The thermodynamical theory of elasto-viscoplasticity for description of nanocrystalline metals

• Autorzy: Perzyna P.
• Języki publikacji: EN

Abstrakty

EN

The main object of the present paper is the development of thermodynamical elasto-viscoplaslic constitutive model describing the behaviour of nanocrystalline metals. Only fcc, bcc and hcp metals will be covered in this description, because they are the classes of metals for which systematic experimental observation data sets are available. Investigation of the deformation mechanisms is important for understanding, controlling and optimizing of the mechanical properties of nanocrystalline metals. Strengthening with grain size refinement in metals and alloys, with an average grain size of 100 nm or larger, has been well characterized by the Hall-Petch (H-P) relationship, where dislocation pile-up against grain boundaries, along with other transgranular dislocations mechanisms, are the dominant strength-cont rolling processes. When the average, and entire range of grain sizes is reduced to less than 100 nm. the dislocation operation becomes increasingly more difficult and grain boundary-mediated processes become increasingly more important. The principal short-range barrier, the Peierls-Nabarro stress. Is important for ultrafine crystalline bcc metals, whereas in ultrafine crystalline fcc and hcp metals, forest dislocations are the primary short-range barriers at lower temperatures. Experimental observations have shown that nanosized grains rotate during plastic deformation and can coalesce along directions of shear, creating larger paths for dislocation movement. The model is developed within the thermodynamic framework of the rate-type covariance constitutive structure with a finite set of the internal state variables. 1 he thermodynamic restrictions have been satisfied and the rate-type constitutive equations have been determined. Fracture criterion based on the evolution of the anisotropic intrinsic microdamage is formulated. The fundamental features of the proposed constitutive theory have been carefully discussed.

Słowa kluczowe

EN

theory of elasticity; theory of plasticity; thermodynamics

PL

teoria plastyczności; elastyczność; termodynamika

• Wydawca: Instytut Podstawowych Problemów Techniki PAN
• Czasopismo: Engineering Transactions
• Rocznik: 2010
• Tom: Vol. 58, iss. 1/2
• Strony: 15--74
• Opis fizyczny: Bibliogr. 62 poz., rys., wykr.

Twórcy

autor

Perzyna P.

• Instytut Podstawowych Problemów Techniki Polskiej Akademii Nauk, Warszawa, Polska

Bibliografia

• 1. R. Abraham, J. E. Marsden, Foundations of Mechanics, Second Edition, Addison-Wesley, Reading Mass., 1988.
• 2. R. Abraham. J. E. Marsden, T. Ratiu, Manifolds, Tensor Analysis and Applications, Springer, Berlin 1988.
• 3. R. J. Asaro, S. SuRESH, Mechanistic models for the activation volume and ratę sensitivity in metals with nanocrystalline grains and nano-scale twins, Acta Materialia, 53, 3369 3382, 2005.
• 4. S. Cheng, E. Ma, Y. M. Wang, L. Y. Kecskes, K. M. Youssef, CC. Kocu. U. P. Trochu n z. K. Han, Tensile properties of in situ consolidated nanocrystalline Cu, Acta Materialia. 53. 1521 1533, 2005.
• 5. B. D. Coleman, W. Noll, The thermodynamics of elastic materials with heat conduction and uiscosity, Arch. Rational Mech. Anal., 13, 167-178, 1963.
• 6. Y.F. Dafalias, Corotational rates for kinematic hardening at large plastic deformations, J. Appl. Mech., 50, 561 565, 1983.
• 7. M. Dao, L. Lu, R. J. Asaro, J. T. M. De Hosson, E. Ma, Toward a quantitative understanding of mechanical behauiour of nanocrystalline metals. Acta Materialia. 55. 12. 4041-4065, 2007.
• 8. W. Dornowski, P. Perzyna. Localization phenomena in thermo-ińscoplastic flow processes under cyclic dynamic loadings, Computer Assisted Mechanics and Engineering Sciences. 7. 117 160, 2000.
• 9. M. K. Duszek-Perzyna, P. Perzyna, On combined isotropic and kinematic hardening effects in plastic flow processes, Int. J. Plasticity, 7, 351-363, 1991.
• 10. M. K. Duszek Perzyna, P. Perzyna, Analysis of the influence of different effects on criteria for adiabatic shear band localization in inelastic solids, [in:] Materiał Instabilities: Theory and Applications, ASME Congress, Chicago, 9-11 November 1994, R.C. Batra and H.M. Zbib [Eds.J, AMD-Vol. 183/MD-Vol.50. ASME, New York, 1994, pp. 59-85.
• 11. H. EBRAHIMI, G. R. Bourne, M. S. Kelly, T. E. Matthews, Mechanical properties of nanocrystalline nickel produced by electrodeposition, NanoStructured Materials. 11. 343 350, 1999.
• 12. T. HANLON, N. Y. KWON, S. Suresh, Grain size effects on the fatigue response nanocrystalline metals, Scripta Mater., 49. 675 680, 2003.
• 13. T. Hani.on, E. D. Tabachnikowa, S. Suresh, Fatigue behaviour of nanon-crystalinne metals and alloys, Int. J. Fatigue, 27. 1147 1158. 2005.,
• 14. A. Glema, T. Lodygowski, W. Sumelka, P. Perzyna, The numerical analysis of the intrinsic anisotropic microdamage evolution in elastic-viscoplastic solids, Int. J. Damage Mechanics. 18. 20.") 231, 2009.
• 15. D. Jia, Y.M. Wang, K.T. Ramesh, E. Ma. Y. T. Zhu, R. ZALIKOV. Deformation behaviour and plastic instabilities of ultrafine-grain titanium, Applied Physics Letters. 79, 611-613. 2001.
• 16. S. P. Jia, K.T. RAMESH, E. Ma. Effects of nanocrystalline = grain sizes on constitutive behaviour and shear bands in iron. Acta Materialia, 51. 3495 3509. 2003.
• 17. S. P. JOSHI, K. T. RameSH, , Grain size dependent shear instabilities in body-centered and face-centered cubic materials Materials Science and Engineering A 493. 65 70. 2008.
• 18. K. Korbel, Z. Nowak, P. Perzyna, R. B. Pęciikkski. Viscoplasticity of nanometals based on Burzyński yield condition, 35th Solid Mechanics Kraków. Poland, September 4 8, 2006.
• 19. K.S. Kumar, S. Suresh, M.F. Chisolm, J.A. Horton, P. Wang. Deformation of electrodeposited nanocrystalline nickel. Acta Materialia. 51. 387 105. 2003.
• 20. R.A. LebENSON. E. M. Bringa, A. Caro. Viscoplastic micromechanical model for the yield strength of nanocrystalline materials. Acta Materialia, 55. 261 271, 2007.
• 21. B. LORET, On the effects of plastic rotation in the finite deformation of anisotropic elasto-plastic materials. Mech. Mater.. 2. 287 304. 1983-
• 22. J. K. MarSDEN, I . J. R. Hughes, Mathematical Foundations of Klosticity. Prentice-Hall, Englewood Cliffs, New York 1983.
• 23. H.C. Mf.yers. Dynamic Behaviour of Materials, John Wiley. New Yok 1994.
• 24. M. A. MEYERS, A. MlSHRA, D.J. BENSON, Mechanical properties of nanocrystaline materials, Progress in Materials Science. 51, 127 556, 2006.
• 25. M. A. Meyers, A. Mishra, D.J. Benson, The deformation physics of metals: Experiments, analysis and computations, JOM, 11 18, 2006.
• 26. M. A. Meyers, C.T. Aimone, Dynamic fraction (spalling) of metals. Próg. Mater 28. 1 96, 1083.
• 27. Z. Nowak. P. Perzyna, R. B. Pęcherski, Description of viscoplastic flow accounting for shear banding, Arch. of Metallurgy and Materials. 52. 217-222, 2007.
• 28. P. Perzyna. The constitutwe eąuations for rate sensitive plastic materials. Quart. Appl. Math.. 20. 321-332. 1963.
• 29. P. Perzyna. Fundamental problems in viscoplasticity. Advances in Applied Mechanics, 9. 343 377. 1966.
• 30. P. Perzyna. Thermodynamic theory oj yiscoplasticity, Advances in Applied Mechanics, 11. 313-354. 1971.
• 31. P. Perzyna. Coupling of dissipative mechanisms of viscoplastic flow. Arch. Mechanics. 29. 607 624. 1977.
• 32. P. Perzyna. Modified theory of viscoplasticity. Application to advanced flow and. instability phenomena. Arch. Mechanics. 32. 403-420, 1980.
• 33. P. Perzyna, Constitutive modelling of dissipative solids for postcritical behaviour and fracture. ASME J. Eng. Materials and Technology. 106. 410-419, 1984.
• 34. P. Perzyna. Internal state variable description of dynamic fracture of ductile solids. Int. J. Solids Structures, 22, 797-818, 1986.
• 35. P. Perzyna. Constitutive modelling for brittle dynamic fracture in dissipatiue solids. Arch. Mechanics, 38, 725-738, 1986.
• 36. P. Perzyna, Temperaturę and rate dependent theory of plasticity of crystalline solids, Revue Phys. Appl.. 23, 445-459. 1988.
• 37. P. Perzyna, Instability phenomena and adiabatic shear band localization in thermoplastic flow processes. Acta Mechanica. 106. 173-205, 1994.
• 38. P. Perzyna, Interactions of elastic-viscoplastic waves and localization phenomena in solids, IUTAM Symposium on Nonlinear Waves in Solids, August 15-20. 1993. Victoria. Canada, J.L. Wegner and F.R. Norwood [Eds.j, ASME 1995, pp. 114-121.
• 39. P. Perzyna. Constitutiue modelling of dissipatiue solids for localization and fracture. in: Localization and Fracture Phenomena in Inelastic Solids, P. Perzyna [Ed.|. Springer. Wien, New York, pp. 99-242, 1998.
• 40. P. Perzyna, Thermo-elasto-viscoplasticity and damage. [in:] Handbook of Materials Be-haviour Models, J. Lemaitre [Ed.], Academic Press, New York, pp. 821-834, 2001.
• 41. P. Perzyna. Thermodynamical theory of inelastic single crystals. Engineering Transactions, 50. 107 164, 2002.
• 42. P. Perzyna, The thermodynamical theory of elasto-viscoplasticity, Engineering Transactions, 53, 235-316, 2005.
• 43. P. Perzyna, The thermodynamical theory of elasto-viscoplasticity accounting for micros-hear banding and induced anisotropy effeets. Mechanics. 27, 25-42. 2008.
• 44. P. Perzyna, Application of the thermodynamical theory of elasto-viscoplasticity in modern manufacturing processes, CISM Courses and Lectures, Springer: Wien New York. 2010 (in print).
• 45. P. Perzyna, G. Z. Voyiadjis, Thermodynamic theory of elasto-viscoplasticity for induced anisotropy effects, McMat 2005, Mechanics and Materials Conference, June 1 3, 2005, Baton Rouge, LA, USA, 2005.
• 46. R. B. Pęcherski, Macroscopic effects of microshear banding in plasticity of metals. Acta Mechanica, 131, 203-224. 1998.
• 47. R. Schwaiger, B. Moser, M. Dao, N. Chollacoop, S. Suresh, Some critical ex-periments on the strain-rate sensitivitty of nanocrystalline nickel, Acta Materialia. 51. 5159-5172, 2003.
• 48. D. A. Shockey, L. Seaman, D. R. Curran, The microstatistical fracture mechanics approach to dynamic fracture problem. Int. J. Fracture. 27, 145 157. 1985.
• 49. C. Triesdell, W. Noi. i.. Tin Non-IAncar Field Thiories of Mechanics, [in:] Handbuch der Physik III 3, S. FlCgge [Ed.], Springer-Verlag, Berlin
• 50. E. Van DER Giessen, Micromechanical and thermodynamic aspects of the plastic spin, Int. .1. Plasticity, 7. 365 386, L991.
• 51. Y. M. Wang. J.Y. Huang, T. Jiao. Y. T. Zm. A. V. II wiza. A normal strain hardening in nanostructered titanium at high strain rates and large strains, J. Mater. Sci.. 42. 1751-1756, 2007.
• 52. Y. M. Wam;. E. Ma, Strain hardening, strain sensitivity, and ductility of nanostructured metals, Materials Science and Engineering, A375-377. 46 52, 2004.
• 53. Y. M. Wang. E. Ma. Three strategics to achieve uniform tensile deformation in nanostructured metal. Acta Materialia, 52. 1699-1709. 2004.
• 54. Y. M. Wang. E. Ma, R. Z. VALIEV, Y. T. ZHU, Tough nanostructured metals and cryogenic temperatures, Adv. Mater., 16. 328-331, 2004.
• 55. Q. Wei, T. Jiao. KI. Ramesh, E. Ma, L. J. Keckes. L. Magness, R. .1. Dowding, V. U. KAZYKHANOV, R. Z. Yaliey, Mechanical behavior and dynamic failure of high-strength ultrafim grained tungsen under uniaxial compression. Acta Materialia. 54. 77 S7. 2006.
• 56. Q. W ii. L. Keckes, T. Jiao. KI'. Hartwig, K.T. Ramesh, E. Ma, Adiabatic shear bending in ultrafine-grained Fe processed by severed plastic defortnation. Acta Materialia. 52. 1859 - 1869, 2004.
• 57. Q. Wei, K.T. Ramesh, E. Ma, L..I. Keckes, R. J. Dowding. V. V. Kazykhanov, R. Z. VALIEV,. Plastic flow localization in bulk tungsten with ultrafine microstructure. Applied Physics Letters, 86. 101907(1-3), 2005.
• 58. Q. Wei. H.T. Zhang. B. E. Schuster, K.T. Ramesh. R. Z. Valiev, L. J. Keckes. R. J. Dowding. L. Magness. K. Cho, Microstructure and mechanical properties of super-strong nanocrystalline tungsten processed by high-pressure torsion. Acta Materialia. 54. 1079-4089. 2006.
• 59. Y..I. Wei. L. Ana.nd. Grain-boundary sliding and separation in połycrystalline metals: Application to nanocrystalline fec metals, .J Mech. Phys. Sol.. 52. 2587 2616. 200 1.
• 60. K.M. Youssef, R. O. Scattergood, K. L. Mirty. J.A. Horton, CC. Koch, Ultrahigh strength and high ductility of bulk nanocrystalline coppir. Appl. Phys. Letters, 87. 091904. 1-3, 2005.
• 61. X. Zhang. H. Wang. R. O. Scattergood, J. Narayan. CC. Koch, Mechanical properties of cyromilled nanocrystalline Zn studied by the miniaturized disk bend test. Acta Materialia. 50. 3527-3533, 2002.
• 62. J.Y. Huang, T. Ungar, Y. M. Wang, E. Ma. R.Z. Yaliky. Nanostruc-tures in the Ti processed by severe plastic deformation. .J. Matei Res., 18. 1908 1017. 2003.