A. S. Smirnov , A. V. Konovalov, O. Yu. Muizemnek
MODELLING AND SIMULATION OF STRAIN RESISTANCE OF ALLOYS TAKING INTO ACCOUNT BARRIER EFFECTS
DOI: 10.17804/2410-9908.2015.1.061-072 The paper proposes a model of strain resistance of alloy under high-temperature deformation. The model describes hardening of alloy due to the increase of dislocation density, as well as the barrier effect of blocking free dislocations, boundaries of grains and subgrains by dispersoids. The model also takes into account the softening processes associated with the recovery and dynamic recrystallization. The model has been tested on the rheological behavior of an Al-Mg alloy named AMg6 at temperatures of 400 and 500 ºC in the range of strain rates from 5 to 25 s-1. It was found in this temperature – strain rate range that the curve of strain resistance of the AMg6 alloy consists of several portions. First there is hardening of the material, then there is material softening, which is again replaced by hardening of the material. With the use of the electron backscatter diffraction technique and transmission electron microscopy, it was found that the main process of softening at investigated temperatures is dynamic recrystallization. The appearance of the second portion of hardening on the strain resistance curve is the inhibition of dynamic recrystallization, as well as manifestation of the barrier effect of blocking free dislocations, grain and subgrain boundaries by dispersoids.
Keywords: Al-Mg alloy, AMg6, strain resistance model, strain resistance, rheology, high temperature deformation, recrystallization, microstructure, dispersoids, barrier effect.  References:
1. Poluhin P.I., Gorelik S.S., Vorontsov V.K. Fizicheskie osnovy plasticheskoi deformatsii [Basic physics of plastic deformation]. Moscow, Metallurgiya Publ., 1982, 584 p. (In Russian).
2. Gorelik S.S., Dobatkin S.V., Kaputkina L.M. Rekristallizatsiya metallov i splavov [Recrystallization of metals and alloys]. Moscow, MISSIS Publ., 2005, 432 p. (In Russian).
3. Doherty R.D., Hughes D.A., Humphreys F.J., Jonas J.J., Juul Jensen D., Kassner M.E., King W.E., McNelley V.R., McQueen H.J., Rollett A.D. Current issues in recrystallization: A review. Materials Science and Engineering A, 1997, vol. 238, no. 2, pp. 219–274.
4. Babich V.K., Gul Yu.P., Dolzhenkov I.E. Deformatsionnoe starenie stali [Strain aging of steel]. Moscow, Metallurgiya Publ., 1972, 320 p.(In Russian).
5. Hähner P., Rizzi E. On the kinematics of Portevin-Le Chatelier bands: Theoretical and numerical modelling. Acta Materialia, 2003, vol. 51, no. 12, pp. 3385–3397.
6. Rizzi E., Hähner P. On the Portevin-Le Chatelier effect: Theoretical modeling and numerical results. International Journal of Plasticity, 2004, vol. 20, no. 1, pp. 121–165.
7. Anjabin N., Karimi Taheri A., Kim H.S. Simulation and experimental analyses of dynamic strain aging of a supersaturated age hardenable aluminum alloy. Materials Science and Engineering A, 2013, vol. 585, pp. 165–173.
8. Zhu S.M., Nie J.F. Serrated flow and tensile properties of a Mg-Y-Nd alloy. Scripta Materialia, 2004, vol. 50, no. 1, pp. 51–55.
9. Wang C., Xu Y., Han E. Serrated flow and abnormal strain rate sensitivity of a magnesium–lithium alloy. Materials Letters, 2006, vol. 60, no. 24, P. 2941–2944.
10. Zhongjun W., Weiping J., Jianzhong C. Study on the Deformation Behavior of Mg-3.6% Er Magnesium Alloy. Journal of Rare Earths, 2007, vol. 25, no. 6, pp. 744–748.
11. Denisov E.K., Mihlik D.V., Shibkov A.A., Zheltov M.A. Discontinuous deformation and structure of alloy Cu-Zn-Sn. Deformatsiya i razrushenie materialov, 2008, no. 9, pp. 6–11. (In Russian).
12. Shibkov A.A., Mazilkin A.A., Protasova S.G., Mihlik D.V., Zolotov A.E., Zheltov M.A., Shuklinov A.V. The influence of impurities on discontinuous deformation of the AMg6 alloy. Deformatsiya i razrushenie materialov, 2008, no. 5, pp. 24–32. (In Russian).
13. Krishtal M.M. Discontinuous fluidity in aluminium-magnesium alloys. Fizika metallov i metallovedenie, 1990, no. 12, pp. 140–143. (In Russian).
14. Mazen A.A. Effect of deformation temperature on the mechanical behavior and deformation mechanisms of Al-Al2O3 metal matrix composites. Journal of Materials Engineering and Performance, 1999, vol. 8, no. 4, pp. 487–495.
15. Puchi-Cabrera E.S. A constitutive description for aluminum-0.1 pct magnesium alloy under hot working conditions. Metallurgical and Materials Transactions A: Physical Metallurgy and Materials Science, 2003, vol. 34, no. 12, pp. 2837–2846.
16. Gouttebroze S., Mo A., Grong Ø., Pedersen K.O., Fjær H.G. A new constitutive model for the finite element simulation of local hot forming of aluminum 6xxx alloys. Metallurgical and Materials Transactions A: Physical Metallurgy and Materials Science, 2008, vol. 39 A, no. 3, pp. 522–534.
17. Zhang P., Li F., Wan Q. Constitutive equation and processing map for hot deformation of SiC particles reinforced metal matrix composites. Journal of Materials Engineering and Performance, 2010, vol. 19, no. 9, pp. 1290–1297.
18. Asgharzadeh H., Simchi A., Kim H.S. Hot deformation of ultrafine-grained Al6063/Al 2O 3 nanocomposites. Journal of Materials Science, 2011, vol. 46, no. 14, pp. 4994–5001.
19. Rajamuthamilselvan M., Ramanathan S. Development of processing map for 7075 Al/20% SiCp composite. Journal of Materials Engineering and Performance, 2012, vol. 21, no. 2, pp. 191–196.
20. Mondal C., Singh A.K., Mukhopadhyay A.K., Chattopadhyay K. Effects of different modes of hot cross-rolling in 7010 aluminum alloy: Part II. Mechanical properties anisotropy. Metallurgical and Materials Transactions A: Physical Metallurgy and Materials Science, 2013,
vol. 44, no. 6, pp. 2764–2777.
21. Mondal C., Singh A.K., Mukhopadhyay A.K., Chattopadhyay K. Effects of different modes of hot cross-rolling in 7010 aluminum alloy: Part I. Evolution of microstructure and texture. Metallurgical and Materials Transactions A: Physical Metallurgy and Materials Science, 2013, vol. 44,
no. 6, pp. 2746–2763.
22. Yang Y., Li F., Yuan Z., Qiao H. A modified constitutive equation for aluminum alloy reinforced by silicon carbide particles at elevated temperature. Journal of Materials Engineering and Performance, 2013, vol. 22, no. 9, pp. 2641–2655.
23. Gangolu S., Rao A.G., Prabhu N., Deshmukh V.P., Kashyap B.P. Hot Workability and Flow Characteristics of Aluminum-5 wV.% B4C Composite. Journal of Materials Engineering and Performance, 2014, vol. 23, iss.4, pp.1366–1373.
24. Shuklinov A.V., Denisov E.K., Mihlik D.V., Zolotov A.E., Zheltov M.A., Shibkov A.A. The transition from a stable to an abrupt deformation caused by the change of composition and structure of Al-Mg alloy. Deformatsiya i razrushenie materialov, 2008, no. 3, pp. 30–35.(In Russian).
25. Mochalov N.A., Galkin A.M., Mochalov S.N., Parfenov D.Yu. Plastometricheskie issledovaniya metallov [Plastometer research of metals]. Moscow, Intermet Inzhiniring Publ., 2003, 318 p. (In Russian).
26. Meng L.J., Sun J., Xing H., Yu W.W., Xue F. Study of low-cycle fatigue of Al6XN austenitic stainless steel. Nuclear Engineering and Design, 2011, vol. 241, no. 8, pp. 2839–2842.
27. Novikov I.I. Teoriya termicheskoi obrabotki metallov [Theory of heat treatment of metals]. Moscow, Metallurgiya Publ., 1978, 391 p. (In Russian).
28. Belyaev A.I., Bochvar O.S., Buynov N.N. Metallovedenie alyuminiya i ego splavov [Physical metallurgy of aluminium and its alloys]. Moscow, Metallurgiya Publ., 1983, 280 p. (In Russian).
29. Kugler G., Turk R. Modelling the dynamic recrystallization under multi-stage hot deformation. Acta Materialia, 2004, vol. 52, no. 15, pp. 4659–4668.
30. Serajzadeh S. Modelling dynamic softening processes during hot working. Materials Science and Engineering A, 2005, vol. 404, no. 1–2, pp. 130–137.
31. Lin Y.C., Chen X.-M. A critical review of experimental results and constitutive descriptions for metals and alloys in hot working. Materials & Design, 2011, vol. 32, no. 4, pp. 1733–1759.
32. Kodzhaspirov G.E., Terentyev M. Modeling the dynamically recrystallized grain size evolution of a superalloy. Materials Physics and Mechanics, 2012, vol. 13, no. 1, pp. 70–76.
33. Rudskoy A.I., Kodzhaspirov G.E., Erentev M.I. Evolution of the structure and properties of Ni-29Cr-9Fe at high-temperature plastic deformation: Experiment and modeling. Deformatsiya i razrushenie materialov, 2013, no. 5, pp. 43–48. (In Russian).
34. Momeni A., Ebrahimi G.R., Jahazi M., Bocher P. Microstructure evolution at the onset of discontinuous dynamic recrystallization: A physics-based model of subgrain critical size. Journal of Alloys and Compounds, 2014, vol. 587, pp. 199–210.
35. Guiqing Ch., Gaosheng F., Wenduan Ja., Chaozeng Ch., Zechang Z. Mathematical model of dynamic recrystallization of aluminum alloy 3003. Metallovedenie i termicheskaja obrabotka metallov, 2013, no. 4, pp. 51–56. (In Russian).
36. Wenduan Ya., Gaosheng F., Guiqing Ch. Kinetic model of dynamic recrystallization of aluminum alloy 1235. Metallovedenie i termicheskaja obrabotka metallov, 2012, no. 4, pp. 23–26. (In Russian).
37. Haimovich A.I., Surkov O.S. Fenomenological model of dynamic recrystallization of aircraft alloys. Vestnik Samarskogo gosudarstvennogo aerokosmicheskogo universiteta, 2009, no. 3–3(27), pp. 150–153. (In Russian).
38. Gourdet S., Montheillet F. A model of continuous dynamic recrystallization. Acta Materialia, 2003, vol. 51, no. 9, pp. 2685–2699.
39. McQueen H.J., Kassner M.E. Comments on a model of continuous dynamic recrystallization proposed for aluminum. Scripta Materialia, 2004, vol. 51, no. 5, pp. 461–465.
40. Hallberg H., Wallin M., Ristinmaa M. Modeling of continuous dynamic recrystallization in commercial-purity aluminum. Materials Science and Engineering: A, 2010, vol. 527, no. 4–5, pp. 1126–1134.
41. Eivani A.R., Zhou J., Duszczyk J. Numerical modeling of subgrain growth of hot extruded Al–4.5Zn–1Mg alloy in the presence of nanosized dispersoids. Computational Materials Science, 2014, vol. 86(15 April) pp. 9–16.
42. Konovalov A.V. Viscoplastic model for the resistance of metals to high-temperature deformation. Metally, 2008, vol. 2008, no. 5, pp. 456–459.
43. Konovalov A.V., Smirnov A.S. Viscoplastic model for the strain resistance of 08Kh18N10T steel at a hot-deformation temperature. Metally, 2008, vol. 2008, no. 2, pp. 138–141.
44. Konovalov A.V., Smirnov A.S., Mazunin V.P., Kokovikhin E.A., Muizemnek O.Yu. Modeling of strain resistance of 08Kh18N10T steel and AMg6 alloy at high rates and temperatures of strains. Deformatsiya i razrushenie materialov, 2012, no. 7, pp. 7–12. (In Russian).
45. Smirnov A.S., Konovalov A.V., Muizemnek O.Yu. Identification of model of strain resistance subject to volume fraction of dynamic recrystallization. Deformatsiya i razrushenie materialov, 2013, no. 9, pp. 7–13. (In Russian).
46. Speedy C.B., Brown R.F., Goodwin G.C. Teoriya ypravleniya. Identifikatsiya i optimalnoe upravlenie [Control theory. Identification and optimal control]. Moscow, Mir Publ., 1973, 248 p. (In Russian).
47. Dziaszyk S., Payton E.J., Friedel F., Marx V., Eggeler G. On the characterization of recrystallized fraction using electron backscatter diffraction: A direct comparison to local hardness in an IF steel using nanoindentation. Materials Science and Engineering: A, 2010, vol. 527, no. 29–30, pp. 7854–7864.
48. Kolychev B.A., Livanov V.A., Elagin V.I. Metallovedenie i termicheskaya obrabotka tsvetnykh metallov i splavov [The metallography and heat treatment of nonferrous metals and alloys]. Moscow, MISSIS Publ., 1999, 416 p. (In Russian).
49. Konovalov A.V., Smirnov A.S. Simulation of strain resistance of AMg6 alloy under hot temperature deformation. Deformatsiya i razrushenie materialov, 2008, no. 5, pp. 33–36. (In Russian).
А. С. Смирнов, А. В. Коновалов, О. Ю. Муйземнек
МОДЕЛИРОВАНИЕ СОПРОТИВЛЕНИЯ ДЕФОРМАЦИИ СПЛАВОВ С УЧЕТОМ БАРЬЕРНЫХ ЭФФЕКТОВ
В работе предложена модель сопротивления деформации сплавов в условиях высокотемпературных деформаций. Модель учитывает упрочнение сплава за счет приращения плотности дислокаций, а также барьерного эффекта блокирования свободных дислокаций, роста границ зерен и субзерен. Также в модели учитываются процессы разупрочнения, связанные с прохождением возврата и динамической рекристаллизации. Модель апробирована на примере реологического поведения Аl-Mg сплава АМг6 при температурах 400 и 500 °С в диапазоне скоростей деформаций 5 – 25 с - 1. В данном температурно-скоростном диапазоне было установлено, что кривая сопротивления деформации сплава АМг6 состоит из нескольких участков. Вначале идет упрочнение материала, затем его разупрочнение, которое опять сменяется упрочнением материала. Используя метод дифракции обратнорассеянных электронов и просвечивающую электронную микроскопию, было выяснено, что основным процессом разупрочнения при исследуемых температурах является динамическая рекристаллизация. Причинами появления второго участка упрочнения на кривой сопротивления деформации является замедление процесса динамической рекристаллизации, а также проявление барьерного эффекта блокирования интерметаллидами свободных дисклокаций, границ зерен и субзерен.
Ключевые слова: Al-Mg сплав, АМг6, модель сопротивления деформации, сопротивление деформации, реология, высокотемпературная деформация, рекристаллизация, микроструктура, интерметаллиды, барьерный эффект Библиография:
1. Полухин П. И., Горелик С. С., Воронцов В. К. Физические основы пластической деформации. ‒ М.: Металлургия, 1982. ‒ 584 с.
2. Горелик С. С., Добаткин С. В., Капуткина Л. М. Рекристаллизация металлов и сплавов. – 3-е изд. ‒ М.: МИССИС, 2005. ‒ 432 с.
3. Current issues in recrystallization: A review / R. D. Doherty, D. A. Hughes, F. J. Humphreys, J. J. Jonas , D. Juul Jensen, M. E. Kassner, W. E. King, T. R. McNelley, H. J. McQueen, A. D. Rollett // Materials Science and Engineering A. ‒ 1997. ‒ Vol. 238, no. 2. ‒ P. 219–274.
4. Бабич В. К., Гуль Ю. П., Долженков И. Е. Деформационное старение стали. ‒ М.: Метеллургия, 1972. ‒ 320 с.
5. Hähner P., Rizzi E. On the kinematics of portevin-le chatelier bands: Theoretical and numerical modelling // Acta Materialia. ‒ 2003. ‒ Vol. 51, no. 12. ‒ P. 3385–3397.
6. Rizzi E., Hähner P. On the Portevin-Le Chatelier effect: Theoretical modeling- and numerical results // International Journal of Plasticity. ‒ 2004. ‒ Vol. 20, no. 1. ‒ P. 121–165.
7. Anjabin N., Karimi Taheri A., Kim H. S. Simulation and experimental analyses of dynamic strain aging of a supersaturated age hardenable aluminum alloy // Materials Science and Engineering A. ‒ 2013. ‒ Vol. 585. ‒ P. 165–173.
8. Zhu S. M., Nie J. F. Serrated flow and tensile properties of a Mg-Y-Nd alloy // Scripta Materialia. ‒ 2004. ‒ Vol. 50, no. 1. ‒ P. 51–55.
9. Wang C., Xu Y., Han E. Serrated flow and abnormal strain rate sensitivity of a magnesium–lithium alloy // Materials Letters. ‒ 2006. ‒ Vol. 60, no. 24. ‒ P. 2941–2944.
10. Zhongjun W., Weiping J., Jianzhong C. Study on the Deformation Behavior of Mg-3.6% Er Magnesium Alloy // Journal of Rare Earths. ‒ 2007. ‒ Vol. 25, no. 6. ‒ P. 744–748.
11. Скачкообразная деформация и структура сплава CU-ZN-SN / Е. К. Денисов, Д. В. Михлик, А. А. Шибков, М. А. Желтов // Деформация и разрушение материалов. ‒ 2008. – № 9. ‒ C. 6–11.
12. Влияние состояния примесей на скачкообразную деформацию сплава АМГ6 / А. А. Шибков, А. А. Мазилкин, С. Г. Протасова, Д. В. Михлик, А. Е. Золотов, М. А. Желтов, А. В. Шуклинов // Деформация и разрушение материалов. ‒ 2008. – № 5. ‒ C. 24–32.
13. Криштал М. М. Прерывистая текучесть в алюминиево-магниевых сплавах // Физика металлов и металловедение. ‒ 1990. – № 12. ‒ C. 140–143.
14. Mazen A. A. Effect of deformation temperature on the mechanical behavior and deformation mechanisms of Al-Al2O3 metal matrix composites // Journal of Materials Engineering and Performance. ‒ 1999. ‒ Vol. 8, no. 4. ‒ P. 487–495.
15. Puchi-Cabrera E. S. A constitutive description for aluminum-0.1 pct magnesium alloy under hot working conditions // Metallurgical and Materials Transactions A: Physical Metallurgy and Materials Science. ‒ 2003. ‒ Vol. 34, no. 12. ‒ P. 2837–2846.
16. A new constitutive model for the finite element simulation of local hot forming of aluminum 6xxx alloys / S. Gouttebroze, A. Mo, Ø. Grong, K. O. Pedersen, H. G. Fjær // Metallurgical and Materials Transactions A: Physical Metallurgy and Materials Science. ‒ 2008. ‒ Vol. 39 A, no. 3. ‒ P. 522–534.
17. Zhang P., Li F., Wan Q. Constitutive equation and processing map for hot deformation of SiC particles reinforced metal matrix composites // Journal of Materials Engineering and Performance. ‒ 2010. ‒ Vol. 19, no. 9. ‒ P. 1290–1297.
18. Asgharzadeh H., Simchi A., Kim H. S. Hot deformation of ultrafine-grained Al6063/Al 2O 3 nanocomposites // Journal of Materials Science. ‒ 2011. ‒ Vol. 46, no. 14. ‒ P. 4994–5001.
19. Rajamuthamilselvan M., Ramanathan S. Development of processing map for 7075 Al/20% SiCp composite // Journal of Materials Engineering and Performance. ‒ 2012. ‒ Vol. 21, no. 2. ‒ P. 191–196.
20. Effects of different modes of hot cross-rolling in 7010 aluminum alloy: Part II. mechanical properties anisotropy / C. Mondal, A. K. Singh, A. K. Mukhopadhyay, K. Chattopadhyay // Metallurgical and Materials Transactions A: Physical Metallurgy and Materials Science. ‒ 2013. ‒ Vol. 44, no. 6. ‒ P. 2764–2777.
21. Effects of different modes of hot cross-rolling in 7010 aluminum alloy: Part I. evolution of microstructure and texture / C. Mondal, A. K. Singh, A. K. Mukhopadhyay, K. Chattopadhyay // Metallurgical and Materials Transactions A: Physical Metallurgy and Materials Science. ‒ 2013. ‒ Vol. 44, no. 6. ‒ P. 2746–2763.
22. A modified constitutive equation for aluminum alloy reinforced by silicon carbide particles at elevated temperature / Y. Yang, F. Li, Z. Yuan, H. Qiao // Journal of Materials Engineering and Performance. ‒ 2013. ‒ Vol. 22, no. 9. ‒ P. 2641–2655.
23. Hot Workability and Flow Characteristics of Aluminum-5 wt.% B4C Composite / S. Gangolu, A. G. Rao, N. Prabhu, V. P. Deshmukh, B. P. Kashyap // Journal of Materials Engineering and Performance. ‒ 2014. ‒ P. 1–8.
24. Переход от устойчивой к скачкообразной деформации, вызванный изменением состава и структуры сплава Al-Mg / А. В. Шуклинов, Е. К. Денисов, Д. В. Михлик, А. Е. Золотов, М. А. Желтов, А. А. Шибков // Деформация и разрушение материалов. ‒ 2008. – № 3. ‒ C. 30–35.
25. Пластометрические исследования металлов. / Н. А. Мочалов, А. М. Галкин, С. Н. Мочалов, Д. Ю. Парфенов ‒ М.: Интермет инжиниринг, 2003. ‒ 318 с.
26. Study of low-cycle fatigue of Al6XN austenitic stainless steel / L. J. Meng, J. Sun, H. Xing, W. Yu, F. Xue // Nuclear Engineering and Design. ‒ 2011. ‒ Vol. 241, no. 8. ‒ P. 2839–2842.
27. Новиков И. И. Теория термической обработки металлов. ‒ М.: Металлургия, 1978. ‒ 391 с.
28. Беляев А. И., Бочвар О. С., Буйнов Н. Н. Металловедение алюминия и его сплавов. ‒ М.: Металлургия, 1983. ‒ 280 с.
29. Kugler G., Turk R. Modeling the dynamic recrystallization under multi-stage hot deformation // Acta Materialia. ‒ 2004. ‒ T. 52, № 15. ‒ C. 4659–4668.
30. Serajzadeh S. Modelling dynamic softening processes during hot working // Materials Science and Engineering A. ‒ 2005. ‒ Vol. 404, no. 1–2. ‒ P. 130–137.
31. Lin Y. C., Chen X.-M. A critical review of experimental results and constitutive descriptions for metals and alloys in hot working // Materials & Design. ‒ 2011. ‒ Vol. 32, no. 4. ‒ P. 1733–1759.
32. Kodzhaspirov G. E., Terentyev M. I. Modeling the dynamically recrystallized grain size evolution of a superalloy // Materials Physics and Mechanics. ‒ 2012. ‒ Vol. 13, no. 1. ‒ P. 70–76.
33. Рудской А. И., Коджаспиров Г. Е., Ерентьев М. И. Эволюция структуры и свойств сплава Ni–29Cr–9Fe при высокотемпературном пластическом деформировании: Эксперимент и моделирование // Деформация и разрушение материалов. ‒ 2013. – № 5. ‒ C. 43–48.
34. Microstructure evolution at the onset of discontinuous dynamic recrystallization: A physics-based model of subgrain critical size / A. Momeni, G. R. Ebrahimi, M. Jahazi, P. Bocher // Journal of Alloys and Compounds. ‒ 2014. ‒ Vol. 587. ‒ P. 199–210.
35. Математическая модель динамической рекристаллизации алюминиевого сплава 3003 / Ч. Гвицин, Ф. Гаошен, Я. Вэндуан, Ч. Чаозен, З. Дзечан // Металловедение и термическая обработка металлов. ‒ 2013. – № 4. ‒ C. 51–56.
36. Вэндуан Я., Гаошэн Ф., Гуицинь Ч. Модель кинетики динамической рекристаллизации алюминиевого сплава 1235 // Металловедение и термическая обработка металлов. ‒ 2012. – № 4. ‒ C. 23–26.
37. Хаймович А. И., Сурков О. С. Феноменологичекие модели динамической рекристаллизации авиационных сплавов // Вестник Самарского государственного аэрокосмического университета. ‒ 2009. – № 3–3. ‒ C. 150–153.
38. Gourdet S., Montheillet F. A model of continuous dynamic recrystallization // Acta Materialia. ‒ 2003. ‒ Vol. 51, no. 9. ‒ P. 2685–2699.
39. McQueen H. J., Kassner M. E. Comments on 'a model of continuous dynamic recrystallization' proposed for aluminum // Scripta Materialia. ‒ 2004. ‒ Vol. 51, no. 5. ‒ P. 461–465.
40. Hallberg H., Wallin M., Ristinmaa M. Modeling of continuous dynamic recrystallization in commercial-purity aluminum // Materials Science and Engineering: A. ‒ 2010. ‒ Vol. 527, no. 4–5. ‒ P. 1126–1134.
41. Eivani A. R., Zhou J., Duszczyk J. Numerical modeling of subgrain growth of hot extruded Al–4.5Zn–1Mg alloy in the presence of nanosized dispersoids // Computational Materials Science. ‒ 2014. ‒ Vol. 86. ‒ P. 9–16.
42. Konovalov A. V. Viscoplastic model for the resistance of metals to high-temperature deformation // Metally. – 2008. – Vol. 2008, no. 5. – P. 456–459
43. Konovalov A. V., Smirnov A. S. Viscoplastic model for the strain resistance of 08Kh18N10T steel at a hot-deformation temperature // Metally. – 2008. – Vol. 2008, no. 2. – P. 138–141.
44. Моделирование реологии стали 08Х18Н10Т и сплава АМг6 при высоких скоростях и температурах деформации / А. В. Коновалов, А. С. Смирнов, В. П. Мазунин, Е. А. Коковихин, О. Ю. Муйземнек // Деформация и разрушение материалов. ‒ 2012. – № 7. ‒ C. 7–12.
45. Смирнов А. С., Коновалов А. В., Муйземнек О. Ю. Идентификация модели сопротивления деформации металлических материалов с учетом объемной доли динамически рекристаллизованных зерен // Деформация и разрушение материалов. ‒ 2013. – № 9. ‒ C. 7–13.
46. Спиди К., Браун Р., Гудвин Д. Теория управления. Идентификация и оптимальное управление. ‒ М.: Мир, 1973. ‒ 248 с.
47. On the characterization of recrystallized fraction using electron backscatter diffraction: A direct comparison to local hardness in an IF steel using nanoindentation / S. Dziaszyk, E. J. Payton, F. Friedel, V. Marx, G. Eggeler // Materials Science and Engineering: A. ‒ 2010. ‒ Vol. 527, no. 29–30. ‒ P. 7854–7864.
48. Jin Z. Y., Cui Z. S. Investigation on strain dependence of dynamic recrystallization behavior using an inverse analysis method // Materials Science and Engineering a-Structural Materials Properties Microstructure and Processing. ‒ 2010. ‒ Vol. 527, no. 13–14. ‒ P. 3111–3119.
49. Коновалов А. В., Смирнов А. С. Моделирование сопротивления деформации сплава АМг6 при температуре горячей деформации // Деформация и разрушение материалов. ‒ 2008. – № 5. ‒ C. 33–36.
     
Библиографическая ссылка на статью
Smirnov A. S., Konovalov A. V., Muizemnek O. Yu. Modelling and Simulation of Strain Resistance of Alloys Taking into Account Barrier Effects // Diagnostics, Resource and Mechanics of materials and structures. -
2015. - Iss. 1. - P. 61-72. - DOI: 10.17804/2410-9908.2015.1.061-072. -
URL: http://dream-journal.org/issues/content/article_18.html (accessed: 30.03.2025).
|
