MSA  Vol.5 No.8 , June 2014
On the Definition of State Variables for an Internal State Variable Constitutive Model Describing Metal Deformation
The quest for an internal state variable constitutive model describing metal deformation is reviewed. First, analogy is drawn between a deformation model and the Ideal Gas Law. The use of strain as a variable in deformation models is discussed, and whether strain serves as an internal state variable is considered. A simple experiment that demonstrated path dependence in copper is described. The importance of defining appropriate internal state variables for a constitutive law relates to the ability to accurately model temperature and strain-rate dependencies in deformation simulations.

Cite this paper
Follansbee, P. (2014) On the Definition of State Variables for an Internal State Variable Constitutive Model Describing Metal Deformation. Materials Sciences and Applications, 5, 603-609. doi: 10.4236/msa.2014.58062.
[1]   Follansbee, P.S. (2014) Fundamentals of Strength—Principles, Experiment, and Application of an Internal State Variable Constitutive Model. the Minerals, Metals, & Materials Society, John Wiley & Sons, Inc., Hoboken.

[2]   Abbott, M.M. and Van Ness, H.C. (1972) Thermodynamics (Schaum’s Outline Series). McGraw-Hill Book Co., New York.

[3]   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. Proceedings 7th International Symposium on Ballistics, The Hague, 19-21 April 1983, 541-547.

[4]   Follansbee, P.S. (1988) The Rate Dependence of Structure Evolution in Copper and Its Influence on the Strain Strain Behavior at Very High Strain Rates. In: Chiem, C.Y., Kunze, H.-D. and Meyer, L.W., Eds., Impact Loading and Dynamic Behaviour of Materials, Verlag, Berlin, 315-322.

[5]   Kocks, U.F, Argon, A.S. and Ashby, M.F. (1975) Thermodynamics and Kinetics of Slip. In: Chalmers, B., Christian, J.W. and Massalski, T.B., Eds., Progress in Materials Science, Pergamon Press, Oxford.

[6]   Mecking, H. and Kocks, U.F. (1981) Kinetics of Flow and Strain-Hardening. Acta Metallurgica, 29, 1865-1875.

[7]   Edington, J.W. (1969) The Influence of Strain Rate on the Mechanical Properties and Dislocation Substructure in Deformed Copper Single Crystals. Philosophical Magazine, 19, 1189-1206.

[8]   Follansbee, P.S. and Kocks, U.F. (1988) A Constitutive Description of the Deformation of Copper Based on the Use of the Mechanical Threshold Stress as an Internal State Variable. Acta Metallurgica, 36, 81-93.

[9]   Lindholm, U.S. (1978) Deformation Maps in the Region of High Dislocation Velocity. In: Kawata, K. and Shiori, J., eds., High Velocity Deformation of Solids, Springer-Verlag, New York, 26-34.

[10]   Barbe, F., Decker, L., Jeulin, D. and Cailletaud, G. (2001) Intergranular and Intragranular Behavior of Polycrystalline Aggregates. Part 1: F. E. Model. International Journal of Plasticity, 17, 513-536.

[11]   Arsenlis, A. and Parks, D.M. (2002) Modeling the Evolution of Crystallographic Dislocation Density in Crystal Plasticity. Journal of the Mechanics and Physics of Solids, 50, 1979-2009.

[12]   Horstemeyer, M.F., Baskes, M.I., Prandil, V.C., Philliber, J. and Vonderheide, S. (2003) Amultiscale Analysis of Fixed-End Simple Shear Using Molecular Dynamics, Crystal Plasticity, and a Macroscopic Internal State Variable Theory. Modelling and Simulation in Materials Science and Engineering, 11, 265-286.