0
Research Papers

Two-Temperature Thermodynamics for Metal Viscoplasticity: Continuum Modeling and Numerical Experiments

[+] Author and Article Information
Shubhankar Roy Chowdhury

Computational Mechanics Laboratory,
Department of Civil Engineering,
Indian Institute of Science,
Bangalore 560012, India
e-mail: shuvorc@civil.iisc.ernet.in

Gurudas Kar

Computational Mechanics Laboratory,
Department of Civil Engineering,
Indian Institute of Science,
Bangalore 560012, India
e-mail: gurudaskar@civil.iisc.ernet.in

Debasish Roy

Professor
Computational Mechanics Laboratory,
Department of Civil Engineering,
Indian Institute of Science,
Bangalore 560012, India
e-mail: royd@civil.iisc.ernet.in

J. N. Reddy

Professor
Advanced Computational Mechanics Laboratory,
Department of Mechanical Engineering,
Texas A&M University,
College Station, TX 77843-3123
e-mail: jnreddy@tamu.edu

1Corresponding author.

Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received August 31, 2016; final manuscript received September 13, 2016; published online October 6, 2016. Editor: Yonggang Huang.

J. Appl. Mech 84(1), 011002 (Oct 06, 2016) (9 pages) Paper No: JAM-16-1425; doi: 10.1115/1.4034726 History: Received August 31, 2016; Revised September 13, 2016

A physics-based model for dislocation mediated thermoviscoplastic deformation in metals is proposed. The modeling is posited in the framework of internal-variables theory of thermodynamics, wherein an effective dislocation density, which assumes the role of the internal variable, tracks permanent changes in the internal structure of metals undergoing plastic deformation. The thermodynamic formulation involves a two-temperature description of viscoplasticity that appears naturally if one considers the thermodynamic system to be composed of two weakly interacting subsystems, namely, a kinetic-vibrational subsystem of the vibrating atomic lattices and a configurational subsystem of the slower degrees-of-freedom (DOFs) of defect motion. Starting with an idealized homogeneous setup, a full-fledged three-dimensional (3D) continuum formulation is set forth. Numerical exercises, specifically in the context of impact dynamic simulations, are carried out and validated against experimental data. The scope of the present work is, however, limited to face-centered cubic (FCC) metals only.

FIGURES IN THIS ARTICLE
<>
Copyright © 2017 by ASME
Your Session has timed out. Please sign back in to continue.

References

Johnson, G. R. , and Cook, W. H. , 1983, “ A Constitutive Model and Data for Metals Subjected to Large Strains, High Strain Rates and High Temperatures,” 7th International Symposium on Ballistics, The Hague, The Netherlands, Vol. 21, pp. 541–547.
Zerilli, F. J. , and Armstrong, R. W. , 1987, “ Dislocation-Mechanics-Based Constitutive Relations for Material Dynamics Calculations,” J. Appl. Phys., 61(5), pp. 1816–1825. [CrossRef]
Aifantis, E. C. , 1987, “ The Physics of Plastic Deformation,” Int. J. Plast., 3(3), pp. 211–247. [CrossRef]
Follansbee, P. , and Kocks, U. , 1988, “ A Constitutive Description of the Deformation of Copper Based on the Use of the Mechanical Threshold Stress as an Internal State Variable,” Acta Metall., 36(1), pp. 81–93. [CrossRef]
Klepaczko, J. , and Rezaig, B. , 1996, “ A Numerical Study of Adiabatic Shear Banding in Mild Steel by Dislocation Mechanics Based Constitutive Relations,” Mech. Mater., 24(2), pp. 125–139. [CrossRef]
Langer, J. , Bouchbinder, E. , and Lookman, T. , 2010, “ Thermodynamic Theory of Dislocation-Mediated Plasticity,” Acta Mater., 58(10), pp. 3718–3732. [CrossRef]
Jou, D. , Casas-Vázquez, J. , and Lebon, G. , 1996, Extended Irreversible Thermodynamics, Springer, Berlin.
Chowdhury, S. R. , Roy, D. , Reddy, J. , and Srinivasa, A. , 2016, “ Fluctuation Relation Based Continuum Model for Thermoviscoplasticity in Metals,” J. Mech. Phys. Solids, 96, pp. 353–368. [CrossRef]
Voyiadjis, G. Z. , and Abed, F. H. , 2005, “ Microstructural Based Models for BCC and FCC Metals With Temperature and Strain Rate Dependency,” Mech. Mater., 37(2), pp. 355–378. [CrossRef]
Lee, E. H. , 1969, “ Elastic-Plastic Deformation at Finite Strains,” ASME J. Appl. Mech., 36(1), pp. 1–6. [CrossRef]
Reddy, J. N. , 2013, An Introduction to Continuum Mechanics, Cambridge University Press, New York.
Gurtin, M. E. , Fried, E. , and Anand, L. , 2010, The Mechanics and Thermodynamics of Continua, Cambridge University Press, New York.
Coleman, B. D. , and Noll, W. , 1963, “ The Thermodynamics of Elastic Materials With Heat Conduction and Viscosity,” Arch. Ration. Mech. Anal., 13(1), pp. 167–178. [CrossRef]
Messerschmidt, U. , 2010, Dislocation Dynamics During Plastic Deformation, Vol. 129, Springer Science & Business Media, Berlin.
Varshni, Y. , 1970, “ Temperature Dependence of the Elastic Constants,” Phys. Rev. B, 2(10), p. 3952. [CrossRef]
Voyiadjis, G. Z. , and Abed, F. H. , 2005, “ Effect of Dislocation Density Evolution on the Thermomechanical Response of Metals With Different Crystal Structures at Low and High Strain Rates and Temperatures,” Arch. Mech., 57(4), pp. 299–343.
Nemat-Nasser, S. , and Li, Y. , 1998, “ Flow Stress of FCC Polycrystals With Application to OFHC Cu,” Acta Mater., 46(2), pp. 565–577. [CrossRef]
Preston, D. L. , Tonks, D. L. , and Wallace, D. C. , 2003, “ Model of Plastic Deformation for Extreme Loading Conditions,” J. Appl. Phys., 93(1), pp. 211–220. [CrossRef]
Samanta, S. , 1971, “ Dynamic Deformation of Aluminium and Copper at Elevated Temperatures,” J. Mech. Phys. Solids, 19(3), pp. 117, 122–123, 135.
Johnson, G. R. , and Cook, W. H. , 1985, “ Fracture Characteristics of Three Metals Subjected to Various Strains, Strain Rates, Temperatures and Pressures,” Eng. Fract. Mech., 21(1), pp. 31–48. [CrossRef]
Gust, W. , 1982, “ High Impact Deformation of Metal Cylinders at Elevated Temperatures,” J. Appl. Phys., 53(5), pp. 3566–3575. [CrossRef]

Figures

Grahic Jump Location
Fig. 1

Comparison of model predictions (solid curves) with experimental results for OFHC copper at strain rate 4000/s. Indicated temperatures correspond to initial values of the adiabatic process. Experimental data are taken from Ref. [17].

Grahic Jump Location
Fig. 2

Model prediction (solid curves) of flow stress at room temperature at very low to very high strain rates. For low strain rate, case simulation is done in isothermal condition. Experimental data are taken from Refs. [4]2 and [17].

Grahic Jump Location
Fig. 3

Comparison of our model prediction (solid curves) to experimental constant-strain stress–strain-rate data at room temperature. Our model successfully exhibits the strain rate sensitivity around the strain rate of 104/s. Experimental data points are taken from Refs. [17] (solid markers) and [18].

Grahic Jump Location
Fig. 4

Model prediction (solid curve) along with experimental data for OFHC copper at high temperatures. Experimental data are reported from Ref. [19].

Grahic Jump Location
Fig. 5

Slices of 3D FE model of deformed cylindrical specimens with temperature contour: (a) test 1: for impact test at 298 K and (b) test 2: for impact test at 718 K (note: figures are not in same length scale)

Grahic Jump Location
Fig. 6

Deformed shape of the cylindrical specimens after impact—model prediction (solid curves) and experimental results obtained from Refs. [20] and [21]: (a) test 1 and (b) test 2

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