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

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

J. N. Reddy

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.

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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].

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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].

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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].

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Fig. 4

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

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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)

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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




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