**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**30184

##### Mathematical Modeling for the Processes of Strain Hardening in Heterophase Materials with Nanoparticles

**Authors:**
Mikhail Semenov ,
Svetlana Kolupaeva,
Tatiana Kovalevskaya,
Olga Daneyko

**Abstract:**

An investigation of the process of deformation hardening and evolution of deformation defect medium in dispersion-hardened materials with face centered cubic matrices and nanoparticles was done. Mathematical model including balance equation for the deformation defects was used.

**Keywords:**
deformation defects,
dispersion-hardened materials,
mathematical modeling,
plastic deformation

**Digital Object Identifier (DOI):**
doi.org/10.5281/zenodo.1077337

**References:**

[1] F. R. N. Nabarro, Z. S. Basinski, and B. Holt, "The plasticity of pure single crystals," Advances in Physics, vol. 13, p. 193, 1964.

[2] R. Berner and H. Kronmuller, Moderne probleme der metallphysik. Berlin: Springer Verlag, 1965.

[3] J. Fridel, Dislocations. Oxford: Pergamon, 1964; Moscow: Mir, 1967.

[4] I. Kovacs and L. Zsoldos, Dislocations and plastic deformation. Budapest: Akademia Publisher, 1973.

[5] U. Kocks and H. Mecking, "Physics and phenomenology of strain hardening: the fcc case,"Progress in Materials Science, vol. 48, p. 171¬273, 2003.

[6] M. Zehetbauer and V. Seumer, "Cold work hardening in stages IV and V of F.C.C. metals - I. Experiments and interpretation: Original research article," Bulletin of the Polish Academy of Sciences, vol. 41, no. 2, pp. 577-588, 1993.

[7] L. E. Popov, V. S. Kobytev, and T. A. Kovalevskaya, Izv. Vyssh. Uchebn. Zaved. Fizika, no. 6, pp. 56-82, 1982.

[8] L. E. Popov, V. S. Kobytev, and T. A. Kovalevskaya, Plasticheskaya defor¬maciya splavov (Plastic deformation of Alloys). Moscow: Metallurgiya, 1984.

[9] V. Essmann, H. Mughrabi, "Annihilation of dislocations during tensile and cyclic deformation and limits of dislocation densities," Phil. Mag. (a), no. 6, pp. 731-756, 1979.

[10] G. A. Malygin, "Dislocation self-organization and crystal plasticity," Physics-Uspekhi, vol. 42, no. 9, pp. 887-916, 1999.

[11] J. Litonski, "Plastic flow of a tube under adiabatic torsion," Bulletin of the Polish Academy of Sciences, vol. 25, pp. 7-14, 1977.

[12] T. Vinh, M. Afzali, and R. A., "Fast fracture of some usual metals at combined high strain and high strain rates," in Proceedings of the Third International Conference on Mechanical Behaviour of Materials, K. J. Miller and R. F. Smith, Eds., Cambridge, England, 1979, pp. 633-642.

[13] R. W. Klopp, R. J. Clifton, and T. G. Shawki, "Pressure-shear impact and the dynamic viscoplastic response of metals," Mechanics of Materials, vol. 4, no. 3-4, pp. 375-385, 1985.

[14] G. R. Johnson and W. H. Cook, "A constitutive model and data for metals subjected to large strains, high strain rates, and high temperatures," in Proceedings of the Seventh International Symposium on Ballistics. Hague, Netherlands, pp. 541-547, 1983.

[15] U. E Kocks, A. S. Argon, and M. E Ashby, "Thermodynamics and kinetics of slip," in Progress in Materials Science, B. Chalmers, J. W. Christian, and T. B. Massalski, Eds., Oxford: Pergamon Press, vol. 19, 1975.

[16] K. G. Hoge and A. K. Mukherjee, "The temperature and strain rate dependence of the flow stress of tantalum," Journal of Materials Science, vol. 12, pp. 1666-1672, 1977.

[17] P. S. Follansbee and U. F Kocks, "A constitutive description of the deformation of copper based on the use of mechanical threshold stress as an internal state variable," Acta Metallurgica, vol. 36, pp. 81-93, 1988.

[18] F. J. Zerilli and R. W. Armstrong, "Dislocation-mechanics-based con¬stitutive relations for material dynamics calculation," Journal of Applied Physics, vol. 5, pp. 1816-1825, 1987.

[19] G. Z. Voyiadjis and F. H. Abed, "Microstructural based models for bcc and fcc metals with temperature and strain rate dependency," Mechanics of Materials, vol. 37, pp. 355-378, 2005.

[20] C. Y. Gao and L. C. Zhang, "A constitutive model for dynamic plasticity of FCC metals," Materials Science and Engineering A, vol. 527, pp. 3138-3143, 2010.

[21] E. Hairer, G. Wanner, Solving Ordinary Differential Equations II: Stiff and Differential-Algebraic Problems. Berlin: Springer, 1996.

[22] J. C. Butcher, Numerical Methods for Ordinary Differential Equations. Chichester, England: John Wiley & Sons, Ltd, 2008.

[23] C. W. Gear, R. D. Skeel, "The development of ODE methods: a symbiosis between hardware and numerical analysis", in: S.G. Nash (Ed.), History of scientific computing, New York: ACM Press, pp. 88-105, 1990.

[24] T. A. Kovalevskaya, 0. I. Daneyko, and S. N. Kolupaeva, "Mathematical simulation of the plastic deformation of crystalline materials with a nanodispersed hardening phase," Russian Physics Journal, vol. 50, no. 11, pp. 1092-1100, 2007.

[25] T. A. Kovalevskaya, 0. I. Daneyko, N. A. Melkozyorova, and S. N. Kolupaeva, "Mathematical modelling of plastic deformation of materials with strengthening nanophase," in Book of abstract Fifteenth International Conference on the Strength of Materials, ICSMA-15, p. 93, 2009.

[26] S. N. Kolupaeva, S. I. Puspesheva, and M. E. Semenov, "Mathematical modeling of temperature and rate dependences of strain hardening in f.c.c. metals," in Abstract Book 11th International Conference on Fracture., Turin (Italy), March 20-25, 2005, p. 847.

[27] M. E. Semenov and S. N. Kolupaeva, "Development of computer programm for the description of plastic deformation by slip," in The 7th Korea-Russia International Symposium on Science and Technology (KORUS 2003), vol. 2, June 2003, pp. 401-404.

[28] S. N. Kolupaeva, T. A. Kovalevskaya, 0. I. Daneyko, M. E. Semenov, N. A. Kulaeva, "Modeling of temperature and rate dependence of the flow stress and evolution of a deformation defect medium in dispersion-hardened materials," Bulletin of the Russian Academy of Sciences: Physics, vol. 74, no. 11, pp. 1527-1531, 2010.

[29] L. E. Popov, T. A. Kovalevskaya, and S. N. Kolupaeva, in Strukturnofa¬zovye sostoyaniya i svoistva metallicheskikh sistem (StructuralPhase research. States and the Properties of Metallic Systems), Tomsk: NTL, pp. 135- 163, 2004.

[30] L. E. Popov, S. N. Kolupaeva, and 0. A. Sergeeva, "Skorost krisral- lographicheskoi plasticheskoi deformasii (Strain Rate of Cristallgrapical Plastic Deformation)," Matematicheskoe Modelimvanie Sistem i Prot- sessov, no. 5, pp. 93-104, 1997.

[31] L. N. Larikov, Yu. E Yurchenko, Teplovye svoistva metallov i splavov (Thermal Properties of Metals and Alloys). Kiev: Naukova dumka, 1985.