Physically Based Constitutive Model for Body Centered Cubic Metals with Applications to Iron
Publication: Journal of Engineering Mechanics
Volume 134, Issue 7
Abstract
A constitutive model is developed in this work to describe the mechanical behavior of body centered cubic metals under a wide range of strain rates and temperatures. The model is based on macromechanical state variables such as stress, strain, and material constants that include threshold and transition temperature as well as micromechanical terms such as mobile dislocation density and burgers vector. The principle of the activation energy and its dependence on temperature, strain rate, and stress is the key point in this proposed model. The model is used to simulate the experimental behavior of pure iron at various temperatures and strain rates in order to obtain the different model parameters. The model shows good capability in capturing the coupling between strain rate and temperature, plastic strain and strain rate, and plastic strain and temperature. The model is used to characterize the hardness of iron at low and high strain rates for a representative strain of 8%.
Get full access to this article
View all available purchase options and get full access to this article.
References
Abed, F. H., and Voyiadjis, G. Z. (2005). “A consistent modified Zerilli-Armstrong flow stress model for BCC and FCC metals for elevated temperatures.” Acta Mech., 175(1–4), 1–18.
Andrews, E. W., Giannakopoulos, A. E., Plisson, E., and Suresh, S. (2002). “Analysis of the impact of a sharp indenter.” Int. J. Solids Struct., 39(15), 281–295.
Anton, R. J., and Subhash, G. (2000). “Dynamic vickers indentation of brittle materials.” Wear, 239(1), 27–35.
Ashby, M. F., and Frost, H. J. (1975). Constitutive relations in plasticity, A. Argon, ed., MIT Press, Cambridge, Mass.
Atkins, A. G., and Tabor, D. (1965). “Plastic indentation in metals with cones.” J. Mech. Phys. Solids, 13(3), 149–164.
Bammann, D. J. (2001). “A model of crystal plasticity containing a natural length scale.” Mater. Sci. Eng., A, 309–310, 406–410.
Bammann, D. J., and Aifantis, E. C. (1982). “On a proposal for a continuum with microstructure.” Acta Mech., 45, 91–121.
Dao, M., Chollacoop, N., Van Vliet, K. J., Venkatesh, T. A., and Suresh, S. (2001). “Computational modeling of the forward and reverse problems in instrumented sharp indentation.” Acta Mater., 49(19), 3899–3918.
Duesbery, M. S., and Vitek, V. (1998). “Plastic anisotropy in b.c.c. transition metals.” Acta Mater., 46(5), 1481–1492.
Follansbee, P. S., and Kocks, U. F. (1988). “A constitutive description of the deformation of copper based on the use of mechanical threshold stress as an internal state variable.” Acta Metall., 36, 81–93.
Freed, A. D., Raj, S. V., and Walker, K. P. (1991). “Stress versus temperature dependent activation energies in creep.” Proc., 3rd Int. Conf. on Constitutive Laws or Engineering Materials (microform), Tucson, Ariz.
Geil, G. W., and Carwile, N. L. (1950). “Tensile properties of ingot iron at low temperatures.” J. Res. Natl. Bur. Stand., 45(2), 129–147.
Gillis, P. P., and Gilman, J. J. (1965). “Dynamical dislocation theory of crystal plasticity.” J. Appl. Phys., 36, 3370–3380.
Gourdin, W. H., and Lassila, D. H. (1996). “Multiple mechanisms in the thermally activated plastic flow of tantalum.” Proc., American Physical Society Topical Conf.: Shock Wave in Condensed Matter, Seattle, 370, 519–522.
Hencky, H. (1923). “Uber einige statisch bestimmte falle des gleichgewichts in plastischen korpern. (Over some statically determined trap of the equilibrium in plastic korpern).” Z. Angew. Math. Mech., 3, 241–251.
Hollomon, J. H. (1944). “The effect of heat treatment and carbon content on the work hardening characteristics of several steels.” Trans. Am. Soc. Met., 32, 123–131.
Jia, D., Rames, K. T., and Ma, E. (2003). “Effects of nanocrystalline and ultrafine grain sizes on constitutive behavior and shear bands in iron.” Acta Mater., 51, 3495–3509.
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.” Proc., 7th Int. Symp. on Ballistics, The Hague, The Netherlands, 541–547.
Klepaczko, J. R. (1987). “Constitutive modelling in dynamic plasticity based on physical state variables: A review.” Int. Proc. Mechanical and Physical Behavior of Materials under Dynamic Loading, Vol. C3/49, Les editions de Physique, Les Ulis., 553–560.
Klopp, R. W., Clifton, R. J., and Shawki, T. G. (1985). “Pressure-shear impact and the dynamic viscoplastic response of metals.” Mech. Mater., 4(3–4), 375–385.
Kocks, U. F., Argon, A. S., and Ashby, M. F. (1975). “Thermodynamics and kinetics of slip.” Progress in materials science, B. Chalmers, J. W. Christian, and T. B. Massalski, eds., Pergamon, Oxford, U.K., 19.
Koeppel, B. J., and Subhash, G. (1999). “Characteristics of residual plastic zone under static and dynamic vickers indentations.” Wear, 224(12), 56–67.
Kubin, L. P., and Estrin, Y. (1990). “Evolution for dislocation densities and the critical conditions for the portevin-le chatelier effect.” Acta Metall. Mater., 38, 697–708.
Lennon, A. M., and Ramesh, K. T. (2004). “The influence of crystal structure on the dynamic behavior of materials at high temperatures.” Int. J. Plast., 20, 269–290.
Littonski, J. (1977). “Plastic flow of a tube under adiabatic torsion.” Bull. Pol. Acad. Sci., 25, 7–14.
Lu, J., Suresh, S., and Ravichandran, G. (2003). “Dynamic indentation for determining the strain rate sensitivity of metals.” J. Mech. Phys. Solids, 51(11–12), 1923–1938.
MacGregor, C. W. (1944). “The true stress-strain tension test—Its role in modern materials testing: Part I.” J. Franklin Inst., 238(2), 111–135.
Miller, A. (1976). “An inelastic constitutive model for monotonic, cyclic, and creep deformation: Part I—Equations development and analytical procedures.” J. Eng. Mater. Technol., 98, 97–105.
Rittel, D., Ravichandran, G., and Venkert, A. (2006). “The mechanical response of pure iron at high strain rates under dominant shear.” Mater. Sci. Eng., A, 432, 191–201.
Stein, D. L., and Low, J. R. (1960). “Mobility of edge dislocations in silicon-iron crystals.” J. Appl. Phys., 31, 362–369.
Sundararajan, G., and Tirupataiah, Y. (2006a). “The localization of plastic flow under dynamic indentation conditions. I: Experimental results.” Acta Mater., 54(3), 565–575.
Sundararajan, G., and Tirupataiah, Y. (2006b). “The localization of plastic flow under dynamic indentation conditions. II: Analysis of results.” Acta Mater., 54(3), 577–586.
Tabor, D. (1951). The hardness of metals, Clarendon Press, Oxford, U.K.
Taylor, G. (1992). “Thermally-activated deformation of BCC metals and alloys.” Prog. Mater. Sci., 36, 29–61.
Vasauskas, V. (2002). “Dynamic hardness during different phases of indentation.” Proc., VDI Berichte: Joint Int. Conf., IMEKO TC3/TC5/TC20, No. 1685, 359–364.
Voyiadjis, G. Z., and Abed, F. H. (2005). “Microstructural based models for bcc and fcc metals with temperature and strain rate dependency.” Math. Comput. Methods Physiol., 37, 355–378.
Yang, J., and Komvopoulos, K. (2004). “Dynamic indentation of an elastic-plastic multilayered medium by a rigid cylinder.” J. Tribol., 126(1), 18–27.
Zerilli, F. J., and Armstrong, R. W. (1987). “Dislocation-mechanics-based constitutive relations for material dynamics calculation.” J. Appl. Phys., 61(5), 1816–1825.
Information & Authors
Information
Published In
Copyright
© 2008 ASCE.
History
Received: Feb 7, 2007
Accepted: Dec 10, 2007
Published online: Jul 1, 2008
Published in print: Jul 2008
Notes
Note. Associate Editor: Dinesh R. Katti
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.