Physically based constitutive model for body centered cubic metals with applications to iron

Journal of Engineering Mechanics

Volumn 134, Issue 7, 2008, Pages 521-529

  Almasri, Amin ^a   Voyiadjis, George Z ^a  

^a Louisiana State University   (United States)

Author keywords

Constitute models; Iron; Strain rate; Temperature

Indexed keywords

ACTIVATION ENERGY; CHEMICAL ACTIVATION; CONSTITUTIVE MODELS; CUBIC BORON NITRIDE; IRON; METALS; PLASTIC DEFORMATION; PLASTICS; STRESSES; TEMPERATURE;

(ABIOTIC AND BIOTIC) STRESS; BODY-CENTERED CUBIC (BCC) METALS; HIGH STRAIN RATE (HSR); IN ORDER; MATERIAL CONSTANTS; MECHANICAL BEHAVIORS; MICRO-MECHANICAL; MOBILE DISLOCATION DENSITIES; MODEL PARAMETERS; PHYSICALLY BASED; PLASTIC STRAINING; PURE IRON; REPRESENTATIVE STRAIN; STATE VARIABLES; TRANSITION TEMPERATURES; WIDE-RANGE;

STRAIN RATE;

ACTIVATION ENERGY; CONSTITUTIVE EQUATION; IRON; MECHANICAL PROPERTY; MICROMECHANICS; STRAIN RATE; TEMPERATURE GRADIENT;

EID: 45849133811     PISSN: 07339399     EISSN: None     Source Type: Journal    
DOI: 10.1061/(ASCE)0733-9399(2008)134:7(521)     Document Type: Article

References (38)

1. 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. AMHCAP0001-597010.1007/s00707-004-0203-1, 175(1-4), 1-18.
2. Andrews, E. W., Giannakopoulos, A. E., Plisson, E., and Suresh, S. (2002). "Analysis of the impact of a sharp indenter." Int. J. Solids Struct. IJSOAD0020-768310.1016/S0020-7683(01)00215-3, 39(15), 281-295.
3. Anton, R. J., and Subhash, G. (2000). "Dynamic vickers indentation of brittle materials." Wear WEARCJ0043-164810.1016/ S0043-1648(99)00364-6, 239(1), 27-35.
4. Ashby, M. F., and Frost, H. J. (1975). Constitutive relations in plasticity, A. Argon, ed., MIT Press, Cambridge, Mass.
5. Atkins, A. G., and Tabor, D. (1965). "Plastic indentation in metals with cones." J. Mech. Phys. Solids JMPSA80022-509610.1016/ 0022-5096(65)90018-9, 13(3), 149-164.
6. Bammann, D. J. (2001). "A model of crystal plasticity containing a natural length scale." Mater. Sci. Eng., A MSAPE30921-5093, 309-310, 406-410.
7. Bammann, D. J., and Aifantis, E. C. (1982). "On a proposal for a continuum with microstructure." Acta Mech. AMHCAP0001-597010.1007/ BF01295573, 45, 91-121.
8. 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. ACMAFD1359-645410.1016/S1359-6454(01)00295-6, 49(19), 3899-3918.
9. Duesbery, M. S., and Vitek, V. (1998). "Plastic anisotropy in b.c.c. transition metals." Acta Mater. ACMAFD1359-645410.1016/ S1359-6454(97)00367-4, 46(5), 1481-1492.
10. 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. AMETAR0001-616010.1016/0001-6160(88)90030-2, 36, 81-93.
11. 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.
12. Geil, G. W., and Carwile, N. L. (1950). "Tensile properties of ingot iron at low temperatures." J. Res. Natl. Bur. Stand. JRNBAG0160-1741, 45(2), 129-147.
13. Gillis, P. P., and Gilman, J. J. (1965). "Dynamical dislocation theory of crystal plasticity." J. Appl. Phys. JAPIAU0021-897910.1063/1.1702998, 36, 3370-3380.
14. 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.
15. 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. ZAMMAX0044-226710.1002/zamm.19230030401, 3, 241-251.
16. Hollomon, J. H. (1944). "The effect of heat treatment and carbon content on the work hardening characteristics of several steels." Trans. Am. Soc. Met. TASEA70096-7416, 32, 123-131.
17. 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. ACMAFD1359-645410.1016/ S1359-6454(03)00169-1, 51, 3495-3509.
18. 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.
19. 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.
20. Klopp, R. W., Clifton, R. J., and Shawki, T. G. (1985). "Pressure-shear impact and the dynamic viscoplastic response of metals." Mech. Mater. MSMSD30167-663610.1016/0167-6636(85)90033-X, 4(3-4), 375-385.
21. 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.
22. Koeppel, B. J., and Subhash, G. (1999). "Characteristics of residual plastic zone under static and dynamic vickers indentations." Wear WEARCJ0043-164810.1016/S0043-1648(98)00328-7, 224(12), 56-67.
23. Kubin, L. P., and Estrin, Y. (1990). "Evolution for dislocation densities and the critical conditions for the portevin-le chatelier effect." Acta Metall. Mater. AMATEB0956-715110.1016/ 0956-7151(90)90021-8, 38, 697-708.
24. 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. IJPLER0749-641910.1016/ S0749-6419(03)00037-8, 20, 269-290.
25. Littonski, J. (1977). "Plastic flow of a tube under adiabatic torsion." Bull. Pol. Acad. Sci., 25, 7-14.
26. Lu, J., Suresh, S., and Ravichandran, G. (2003). "Dynamic indentation for determining the strain rate sensitivity of metals." J. Mech. Phys. Solids JMPSA80022-509610.1016/j.jmps.2003.09.007, 51(11-12), 1923-1938.
27. MacGregor, C. W. (1944). "The true stress-strain tension test-Its role in modern materials testing: Part I." J. Franklin Inst. JFINAB0016-0032, 238(2), 111-135.
28. Miller, A. (1976). "An inelastic constitutive model for monotonic, cyclic, and creep deformation: Part I-Equations development and analytical procedures." J. Eng. Mater. Technol. JEMTA80094-4289, 98, 97-105.
29. 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 MSAPE30921-509310.1016/ j.msea.2006.05.154, 432, 191-201.
30. Stein, D. L., and Low, J. R. (1960). "Mobility of edge dislocations in silicon-iron crystals." J. Appl. Phys. JAPIAU0021-897910.1063/ 1.1735574, 31, 362-369.
31. Sundararajan, G., and Tirupataiah, Y. (2006a). "The localization of plastic flow under dynamic indentation conditions. I: Experimental results." Acta Mater. ACMAFD1359-645410.1016/j.actamat.2005.09.022, 54(3), 565-575.
32. Sundararajan, G., and Tirupataiah, Y. (2006b). "The localization of plastic flow under dynamic indentation conditions. II: Analysis of results." Acta Mater. ACMAFD1359-645410.1016/j.actamat.2005.09.021, 54(3), 577-586.
33. Tabor, D. (1951). The hardness of metals, Clarendon Press, Oxford, U.K.
34. Taylor, G. (1992). "Thermally-activated deformation of BCC metals and alloys." Prog. Mater. Sci. PRMSAQ0079-642510.1016/ 0079-6425(92)90004-Q, 36, 29-61.
35. Vasauskas, V. (2002). "Dynamic hardness during different phases of indentation." Proc., VDI Berichte: Joint Int. Conf., IMEKO TC3/TC5/ TC20, No. 1685, 359-364.
36. 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. 45TGAW, 37, 355-378.
37. Yang, J., and Komvopoulos, K. (2004). "Dynamic indentation of an elastic-plastic multilayered medium by a rigid cylinder." J. Tribol. JOTRE90742-478710.1115/1.1609489, 126(1), 18-27.
38. Zerilli, F. J., and Armstrong, R. W. (1987). "Dislocation-mechanics-based constitutive relations for material dynamics calculation." J. Appl. Phys. JAPIAU0021-897910.1063/ 1.338024, 61(5), 1816-1825.