Multilevel models of crystal plasticity and viscoplasticity in multiphase polycrystalline materials

Abstract


The paper considers the problem of modelling the processes of inelastic deformation of polycrystalline materials with regard to microstructure, physical mechanisms and their carriers. At present physical approach based on an explicit introduction of variables (responsible for these mechanisms) into the mathematical model is widely spread. It is necessary to consider deeper scale levels than a macroscopic one for description of such models. That is why this type of model can be considered as a multilevel model. Classification features in multilevel models based on the physical theory of plasticity may be: hypothesis transition between scale levels, the number of the scale levels involved in the consideration and physical model lying in the low level. The fact that physical laws of meso- and microlevel are quite universal, this class of models can be used to analyze a wide range of materials and processes, and their scope is constantly increasing. To be more exact, these are multiphase materials, both widely used and newly developed and implemented in production, for example, steel and titanium alloys. Analysis of meso-and microstructure shows the dependence of the response of the material at the macro level on its current state. The peculiarity of such materials is a high degree of heterogeneity of stress and strain fields arising due to the physical heterogeneity of the individual phases of polycrystal. The present paper provides a review of multilevel models of plasticity theory based on the explicit consideration of carriers and mechanisms of inelastic deformation. The review contains different aspects of application of various modifications of multilevel physical models for description of behavior of multiphase materials that are widely used in industry. Special attention is paid to critical analysis of models.

About the authors

N S Kondratev

Perm National Research Polytechnic University

P V Trusov

Perm National Research Polytechnic University

References

  1. Линь Т.Г. Физическая теория пластичности // Проблемы теории пластичности. Сер. Новое в зарубежной механике. Вып. 7. - М.: Мир, 1976. - С. 7-68.
  2. Панин В.Е., Гриняев Ю.В. Физическая мезомеханика - новая парадигма на стыке физики и механики // Физическая мезомеханика. - 2003. - Т. 6, № 4. - С. 9-36.
  3. Трусов П.В., Ашихмин В.Н., Швейкин А.И. Двухуровневая модель упругопластического деформирования поликристаллических материалов // Механика композиционных материалов и конструкций. - 2009. - Т. 15, № 3. - С. 327-344.
  4. Трусов П.В., Волегов П.С. Физические теории пластичности: теория и приложения к описанию неупругого деформирования материалов. Ч. 1: Жесткопластические и упругопластические модели // Вестник ПНИПУ. Механика. - 2011. - № 1. - С. 5-45.
  5. Трусов П.В., Волегов П.С. Физические теории пластичности: теория и приложения к описанию неупругого деформирования материалов. Ч. 2: Вязкопластические и упруговязкопластические модели // Вестник ПНИПУ. Механика. - 2011. - № 2. - С. 101-131.
  6. Трусов П.В., Волегов П.С. Физические теории пластичности: теория и приложения к описанию неупругого деформирования материалов. Ч. 3: Теории упрочнения, градиентные теории // Вестник ПНИПУ. Механика. - 2011. - № 3. - С. 146-197.
  7. Трусов П.В., Волегов П.С. Определяющие соотношения с внутренними переменными и их применение для описания упрочнения в монокристаллах // Физическая мезомеханика. - 2009. - Т. 12, № 5. - С. 65-72.
  8. Трусов П.В., Волегов П.С., Кондратьев Н.С. Физические теории пластичности - Пермь: Изд-во Пермского национального исследовательского политехнического университета, 2013. - 244 с.
  9. Трусов П.В., Швейкин А.И., Нечаева Е.С., Волегов П.С. Многоуровневые модели неупругого деформирования материалов и их применение для описания эволюции внутренней структуры // Физическая мезомеханика. -2012. - Т. 15, № 1. - С. 33-56.
  10. Трусов П.В., Швейкин А.И. Многоуровневые физические модели моно- и поликристаллов. Статистические модели // Физическая мезомеханика. - 2011. - Т. 14, № 4. - С. 17-28.
  11. Трусов П.В., Швейкин А.И. Многоуровневые физические модели моно- и поликристаллов. Прямые модели // Физическая мезомеханика. - 2011. - Т. 14, № 5. - С. 5-30.
  12. Трусов П.В., Швейкин А.И. Теория пластичности. - Пермь: Изд-во Пермского национального исследовательского политехнического университета, 2011. - 419 с.
  13. Физическая мезомеханика и компьютерное конструирование материалов: в 2 т. / В.Е. Панин, В.Е. Егорушкин, П.В. Макаров [и др.]. - Новосибирск: Наука, 1995. - Т. 1. - 298 с. - Т. 2. - 320 с.
  14. Alley E.S., Neu R.W. A hybrid crystal plasticity and phase transformation model for high carbon steel // Computational Mechanics. - 2013. - Vol. 52. - Iss. 2. - P. 237-255.
  15. Al-Abbasi F.M., Nemes J.A. Micromechanical modeling of dual phase steels // International Journal of Mechanical Sciences. - 2003. - Vol. 45. - P. 1449-1465.
  16. Ankem S., Margolin H. The role of elastic interaction stresses on the onset of plastic flow for oriented two ductile phase structures // Metall. Trans. A. - Vol. 11. - P. 963-972.
  17. Ashby M.The deformation of plastically non-homogeneous alloys // Philosophical Magazine. - 1970. - Vol. 21. - P. 399-324.
  18. Bailey J.E., Hirsch P.B. The dislocation distribution, flow stress, and stored energy in cold-worked polycrystalline silver // Philos. Mag. - 1960. - Vol. 5 (53). - P. 485-497.
  19. Berecz T., Szabó P.J. Misorientation between austenite and σ-phase in duplex stainless steel // Periodicapolytechnica ser. mech. eng. - 2005. - Vol. 49. - No. 49. - P. 123-130.
  20. Hot deformation of duplex stainless steels / J.M. Cabrera, A. Mateo, L. Llanes, J.M. Prado, M. Anglada // J. Mater. Process. Tech. - 2003. - Vol. 143-144. - P. 321-325.
  21. Computational crystal plasticity: from single crystal to homogenized polycrystals / G. Cailletaud, O. Diard, F. Feyel, S. Forest // Technischemechanik. - 2003. - Vol. 23. - P. 130-145.
  22. Chen, Yang J.R. Effects of solution treatment and continuous cooling duplex stainless steel // Materials Science and Engineering A. - 2001. - Vol. A311. - P. 28-41.
  23. Cizek P., Wynne B.P., Rainforth W.M. EBSD investigation of the effect of strain path changes on the microstructure and texture of duplex stainless steel during hot deformation // Journal of Physics: Conference Series - 2006. - Vol. 26. -P. 331-334.
  24. Diercks D.R., Burke W.F. Elevated-temperature properties of austenitic stainless steels // ASME. - 1974. - P. 19-30.
  25. Eiken J., Böttger B., Steinbach I. Multiphase-field approach for multicomponent alloys with extrapolation scheme for numerical application // Physical Review - 2006. - Vol. 73. - P. 1-9.
  26. Grain and subgrain structures developed by hot working in as-cast 434 stainless steel / E. Evangelista, P. Mengucci, J. Bowles, H.J. McQueen // High Temp. Mater. Process. - 1993. - Vol. 12. - P. 57-66.
  27. Faccoli M., Roberti R. Study of hot deformation behaviour of 2205 duplex stainless steel through hot tension tests // J. Mater. Sci. - 2013. - Vol. 48. - No. 15. - P. 5196-5203.
  28. Hot deformation characteristics of 2205 duplex stainless steel based on the behavior of constituent phases / H. Farnousha, A. Momenia, K. Dehghania, J.А. Mohandesia, H. Keshmiri // Mater. Design. - 2010. - Vol. 31. - No. 1. - P. 220-226.
  29. Fleck N.A., Hutchinson J.W. Strain gradient plasticity // Adv. Appl. Mech. - 1997. - Vol. 33. - P. 295-361.
  30. Forest S. Strain gradient crystal plasticity: thermomechanical formulations and applications // Journal of the Mechanical Behaviour of Materials. - 2002. - Vol. 13. - P. 219-232.
  31. Franciosi P., Berveiller M., Zaoui A. Latent hardening in copper and aluminum single-crystals // Acta Metall. - 1980. - Vol. 28. - Iss. 3. - P. 273-283.
  32. Gardey B., Bouvier S., Bacroix B. Correlation between the macroscopic behavior and the microstructural evolutions during large plastic deformation of a dual-phase steel // Met. Mater. Trans. A. - 2005. - Vol. 36. - P. 2937-2945.
  33. Garofalo F. An empirical relation defining the stress dependence of minimum creep rate in metals // Trans. Met. Soc. AIME. - 1963. - Vol. 227. - P. 351-359.
  34. A multiscale crystal plasticity analysis of deformation in a two-phase steel / J. Gaskell, F. Dunne, D. Farrugia, J. Lin // Journal of Multiscale Modelling. - 2008. - Vol. 1. - No. 1. - P. 1-19.
  35. Germain P. La m´ethode des puissancesvirtuelles en m´ecanique des milieuxcontinus, premi`erepartie: th´eorie du second gradient // J. de M´ecanique. - 1973. - Vol. 12. - P. 235-274.
  36. Grujicic M., Batchu S. A crystal plasticity materials constitutive model for polysynthetically-twinned γ-TiAl+α2-Ti3Al single crystals // Journal of Materials Science. - 2001. - Vol. 36. - P. 2851-2863.
  37. Modeling of static recrystallization kinetics by coupling crystal plasticity fem and multiphase field calculations / O. Güvenc, T. Henke, G. Laschet, B. Böttger, M. Apel, M. Bambach, G. Hirt // Computer methods in materials science. - 2013. - Vol. 13. - No. 2. - P. 368-374.
  38. Hartig Ch., Mecking H. Finite element modelling of two phase Fe-Cu polycrystals // Computational Materials Science. - 2005. - Vol. 32. - P. 370-377.
  39. Jain M., Christmana T. Processing of submicron grain 304 stainless steel // J. Mater. Res. - 1996. - Vol. 11. - No. 11. - P. 2677-2680.
  40. An experimental analysis and modeling of the work-softening transient due to dynamic recrystallization / E.S. Puchi-Cabrera, M.H. Staia, J.D. Guérin, J. Lesage, M. Dubar, D. Chicot // International Journal of Plasticity. - 2014. - Vol. 54. - P. 113-131.
  41. Kitagawa H., Tomita Y. Note on incremental stress-strain relations of elasto-plastic materials referred to a convected coordinate systems // J. Appl. Math. Mech. - 1972. - Vol. 52 (3). - P. 183-186.
  42. Effect of aging time and temperature on mechanical properties and microstructural evolution of 2205 ferritic-austenitic stainless steel / H. Keshmi, A. Momeni, K. Dehghani, G.R. Ebrahimi, G. Heidari // Journal of Materials Science and Technology. - 2009. - Vol. 25. - P. 597-602.
  43. Kroner E. Initial studies of a plasticity theory based upon statistical mechanics // Inelastic Behaviour of Solids - 1969. - P. 137-147.
  44. Kuc D., Niewielski G. Technological plasticity and structure in stainless steels during hot-working // Journal of Achievements in Materials and Manufacturing Engineering. - 2009. - Vol. 32. - Iss. 2. - P. 154-161.
  45. Atomic-scale simulations of the interaction be-tween a moving dislocation and a bcc/fcc phase boundary / G. Lasko, D. Saraev, S. Schmauder, P. Kizler // Computational Materials Science. - 2005. - Vol. 32. - P. 418-425.
  46. Masima M., Sachs G.O. Mechanische Eigenschaften von Messingkristallen // Z. Physik. - 1928. - B. 50. - S. 161-186.
  47. Mayeur J.R., McDowell D.L. A three-dimensional crystal plasticity model for duplex Ti-6Al-4V // Int. J. Plasticity. - 2007. - Vol. 23 - P. 1457-1485.
  48. Mindlin R.D., Eshel N.N. On first strain gradient theories in linear elasticity // Int. J. Solids Structures. - 1968. - Vol. 4. - P. 109-124.
  49. Perdahcıoğlu E.S., Geijselaers H.J.M. Constitutive modeling of two phase materials using the mean field method for homogenization // International Journal of Material Forming. - 2011. - Vol. 4 (2). - P. 93-102.
  50. Perdahcıoğlu E.S., Geijselaers H.J.M. A constitutive model for multi-phase steels // AIP Conference Proceedings. - 2011. - Vol. 1315. - Iss. 1. - P. 3-9.
  51. Sachs G. Zur Ableitungeiner Fliessbedingung // Z. Verein Deut. Ing. - 1928. - В.72. - S. 734-736.
  52. Deformation mechanisms and microtensile behavior of single colony Ti-6242Si / M.F. Savage, J. Tatalovich, M. Zupan, K.J. Hemker, M.J. Mills // Mater. Sci. Eng. A. - 2001. - Vol. 319-321. - P. 398-403.
  53. Sellars C.M., Tegart W.J. La relation entre la résistance et la structure dans la deformation à chaud // Memories Scientifiques Rev. Métallurg. - 1966. - Vol. 63. - P. 731-746.
  54. Sellars C.M. Modelling microstructural development during hot rolling // Mats. Sci. Tech. - 1990. - Vol. 6. - P. 1072-1081.
  55. Shanthraj P., Zikry M.A. Dislocation density evolution and interactions in crystalline materials // Acta Mater. - 2011. - Vol. 59. - Iss. 20. - P. 7695-7702.
  56. Steinbach I., Pezzolla F. A generalized field method for multiphase transformations using interface fields // Physica D. - 1999. - Vol. 134 (4). - P. 385-393.
  57. Rajabi D., Abedi A., Ebrahimi Gh. Study on static recrystallization process in duplex stainless steel 2205 // International Journal of ISSI. - 2011. - Vol. 8. - No. 2. - P. 20-23.
  58. Overview of constitutive laws, kinematics, homogenization and multiscale methods in crystal plasticity finite-element modeling: Theory, experiments, applications / F. Roters, P. Eisenlohr, L. Hantcherli, D. Tjahjanto, T. Bieler, D. Raabe // Acta Materialia. - 2010. - Vol. 58. - P. 1152-1211.
  59. Multiscale modeling of hot-working with dynamic recrystallization by coupling microstructure evolution and macroscopic mechanical behavior / T. Takaki, C. Yoshimoto, A. Yamanaka, Y. Tomita // Int. J. Plasticity. - 2014. - Vol. 52. - P. 105-116.
  60. Elastic-plastic behaviour of dual-phase, high-strength steel under strain-path changes / V. Tarigopula, O.S. Hopperstad, M. Langseth, A.H. Clausen // European Journal of Mechanics - A/Solids. - 2008. - Vol. 27. - P. 764-782.
  61. Taylor G.I. Plastic strain in metals // J. Inst. Metals. - 1938. - Vol. 62. - P. 307-324.
  62. Taylor G.I., Elam C.F. The distortion of an aluminium crystal during a tensile test // Proc. Roy. Soc. (London). - 1923. - Ser. A 102. - P. 643-647.
  63. Taylor G.I., Elam C.F. The plastic extension and fracture of aluminium crystals // Proc. Roy. Soc. (London). - 1925. - Ser. A 108. - P. 28-51.
  64. Tinga T., Geers M.G.D., Brekelmans W.A.M. Micromechanical model of a single crystal nickel-based superalloy // 25th international congress of the aeronautical sciences. - Germany, Hamburg, 2006. - P. 1-9.
  65. Turteltaub S., Suiker A.S.J. Grain size effects in multiphase steels assisted by transformation-induced plasticity // Int. J. Solids and Structures - 2006. - Vol. 43. - P. 7322-733.
  66. Wu Q., Shanthraj P., Zikry M.A. Modeling the heterogeneous effects of retained austenite on the behavior of martensitic high strength steels // Int. J. Fracture -2013. - Vol. 184. - Iss. 1-2. - P. 241-252.
  67. Micromechanical modeling of the work-hardening behavior of single- and dual-phase steels under two-stage loading paths / K. Yoshida, R. Brenner, B. Bacroix, S. Bouvier // Materials Science and Engineering A. - 2011. - Vol. 528. - P. 1037-1046.
  68. Zambaldi C., Raabe D. Crystal plasticity modelling and experiments for deriving microstructure-property relationships in γ-TiAl based alloys // Journal of Physics: Conference Series. - 2010. - Vol. 240. - P. 1-4. doi: 10.1088/1742-6596/240/1/012140
  69. Zieli´nski W., ´Swi˛atnicki W., Barstch M., Messerschmidt U. Non-uniform distribution of plastic strain in duplex steel during TEM in situ deformation // Materials Chemistry and Physics. - 2003. - Vol. 81. - P. 476-479.
  70. Zikry M.A. Kao M. Inelastic microstructural failure mechanisms in crystalline materials with high angle grain boundaries // J. Mech. Phys. Solids - 1996. - Vol. 44 (11) - P. 1765-1798.

Statistics

Views

Abstract - 43

PDF (Russian) - 23

Cited-By


PlumX


Copyright (c) 2015 Kondratev N.S., Trusov P.V.

Creative Commons License
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.

This website uses cookies

You consent to our cookies if you continue to use our website.

About Cookies