Research Papers

Extension of Generalized Plasticity Model for Thermocyclic Loading

[+] Author and Article Information
J. C. Sobotka

Post-Doctoral Researcher
e-mail: sobotka@illinois.edu

R. H. Dodds

Professor Emeritus
e-mail: rdodds@illinois.edu
University of Illinois at Urbana-Champaign,
Urbana, IL 61801

1Corresponding author.

Contributed by the Materials Division of ASME for publication in the JOURNAL OF ENGINEERING MATERIALS AND TECHNOLOGY. Manuscript received February 1, 2013; final manuscript received September 12, 2013; published online November 19, 2013. Assoc. Editor: Georges Cailletaud.

J. Eng. Mater. Technol 136(1), 011003 (Nov 19, 2013) (8 pages) Paper No: MATS-13-1022; doi: 10.1115/1.4025758 History: Received February 01, 2013; Revised September 12, 2013

This work extends the generalized plasticity model for structural metals under cyclic loading proposed by Lubliner et al. (1993, “A New Model of Generalized Plasticity and its Numerical Implementation,” Int. J. Solids Struct., 22, pp. 3171–3184) to incorporate temperature-dependence into the elastic-plastic response. Proposed flow equations satisfy the Clausius–Duhem inequality through a thermodynamically consistent energy functional and retain key aspects of conventional plasticity models: Mises yield surface, normal plastic flow, and additive decomposition of strain. Uniaxial specialization of the 3D rate equations leads to a simple graphical method to estimate model properties. The 3D integration scheme based on backward Euler discretization leads to a scalar quadratic expression to determine the plastic strain rate multiplier and has a symmetric algorithmic tangent matrix. Both properties of the integration lead to a computationally efficient implementation especially suited to large-scale, finite element analyses. In comparison studies using experimental data from a Cottrell–Stokes test, the modified rate equations for the generalized plasticity model capture a thermally activated increase in the flow stress.

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Lubliner, J., 1974, “A Simple Theory of Plasticity,” Int. J. Solids Struct., 10, pp. 313–319. [CrossRef]
Eisenberg, M. A., and Phillips, A., 1971, “A Theory of Plasticity With Non-Coincident Yield and Loading Surfaces,” Acta Mech., 11, pp. 247–260. [CrossRef]
Lubliner, J., 1975, “On Loading, Yield, and Quasi-Yield Hypersurfaces in Plasticity Theory,” Int. J. Solids Struct., 11, pp. 1011–1015. [CrossRef]
Lubliner, J., 1980, “An Axiomatic Model of Rate-Independent Plasticity,” Int. J. Solids Struct., 14, pp. 709–713. [CrossRef]
Lubliner, J., 1984, “A Maximum-Dissipation Principle in Generalized Plasticity,” Acta Mech.52, pp. 225–237. [CrossRef]
Lubliner, J., 1987, “On Uniqueness of Solutions in Generalized Plasticity at Infinitesimal Deformation,” Int. J. Solids Struct., 23, pp. 261–266. [CrossRef]
Lubliner, J., 1987, “Non-Isothermal Generalized Plasticity,” Thermomechanical Couplings in Solids, H. D.Bui and Q. S.Nguyen, eds., Elsevier Science, New York, pp. 121–133.
Lubliner, J., Taylor, R. L., and Auricchio, F., 1993, “A New Model of Generalized Plasticity and Its Numerical Implementation,” Int. J. Solids Struct., 22, pp. 3171–3184. [CrossRef]
Auricchio, F., and Taylor, R. L., 1995, “Two Material Models for Cyclic Plasticity: Nonlinear Kinematic Hardening and Generalized Plasticity,” Int. J. Plast., 11, pp. 65–98. [CrossRef]
Auricchio, F., 1997, “A Viscoplasticity Constitutive Equation Bounded Between Two Generalized Plasticity Models,” Int. J. Plast., 13, pp. 697–721. [CrossRef]
Auricchio, F., and Taylor, R., 1994, “A Generalized Visco-Plasticity Model and Its Algorithmic Implementation,” Comput. Struct., 53, pp. 637–647. [CrossRef]
Auricchio, F., and Petrini, L., 2004, “A Three-Dimensional Model Describing Stress-Temperature Induced Solid Phase Transformations: Solution Algorithm and Boundary Value Problems,” Int. J. Numer. Methods Eng., 61, pp. 807–836. [CrossRef]
Auricchio, F., Reali, A., and Stefanelli, U., 2007, “A Three-Dimensional Model Describing Stress-Induced Solid Phase Transformation With Permanent Inelasticity,” Int. J. Plast., 23, pp. 207–226. [CrossRef]
Auricchio, F., Taylor, R., and Lubliner, J., 1997, “Shape-Memory Alloys: Macromodelling and Numerical Simulations of the Superelastic Behavior,” Comput. Methods Appl. Mech. Eng., 146, pp. 281–312. [CrossRef]
Lubliner, J., and Auricchio, F., 1996, “Generalized Plasticity and Shape-Memory Alloys,” Int. J. Solids Struct., 33, pp. 991–1003. [CrossRef]
McDowell, D. L., 1992, “A Nonlinear Kinematic Hardening Theory for Cyclic Thermoplasticity and Thermoviscoplasticity,” Int. J. Plast.8, pp. 693–728. [CrossRef]
Cassenti, B. N., 1983, “Research and Development Program for the Development of Advanced Time-Temperature Dependent Constitutive Relationships—Vol. 1—Theoretical Discussion,” Contractor Final Report No. NASA CR-168191.
Simo, J. C., and Taylor, R. L., 1985, “Consistent Tangent Operators for Rate-Independent Elastoplasticity,” Comput. Methods Appl. Mech. Eng., 48, pp. 101–118. [CrossRef]
Chaboche, J. L., 1986, “Time-Independent Constitutive Theories for Cyclic Plasticity,” Int. J. Plast., 2, pp. 149–188. [CrossRef]
Chaboche, J. L., 2008, “A Review of Some Plasticity and Viscoplasticity Constitutive Theories,” Int. J. Plast., 24, pp. 1642–1693. [CrossRef]
Chaboche, J. L., and Rousselier, G., 1983, “On the Plastic and Viscoplastic Constitutive Equations—Part I: Rules Developed With Internal Variable Concept,” ASME J. Pressure Vessel Technol., 105, pp. 153–158. [CrossRef]
Ohno, N., and Wang, J., 1993, “Kinematic Hardening Rules With Critical State of Dynamic Recovery, Part I: Formulation and Basic Features for Ratchetting Behavior,” Int. J. Plast., 9, pp. 375–390. [CrossRef]
Jiang, Y., and Sehitoglu, H., 1996, “Modeling of Cyclic Ratchetting Plasticity, Part I: Development of Constitutive Relations,” ASME J. Appl. Mech., 63, pp. 720–725. [CrossRef]
Frederick, C. O., and Armstrong, P. J., 2007, “A Mathematical Representation of the Multiaxial Bauschinger Effect,” Mater. High. Temp., 24, pp. 1–26. [CrossRef]
Ohno, N., and Wang, J., 1992, “Nonisothermal Constitutive Modeling of Inelasticity Based on Bounding Surface,” Nucl. Eng. Des., 133, pp. 369–281. [CrossRef]
Cottrell, A. H., and Stokes, R. J., 1955, “Effects of Temperature on the Plastic Properties of Aluminum Crystals,” Proc. R. Soc. London, Ser. A, 233, pp. 17–34. [CrossRef]
Picu, R. C., Vincze, G. T., and Gracio, J. J., 2011, “Deformation and Microstructure-Independent Cottrell–Stokes Ratio in Commercial Al Alloys,” Int. J. Plast., 27, pp. 1045–1054. [CrossRef]
Swaminathan, B., Lambros, J., and Sehitoglu, H., “Mechanical Response of a Nickel Superalloy Under Thermal and Mechanical Cyclic: Uniaxial and Biaxial Stress States,” J. Strain Anal. Eng. Des. (in press).


Grahic Jump Location
Fig. 1

Uniaxial description of renewed plasticity effect described by the GP model

Grahic Jump Location
Fig. 2

Key material properties to calibrate the GP model using experimental results generated from uniaxial stress–strain data. All material properties for the GP model can be determined from features marked on this curve except δu which fits the nonlinear curvature of the material response after yield. The parameter τ reflects the level of isotropic to kinematic hardening in the material and does not vary with temperature. Circled numbers mark curves 1, 2, and 3.

Grahic Jump Location
Fig. 3

Fit of the (a) temperature-dependent, GP model, (b) the BL model, and (c) the MBFA model with two backstress terms to stress–strain data of Hastelloy X from Swaminathan et al. [28]. The figure shows the stress–strain response fit of these models to experimental data under monotonic and isothermal (20 °C and 600 °C) loading conditions at a constant strain rate.

Grahic Jump Location
Fig. 4

Comparison of experimental data for Hastelloy X under a CS loading protocol with computational results using the present temperature-dependent, GP model, the BL model, and the MBFA model with two backstress terms

Grahic Jump Location
Fig. 5

Comparison of experimental data for Hastelloy X under an inverse CS loading protocol with computational results using the present temperature-dependent, GP model, the BL model, and the MBFA model with two backstress terms




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