0
Research Papers

Modified Maximum Mechanical Dissipation Principle for Rate-Independent Metal Plasticity

[+] Author and Article Information
Jun Chen

e-mail: jun_chen@sjtu.edu.cnDepartment of Plasticity Technology,
Shanghai Jiao Tong University,
Shanghai 200030, China

Xinhai Zhu

Livermore Software Technology Corporation,
Livermore, CA 94551

Jian Cao

Department of Mechanical Engineering,
Northwestern University,
Evanston, IL 60208

1Corresponding author.

Manuscript received November 30, 2012; final manuscript received January 4, 2013; accepted manuscript posted February 14, 2013; published online August 21, 2013. Editor: Yonggang Huang.

J. Appl. Mech 80(6), 061020 (Aug 21, 2013) (9 pages) Paper No: JAM-12-1536; doi: 10.1115/1.4023685 History: Received November 30, 2012; Revised January 04, 2013; Accepted February 14, 2013

The approach regarding the plastic process as a constrained optimization problem (Simo, J. C., and Hughes, T. J. R., 1998, Computational Inelasticity, Springer, New York) is discussed and found to be limited in considering nonlinear kinematic hardening and mechanical dissipation. These limitations are virtually common in elastoplastic modeling in both theoretical studies and industrial applications. A modified maximum mechanical dissipation principle is proposed to overcome the limitations and form an energy-based framework of nonlinear hardening laws. With the control functions introduced into the framework, not only are the relationships between existing hardening models clarified against their ad hoc origins, but modeling nonsaturating kinematic hardening behavior is also achieved. Numerical examples are presented to illustrate the capability of the nonsaturating kinematic hardening model to describe the phenomena of the permanent softening as well as the cyclic loading. These applications indicate the concept of the control function can be nontrivial in material modeling. Finally, the methodology is also extended to incorporate the multiterm approach.

FIGURES IN THIS ARTICLE
<>
Copyright © 2013 by ASME
Your Session has timed out. Please sign back in to continue.

References

Cao, J., Lee, W., Cheng, H. S., Seniw, M., Wang, H.-P., and Chung, K., 2009, “Experimental and Numerical Investigation of Combined Isotropic-Kinematic Hardening Behavior of Sheet Metals,” Int. J. Plast., 25(5), pp. 942–972. [CrossRef]
Kim, D., Lee, W., Kim, J., Chung, K.-H., Kim, C., Okamoto, K., Wagoner, R. H., and Chung, K., 2010, “Macro-Performance Evaluation of Friction Stir Welded Automotive Tailor-Welded Blank Sheets—Part II : Formability,” Int. J. Solids Struct., 47(7–8), pp. 1063–1081. [CrossRef]
Chung, K., Lee, W., Kim, D., Kim, J., Chung, K.-H., Kim, C., Okamoto, K., and Wagoner, R. H., 2010, “Macro-Performance Evaluation of Friction Stir Welded Automotive Tailor-Welded Blank Sheets—Part I : Material Properties,” Int. J. Solids Struct., 47(7–8), pp. 1048–1062. [CrossRef]
Dafalias, Y. F., Kourousis, K. I., and Saridis, G. J., 2008, “Corrigendum to ‘Multiplicative AF Kinematic Hardening in Plasticity' (International Journal of Solids and Structures 45 (2008) 2861–2880),” Int. J. Solids Struct., 45(17), pp. 4878. [CrossRef]
Dafalias, Y. F., Kourousis, K. I., and Saridis, G. J., 2008, “Multiplicative AF Kinematic Hardening in Plasticity,” Int. J. Solids Struct., 45(10), pp. 2861–2880. [CrossRef]
Abdel-Karim, M., 2009, “Modified Kinematic Hardening Rules for Simulations of Ratchetting,” Int. J. Plast., 25(8), pp. 1560–1587. [CrossRef]
Sansour, C., Karsaj, I., and Soric, J., 2006, “On Free Energy-Based Formulations for Kinematic Hardening and the Decomposition F = F(P)F(E),” Int. J. Solids Struct., 43(25–26), pp. 7534–7552. [CrossRef]
Armstrong, P. J., and Frederick, C. O., 1966, “A Mathematical Representation of the Multiaxial Bauschinger Effect,” Technical Report, Berkeley Nuclear Laboratories, Berkeley, UK.
Chaboche, J. L., 1986, “Time-Independent Constitutive Theories for Cyclic Plasticity,” Int. J. Plast., 2(2), pp. 149–188. [CrossRef]
Badreddine, H., Saanouni, K., and Dogui, A., 2010, “On Non-Associative Anisotropic Finite Plasticity Fully Coupled With Isotropic Ductile Damage for Metal Forming,” Int. J. Plast., 26(11), pp. 1541–1575. [CrossRef]
Arghavani, J., Auricchio, F., and Naghdabadi, R., 2011, “A Finite Strain Kinematic Hardening Constitutive Model Based on Hencky Strain: General Framework, Solution Algorithm and Application to Shape Memory Alloys,” Int. J. Plast., 27(6), pp. 940–961. [CrossRef]
Halphen, B., and NguyenQuoc, S., 1975, “On Generalized Standard Materials,” J. Mec., 14(1), pp. 39–63.
Lemaitre, J., and Chaboche, J.-L., 1990, Mechanics of Solid Materials, Cambridge University Press, Cambridge, UK.
Simo, J. C., and Hughes, T. J. R., 1998, Computational Inelasticity, Interdisciplinary Applied Mathematics, Springer, New York.
Voyiadjis, G. Z., and AbuAl-Rub, R. K., 2003, “Thermodynamic Based Model for the Evolution Equation of the Backstress in Cyclic Plasticity,” Int. J. Plast., 19(12), pp. 2121–2147. [CrossRef]
Boyd, S. P., and Vandenberghe, L., 2004, Convex Optimization , Cambridge University Press, New York.
Ziegler, H., 1983, An Introduction to Thermomechanics, North-Holland Series in Applied Mathematics and Mechanics, North-Holland Publishers, Amsterdam.
Erlicher, S., and Point, N., 2006, “Endochronic Theory, Non-Linear Kinematic Hardening Rule and Generalized Plasticity: A New Interpretation Based on Generalized Normality Assumption,” Int. J. Solids Struct., 43(14–15), pp. 4175–4200. [CrossRef]
Ohno, N., and Wang, J. D., 1993, “Kinematic Hardening Rules With Critical State of Dynamic Recovery, Part I: Formulation and Basic Features for Ratchetting Behavior,” Int. J. Plast., 9(3), pp. 375–390. [CrossRef]
Ohno, N., and Wang, J. D., 1993, “Kinematic Hardening Rules With Critical State of Dynamic Recovery—Part II: Application to Experiments of Ratchetting Behavior,” Int. J. Plast., 9(3), pp. 391–403. [CrossRef]
Ristinmaa, M., Wallin, M., and Ottosen, N., 2007, “Thermodynamic Format and Heat Generation of Isotropic Hardening Plasticity,” Acta Mech., 194(1), pp. 103–121. [CrossRef]
Henann, D. L., and Anand, L., 2009, “A Large Deformation Theory for Rate-Dependent Elastic-Plastic Materials With Combined Isotropic and Kinematic Hardening,” Int. J. Plast., 25(10), pp. 1833–1878. [CrossRef]
Mises, R. V., 1928, “Mechanik Der Plastischen Formänderung Von Kristallen,” ZAMM, 8(3), pp. 161–185. [CrossRef]
Hill, R., 1948, “A Theory of the Yielding and Plastic Flow of Anisotropic Metals,” Proc. R. Soc. London, Ser. A, 193(1033), pp. 281–297. [CrossRef]
Barlat, F., Yoon, J. W., and Cazacu, O., 2007, “On Linear Transformations of Stress Tensors for the Description of Plastic Anisotropy,” Int. J. Plast., 23(5), pp. 876–896. [CrossRef]
Haddadi, H., Bouvier, S., Banu, M., Maier, C., and Teodosiu, C., 2006, “Towards an Accurate Description of the Anisotropic Behaviour of Sheet Metals Under Large Plastic Deformations: Modelling, Numerical Analysis and Identification,” Int. J. Plast., 22(12), pp. 2226–2271. [CrossRef]
Voyiadjis, G. Z., Shojaei, A., and Li, G., 2011, “A Thermodynamic Consistent Damage and Healing Model for Self Healing Materials,” Int. J. Plast., 27(7), pp. 1025–1044. [CrossRef]
Chaboche, J. L., 2008, “A Review of Some Plasticity and Viscoplasticity Constitutive Theories,” Int. J. Plast., 24(10), pp. 1642–1693. [CrossRef]
Prager, W., 1956, “A New Method of Analyzing Stresses and Strains in Work Hardening Plastic Solids,” ASME J. Applied Mech., 23(1), pp. 493–496.
Chen, X., Jiao, R., and Kim, K. S., 2005, “On the Ohno–Wang Kinematic Hardening Rules for Multiaxial Ratcheting Modeling of Medium Carbon Steel,” Int. J. Plast., 21(1), pp. 161–184. [CrossRef]
Abdel-Karim, M., 2010, “An Evaluation for Several Kinematic Hardening Rules on Prediction of Multiaxial Stress-Controlled Ratchetting,” Int. J. Plast., 26(5), pp. 711–730. [CrossRef]
Truesdell, C., Noll, W., and Antman, S. S., 2004, The Non-Linear Field Theories of Mechanics, Springer, Berlin. [CrossRef]
Xiao, Y., Chen, J., and Cao, J., 2012, “A Generalized Thermodynamic Approach for Modeling Nonlinear Hardening Behaviors,” Int. J. Plast., 38(0), pp. 102–122. [CrossRef]
Chaboche, J. L., Dang-Van, K., and Cordier, G., 1979, “Modelization of the Strain Memory Effect on the Cyclic Hardening of 316 Stainless Steel,” Proceedings of the 5th International Conference on Structural Mechanics in Reactor Technology (SMiRT), Berlin, August 13–17.
Chaboche, J. L., 1991, “On Some Modifications of Kinematic Hardening to Improve the Description of Ratchetting Effects,” Int. J. Plast., 7(7), pp. 661–678. [CrossRef]
Guo, S., Kang, G., and Zhang, J., 2011, “Meso-Mechanical Constitutive Model for Ratchetting of Particle-Reinforced Metal Matrix Composites,” Int. J. Plast., 27(12), pp. 1896–1915. [CrossRef]
Zienkiewicz, O. C., and Taylor, R. L., 2005, The Finite Element Method for Solid and Structural Mechanics, Elsevier Butterworth–Heinemann, Woburn, MA.
Chun, B. K., Kim, H. Y., and Lee, J. K., 2002, “Modeling the Bauschinger Effect for Sheet Metals—Part II: Applications,” Int. J. Plast., 18(5–6), pp. 597–616. [CrossRef]
Geng, L., Shen, Y., and Wagoner, R. H., 2002, “Anisotropic Hardening Equations Derived From Reverse-Bend Testing,” Int. J. Plast., 18(5–6), pp. 743–767. [CrossRef]
Chun, B. K., Jinn, J. T., and Lee, J. K., 2002, “Modeling the Bauschinger Effect for Sheet Metals—Part I: Theory,” Int. J. Plast., 18(5–6), pp. 571–595. [CrossRef]

Figures

Grahic Jump Location
Fig. 1

Comparing the behaviors of the NSK-I model, the Swift isotropic hardening model and the Armstrong–Frederick model under tension loading

Grahic Jump Location
Fig. 2

Comparing the behaviors of the NSK-I model, the Swift isotropic hardening model and the Armstrong–Frederick model under tension-compression (T-C) loading

Grahic Jump Location
Fig. 3

Modeling the cyclic behavior of DP590 with NSK-I model

Grahic Jump Location
Fig. 4

The schematic curve of the NSK-II model under tension-compression loading

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