Hostname: page-component-7c8c6479df-xxrs7 Total loading time: 0 Render date: 2024-03-29T00:20:15.970Z Has data issue: false hasContentIssue false

A Gurson Yield Function for Anisotropic Porous Sheet Metals and its Applications to Failure Prediction of Aluminum Sheets

Published online by Cambridge University Press:  05 May 2011

D.-A. Wang*
Affiliation:
Department of Mechanical Engineering, The University of Michigan, Ann Arbor, MI 48109, U.S.A.
W. Y. Chien*
Affiliation:
Department of Mechanical Engineering, The University of Michigan, Ann Arbor, MI 48109, U.S.A.
K. C. Liao*
Affiliation:
Department of Mechanical Engineering, Mingchi Institute of Technology, Taipei Hsien, Taiwan 243, R.O C.
J. Pan*
Affiliation:
Department of Mechanical Engineering, The University of Michigan, Ann Arbor, MI 48109, U.S.A.
S. C. Tang*
Affiliation:
Department of Mechanical Engineering, The University of Michigan, Ann Arbor, MI 48109, U.S.A.
*
*Graduate student
*Graduate student
**Assistant Professor
***Professor
****Visiting Scholar
Get access

Abstract

An approximate anisotropic yield function is presented for anisotropic sheet metals containing spherical voids. Hill's quadratic anisotropic yield function is used to describe the anisotropy of the matrix. The proposed yield function is validated using a three-dimensional finite element analysis of a unit cell model under different straining paths. The results of the finite element computations are shown in good agreement with those based on the yield function with three fitting parameters. For demonstration of applicability, the anisotropic Gurson yield function is adopted in a combined necking and shear localization analysis to model the failure of AA6111 aluminum sheets under biaxial stretching conditions.

Type
Articles
Copyright
Copyright © The Society of Theoretical and Applied Mechanics, R.O.C. 2003

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

1Worswick, M. J., Pilkey, A. K., Lloyd, D. and Court, S., “Damage Characterization and Damage Percolation Modelling in Aluminum Alloy Sheet,” SAE Paper 2000-01-0773, Society of Automotive Engineers, Warrendale, PA (2000).CrossRefGoogle Scholar
2Gurson, A. L., “Continuum Theory of Ductile Rupture by Void Growth: Part I – Yield Criteria and Flow Rules for Porous Ductile Media,” J. Eng. Mater. Tech., 99, pp. 215 (1977).CrossRefGoogle Scholar
3Yamamoto, H., “Conditions for Shear Localization in the Ductile Fracture of Void Containing Materials,” Int. J. Fract., 11, pp. 347365 (1978).CrossRefGoogle Scholar
4Needleman, A. and Triantafyllidis, N., “Void Growth and Local Necking in Biaxial Stretched Sheets,” J. Eng. Mater. Tech., 100, pp. 164169 (1978).CrossRefGoogle Scholar
5Saje, M., Pan, J. and Needleman, A., “Void Nucleation Effects on Shear Localization in Porous Plastic Solids,” Int. J. Fract., 19, pp. 163182 (1982).CrossRefGoogle Scholar
6Tvergaard, V., “Influence of Voids on Shear Band Instabilities Under Plane Strain Conditions,” Int. J. Fract., 17, pp. 389407 (1981).CrossRefGoogle Scholar
7Mear, M. E. and Hutchinson, J. W., “Influence of Yield Surface Curvature on Flow Localization in Dilatant Plasticity,” Mech. Mater., 4, pp. 395407 (1985).CrossRefGoogle Scholar
8Tvergaard, V., “On Localization in Ductile Materials Containing Spherical Voids,” Int. J. Fract., 18, pp. 237252 (1982).CrossRefGoogle Scholar
9Pan, J., Saje, M. and Needleman, A., “Localization of Deformation in Rate Sensitive Porous Plastic Solids,” Int. J. Fract., 21, pp. 261278 (1983).CrossRefGoogle Scholar
10Tvergaard, V. and Needleman, A., “Analysis of the Cup-Cone Fracture in a Round Tensile Bar,” Acta Metal., 32, pp. 157169 (1984).CrossRefGoogle Scholar
11Graf, A. and Hosford, W. F., “Calculations of Forming Limit Diagrams,” Metall. Trans., 21A, pp. 8794 (1990).CrossRefGoogle Scholar
12Hill, R., “A Theory of the Yielding and Plastic Flow of Anisotropic Metals,” Roy. Soc. London Proc., 193A, pp. 281297 (1948).Google Scholar
13Hosford, W. F., “On Yield Loci of Anisotropic Cubic Metals,” Proc. 7th North Am. Metalworking Res. Conf., SME, Dearborn, MI, pp. 191196 (1979).Google Scholar
14Liao, K.-C., Pan, J. and Tang, S. C., “Approximate Yield Criteria for Anisotropic Porous Ductile Sheet Metals,” Mech. Mater., 26, pp. 213226 (1997).CrossRefGoogle Scholar
15Hill, R., “Theoretical Plasticity of Textured Aggregates,” Math. Proc. Camb. Phil. Soc., 85, pp. 179191 (1979).CrossRefGoogle Scholar
16Chien, W. Y., Pan, J. and Tang, S. C., “Modified Anisotropic Gurson Yield Criterion for Porous Ductile Sheet Metals,” J. Eng. Mater. Tech., 123, pp. 409416 (2001).CrossRefGoogle Scholar
17Barlat, 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., “Yield Function Development for Aluminum Alloy Sheets,” J. Mech. Phys. Solids, 45, pp. 17271763 (1997).CrossRefGoogle Scholar
18Yoon, J. W., Barlat, F. and Dick, R. E., “Sheet Metal Forming Simulation for Aluminum Alloy Sheets,” SAE Paper 2000-01-0774, Society of Automotive Engineers, Warrendale, PA (2000).Google Scholar
19Liao, K.-C, Friedman, P. A., Pan, J. and Tang, S. C., “Texture Development and Plastic Anisotropy of B.C.C. Strain Hardening Sheet Metals,” Int. J. Solids Struct., 35, pp. 52055236 (1998).CrossRefGoogle Scholar
20Wang, D.-A., Pan, J. and Liu, S.-D., “An Anisotropic Gurson Yield Criterion for Porous Ductile Sheet Metals with Planar Anisotropy,” submitted for publication in Int. J. Damage Mech. (2002).Google Scholar
21Hibbitt, H. D., Karlsson, B. I. and Sorensen, E. P., ABAQUS User Manual, Version 6-2 (2001).Google Scholar
22Chien, W. Y., Pan, J. and Tang, S. C., “A Combined Necking and Shear Localization Analysis of Aluminum Sheet Failure Under Biaxial Stretching Conditions,” to be submitted for publication (2002).Google Scholar
23Hill, R., “Acceleration Waves in Solids,” J. Mech. Phys. Solids, 10, pp. 116 (1962).CrossRefGoogle Scholar
24Rice, J. R., “The Localization of Plastic Deformation,” Proc. 14th Int. Cong. Theor. Appl. Mech., ed. Koiter, W. T., Delft, North-Holland, 1, pp. 207220 (1976).Google Scholar
25Jain, M., Allin, J. and Lloyd, D. J., “Fracture Limit Prediction Using Ductile Fracture Criteria for Forming of an Automotive Aluminum Sheet,” Int. J. Mech. Sci., 41, pp. 12731288 (1999).CrossRefGoogle Scholar