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Title: Constitutive Modeling of Magnesium Alloy Sheets

Abstract

Magnesium alloy sheets have unique mechanical properties: high in-plane anisotropy/asymmetry of yield stress and hardening response, which have not been thoroughly studied. The unusual mechanical behavior of magnesium alloys has been understood by the limited symmetry crystal structure of h.c.p metals and thus by deformation twinning. In this paper, the phenomenological continuum plasticity models considering the unusual plastic behavior of magnesium alloy sheet were developed for a finite element analysis. A new hardening law based on two-surface model was developed to consider the general stress-strain response of metal sheets such as Bauschinger effect, transient behavior and the unusual asymmetry. Three deformation modes observed during the continuous tension/compression tests were mathematically formulated with simplified relations between the state of deformation and their histories. In terms of the anisotropy and asymmetry of the initial yield stress, the Drucker-Prager's pressure dependent yield surface was modified to include the anisotropy of magnesium alloys. Also, characterization procedures of material parameters for the constitutive equations were presented and finally the correlation of simulation with measurements was performed to validate the proposed theory.

Authors:
; ;  [1];  [2];  [3];  [4]
  1. Department of Materials Science and Engineering, 2041 College Road, Ohio State University, Columbus, OH 43210 (United States)
  2. Department of Mechanical Engineering, Scott Laboratory, 201 West 19th Avenue, Ohio State University, Columbus, OH 43210 (United States)
  3. School of Materials Science and Engineering, Intelligent Textile System Research Center, Seoul National University, 56-1, Shinlim-Dong, Kwanak-Ku, Seoul 151-742 (Korea, Republic of)
  4. Division of Mechanical Engineering and Mechatronics, Kangwon National University, 192-1 Hyoja 2-Dong, Chunchon, Gangwon-Do, 200-701 (Korea, Republic of)
Publication Date:
OSTI Identifier:
21061741
Resource Type:
Journal Article
Resource Relation:
Journal Name: AIP Conference Proceedings; Journal Volume: 908; Journal Issue: 1; Conference: NUMIFORM 2007: 9. international conference on numerical methods in industrial forming processes, Porto (Portugal), 17-21 Jun 2007; Other Information: DOI: 10.1063/1.2740887; (c) 2007 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
36 MATERIALS SCIENCE; ANISOTROPY; ASYMMETRY; COMPRESSION; COMPUTERIZED SIMULATION; CORRELATIONS; CRYSTAL STRUCTURE; CRYSTALS; DEFORMATION; FINITE ELEMENT METHOD; HARDENING; MAGNESIUM ALLOYS; PLASTICITY; PRESSURE DEPENDENCE; SHEETS; STRAINS; STRESSES; SURFACES; SYMMETRY; TRANSIENTS; TWINNING

Citation Formats

Lee, M. G., Piao, K., Wagoner, R. H., Lee, J. K., Chung, K., and Kim, H. Y. Constitutive Modeling of Magnesium Alloy Sheets. United States: N. p., 2007. Web. doi:10.1063/1.2740887.
Lee, M. G., Piao, K., Wagoner, R. H., Lee, J. K., Chung, K., & Kim, H. Y. Constitutive Modeling of Magnesium Alloy Sheets. United States. doi:10.1063/1.2740887.
Lee, M. G., Piao, K., Wagoner, R. H., Lee, J. K., Chung, K., and Kim, H. Y. Thu . "Constitutive Modeling of Magnesium Alloy Sheets". United States. doi:10.1063/1.2740887.
@article{osti_21061741,
title = {Constitutive Modeling of Magnesium Alloy Sheets},
author = {Lee, M. G. and Piao, K. and Wagoner, R. H. and Lee, J. K. and Chung, K. and Kim, H. Y.},
abstractNote = {Magnesium alloy sheets have unique mechanical properties: high in-plane anisotropy/asymmetry of yield stress and hardening response, which have not been thoroughly studied. The unusual mechanical behavior of magnesium alloys has been understood by the limited symmetry crystal structure of h.c.p metals and thus by deformation twinning. In this paper, the phenomenological continuum plasticity models considering the unusual plastic behavior of magnesium alloy sheet were developed for a finite element analysis. A new hardening law based on two-surface model was developed to consider the general stress-strain response of metal sheets such as Bauschinger effect, transient behavior and the unusual asymmetry. Three deformation modes observed during the continuous tension/compression tests were mathematically formulated with simplified relations between the state of deformation and their histories. In terms of the anisotropy and asymmetry of the initial yield stress, the Drucker-Prager's pressure dependent yield surface was modified to include the anisotropy of magnesium alloys. Also, characterization procedures of material parameters for the constitutive equations were presented and finally the correlation of simulation with measurements was performed to validate the proposed theory.},
doi = {10.1063/1.2740887},
journal = {AIP Conference Proceedings},
number = 1,
volume = 908,
place = {United States},
year = {Thu May 17 00:00:00 EDT 2007},
month = {Thu May 17 00:00:00 EDT 2007}
}
  • To examine the deformation characteristic of type 5000 and 6000 aluminum alloy sheets, uniaxial tension, biaxial stretching and in-plane cyclic tension-compression experiments were performed, and from these, r-values (r{sub 0}, r{sub 45} and r{sub 90}), yield loci and cyclic stress-strain responses were obtained. For the accurate description of anisotropies of the materials, high-ordered anisotropic yield functions, such as Gotoh's biquadratic yield function and Barlat's Yld2000-2d, are necessary. Furthermore, for the simulation of cyclic behavior, an advanced kinematic hardening model, such as Yoshida-Uemori model (Y-U model), should be employed. The effect of the selection of material models on the accuracy ofmore » the springback prediction was discussed by performing hat bending FE simulation using several yield functions and two types of hardening laws (the isotropic hardening model and Y-U model).« less
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  • The main aim of this paper is to study the flow behavior of the AZ31B magnesium alloy by means of tensile tests performed in extended ranges of temperature and strain rates. The flow stress-strain curves analyzed by power law type constitutive equation can only fit well with experimental curves at the work-hardening stage. A new mathematical model is studied to describe the softening behavior of material based on tensile experiments. The relative parameters are obtained by fitting the equation with the experimental data. The genetic algorithm has been used to obtain the global optimal fitting parameters. The comparison between themore » fitted and experimental data proves the effectiveness of the model. The results indicate that this model leads to a better simulation of the flow stress during the softening stage than that of the power law equation. Based on this model, the deep drawing process has been simulated with the commercial finite element code FORGE registered. The punch load and thickness distribution of AZ31 sheet have been studied. The study of the results is helpful to the application of the stamping technology for the magnesium alloy sheet.« less
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