” J. Mech. Phys. Solids, 45, p. 1727.
Liao,  K.-C., Pan,  J., and Tang,  S. C., 1997, “Approximate yield criteria for anisotropic porous ductile sheet metals,” Mech. Mater. 26, p. 213.
Chen, B., Wu, P. D., MacEwen, S. R., Xia, Z. C., Tang, S. C., and Huang, Y., 2000, “Dilational plasticity for porous anisotropic aluminum sheet based on Barlat et al.’s model,” Presented at SAE 2000 World Congress, Detroit, MI, Mar. 6–9.
Hom,  C. L., and McMeeking,  R. M., 1989, “Void growth in elastic-plastic materials,” ASME J. Appl. Mech., 56, p. 309.
Jeong,  H.-Y., and Pan,  J., 1995, “A macroscopic constitutive law for porous solids with pressure-sensitive matrices and its implications to plastic flow localization,” Int. J. Solids Struct., 32, p. 3669.
Liao,  K.-C, Friedman,  P. A., Pan,  J., and Tang,  S. C., 1998, “Texture development and plastic anisotropy of B. C. C. strain hardening sheet metals,” Int. J. Solids Struct., 35, p. 5205.
Hibbitt, H. D., Karlsson, B. I., and Sorensen, E. P., 1998, ABAQUS User Manual, Version 5–8.
Pardoen,  T., and Hutchinson,  J. W., 2000, “An extended model for void growth and coalescence,” J. Mech. Phys. Solids, 48, p. 2467.
Huang,  H.-M., Pan,  J., and Tang,  S. C., 2000, “Failure prediction in anisotropic sheet metals under forming operation with consideration of rotating principal stretch directions,” Int. J. Plast., 16, p. 611.
Huang, H.-M., Pan, J., and Tang, S. C., 2001, “Failure prediction in anisotropic sheet metals containing voids under biaxial straining conditions with pre-bending/unbending,” Int. J. Plast.
Chien, W. Y., Huang, H.-M., Pan, J., and Tang, S. C., 2000, “Approximate yield criterion for anisotropic porous sheet metals and its applications to failure prediction of sheet metals under forming processes,” to appear in Multiscale Deformation and Fracture in Materials and Structures, The James Rice 60th Anniversary Volume, T.-J. Chuang and J. W. Rudnicki, eds., Kluwer Academic Publisher, The Netherlands.
Tandon,  G. P., and Weng,  G. J., 1988, “A theory of particle-reinforced plasticity,” ASME J. Appl. Mech., 55, p. 126.

Figures

Grahic Jump Location
A three-dimensional model containing a periodic array of voids
Grahic Jump Location
One-eighth of the voided cube model
Grahic Jump Location
Finite element computational results (open symbols) and the results based on the unmodified anisotropic Gurson yield criteria (curves) for: (a) R=0.8 and (b) R=1.6
Grahic Jump Location
Finite element computational results (open symbols) and the results based on the modified anisotropic Gurson yield criteria (curves) for: (a) R=0.8 and (b) R=1.6
Grahic Jump Location
The macroscopic stress-strain relations based on the finite element results, and the unmodified and modified anisotropic Gurson yield criterion under uniaxial tensile conditions for (a) f=0.01 and R=0.8; (b) f=0.01 and R=1.6; (c) f=0.09 and R=0.8; (d) f=0.09 and R=1.6
Grahic Jump Location
The macroscopic stress-strain relations based on the finite element results, and the unmodified and modified anisotropic Gurson yield criterion under equal biaxial tensile conditions for (a) f=0.01 and R=0.8; (b) f=0.01 and R=1.6; (c) f=0.09 and R=0.8; (d) f=0.09 and R=1.6
Grahic Jump Location
The deformed meshes with f=0.01 under uniaxial tensile conditions at E11=0.5 for (a) R=0.8; (b) R=1.6
Grahic Jump Location
The deformed meshes with f=0.01 under equal biaxial tensile conditions at E11=0.25 for (a) R=0.8; (b) R=1.6

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In