Prediction of Forming Limit Diagram Based on Damage Coupled Kinematic-Isotropic Hardening Model Under Nonproportional Loading

[+] Author and Article Information
C. L. Chow, X. J. Yang

Department of Mechanical Engineering, University of Michigan-Dearborn, Dearborn, MI 48128

E. Chu

Alcoa Inc., Alcoa Technical Center, Alcoa Center, PA 15069-0001

J. Eng. Mater. Technol 124(2), 259-265 (Mar 26, 2002) (7 pages) doi:10.1115/1.1431908 History: Received December 13, 2000; Revised April 03, 2001; Online March 26, 2002
Copyright © 2002 by ASME
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Sing,  W. M., and Rao,  K. P., 1997, “Study of Sheet Metal Failure Mechanisms Based on Stress-state Conditions,” J. Mater. Process. Technol., 67, pp. 201–206.
Arrieux,  R., 1995, “Determination and Use of the Forming Limit Stress Diagrams,” J. Mater. Process. Technol., 53, pp. 47–56.
Takuda,  H., Mori,  K., Takakura,  N., and Yamaguchi,  K., 2000, “Finite Element Analysis of Limit Strains in Biaxial Stretching of Sheet Metals Allowing for Ductile Fracture,” Int. J. Mech. Sci., 42, pp. 785–798.
Laukonis,  J. V., and Ghosh,  A. K., 1978, “Effect of Strain Path Changes on the Formability of Sheet Metals,” Metall. Trans. A, 9A, pp. 1849–1856.
Graf,  A. F., and Hosford,  W., 1993, “Calculation of Forming Limit Diagrams for Changing Strain Paths,” Metall. Trans. A, 24A, pp. 2497–2501.
Graf,  A. F., and Hosford,  W., 1994, “The Influence of Strain-Path Changes on Forming Limit Diagram of AL 6111-T4,” Int. J. Mech. Sci., 36, pp. 897–910.
Barata da Rocha,  A., Barlat,  F., and Jalinier,  J. M., 1984, “Prediction of the Forming Limit Diagram of Anisotropic Sheets in Linear and Nonlinear Loading,” Mater. Sci. Eng., 68, pp. 151–164.
Wang,  J., and Chow,  C. L., 1989, “Hysteretic Effects of Damage and Stress on Ductile Fracture Characterization,” Eng. Fract. Mech., 34, pp. 209–220.
Chow,  C. L., Yu,  L. G., and Demeri,  M. Y., 1997, “A Unified Damage Approach for Predicting Forming Limit Diagrams,” ASME J. Eng. Mater. Technol., 119, pp. 346–353.
Hayakawa,  K., and Murakami,  S., 1997, “Thermodynamical Modeling of Elastic-Plastic Damage and Experimental Validation of Damage Potential,” Int. J. Damage Mech., 6, pp. 333–363.
Chaboche,  J. L., 1992, “Damage Induced Anisotropy: On the Difficulties Associated with the Active/Passive Unilateral Condition,” Int. J. Damage Mech., 1, pp. 148–171.
Ju,  J. W., 1990, “Isotropic and Anisotropic Damage Variable in Continuum Damage Mechanics,” J. Eng. Mech., 116, pp. 2764–2770.
Demeri, M. Y., Chow, C. L., and Tai, W. H., 1998, “Predication and Experimental Validation of Path-dependent Forming Limit Diagram of VDIF Steel,” Developments in Sheet Metal Stamping, SAE SP-1322, pp. 53–58.
Chow,  C. L., and Tai,  W. H., 2000, “Damage Based Formability Analysis of Sheet Metal with LS-DYNA,” Int. J. Damage Mech., 9, No. 3, pp. 241–254.
Chow, C. L., Yang, X. J., and Chu, E., 2000, “Viscoplastic Constitutive Modelling of Anisotropic Damage under Nonproportional Loading,” International Mechanical Engineering Congress and Exposition, Proceedings of the ASME Manufacturing Engineering Division, MED- Vol. 11, pp. 705–711.
Chow,  C. L., and Yang,  X. J., 2001, “Prediction of Forming Limit Diagram Based on Damage Criterion under Nonproportional Loading,” J. Mech. Eng. Sci., 215, 405–414.
Hill,  R., 1948, “A Theory of Yield and Plastic Flow of Anisotropic Metals,” Proc. R. Soc. London, Ser. A, A193, pp. 281–297.
Prager,  W., 1955, “The Theory of Plasticity: a Survey of Recent Achievements,” Proc. Inst. Mech. Eng., 169, pp. 41–57.
Chaboche,  J. L., and Jung,  O., 1998, “Application of a Kinematic Hardening Viscoplasticity Model with Thresholds to the Residual Stress Relaxation,” Int. J. Plast., 13, pp. 785–807.
Moosbrugger,  J. C., 2000, “Anisotropic Nonlinear Hardening Rule Parameters from Reversed Proportional Axial-torsional Cycling,” ASME J. Eng. Mater. Technol., 122, pp. 18–28.
Wu,  H. C., Hong,  H. K., and Shiao,  Y. P., 1999, “Anisotropic Plasticity with Application to Sheet Metals,” Int. J. Mech. Sci., 41, 703–724.
Chaboche,  I. L., 1993, “Cyclic Viscoplastic Constitutive Equations, Part I: A Thermodynamically Consistent Formulation,” ASME J. Appl. Mech., 60, pp. 813–820.
Mroz,  Z., 1967, “On the Description of Anisotropic Work Hardening,” J. Mech. Phys. Solids, 15, pp. 163–175.
Dafalias,  Y. F., and Popov,  E. P., 1976, “Plastic Internal Variables Formalism of Cyclic Plasticity,” ASME J. Appl. Mech., 98, pp. 645–651.
McDowell,  D. L., 1985, “An Experimental Study of the Structure of Constitutive Equations for Nonproportional Cyclic Plasticity,” ASME J. Eng. Mater. Technol., 107, pp. 307–315.
Geng, L., and Wagoner, R. H., 2000, “Springback Analysis with a Modified Hardening Model,” Sheet Metal Forming: Sing Tang 65th Anniversary Volume, SAE SP-1536, pp. 21–31.
Armstrong, P. J., and Frederick, C. O.1966, “A Mathematical Representation of the Multiaxial Bauschinger Effect,” CEGB Report RD/B/N73 1, Central Electricity Generating Board.
Chow,  C. L., and Yang,  X. J., 2001, “Effect of Principal Damage Plane Rotation on Anisotropic Damage Plastic Model,” Int. J. Damage Mech., 10, No. 1, pp. 43–55.
Chow,  C. L., and Chen,  X. F., 1992, “An Anisotropic Model of Damage Mechanics Based on Endochronic Theory of Plasticity,” Int. J. Fract., 55, pp. 115–130.
Chow,  C. L., and Wang,  J., 1988, “Ductile Fracture Characterization with an Anisotropic Continuum Damage Theory,” Eng. Fract. Mech., 30, pp. 547–563.
Chow, C. L., Yu, L. G., and Demeri, M. Y., 1996, “Prediction of Forming Limit Diagram with Damage Analysis,” SAE Technical Paper Series 960598, pp. 73–80.


Grahic Jump Location
FLDs with equibiaxial prestrains
Grahic Jump Location
FLDs with prestrains normal to RD
Grahic Jump Location
Experimental and predicted FLDs for as-received and prestrained specimens



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