Fluctuation relation based continuum model for thermoviscoplasticity in metals |
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| Institution: | 1. Computational Mechanics Lab., Department of Civil Engineering, Indian Institute of Science, Bangalore 560012, India;2. Advanced Computational Mechanics Lab., Department of Mechanical Engineering, Texas A&M University, College Station, TX 77843-3123, USA;3. Department of Mechanical Engineering, Texas A&M University, College Station, TX 77843-3123, USA;1. Lyles School of Civil Engineering, Purdue University, West Lafayette, IN 47907, USA;2. Department of Chemical and Environmental Engineering, University of California, Riverside, CA 92521, USA;3. Materials Science and Engineering, University of California, Riverside, CA 92521, USA;1. Division of Solid Mechanics, Lund University, P.O. Box 118, 221 00 Lund, Sweden;2. European Spallation Source AB, P.O. Box 176, 221 00 Lund, Sweden;3. MAX IV Laboratory, Lund University, P.O. Box 118, 221 00 Lund, Sweden |
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| Abstract: | A continuum plasticity model for metals is presented from considerations of non-equilibrium thermodynamics. Of specific interest is the application of a fluctuation relation that subsumes the second law of thermodynamics en route to deriving the evolution equations for the internal state variables. The modelling itself is accomplished in a two-temperature framework that appears naturally by considering the thermodynamic system to be composed of two weakly interacting subsystems, viz. a kinetic vibrational subsystem corresponding to the atomic lattice vibrations and a configurational subsystem of the slower degrees of freedom describing the motion of defects in a plastically deforming metal. An apparently physical nature of the present model derives upon considering the dislocation density, which characterizes the configurational subsystem, as a state variable. Unlike the usual constitutive modelling aided by the second law of thermodynamics that merely provides a guideline to select the admissible (though possibly non-unique) processes, the present formalism strictly determines the process or the evolution equations for the thermodynamic states while including the effect of fluctuations. The continuum model accommodates finite deformation and describes plastic deformation in a yield-free setup. The theory here is essentially limited to face-centered cubic metals modelled with a single dislocation density as the internal variable. Limited numerical simulations are presented with validation against relevant experimental data. |
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| Keywords: | Plastic deformation Two-temperature model Kinetic vibrational and configurational subsystem Entropy production Fluctuation theorem Yield-free theory |
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