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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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Figures

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Fig. 1

Uniaxial description of renewed plasticity effect described by the GP model

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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.

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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.

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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

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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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