МЕТОДЫ И РЕЗУЛЬТАТЫ ИССЛЕДОВАНИЯ ЭФФЕКТА ПОРТЕВЕНА – ЛЕ ШАТЕЛЬЕ: ФИЗИЧЕСКИ-ОРИЕНТИРОВАННЫЕ КОНТИНУАЛЬНЫЕ И МНОГОУРОВНЕВЫЕ МОДЕЛИ

Трусов, П.В.; Герасимов, Р.М.

doi:10.15593/perm.mech/2023.5.10

МЕТОДЫ И РЕЗУЛЬТАТЫ ИССЛЕДОВАНИЯ ЭФФЕКТА ПОРТЕВЕНА – ЛЕ ШАТЕЛЬЕ: ФИЗИЧЕСКИ-ОРИЕНТИРОВАННЫЕ КОНТИНУАЛЬНЫЕ И МНОГОУРОВНЕВЫЕ МОДЕЛИ

П.В. Трусов, Р.М. Герасимов

Сведения об авторах

П.В. Трусов
Пермский национальный исследовательский политехнический университет, Пермь, Российская Федерация
Р.М. Герасимов
Пермский национальный исследовательский политехнический университет, Пермь, Российская Федерация

https://doi.org/10.15593/perm.mech/2023.5.10

Эффекты прерывистой пластичности, несмотря на почти 200-летнюю историю с момента своего открытия, продолжают являться объектами интенсивного изучения механиками, материаловедами, технологиями в области обработки металлов и сплавов пластическим деформированием. С развитием экспериментальных методов и инструментальной базы обнаруживаются все новые механизмы, ответ- ственные за нарушение монотонности отклика (напряжений) при монотонных воздействиях (ростом деформаций). Для описания данных эффектов предложены и продолжают разрабатываться конститу- тивные модели (определяющие соотношения), основанные на различных (макрофеноменологическом, термодинамическом, структурно-механическом, физическом) подходах. Несмотря на разнообразие причин возникновения прерывистой пластичности, общепризнанной являет- ся необходимость для построения корректных конститутивных моделей анализировать процессы, реализуе- мые при неупругом деформировании на мезо- и микроуровне, описывать эволюционирующую структуру материалов на различных масштабных уровнях. В связи с этим наиболее перспективными для формулировки определяющих соотношений в настоящее время представляется применение физически-ориентированных моделей. В предлагаемой статье приводится краткий обзор работ, посвященных построению физически- ориентированных конститутивных моделей, пригодных для исследования эффектов прерывистой пла- стичности. В первой части обзора приведены модели, базирующиеся в основном на феноменологиче- ском подходе к формулировке совокупности уравнений для исследования эволюции дефектной струк- туры моно- и поликристаллических сплавов, в большинстве своем использующие континуальное описа- ние. Особое внимание при создании физически-ориентированных моделей уделяется рассмотрению взаимовлияние дефектов различной природы, включая взаимодействие примесных атомов с дислока- циями. Во второй части обзора рассмотрены работы, основанные на введении внутренних переменных, многоуровневом физически-ориентированном подходе. К сожалению, моделей второго класса в настоя- щее время имеется очень ограниченное количество; тем не менее, авторы считают их наиболее пер- спективными для построения конститутивных моделей, адекватно описывающих эффекты прерывистой пластичности.

Ключевые слова

обзорпрерывистая пластичностьконститутивные моделифизически- ориентированные континуальные и многоуровневые модели.

Methods and results of studying the Portevin – Le Chatelier effect: physically-oriented continuous and multilevel models

The effects of intermittent plasticity, despite almost 200 years of history since its discovery, are still intensively studied by mechanics, materials scientists, and technologists processing metals and alloys by plastic deformation. With the development of experimental methods and instrumentation, more and more new mechanisms are being discovered that are responsible for the violation of the monotonicity of the response (stresses) under monotonic effects (growth of strains). To describe these effects, constitutive models (constitutive relations) based on various (macrophenomenological, thermodynamic, structural-mechanical, physical) approaches have been proposed and continue to be developed. Despite the variety of reasons for the emergence of discontinuous plasticity, it is generally recognized that in order to build correct constitutive models, it is necessary to analyze the processes that occur during inelastic deformation at the meso- and microlevels, and to describe the evolving structure of materials at various scale levels. Thus the use of physically oriented models is the most promising area of studies for the formulation of constitutive relations. The proposed article provides a brief overview of works constructing physically-oriented constitutive models suitable for studying the effects of discontinuous plasticity. The first part of the review presents models based mainly on the phenomenological approach to the formulation of a set of equations for studying the evolution of the defect structure of single- and polycrystal- line alloys, most of which use the continuum description. When creating physically-oriented mod- els, special attention is paid to the consideration of the mutual influence of defects of various natures, including the interaction of impurity atoms with dislocations. The second part of the re- view considers works based on the introduction of internal variables, a multilevel physically- oriented approach. Unfortunately, second-class models are currently very limited; nevertheless, the authors consider them the most promising for constructing constitutive models that adequate- ly describe the effects of discontinuous plasticity.

Keywords

reviewdiscontinuous plasticityconstitutive modelsphysically oriented continual and multilevel models

Литература

1.Kottrel A.X. Dislokaciiu i plastichcecko techenie b krictallax. - M.: GNTII lit-rib no cephoi i chteni metalurgii, 1958. - 267 c. Scholar
2.Petuxob B.B. O nopore podivnokosti dislokaciiu b primecshx nopuprovodnikax // Журnal texhnichckoi fizikii. - 1990. - T. 60, bm. 10. - C. 64-68. Scholar
3.Petuxob B.B. Pazlinhne tihs dinamikii dislokaciiu kak cldestivie ix dinamicchokoro ctaerii // Журnal texhnichckoi fizikii. - 2003. - T. 73, bm. 7. - C. 82-87. Scholar
4.Petuxob B.B. Dinamichckoe ctaerine dislokaciiu b materialax c buchokm krictallichckom pelebop: konkurenciia difpuziiu i vnlechenie primecsei // Krictallografii. - 2009. - T. 54, № 1. - C. 85-91. Scholar
5.Petuxob B.B. Ob uprochenii krictallob poscrdctbom immobiliaciiu dislokaciiu podivnkhimi primecsii // Krictallografii. - 2011. - T. 56, № 1. - C. 65-71. Scholar
6.Tpucob P.B., Cheyulina E.A. Prepbrisiata tekycteb: modeli, osnovanhne ha fizichckix teoriix plastichctii // Vestnik PIHIIIIY. Mexanika. - 2017. - № 1. - C. 134-163. DOI: 10.15593/pem.mech/2017.1.09 Scholar
7.Tpucob P.B., Cheyulina E.A. Metohi i pezylatbi isclodobaniia zfpckta Portbena - Jle Шatleb: zckepiemhnti i makpofenomelnoligichckie modeli // Vestnik PIHIIIIY. Mexanika. - 2023. - № 5. - C. 99-131. Scholar
8.Tpucob P.B., Шveikii A.I. Mhoroqopbneshie modeli mono- i nolikrictallichckix materialob: teoriia, aligortihmi, primepbri mpenhenii. - Hovocibipck: Izhdatelctbo CO PAH, 2019. - 605 c. DOI: 10.15372/MULTILEVEL2019TPV Scholar
9.Фридель Ж. Dislokaciiu. - M.: Мир, 1967. - 644 c. Scholar
10.Aboulfadl H. et al. Dynamic strain aging studied at the atomic scale / H. Aboulfadl, J. Deges, P. Choi, D. Raabe // Acta Materialia. – 2015. – Vol. 86. – P. 34–42. DOI: 10.1016/j.actamat.2014.12.028 Scholar
11.Acharya A. A model of crystal plasticity based on the theory of continuously distributed dislocations // J. Mechanics and Physics of Solids. – 2001. – Vol. 49. – P. 761–784. DOI: 10.1016/S0022-5096(00)00060-0 Scholar
12.Acharya A. Driving forces and boundary conditions in continuum dislocation mechanics // Proc. R. Soc. Lond. A. – 2003. – Vol. 459. – P. 1343–1363. DOI: 10.1098/rspa.2002.1095 Scholar
13.Acharya A., Roy A. Size effects and idealized dislocation microstructure at small scales: predictions of a phenomenological model of mesoscopic field dislocation mechanics: part I // Journal of the Mechanics and Physics of Solids. – 2006. – Vol. 54. – P. 1687- 1710. DOI: 10.1016/j.jmps.2006.01.009 Scholar
14.Aqaram S. et al. Dislocation density based crystal plasticity model incorporating the effect of precipitates in IN718 under monotonic and cyclic deformation / S. Aqaram, A.K. Kanjarla, B. Bhuvaraghan, S.M. Srinivasan // Int. J. Plasticity. – 2021. – Vol. 141. – P. 102990 (19 p.). DOI: 10.1016/j.ijplas.2021.102990 Scholar
15.Ananthakrishna G. On the dynamical mechanism of cross-over from chaotic to turbulent states // Pramana - J. Phys. – 2005. – Vol. 64, no. 3. – P. 343–352. DOI: 10.1007/BF02704562 Scholar
16.Ananthakrishna G. Current theoretical approaches to collective behavior of dislocations // Physics Reports. – 2007. – Vol. 440. – P. 113–259. DOI: 10.1016/j.physrep.2006.10.003 Scholar
17.Ananthakrishna G., Valsakumar M.C. Repeated yield drop phenomenon: a temporal dissipative structure // J. Physics D: Applied Physics. – 1982. – Vol. 15(12), L171-L175. DOI: 10.1088/0022-3727/15/12/003 Scholar
18.Arsenault R.J., Patu S., Esterling D.M. Computer simulation of solid solution strengthening in FCC alloys: Part I. Friedel and Mott limits // Metallurgical Transaction A. – 1989. – Vol. 20. – P. 1411–1418. DOI: 10.1007/BF02665498 Scholar
19.Balik J., Lukáč P. Influence of solute mobility on dislocation motion. I. Basic model // Czech. J. Phys. – 1989a. – B. 39. – P. 447–457. DOI: 10.1007/BF01597802 Scholar
20.Balik J., Lukáč P. Influence of solute mobility on dislocation motion. II. Application of the basic model // Czech. J. Phys. – 1989b. – B. 39. – P. 1138–1146. DOI: 10.1007/BF01605398 Scholar
21.Van den Beukel A. Theory of the effect of dynamic strain aging // Phys. Stat. Sol. A. – 1975. – Vol. 30. – P. 197–206. DOI: 10.1002/pssa.2210300120 Scholar
22.Benallal A. et al. Dynamic strain aging and related instabilities: experimental, theoretical and numerical aspects / A. Benallal, T. Berstad, T. Børvik, A.H. Clausen, O.S. Hopperstad // European Journal of Mechanics – A/Solids. – 2006. – Vol. 25, is. 3. – P. 397–424. DOI: 10.1016/j.euromechsol.2005.10.007 Scholar
23.Bharathi M.S., Rajesh S., Ananthakrishna G. A dynamical model for the Portevin – Le Chatelier bands // Scripta Materialia. – 2003. – Vol. 48, no. 9. – P. 1355–1360. DOI: 10.1016/s1359-6462(02)00653-x Scholar
24.Bilby B.A. On the interactions of dislocations and solute atoms // Proc. Physical Society. Sect. A. – 1950. – Vol. 63, is. 3. – P. 191–200. DOI: 10.1088/0370-1298/63/3/302 Scholar
25.Böhlke T. et al. Geometrically non-linear modeling of the Portevin–Le Chatelier effect / T. Böhlke, G. Bondár, Y. Estrin, M.A. Lebyodkin // Computational Materials Science. – 2009. – Vol. 44, is. 4. – P. 1076–1088. DOI: 10.1016/j.commatsci.2008.07.036 Scholar
26.Brechet Y., Estrin Y. On the influence of precipitation on the Portevin-Le Chatelier effect // Acta Metall. Mater. – 1995. – Vol. 43, no. 3. – P. 955–963. DOI: 10.1016/0956-7151(94)00334-E Scholar
27.Brechtl J. et al. Entropy modeling on serrated flows in carburized steels / J. Brechtl, B. Chen, X. Xie, Y. Ren, J.D. Venable, P.K. Liaw, S.J. Zinkle // Materials Science & Engineering A. – 2019. – Vol. 753. – P. 135–145. DOI: 10.1016/j.msea.2019.02.096 Scholar
28.Brindley B.J., Worthington P.J. Yield-point phenomena in substitutional alloys // Metallurgical Reviews. – 1970. – Vol. 15, is. 1. – P. 101–114. DOI: 10.1179/mtlr.1970.15.1.101 Scholar
29.Bryukhanov I.A. Dynamics of edge dislocation in Cu–Ni solid solution alloys at atomic scale // Int. J. Plasticity. – 2020. – Vol. 135. – P. 102834. DOI: 10.1016/j.ijplas.2020.102834 Scholar
30.Bullough R., Newman R.C. The flow of impurities to an edge dislocation // Proc. Royal Society of London. Series A, Mathematical and Physical Sciences. – 1959. – Vol. 249, no. 1258. – P. 427–440. Scholar
31.Bullough R., Newman R.C. The growth of impurity atmospheres round dislocations // Proc. Royal Society of London. Series A, Mathematical and Physical Sciences. – 1962a. – Vol. 266, no. 1325. – P. 198–208. DOI:10.1098/rspa.1962.0056 Scholar
32.Bullough R., Newman R.C. Impurity Precipitation on Dislocations-A Theory of Strain Ageing // Proc. Royal Society of London. Series A, Mathematical and Physical Sciences. –1962b. – Vol. 266, no. 1325. – P. 209–221. DOI: 10.1098/rspa.1962.0057 Scholar
33.Bullough R., Newman R.C. The kinetics of migration of point defects to dislocations // Rep. Prog. Phys. – 1970. – Vol. 33, no. 1. – P. 101–148. DOI: 10.1088/ 0034-4885/33/1/303 Scholar
34.Butt M.Z., Feltham P. Solid-solution hardening (Review) // J. Material Science. – 1993. – Vol. 28. – P. 2557–2576. DOI: 10.1007/BF00356192 Scholar
35.Cahn R.W., Davies R.G. X-ray evidence for segregation of solute to stacking faults in a copper-aluminium alloy // Philosophical Magazine. – 1960. – Vol.5, Is.59. – P.1119-1126. DOI: 10.1080/14786436008238320 Scholar
36.Cai W. et al. A non-singular continuum theory of dislocations / W. Cai, A. Arsenlis, C.R. Weinberger, V.V. Bulatov // J. Mechanics and Physics of Solids. – 2006. – Vol. 54. – P. 561- 587. DOI: 10.1016/j.jmps.2005.09.005 Scholar
37.Chen H. et al. Effects of nanosized precipitates on the Portevin - Le Chatelier behavior: Model prediction and experimental verification / H. Chen, Z. Chen, Y. Chen, G. Ji, S. Zhong, H. Wang, Y. Ke, Y. Brechet // Materialia - 2021. - Vol. 21. - P. 101299. DOI: 10.1016/j.mtla.2021.101299 Scholar
38.Cheng J., Nemat- Nasser S. A model for experimentallyobserved high- strain- rate dynamic strain aging in titanium // Acta mater. - 2000. - Vol. 48. - P. 3131- 3144. DOI: 10.1016/S1359- 6454(00)00124- 5 Scholar
39.Cochardt A.W., Schoek G., Wiedersich H. Interaction between dislocations and interstitial atoms in body- centered cubic metals // Acta Metallurgica. - 1955. - Vol. 3, no. 6. - P. 533- 537. DOI: 10.1016/0001- 6160(55)90111- 5 Scholar
40.Cottrell A.H. A note on the Portevin - Le Chatelier effect // Philosophical Magazine and Journal of Science. - 1953. - Vol. 44, is. 355. - P. 829- 832. DOI: 10.1080/14786440808520347 Scholar
41.Cottrell A.H., Bilby B.A. Dislocation theory of yielding and strain ageing of iron // Proc. Phys. Soc. A. - 1949. - Vol. 62. - P. 49- 62. DOI: 10.1088/0370- 1298/62/1/308 Scholar
42.Cottrell A.H., Jaswon M.A. Distribution of solute atoms round a slow dislocation // Proc. R. Soc. - 1949. - Vol. 199. - P. 104- 114. DOI: 10.1098/rspa.1949.0128 Scholar
43.Curtin W.A., Olmsted D.L., Hector Jr., L.G. A predictive mechanism for dynamic strain ageing in aluminium- magnesium alloy // Nat. Mater. - 2006. - Vol. 5. - P. 875- 880. DOI: 10.1038/nmat1765 Scholar
44.Estrin Y. 2. Dislocation- density- related constitutive modeling. - In: Unified Constitutive Laws of Plastic Deformation (Editors A.S. Krausz, K. Krausz). - Academic Press, 1996. - P. 69- 106. DOI: 10.1016/b978- 012425970- 6/50003- 5 Scholar
45.Estrin Y., Kubin L.P. Local strain hardening and nonuniformity of plastic deformation // Actu metall. - 1986. - Vol. 34, no. 12. - P. 2455- 2464. DOI: 10.1016/0001- 6160(86)90148- 3 Scholar
46.Estrin Y., Kubin L.P. Plastic instabilities: phenomenology and theory // Materials Science and Engineering A. - 1991. - Vol. 137. - P. 125- 134. DOI: 10.1016/0921- 5093(91)90326- I Scholar
47.Estrin Y., Ling C.P., McCormick P.G. Localization of plastic flow: spatial vs temporal instabilities // Acta metall. mater. - 1991. - Vol. 39, no. 11. - P. 2943- 2949. DOI: 10.1016/0956- 7151(91)90110- M Scholar
48.Estrin Y., McCormick P.G. Modelling the transient flow behaviour of dynamic strain ageing materials // Acta metall. mater. - 1991. - Vol. 39, no. 12. - P. 2977- 2983. DOI: 10.1016/0956- 7151(91)90030- 5 Scholar
49.Fleischer R.L. Solution hardening // Acta Metallurgica. - 1961. - Vol. 9, is. 11. - P. 996- 1000. DOI: 10.1016/0001- 6160(61)90242- 5 Scholar
50.Follansbee P.S., Kocks U.F. A constitutive description of copper based on the use of the mechanical threshold stress as an Internal State Variable // Acta Metall. 1988. - Vol. 36. - P. 81- 93. DOI: 10.1016/0001- 6160(88)90030- 2 Scholar
51.Fressengeas C. et al. Dynamic strain aging: A coupled dislocation - solute dynamic model // C. Fressengeas, A.J. Beaudoin, M. Leboydkin, L.P. Kubine, Y. Estrin // Materials Science and Engineering A. - 2005. - Vol. 400- 401. - P. 226- 230. DOI: 10.1016/j.mse.2005.02.073 Scholar
52.Fuentes- Samaniego R., Gasca- Neri R., Hirth J.P. Solute drag on moving edge dislocations // Philosophical Magazine A. - 1984. - Vol. 49, no. 1. - P. 31- 43. DOI: 10.1080/01418618408233426 Scholar
53.Graff S. et al. Strain localization phenomena associated with static and dynamic strain ageing in notched specimens: experiments and finite element simulations // S. Graff, S. Forest, J.- L. Strudel, C. Prioul, P. Pilvin, J.- L. Bechade // Materials Science and Engineering: A. - 2004. - Vol. 387. - P. 181- 185. DOI: 10.1016/j.mse.2004.02.083 Scholar
54.Gupta S., Beaudoin Jr A.J., Chevy J. Strain rate jump induced negative strain rate sensitivity (NSRS) in aluminum alloy 2024: Experiments and constitutive modeling // Materials Science & Engineering A. - 2017. - Vol. 683. - P. 143- 152. DOI: 10.1016/j.mse.2016.12.010 Scholar
55.Gupta S. et al. Crystal plasticity modeling of the effects of crystal orientation and grain- to- grain interactions on DSA- induced strain localization in Al- Li alloys // S. Gupta, V. Taupin, C. Fressengeas, J. Chevy // Materialia. - 2019. - Vol. 8. - P. 100467 (12 p.) DOI: 10.1016/j.mtla.2019.100467 Scholar
56.Hahn G.T. A model for yielding with special reference to the yield- point phenomena of iron and related bcc metals // Acta Metallurgica. - 1962. - Vol. 10, is. 8. - P. 727- 738. DOI: 10.1016/0001- 6160(62)90041- x Scholar
57.Ham F.S. Stress- assisted precipitation on dislocations // J. Applied Physics, - 1959. - Vol. 30, no. 6. - P. 915- 926. DOI: 10.1063/1.1735262 Scholar
58.Hahner P., Rizzi E. On the kinematics of Portevin - Le Chatelier bands: theoretical and numerical modelling // Acta Materialia - 2003. - Vol. 51, is. 12. - P. 3385- 3397. DOI: 10.1016/S1359- 6454(03)00122- 8 Scholar
59.Hahner P., Zaiser M. From mesoscopic heterogeneity of slip to macroscopic fluctuations of stress and strain // Acta Materialia - 1997. - Vol. 45, is. 3. - P. 1067- 1075. DOI: 10.1016/S1359- 6454(96)00227- 3 Scholar
60.Harper S. Precipitation of carbon and nitrogen in cold- worked alpha- iron // Physical Review. - 1951. - Vol. 83, no. 4. - P. 709- 712. DOI: 10.1103/PhysRev.83.709 Scholar
61.Hossain M.Z., Marian J. Stress- dependent solute energetics in W- Re alloys from first- principles calculations // Acta Materialia. - 2014. - Vol. 80. - P. 107- 117. DOI: 10.1016/j.actamat.2014.07.028 Scholar
62.Hu S.Y. et al. Dynamic drag of solute atmosphere on moving edge dislocations- Phase- field simulation // S.Y. Hu, J. Choi, Y.L. Li, L.Q. Chen // J. Appl. Phys. - 2004. - Vol. 96, no. 1. - P. 229- 236. DOI: 10.1063/1.1755858 Scholar
63.Johnston W.G., Gilman J.J. Dislocation multiplication in lithium fluoride crystals // J. Applied Physics. - 1960. - Vol. 31, no. 4. - P. 632- 643. DOI: 10.1063/1.1735655 Scholar
64.Klose F.B. et al. Plastic instabilities with propagating deformation bands in Cu- Al alloys // F.B. Klose, J. Weidenmuller, A. Ziegenbein, P. Hahner, H. Neuhauser // Philosophical Magazine. - 2004. - Vol. 84, no. 3- 5. - P. 467- 480. DOI: 10.1080/14786430310001610320 Scholar
65.Klusemann B. et al. Thermomechanical characterization of Portevin - Le Chatelier bands in AlMg3 (AA5754) and modeling based on a modified Estrin - McCormick approach // B. Klusemann, G. Fischer, T. Bohlke, B. Svendsen // International Journal of Plasticity. - Vol. 67. - P. 192- 216. DOI: 10.1016/j.ijplas.2014.10.011 Scholar
66.Kocks U.F. Kinetics of solution hardening // Metall. Mater. Trans. A. - 1985. - Vol. 16A. - P. 2109- 2129. DOI: 10.1007/BF02670415 Scholar
67.Kocks U.F., Mecking H. Physics and phenomenology of strain hardening: the FCC case // Progress in Materials Science. - 2003. - Vol. 48. - P. 171- 273. DOI: 10.1016/S0079- 6425(02)00003- 8 Scholar
68.Kok S. et al. Simulation of the Portevin-Le Chatelier effect using polycrystal plasticity / S. Kok, A.J. Beaudoin, D.A. Tortorelli, M. Lebyodkin, L. Kubin, C. Fressengeas // J. Phys. IV. - 2003a. - Vol. 105. - P. 191-197. DOI: 10.051/jp4:2 0030187 Scholar
69.Kok S. et al. Spatial coupling in jerky flow using polycrystal plasticity / S. Kok, M.S. Bharathi, A.J. Beaudoin, C. Fressengeas, G. Ananthakrishna, L.P. Kubin, M. Lebyodkin // Acta Materialia. - 2003b. - Vol. 51. - P. 3651-3662. DOI: 10.1016/S1359-6454(03)00114-9 Scholar
70.Kreya J., Kozeschnik E. State parameter-based constitutive modelling of stress strain curves in Al-Mg solid solutions // Int. J. Plasticity. - 2018. - Vol. 103. - P. 67-80. DOI: 10.1016/j.ijplas.2018.01.001 Scholar
71.Kubin L.P., Chihab K., Estrin Y. The rate dependence of the Portevin-Le Chatelier effect // Acta metall. - 1988. - Vol. 36, no. 10. - P. 2707-2718. DOI: 10.1016/0001-6160(88)90117-4 Scholar
72.Kubin L.P., Estrin Y. The Portevin - Le Chatelier effect in deformation with constant stress rate // Acta Metall. - 1985. - Vol. 33. - P. 397-407. DOI: 10.1016/0001-6160(85)90082-3 Scholar
73.Kubin L.P., Estrin Y. Evolution of dislocation densities and the critical conditions for the Portevin - Le Chatelier effect // Acta Metall. Mater. - 1990. - Vol. 38, no. 5. - P. 697-708. DOI: 10.1016/0956-7151(90)90021-8 Scholar
74.Kubin L., Estrin Y. Dynamic strain ageing and the mechanical response of alloys // J. de Physique III, EDP Sciences. - 1991. - Vol. 1, no. 6. - P. 929-943. DOI: 10.1051/jp3:1991166 Scholar
75.Kumar J., Sarmah R., Ananthakrishna G. General framework for acoustic emission during plastic deformation // Physical Review B. - 2015. - Vol. 92. - P. 144109 (11 p.). DOI: 10.1103/PhysRevB.92.144109 Scholar
76.Labusch R. A statistical theory of solid solution hardening // Phys. Stat. Sol. - 1970. - Vol. 41, no. 2. - P. 659-669. DOI: 10.1002/pssb.19700410221 Scholar
77.Labusch R. Statistische theorie der mischkristallhartung // Acta Metallurgica. - 1972. - Vol. 20, is. 7. - P. 917-927. DOI: 10.1016/0001-6160(72)90085-5 Scholar
78.Lane Rohrer C. Cluster/dislocation interactions in dilute aluminum-based solid solutions // J. Materials Research. - 1995. - Vol. 10, is. 3. - P. 578-590. DOI: 10.1557/JMR.1995.0578 Scholar
79.Lazar M., Maugin G. Nonsingular stress and strain fields of dislocations and disclinations in first strain gradient elasticity // Int. J. Eng. Sci. - 2005. - Vol. 43. - P. 1157-1184. DOI: 10.1016/j.ijengsci.2005.01.006 Scholar
80.Lebyodkin M. et al. Statistical behaviour and strain localization patterns in the Portevin - Le Chatelier effect // M. Lebyodkin, Y. Brechet, Y. Estrin, L. Kubin // Acta Materialia. - 1996. - Vol. 44, is. 11. - P. 4531-4541. DOI: 10.1016/1359-6454(96)00076-6 Scholar
81.Lee S.-Y. et al. Serrated flow accompanied with dynamic type transition of the Portevin - Le Chatelier effect in austenitic stainless steel / S.-Y. Lee, S. Chettri, R. Sarmah, C. Takushima, J.-I. Hamada, N. Nakada // J. Materials Science & Technology. - 2023. - Vol. 133. - P. 154-164. DOI: 10.1016/j.jmst.2022.06.020 Scholar
82.Li X. et al. Electroplasticity mechanism study based on dislocation behavior of Al6061 in tensile process / X. Li, Z. Xu, P. Guo, L. Peng, X. Lai // J. Alloys and Compounds. - 2022. - Vol. 910. - P. 164890 (13 p.). DOI: 10.1016/j.jallcom.2022.164890 Scholar
83.Liepnt V.P., Sietsma J. A revised criterion for the Portevin-Le Chatelier effect based on the strain-rate sensitivity of the work-hardening rate // Metallurgical and Materials transactions A. - 2011. - Vol. 42. - P. 4008-4014. DOI: 10.1007/s11661-011-0850-5 Scholar
84.Lin Y.C. et al. A physically-based model considering dislocation-solute atom dynamic interactions for a nickel-based superalloy at intermediate temperatures / Y.C. Lin, H. Yang, D.- G. He, J. Chen // Materials and Design. - 2019. - Vol. 183. - P. 108122. DOI: 10.1016/j.matdes.2019.108122 Scholar
85.Ling C.P., McCormick P.G., Estrin Y. A load perturbation method of examining dynamic strain ageing // Acta metall. mater. - 1993. - Vol. 41, no. 11. - P. 3323-3330. DOI: 10.1016/0956-7151(93)90061-V Scholar
86.Louat N. On the theory of the Portevin - Le Chatelier effect // Scripta Metallurgica. - 1981. - Vol. 15, is. 11. - P. 1167-1170. DOI: 10.1016/0036-9748(81)90290-8 Scholar
87.Ma N. et al. Segregation and wetting transition at dislocations / N. Ma, C. Shen, S.A. Dregia, Y. Wang // Metallurgical and Materials Trans. A. - 2006. - Vol. 37A. - P. 1773-1783. DOI: 10.1007/s11661-006-0119-6 Scholar
88.Marchenko A. et al. Crystal plasticity simulation of strain aging phenomena in \(\alpha\) -titanium at room temperature / A. Marchenko, M. Maziere, S. Forest, J.-L. Strudel // Int. J. Plasticity. - 2016. - Vol. 85. - P. 1-33. DOI: 10.1016/j.ijplas.2016.05.007 Scholar
89.McCormick P.G. A model for the Portevin - Le Chatelier effect in substitutional alloys // Acta Metallurgica. - 1972. - Vol. 20, is. 3. - P. 351-354. DOI: 10.1016/0001-6160(72)90028-4 Scholar
90.McCormick P.G. Theory of flow localization due to dynamic strain ageing // Acta Metallurgica. - 1988. - Vol. 36, is. 12. - P. 3061-3067. DOI: 10.1016/0001-6160(88) 90043-0 Scholar
91.McCormick P.G., Estrin Y. Transient flow behaviour associated with dynamic strain ageing // Scripta Metallurgica. - 1989. - Vol. 23. - P. 1231-1234. DOI: 10.1016/0036-9748(89)90332-3 Scholar
92.McCormick P.G., Ling C.P. Numerical modelling of the Portevin - Le Chatelier effect // Acta Metallurgica et Materialia. - 1995. - Vol. 43, is. 5. - P. 1969-1977. DOI: 10.1016/0956-7151(94)00390-4 Scholar
93.Meisel L.V. Stress-assisted diffusion to dislocations and its role in strain aging // J. Applied Physics. - 1967. - Vol. 38, no. 12. - P. 4780-4784. DOI: 10.1063/1.1709219 Scholar
94.Mott N.F., Nabarro F.R.N. An attempt to estimate the degree of precipitation hardening, with a simple model // Proc. Physical Society. - 1940. - Vol. 52, no. 1. - P. 86-89. DOI 10.1088/0959-5309/52/1/312 Scholar
95.Mott N.F., Nabarro F.R.N. Dislocation theory and transient creep // Report of a Conference on the Strength of Solids, The Physical Society, London. - 1948. - P. 1-19 Scholar
96.Nabarro F.R.N. The theory of solution hardening // Philosophical Magazine. - 1977. - Vol. 35, is. 3. - P. 613-622. DOI: 10.1080/14786437708235994 Scholar
97.Nabarro F.R.N. Distribution of solute atoms round a moving dislocation // Materials Science and Engineering A. - 2005. - Vol. 400-401. - P. 22-24. DOI: 10.1016/j.msea.2005.03.046 Scholar
98.Nakajima K. Stacking faults in copper-nickel alloys // J. Phys. Soc. Jpn. - 1959. - Vol. 14. - P. 1825-1826. DOI: 10.1143/JPSJ.14.1825 Scholar
99.Ovi H., Lilleodden E.T. New insights into plastic instability in precipitation strengthened Al-Li alloys // Acta Materialia. - 2015. - Vol. 89. - P. 88-97. DOI: 10.1016/j.actamat.2015.01.065 Scholar
100.Petukhov B.V. Hardening of crystals caused by the dynamic aging of dislocations // Crystallography Reports. - 2003. - Vol. 48, no. 5. - P. 813-818. DOI: 10.1134/1.1612600 Scholar
101.Petukhov B.V. Role of the static and dynamic aging of dislocations in the kinetics of deformation of doped crystals // Physics of the Solid State. - 2014. - Vol. 56, no. 6. - P. 1180-1186. DOI: 10.1134/S1063783414060316 Scholar
102.Picu R.C. A mechanism for the negative strain-rate sensitivity of dilute solid solutions // Acta Materialia. - 2004. - Vol. 52. - P. 3447-3458. DOI: 10.1016/j.actamat.2004.03.042 Scholar
103.Picu R.C. et al. Effect of solute distribution on the strain rate sensitivity of solid solutions / R.C. Picu, G. Vincze, J.J. Gracio, F. Barlat // Scripta Materialia. - 2006. - Vol. 54, is. 1. - P. 71-75. DOI: 10.1016/j.scriptamat.2005.09.002 Scholar
104.Portevin A., Le Chatelier F. Sur un phenomene observe lors de l'essai de traction d'alliances en cours de transformation // Compt. Rend. Acad. Sci. Paris. - 1923. - Vol. 176. - P. 507-510. Scholar
105.Rajesh S., Ananthakrishna G. Relaxation oscillations and negative strain rate sensitivity in the Portevin - Le Chatelier effect // Physical Review E. - 2000. - Vol. 61, no. 4. - P. 3664-3674. DOI: 10.1103/physreve.61.3664 Scholar
106.Ren S.-C. et al. Numerical investigation of dynamic strain ageing and slant ductile fracture in a notched specimen and comparison with synchrotron tomography 3D-DVC / S.-C. Ren, G. Rousselier, T.F. Morgeneyer, M. Maziere, S. Forest // Procedia Structural Integrity. - 2016. - Vol. 2. - P. 3385-3392. DOI: 10.1016/j.prostr.2016.06.422 Scholar
107.Ren S. et al. A constitutive model accounting for strain ageing effects on work-hardening. Application to a C-Mn steel / S. Ren, M. Maziere, S. Forest, T.F. Morgeneyer, G. Rousselier // Comptes Rendus Mecanique. - 2017. - Vol. 345. - P. 908-921. DOI: 10.1016/j.crme.2017.09.005 Scholar
108.Ren S. et al. Effect of Luders and Portevin-Le Chatelier localization bands on plasticity and fracture of notched steel specimens studied by DIC and FE simulations / S.C. Ren, T.F. Morgeneyer, M. Maziere, S. Forest, G. Rousselier // Int. J. Plasticity. - 2021. - Vol. 136. - P. 102880 (28 p.). DOI: 10.1016/j.ijplas.2020.102880 Scholar
109.Rowlands B.S., Rae C., Galindo-Nava E. The Portevin - Le Chatelier effect in nickel-base superalloys: Origins, consequences and comparison to strain ageing in other alloy systems // Progress in Materials Science. - 2023. - Vol. 132. - P. 101038 (66 p.). DOI: 10.1016/j.pmatsci.2022.101038 Scholar
110.Sarkar A. et al. Comparative study of the Portevin - Le Chatelier effect in interstitial and substitutional alloy / A. Sarkar, A. Chatterjee, P. Barat, P. Mukherjee // Materials Science and Engineering A. - 2007. - Vol. 459. - P. 361-365. DOI: 10.1016/j.msea.2007.01.006 Scholar
111.Sarmah R., Ananthakrishna G. Influence of system size on spatiotemporal dynamics of a model for plastic instability: Projecting low-dimensional and extensive chaos // Physical Review E. - 2013. - Vol. 87. - P. 052907 (15 p.). DOI:10.1103/PhysRevE.87.052907 Scholar
112.Sarmah R., Ananthakrishna G. Correlation between band propagation property and the nature of serrations in the Portevin - Le Chatelier effect // Acta Materialia. - 2015. - Vol. 91. - P. 192-201. DOI: 10.1016/j.actamat.2015.03.027 Scholar
113.Schoeck G., Seeger A. The flow stress of iron and its dependence on impurities // Acta Metall. - 1959. - Vol. 7. - P. 469-477. DOI: 10.1016/0001-6160(59)90028-8 Scholar
114.Sills R.B., Cai W. Solute drag on perfect and extended dislocations // Philosophical Magazine. - 2016. - Vol. 96, is. 10. - P. 895-921. DOI: 10.1080/14786435.2016.1142677 Scholar
115.Sleeswyk A.W. Slow strain-hardening of ingot iron // Acta Metallurgica. - 1958. - Vol. 6, is. 9. - P. 598-603. DOI: 10.1016/0001-6160(58)90101-9 Scholar
116.Snoek J.L. Effect of small quantities of carbon and nitrogen on the elastic and plastic properties of iron // Physica. - 1941. - Vol. 8, is. 7. - P. 711-733. DOI: 10.1016/S0031-8914(41)90517-7 Scholar
117.Soare M.A., Curtin W.A. Solute strengthening of both mobile and forest dislocations: The origin of dynamic strain aging in fcc metals // Acta Materialia. - 2008a. - Vol. 56. - P. 4046-4061. DOI: 10.1016/j.actamat.2008.04.027 Scholar
118.Soare M.A., Curtin W.A. Single-mechanism rate theory for dynamic strain aging in fcc metals // Acta Materialia. - 2008b. - Vol. 56. - P. 4091-4101. DOI: 10.1016/j.actamat.2008.04.030 Scholar
119.Stukowski A. et al. Thermally-activated non-Schmid glide of screw dislocations in W using atomistically-informed kinetic Monte Carlo simulations / A. Stukowski, D. Cereceda, T.D. Swinburne, J. Marian // Int. J. Plasticity. - 2015. - Vol. 65. - P. 108-130. DOI: 10.1016/j.ijplas.2014.08.015 Scholar
120.Suzuki H. Chemical interaction of solute atoms with dislocations // Sci. Rep. Res. Inst. Tohoku Univ. A. - 1952. - Vol. 4. - P. 455-463. DOI: 10.50974/00041613 Scholar
121.Suzuki H. Segregation of solute atoms on stacking faults // J. Phys. Soc. Jpn. - 1962. - Vol. 17. - P. 322-325. DOI: 10.1143/JPSJ.17.322 Scholar
122.Svoboda J. et al. Kinetics of interaction of impurity interstitials with dislocations revisited / J. Svoboda, W. Ecker, V.I. Razumovsky, G.A. Zickler, F.D. Fischer // Progress in Materials Science. - 2019. - Vol. 101. - P. 172-206. DOI: 10.1016/j.pmatsci.2018.10.001 Scholar
123.Takeuchi S., Argon A.S. Glide and climb resistance to the motion of an edge dislocation due to dragging a Cottrell atmosphere // Philos. Mag. A. - 1979. - Vol. 40. - P. 65-75. DOI: 10.1080/01418617908234833 Scholar
124.Tamimi S., Andrade-Campos A., Pinho-da-Cruz J. Modelling the Portevin - Le Chatelier effects in aluminium alloys: a review // J. Mech. Behav. Mater. - 2015. - Vol. 24, no. 3-4. - P. 67-78. DOI: 10.1515/jmbm-2015-0008 Scholar
125.Tsuzuki H., Branicio P.S., Rino J.P. Molecular dynamics simulation of fast dislocations in copper // Acta Materialia. - 2009. - Vol. 57. - P. 1843-1855. DOI: 10.1016/j.actamat.2008.12.025 Scholar
126.Varadhan S., Beaudoin A.J., Fressengeas C. Lattice incompatibility and strain-aging in single crystals // J. Mechanics and Physics of Solids. - 2009. - Vol. 57. - P. 1733-1748. DOI: 10.1016/j.jmps.2009.06.007 Scholar
127.Varschavsky A., Donoso E. Modelling solute segregation to partial dislocations for DSC evaluations // J. Thermal Analysis. - 1997a. - Vol. 48. - P. 1229-1248. DOI: 10.1007/BF01983434 Scholar
128.Varschavsky A., Donoso E. Modelling the kinetics of solute segregation to partial dislocations for isothermal microcalorimetric evaluations // J. Thermal Analysis. - 1997b. - Vol. 50. - P. 533-545. DOI: 10.1007/BF01979026 Scholar
129.Wilcox B.A., Smith G.C. The Portevin - Le Chatelier effect in hydrogen charged nickel // Acta Metallurgica. - 1964. - Vol. 12. - P. 371-376. DOI: 10.1016/0001-6160(64)90006-9 Scholar
130.Xu J. et al. Dynamic strain ageing in an AlMg alloy at different strain rates and temperatures: Experiments and constitutive modelling / J. Xu, B. Holmedal, O.S. Hopperstad, T. Manik, K. Marthinsen // Int. J. Plasticity. - 2022. - Vol. 151. - P. 103215 (24 p.). DOI: 10.1016/j.ijplas.2022.103215 Scholar
131.Xu Z., Picu R.C. Dislocation-solute cluster interaction in Al-Mg binary alloys // Modelling Simul. Mater. Sci. Eng. - 2006. - Vol. 14. - P. 195-206. DOI: 10.1088/0965-0393/14/2/005 Scholar
132.Xu Z., Picu R.C. Effect of residual and pre-existing solute clusters on dynamic strain ageing in dilute solid solutions // Modelling Simul. Mater. Sci. Eng. - 2007. - Vol. 15. - P. 385-396. DOI: 10.1088/0965-0393/15/5/001 Scholar
133.Yoshinaga H., Morozumi S. A Portevin - Le Chatelier effect expected from solute atmosphere dragging // The Philosophical Magazine: A Journal of Theoretical Experimental and Applied Physics. Series 8. - 1971a. - Vol. 23, is. 186. - P. 1351-1366. DOI: 10.1080/14786437108217007 Scholar
134.Yoshinaga H., Morozumi S. The solute atmosphere round a moving dislocation and its dragging stress // The Philosophical Magazine: A Journal of Theoretical Experimental and Applied Physics. Series 8. - 1971b. - Vol. 23, is. 186. - P. 1367-1385. DOI: 10.1080/14786437108217008 Scholar
135.Zaiser M., Hahner P. Oscillatory modes of plastic deformation: theoretical concepts // Physica Status Solidi B. - 1997. - Vol. 199, no. 2. - P. 267-330. DOI: 10.1002/1521-3951(199702)199:2<267::AID-PSSB267>3.0. CO;2- Q Scholar
136.Zaiser M. et al. On the relations between strain and strain-rate softening phenomena in some metallic materials: a computational study / M. Zaiser, M. Glazov, L.A. Lalli, O. Richmond // Computational Materials Science. - 1999. - Vol. 15, no. 1. - P. 35-49. DOI: 10.1016/s0927-0256(98)00131-1 Scholar
137.Zhang D., Picu R.C. Solute clustering in Al-Mg binary alloys // Modelling Simul. Mater. Sci. Eng. - 2004. - Vol. 12. - P. 121-132. DOI: 10.1088/0965-0393/12/1/011 Scholar
138.Zhang F., Curtin W.A. Atomistically informed solute drag in Al-Mg // Modelling Simul. Mater. Sci. Eng. - 2008. - Vol. 16. - P. 055006 (18 p.). DOI: 10.1088/0965-0393/16/5/055006 Scholar
139.Zhang S., McCormick P., Estrin Y. The morphology of Portevin-Le Chatelier bands: Finite element simulation for Al-Mg- Si // Acta Materialia - 2001. - Vol. 49, is. 6. - P. 1087-1094. DOI: 10.1016/S1359-6454(00)00380-3 Scholar
140.Zhao Y., Marian J. Direct prediction of the solute softening-to-hardening transition in W-Re alloys using stochastic simulations of screw dislocation motion // Modell. Simul. in Mater. Sci. Eng. - 2018. - Vol. 26. - P. 045002 (16 p.). DOI: 10.1088/1361-651X/aaaeef Scholar
141.Zhao T., Dezerald L., Marian J. Electronic structure calculations of oxygen atom transport energetics in the presence of screw dislocations in tungsten // Metals. - 2019. - Vol. 9, no. 2. - P. 252 (14 p.). DOI: 10.3390/met9020252 Scholar
142.Zhao Y. et al. Simulating the mechanisms of serrated flow in interstitial alloys with atomic resolution over diffusive timescales // Y. Zhao, L. Dezerald, M. Pozuelo, X. Zhou, J. Marian // Nature Communications. - 2020. - Vol. 11. - P. 1227 (8 p.). DOI: 10.1038/s41467-020-15085-3 Scholar
143.Zhu A.-W. Evolution of size distribution of shearable ordered precipitates under homogeneous deformation: Application to an Al-Li-alloy // Acta mater. - 1997. - Vol. 45, no. 10. - P. 4213-4223. DOI: 10.1016/S1359-6454(97)00077-3 Scholar
144.Zhu A.-W. Strain localization and formation of heterogeneous distribution of shearable ordered precipitates: Application to an Al-10at.%Li single crystal // Acta mater. - 1998. - Vol. 46, no. 9. - P. 3211-3220. DOI: 10.1016/S1359-6454(97)00488-6 Scholar

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МЕТОДЫ И РЕЗУЛЬТАТЫ ИССЛЕДОВАНИЯ ЭФФЕКТА ПОРТЕВЕНА – ЛЕ ШАТЕЛЬЕ: ФИЗИЧЕСКИ-ОРИЕНТИРОВАННЫЕ КОНТИНУАЛЬНЫЕ И МНОГОУРОВНЕВЫЕ МОДЕЛИ

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Methods and results of studying the Portevin – Le Chatelier effect: physically-oriented continuous and multilevel models

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