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<article article-type="research-article" dtd-version="1.3" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xml:lang="ru"><front><journal-meta><journal-id journal-id-type="publisher-id">blackmet</journal-id><journal-title-group><journal-title xml:lang="ru">Известия высших учебных заведений. Черная Металлургия</journal-title><trans-title-group xml:lang="en"><trans-title>Izvestiya. Ferrous Metallurgy</trans-title></trans-title-group></journal-title-group><issn pub-type="ppub">0368-0797</issn><issn pub-type="epub">2410-2091</issn><publisher><publisher-name>National University of Science and Technology "MISIS"</publisher-name></publisher></journal-meta><article-meta><article-id pub-id-type="doi">10.17073/0368-0797-2024-2-167-175</article-id><article-id custom-type="elpub" pub-id-type="custom">blackmet-2707</article-id><article-categories><subj-group subj-group-type="heading"><subject>Research Article</subject></subj-group><subj-group subj-group-type="section-heading" xml:lang="ru"><subject>МАТЕРИАЛОВЕДЕНИЕ</subject></subj-group><subj-group subj-group-type="section-heading" xml:lang="en"><subject>MATERIAL SCIENCE</subject></subj-group></article-categories><title-group><article-title>Внутренние напряжения и их источники в сталях с ОЦК-кристаллической решеткой</article-title><trans-title-group xml:lang="en"><trans-title>Internal stresses and their sources in steels with BCC lattice</trans-title></trans-title-group></title-group><contrib-group><contrib contrib-type="author" corresp="yes"><contrib-id contrib-id-type="orcid">https://orcid.org/0000-0001-8823-4562</contrib-id><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Попова</surname><given-names>Н. А.</given-names></name><name name-style="western" xml:lang="en"><surname>Popova</surname><given-names>N. A.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Наталья Анатольевна Попова, к.т.н., научный сотрудник научно-учебной лаборатории «Наноматериалы и нанотехнологии»</p><p>Россия, 634003, Томск, пл. Соляная, 2</p></bio><bio xml:lang="en"><p>Natal’ya A. Popova, Cand. Sci. (Eng.), Research Associate of the Scientific and Educational Laboratory “Nanomaterials and Nanotechnologies”</p><p>2 Solyanaya Sqr., Tomsk 634003, Russian Federation</p></bio><email xlink:type="simple">natalya-popova-44@mail.ru</email><xref ref-type="aff" rid="aff-1"/></contrib><contrib contrib-type="author" corresp="yes"><contrib-id contrib-id-type="orcid">https://orcid.org/0000-0002-0396-9541</contrib-id><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Никоненко</surname><given-names>Е. Л.</given-names></name><name name-style="western" xml:lang="en"><surname>Nikonenko</surname><given-names>E. L.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Елена Леонидовна Никоненко, к.ф.-м.н., доцент кафедры физики, химии, теоретической механики, Томский государственный архитектурно-строительный университет; старший преподаватель, Национальный исследовательский Томский политехнический университет</p><p>Россия, 634003, Томск, пл. Соляная, 2</p><p>Россия, 634050, Томск, пр. Ленина, 30</p></bio><bio xml:lang="en"><p>Elena L. Nikonenko, Cand. Sci. (Phys.-Math.), Assist. Prof. of the Chair of Physics, Chemistry, Theoretical Mechanics, Tomsk State University of Architecture and Building; Senior Lecturer, National Research Tomsk Polytechnic University</p><p>2 Solyanaya Sqr., Tomsk 634003, Russian Federation</p><p>30 Lenina Ave., Tomsk, 634050, Russian Federation</p></bio><email xlink:type="simple">vilatomsk@mail.ru</email><xref ref-type="aff" rid="aff-2"/></contrib><contrib contrib-type="author" corresp="yes"><contrib-id contrib-id-type="orcid">https://orcid.org/0000-0003-3602-5739</contrib-id><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Порфирьев</surname><given-names>М. А.</given-names></name><name name-style="western" xml:lang="en"><surname>Porfir’ev</surname><given-names>M. A.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Михаил Анатольевич Порфирьев, научный сотрудник управления научных исследований</p><p>Россия, 654007, Кемеровская обл. – Кузбасс, Новокузнецк, ул. Кирова, 42</p></bio><bio xml:lang="en"><p>Mikhail A. Porfir’ev, Research Associate of Department of Scientific Researches</p><p>42 Kirova Str., Novokuznetsk, Kemerovo Region – Kuzbass 654007, Russian Federation</p></bio><email xlink:type="simple">mporf372@gmail.com</email><xref ref-type="aff" rid="aff-3"/></contrib><contrib contrib-type="author" corresp="yes"><contrib-id contrib-id-type="orcid">https://orcid.org/0000-0002-3394-7941</contrib-id><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Крюков</surname><given-names>Р. Е.</given-names></name><name name-style="western" xml:lang="en"><surname>Kryukov</surname><given-names>R. E.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Роман Евгеньевич Крюков, д.т.н., доцент кафедры металлургии черных металлов</p><p>Россия, 654007, Кемеровская обл. – Кузбасс, Новокузнецк, ул. Кирова, 42</p></bio><bio xml:lang="en"><p>Roman E. Kryukov, Dr. Sci. (Eng.), Assist. Prof. of the Chair of Ferrous Metallurgy</p><p>42 Kirova Str., Novokuznetsk, Kemerovo Region – Kuzbass 654007, Russian Federation</p></bio><email xlink:type="simple">rek_nzrmk@mail.ru</email><xref ref-type="aff" rid="aff-3"/></contrib></contrib-group><aff-alternatives id="aff-1"><aff xml:lang="ru"><institution>Томский государственный архитектурно-строительный университет</institution><country>Россия</country></aff><aff xml:lang="en"><institution>Tomsk State University of Architecture and Building</institution><country>Russian Federation</country></aff></aff-alternatives><aff-alternatives id="aff-2"><aff xml:lang="ru"><institution>Томский государственный архитектурно-строительный университет; Национальный исследовательский Томский политехнический университет</institution><country>Россия</country></aff><aff xml:lang="en"><institution>Tomsk State University of Architecture and Building; National Research Tomsk Polytechnic University</institution><country>Russian Federation</country></aff></aff-alternatives><aff-alternatives id="aff-3"><aff xml:lang="ru"><institution>Сибирский государственный индустриальный университет</institution><country>Россия</country></aff><aff xml:lang="en"><institution>Siberian State Industrial University</institution><country>Russian Federation</country></aff></aff-alternatives><pub-date pub-type="collection"><year>2024</year></pub-date><pub-date pub-type="epub"><day>20</day><month>04</month><year>2024</year></pub-date><volume>67</volume><issue>2</issue><fpage>161</fpage><lpage>175</lpage><permissions><copyright-statement>Copyright &amp;#x00A9; Попова Н.А., Никоненко Е.Л., Порфирьев М.А., Крюков Р.Е., 2024</copyright-statement><copyright-year>2024</copyright-year><copyright-holder xml:lang="ru">Попова Н.А., Никоненко Е.Л., Порфирьев М.А., Крюков Р.Е.</copyright-holder><copyright-holder xml:lang="en">Popova N.A., Nikonenko E.L., Porfir’ev M.A., Kryukov R.E.</copyright-holder><license xml:lang="ru" license-type="creative-commons-attribution" xlink:href="https://creativecommons.org/licenses/by/4.0/" xlink:type="simple"><license-p>Данная работа распространяется под лицензией Creative Commons Attribution 4.0.</license-p></license><license xml:lang="en" license-type="creative-commons-attribution" xlink:href="https://creativecommons.org/licenses/by/4.0/" xlink:type="simple"><license-p>This work is licensed under a Creative Commons Attribution 4.0 License.</license-p></license></permissions><self-uri xlink:href="https://fermet.misis.ru/jour/article/view/2707">https://fermet.misis.ru/jour/article/view/2707</self-uri><abstract><p>Методом просвечивающей дифракционной электронной микроскопии выполнены исследования тонкой структуры сталей промышленного назначения, которые обладают ОЦК-кристаллической решеткой (перлитные, феррито-перлитные и мартенситные). Проанализирована внутренняя структура зерен, определены скалярная плотность дислокаций в различных участках материала, источники внутренних напряжений и их амплитуда. Использование метода, основанного на анализе изгибных экстинкционных контуров, позволяет изучать внутренние напряжения. Изучение внутренних напряжений и их источников проведено на примере рельсовой стали Э76ХФ со структурой пластинчатого перлита после сверхдлительной эксплуатации (пропущенный тоннаж – 1770 млн т брутто). Места проведения исследования металла рельсов: вдоль центральной оси симметрии (поверхность катания) и вдоль радиуса скругления (рабочая выкружка) головки рельса на расстояниях 0, 2 и 10 мм от поверхности. По мере приближения к поверхности головки, независимо от направления исследований (вдоль радиуса скругления выкружки или вдоль оси симметрии) пластинчатый перлит постепенно заменяется на разрушенный с образованием феррито-карбидной смеси и формированием фрагментированной структуры, причем эти процессы более интенсивно протекают в рабочей выкружке. Вдоль всей центральной оси симметрии головки рельса (поверхность катания) имеет место пластический изгиб-кручение кристаллической решетки, вдоль радиуса скругления головки рельса (рабочая выкружка) на расстоянии 10 мм от поверхности – также пластический, а на расстоянии от 0 до 2 мм – упругопластический. Основным источником внутренних моментных (дальнодействующих) напряжений в рельсовой стали является избыточная плотность дислокаций. На примере стали мартенситного класса 34ХН3МФА с использованием матричных уравнений определен тип изгибного экстинкционного контура. При малых степенях пластической деформации экстинкционные контуры являются контурами изгиба или кручения, при больших степенях – контурами смешанного типа.</p></abstract><trans-abstract xml:lang="en"><p>The paper studies fine structure of industrial steels with BCC lattice (pearlite, ferrite-pearlite and martensite) using transmission diffraction electron microscopy. The internal structure of the grains was analyzed; the scalar density of dislocations in various parts of the material, the sources of internal stresses and their amplitude were determined. The use of a method based on the analysis of bending extinction contours allowed us to study internal stresses. We analyzed the internal stresses and their sources using the example of 0.76С–Cr–V–Fe rail steel with a lamellar pearlite structure after ultra long-term operation with the tonnage of 1770 million gross tons. The metal of the rails was examined along the central axis of symmetry (rolling surface) and the rounding radius (working fillet) of the railhead at distances of 0, 2 and 10 mm from the surface. As one approaches the head surface, regardless of the research direction (along the fillet rounding radius or along the axis of symmetry), the lamellar pearlite is gradually replaced by destroyed pearlite with formation of a ferrite-carbide mixture and formation of a fragmented structure. These processes occur more intensively in the working fillet. Along the entire central axis of symmetry of the rail head (rolling surface), there is a plastic bending-torsion of the crystal lattice, along the rounding radius of the rail head (working fillet) at a distance of 10 mm from the surface – also plastic, and at a distance from 0 to 2 mm – elastic-plastic. The main source of internal torque (long-acting) stresses in rail steel is the excessive density of dislocations. Using the example of 34CrNi3MoVN steel of the martensitic class, the type of bending extinction contour was determined using mathematical equations. At low degrees of plastic deformation, extinction contours are contours of bending or torsion, at high degrees they are of a mixed type.</p></trans-abstract><kwd-group xml:lang="ru"><kwd>электронная микроскопия</kwd><kwd>ОЦК-кристаллическая решетка</kwd><kwd>изгибной экстинкционный контур</kwd><kwd>кривизна-кручение</kwd><kwd>скалярная плотность дислокаций</kwd><kwd>избыточная плотность дислокаций</kwd><kwd>внутренние напряжения</kwd><kwd>источники</kwd></kwd-group><kwd-group xml:lang="en"><kwd>electron microscopy</kwd><kwd>BCC lattice</kwd><kwd>bending extinction contour</kwd><kwd>curvature-torsion</kwd><kwd>scalar dislocation density</kwd><kwd>excess dislocation density</kwd><kwd>internal stresses</kwd><kwd>sources</kwd></kwd-group><funding-group><funding-statement xml:lang="ru">Работа выполнена в рамках государственного задания Министерства науки и высшего образования Российской Федерации (тема № FEMN-2023-0003).</funding-statement><funding-statement xml:lang="en">The work was carried out within the framework of the state task of the Ministry of Science and Higher Education of the Russian Federation (subject No. FEMN-2023-0003).</funding-statement></funding-group></article-meta></front><back><ref-list><title>References</title><ref id="cit1"><label>1</label><citation-alternatives><mixed-citation xml:lang="ru">Koneva N.A., Kozlov E.V., Trishkina L.I. Internal field sources, their screening and the flow stress. Materials Science and Engineering: A. 2001;319-321:156–159. https://doi.org/10.1016/S0921-5093(01)00945-5</mixed-citation><mixed-citation xml:lang="en">Koneva N.A., Kozlov E.V., Trishkina L.I. Internal field sources, their screening and the flow stress. Materials Science and Engineering: A. 2001;319-321:156–159. https://doi.org/10.1016/S0921-5093(01)00945-5</mixed-citation></citation-alternatives></ref><ref id="cit2"><label>2</label><citation-alternatives><mixed-citation xml:lang="ru">Конева Н.А., Козлов Э.В. Дислокационная структура и физические механизмы упрочнения металлических материалов. В кн.: Перспективные материалы. Структура и методы исследования (учебное пособие) / Под ред. Д.Л. Мерсона. Тула: ТГУ; Москва: МИСиС; 2006:267–320.</mixed-citation><mixed-citation xml:lang="en">Koneva N.A., Kozlov E.V. Dislocation structure and physical mechanisms of hardening of metal materials. In: Promising Materials. Structure and Methods of Research (Tutorial). Merson D.L. ed. Tula: TGU; Moscow: MISiS; 2006:267–320. (In Russ.).</mixed-citation></citation-alternatives></ref><ref id="cit3"><label>3</label><citation-alternatives><mixed-citation xml:lang="ru">Ovid’ko I.A., Valiev R.Z., Zhu Y.T. Review on superior strength and enhanced ductility of metallic nanomaterials. Progress in Materials Science. 2018:94:462–540. https://doi.org/10.1016/j.pmatsci.2018.02.002</mixed-citation><mixed-citation xml:lang="en">Ovid’ko I.A., Valiev R.Z., Zhu Y.T. Review on superior strength and enhanced ductility of metallic nanomaterials. Progress in Materials Science. 2018:94:462–540. https://doi.org/10.1016/j.pmatsci.2018.02.002</mixed-citation></citation-alternatives></ref><ref id="cit4"><label>4</label><citation-alternatives><mixed-citation xml:lang="ru">Закономерности пластической деформации в высокопрочных и нанокристаллических металлических материалах / А.Н. Тюменцев, А.Д. Коротаев, И.А. Дитенберг, Ю.П. Пинжин, В.М. Чернов. Новосибирск: СО РАН Наука; 2018:256.</mixed-citation><mixed-citation xml:lang="en">Tyumentsev A.N., Korotaev A.D., Ditenberg I.A., Pin­zhin Yu.P., Chernov V.M. Patterns of Plastic Deformation in High-Strength and Nanocrystalline Metallic Materials. Novosibirsk: SB RAS Nauka; 2018:256. (In Russ.).</mixed-citation></citation-alternatives></ref><ref id="cit5"><label>5</label><citation-alternatives><mixed-citation xml:lang="ru">Yang M., Pan Yu., Yuan F., Zhu Yu., Wu X. Back stress strengthening and strain hardening in gradient structure. Materials Research Letters. 2016;4(3):145–151. https://doi.org/10.1080/21663831.2016.1153004</mixed-citation><mixed-citation xml:lang="en">Yang M., Pan Yu., Yuan F., Zhu Yu., Wu X. Back stress strengthening and strain hardening in gradient structure. Materials Research Letters. 2016;4(3):145–151. https://doi.org/10.1080/21663831.2016.1153004</mixed-citation></citation-alternatives></ref><ref id="cit6"><label>6</label><citation-alternatives><mixed-citation xml:lang="ru">Конева Н., Киселева С., Попова Н. Эволюция структуры и внутренние поля напряжений. Аустенитная сталь. Германия: LAP LAMBER Academic Publishing; 2017:156.</mixed-citation><mixed-citation xml:lang="en">Koneva N., Kiseleva S., Popova N. Evolution of the Structure and Internal Stress Fields. Austenitic Steel. Germany: LAP LAMBER Academic Publishing; 2017:156. (In Russ.).</mixed-citation></citation-alternatives></ref><ref id="cit7"><label>7</label><citation-alternatives><mixed-citation xml:lang="ru">Kundu A., Field D.P. Geometrically necessary dislocation density evolution in interstitial free steel at small plastic strains. Metallurgical and Materials Transactions A. 2018;49:3274–3282. https://doi.org/10.1007/s11661-018-4693-1</mixed-citation><mixed-citation xml:lang="en">Kundu A., Field D.P. Geometrically necessary dislocation density evolution in interstitial free steel at small plastic strains. Metallurgical and Materials Transactions A. 2018;49:3274–3282. https://doi.org/10.1007/s11661-018-4693-1</mixed-citation></citation-alternatives></ref><ref id="cit8"><label>8</label><citation-alternatives><mixed-citation xml:lang="ru">Kundu A., Field D.P., Chakraborti P.C. Effect of strain and strain rate on the development of deformation heteroge­neity during tensile deformation of a solution annealed 304 LN austenitic stainless steel: An EBSD study. Materials Science and Engineering: A. 2019;773:138854. https://doi.org/10.1016/j.msea.2019.138854</mixed-citation><mixed-citation xml:lang="en">Kundu A., Field D.P., Chakraborti P.C. Effect of strain and strain rate on the development of deformation heteroge­neity during tensile deformation of a solution annealed 304 LN austenitic stainless steel: An EBSD study. Materials Science and Engineering: A. 2019;773:138854. https://doi.org/10.1016/j.msea.2019.138854</mixed-citation></citation-alternatives></ref><ref id="cit9"><label>9</label><citation-alternatives><mixed-citation xml:lang="ru">Muñoz J.A., Komissarov A. Back stress and strength cont­ributions evolution of a heterogeneous austenitic stainless steel obtained after one pass by equal channel angular sheet extrusion (ECASE). The International Journal of Advanced Manufacturing Technology. 2020;109:607–617. https://doi.org/10.1007/s00170-020-05630-1</mixed-citation><mixed-citation xml:lang="en">Muñoz J.A., Komissarov A. Back stress and strength cont­ributions evolution of a heterogeneous austenitic stainless steel obtained after one pass by equal channel angular sheet extrusion (ECASE). The International Journal of Advanced Manufacturing Technology. 2020;109:607–617. https://doi.org/10.1007/s00170-020-05630-1</mixed-citation></citation-alternatives></ref><ref id="cit10"><label>10</label><citation-alternatives><mixed-citation xml:lang="ru">Ivanov Yu.F., Gromov V.E., Yuriev A.A., Kormyshev V.E., Rubannikova Yu.A., Semin A.P. Deformation strengthening mechanisms of rails in extremely long-term operation. Journal of Materials Research and Technology. 2021;11: 710–718. https://doi.org/10.1016/J.JMRT.2020.12.107</mixed-citation><mixed-citation xml:lang="en">Ivanov Yu.F., Gromov V.E., Yuriev A.A., Kormyshev V.E., Rubannikova Yu.A., Semin A.P. Deformation strengthening mechanisms of rails in extremely long-term operation. Journal of Materials Research and Technology. 2021;11: 710–718. https://doi.org/10.1016/J.JMRT.2020.12.107</mixed-citation></citation-alternatives></ref><ref id="cit11"><label>11</label><citation-alternatives><mixed-citation xml:lang="ru">Yuriev A.A., Ivanov Yu.F., Gromov V.E., Rubanni­kova Yu.A., Starostenkov M.D., Tabakov P.Y. Structure and properties of lengthy rails after extreme long-term operation. MRF; 2021;106:193. https://doi.org/10.21741/9781644901472</mixed-citation><mixed-citation xml:lang="en">Yuriev A.A., Ivanov Yu.F., Gromov V.E., Rubanni­kova Yu.A., Starostenkov M.D., Tabakov P.Y. Structure and properties of lengthy rails after extreme long-term operation. Mate­rials Research Forum; 2021;106:193. https://doi.org/10.21741/9781644901472</mixed-citation></citation-alternatives></ref><ref id="cit12"><label>12</label><citation-alternatives><mixed-citation xml:lang="ru">Ivanov Yu.F., Gleser A.M., Kuznetsov R.V., Gromov V.E., Shliarova Yu.A., Semin A.P., Sundeev R.V. Fine structure formation in rails under ultra long-term operation. Materials Letters. 2022;309(4):131378. https://doi.org/10.1016/j.matlet.2021.131378</mixed-citation><mixed-citation xml:lang="en">Ivanov Yu.F., Gleser A.M., Kuznetsov R.V., Gromov V.E., Shliarova Yu.A., Semin A.P., Sundeev R.V. Fine structure formation in rails under ultra long-term operation. Materials Letters. 2022;309(4):131378. https://doi.org/10.1016/j.matlet.2021.131378</mixed-citation></citation-alternatives></ref><ref id="cit13"><label>13</label><citation-alternatives><mixed-citation xml:lang="ru">Смирнов А.Н., Козлов Э.В. Субструктура, внутренние поля напряжений и проблема разрушения паропроводов из стали 12Х1МФ. Кемерово: Кузбассвузиздат; 2004:163.</mixed-citation><mixed-citation xml:lang="en">Smirnov A.N., Kozlov E.V. Substructure, Internal Stress Fields and the Problem of Destruction of Steam Pipelines Made of 12Kh1MF Steel. Kemerovo: Kuzbassvuzizdat; 2004:163. (In Russ.).</mixed-citation></citation-alternatives></ref><ref id="cit14"><label>14</label><citation-alternatives><mixed-citation xml:lang="ru">Сварка модулированным током. Структурно-фазовое состояние и поля внутренних напряжений в сварных соединениях конструкционных сталей / А.Н. Смирнов, А.Ф. Князьков, В.Л. Князьков и др. Москва: Инновационное машиностроение; Кемерово: Сибирская издательская группа; 2017:328.</mixed-citation><mixed-citation xml:lang="en">Smirnov A.N., Knyaz’kov A.F., Knyaz’kov V.L., etc. Modulated Current Welding. Structural-Phase State and Internal Stress Fields in Welded Joints of Structural Steels. Moscow: Innovatsionnoe mashinostroenie; Kemerovo: Sibirskaya izdatel’skaya gruppa; 2017:328. (In Russ.).</mixed-citation></citation-alternatives></ref><ref id="cit15"><label>15</label><citation-alternatives><mixed-citation xml:lang="ru">Смирнов А.Н., Князьков А.Ф., Князьков В.Л. и др. Структурно-фазовое состояние, контроль и испытания сварных соединений аустенитных нержавеющих сталей. Кемерово: Сибирская издательская группа; 2021:248.</mixed-citation><mixed-citation xml:lang="en">Smirnov A.N., Knyaz’kov A.F., Knyaz’kov V.L., etc. Structural-Phase State, Control and Testing of Welded Joints of Austenitic Stainless Steels. Kemerovo: Sibirskaya izdatel’skaya gruppa; 2021:248. (In Russ.).</mixed-citation></citation-alternatives></ref><ref id="cit16"><label>16</label><citation-alternatives><mixed-citation xml:lang="ru">Panin V.E., Egorushkin V.E. Fundamental role of local curvature of crystal structure in plastic deformation and fracture of solids. Physical Mesomechanics of Multilevel Systems 2014: AIP Conference Proceedings. 2014;1623(1):475–478. https://doi.org/10.1063/1.4898985</mixed-citation><mixed-citation xml:lang="en">Panin V.E., Egorushkin V.E. Fundamental role of local curvature of crystal structure in plastic deformation and fracture of solids. Physical Mesomechanics of Multilevel Systems 2014: AIP Conference Proceedings. 2014;1623(1):475–478. https://doi.org/10.1063/1.4898985</mixed-citation></citation-alternatives></ref><ref id="cit17"><label>17</label><citation-alternatives><mixed-citation xml:lang="ru">Панин В.Е., Панин А.В., Елсукова Т.Ф., Попкова Ю.Ф. Фундаментальная роль кривизны кристаллической структуры в пластичности и прочности твердых тел. Физическая мезомеханика. 2014;17(6):7–18.</mixed-citation><mixed-citation xml:lang="en">Panin V.E., Panin A.V., Elsukova T.F., Popkova Yu.F. The fundamental role of the curvature of the crystal structure in the plasticity and strength of solids. Fizicheskaya mezomekhanika. 2014;17(6):7–18. (In Russ.).</mixed-citation></citation-alternatives></ref><ref id="cit18"><label>18</label><citation-alternatives><mixed-citation xml:lang="ru">Cattivelli A., Roy M.J., Burke M.G, Dhers J., Lee T.L., Francis J.A. Internal stresses in a clad pressure vessel steel du­ring post weld heat treatment and their relevance to underclad cracking. International Journal of Pressure Vessels and Piping. 2021;193:104448. https://doi.org/10.1016/j.ijpvp.2021.104448</mixed-citation><mixed-citation xml:lang="en">Cattivelli A., Roy M.J., Burke M.G, Dhers J., Lee T.L., Francis J.A. Internal stresses in a clad pressure vessel steel du­ring post weld heat treatment and their relevance to underclad cracking. International Journal of Pressure Vessels and Piping. 2021;193:104448. https://doi.org/10.1016/j.ijpvp.2021.104448</mixed-citation></citation-alternatives></ref><ref id="cit19"><label>19</label><citation-alternatives><mixed-citation xml:lang="ru">Fang X.-Y., Zhang H.-N., Ma D.-W., Wu Z.-J., Huang W. Influence of welding residual stress on subsurface fatigue crack propagation of rail. Engineering Fracture Mechanics. 2022;271:108642. https://doi.org/10.1016/j.engfracmech.2022.108642</mixed-citation><mixed-citation xml:lang="en">Fang X.-Y., Zhang H.-N., Ma D.-W., Wu Z.-J., Huang W. Influence of welding residual stress on subsurface fatigue crack propagation of rail. Engineering Fracture Mechanics. 2022;271:108642. https://doi.org/10.1016/j.engfracmech.2022.108642</mixed-citation></citation-alternatives></ref><ref id="cit20"><label>20</label><citation-alternatives><mixed-citation xml:lang="ru">Эволюция фазового состава, дефектной структуры, внут­ренних напряжений и перераспределение углерода при отпуске литой конструкционной стали / Э.В. Козлов, Н.А. Попова, О.В. Кабанина, С.И. Климашин, В.Е. Громов. Новокузнецк: изд. СибГИУ; 2007:177.</mixed-citation><mixed-citation xml:lang="en">Kozlov E.V., Popova N.A., Kabanina O.V., Klimashin S.I., Gromov V.E. Evolution of Phase Composition, Defective Structure, Internal Stresses and Carbon Redistribution during Tempering of Cast Structural Steel. Novokuznetsk: SibSIU; 2007:177. (In Russ.).</mixed-citation></citation-alternatives></ref><ref id="cit21"><label>21</label><citation-alternatives><mixed-citation xml:lang="ru">Kassner M.E., Geantil P., Levine L.E. Long range internal stresses in single-phase crystalline materials. International Journal of Plasticity. 2013;45:44–60. https://doi.org/10.1016/j.ijplas.2012.10.003</mixed-citation><mixed-citation xml:lang="en">Kassner M.E., Geantil P., Levine L.E. Long range internal stresses in single-phase crystalline materials. International Journal of Plasticity. 2013;45:44–60. https://doi.org/10.1016/j.ijplas.2012.10.003</mixed-citation></citation-alternatives></ref><ref id="cit22"><label>22</label><citation-alternatives><mixed-citation xml:lang="ru">Zhang Y., Yu T., Xu R., Thorborg J., Liu W., Tischler J., Godfrey A., Jensen D.J. Local residual stresses and microstructure within recrystallizing grains in iron. Materials Characterization. 2022;191:112113. https://doi.org/10.1016/j.matchar.2022.112113</mixed-citation><mixed-citation xml:lang="en">Zhang Y., Yu T., Xu R., Thorborg J., Liu W., Tischler J., Godfrey A., Jensen D.J. Local residual stresses and microstructure within recrystallizing grains in iron. Materials Characterization. 2022;191:112113. https://doi.org/10.1016/j.matchar.2022.112113</mixed-citation></citation-alternatives></ref><ref id="cit23"><label>23</label><citation-alternatives><mixed-citation xml:lang="ru">Glezer A.M., Kozlov E.V., Koneva N.A., Popova N.A., Kurzina I.A. Plastic Deformation of Nanostructured Mate­rials. Boca Raton, London, New York: CRC Press, Taylor &amp; Francis Group; 2017:334. http://dx.doi.org/10.1201/9781315111964</mixed-citation><mixed-citation xml:lang="en">Glezer A.M., Kozlov E.V., Koneva N.A., Popova N.A., Kurzina I.A. Plastic Deformation of Nanostructured Materials. Boca Raton, London, New York: CRC Press, Taylor &amp; Francis Group; 2017:334. http://dx.doi.org/10.1201/9781315111964</mixed-citation></citation-alternatives></ref><ref id="cit24"><label>24</label><citation-alternatives><mixed-citation xml:lang="ru">Valiev R.Z., Zhilyaev A.P., Langdon T.G. Bulk Nanostructured Materials: Fundamentals and Applications. Hoboken: Wiley/TMS; 2014:440. https://doi.org/10.1002/9781118742679</mixed-citation><mixed-citation xml:lang="en">Valiev R.Z., Zhilyaev A.P., Langdon T.G. Bulk Nanostructured Materials: Fundamentals and Applications. Hoboken: Wiley/TMS; 2014:440. https://doi.org/10.1002/9781118742679</mixed-citation></citation-alternatives></ref><ref id="cit25"><label>25</label><citation-alternatives><mixed-citation xml:lang="ru">Vinogradov A., Estrin Y. Analytical and numerical approaches to modelling severe plastic deformation. Progress in Mate­rials Science. 2018;95:172–242. https://doi.org/10.1016/j.pmatsci.2018.02.001</mixed-citation><mixed-citation xml:lang="en">Vinogradov A., Estrin Y. Analytical and numerical approaches to modelling severe plastic deformation. Progress in Mate­rials Science. 2018;95:172–242. https://doi.org/10.1016/j.pmatsci.2018.02.001</mixed-citation></citation-alternatives></ref><ref id="cit26"><label>26</label><citation-alternatives><mixed-citation xml:lang="ru">Wilde G., Divinski S. Grain boundaries and diffusion phenomena in severely deformed materials. Materials Transactions. 2019;60(7):1302–1315. https://doi.org/10.2320/matertrans.MF201934</mixed-citation><mixed-citation xml:lang="en">Wilde G., Divinski S. Grain boundaries and diffusion phenomena in severely deformed materials. Materials Transactions. 2019;60(7):1302–1315. https://doi.org/10.2320/matertrans.MF201934</mixed-citation></citation-alternatives></ref><ref id="cit27"><label>27</label><citation-alternatives><mixed-citation xml:lang="ru">Буркин С.П., Шимов Г.В., Андрюкова Е.А. Остаточные напряжения в металлопродукции. Екатеринбург: изд. Уральского университета; 2015:248.</mixed-citation><mixed-citation xml:lang="en">Burkin S.P., Shimov G.V., Andryukova E.A. Residual Stresses in Metal Products. Ekateriburg: izd. Ural’skogo universiteta; 2015:248. (In Russ.).</mixed-citation></citation-alternatives></ref><ref id="cit28"><label>28</label><citation-alternatives><mixed-citation xml:lang="ru">Экспериментальная механика. В 2-х книгах / Пер. с англ.; под ред. А. Кобаяси. Москва: Мир; 1990.</mixed-citation><mixed-citation xml:lang="en">Handbook on Experimental Mechanics. 2nd ed. Kobayashi A. ed. VCH; 1993:1074.</mixed-citation></citation-alternatives></ref><ref id="cit29"><label>29</label><citation-alternatives><mixed-citation xml:lang="ru">Reynolds A.P., Tang W., Gnaupel-Herold T., Prask H. Structure, properties, and residual stress of 304L stainless steel friction stir welds. Scripta Materialia. 2003;48(9):1289–1294. https://doi.org/10.1016/S1359-6462(03)00024-1</mixed-citation><mixed-citation xml:lang="en">Reynolds A.P., Tang W., Gnaupel-Herold T., Prask H. Structure, properties, and residual stress of 304L stainless steel friction stir welds. Scripta Materialia. 2003;48(9):1289–1294. https://doi.org/10.1016/S1359-6462(03)00024-1</mixed-citation></citation-alternatives></ref><ref id="cit30"><label>30</label><citation-alternatives><mixed-citation xml:lang="ru">Cihak U., Staron P., Clemens H., Homeyer J., Stockin­ger M., Tockner J. Characterization of residual stresses in turbine discs by neutron and high-energy X-ray diffraction and comparison to finite element modeling. Materials Science and Engineering: A. 2006;437(1):75–82. https://doi.org/10.1016/j.msea.2006.04.049</mixed-citation><mixed-citation xml:lang="en">Cihak U., Staron P., Clemens H., Homeyer J., Stockin­ger M., Tockner J. Characterization of residual stresses in turbine discs by neutron and high-energy X-ray diffraction and comparison to finite element modeling. Materials Science and Engineering: A. 2006;437(1):75–82. https://doi.org/10.1016/j.msea.2006.04.049</mixed-citation></citation-alternatives></ref><ref id="cit31"><label>31</label><citation-alternatives><mixed-citation xml:lang="ru">Withers P.J. Mapping residual and internal stress in mate­rials by neutron diffraction. Comptes Rendus Physique. 2007; 8(7-8):806–820. https://doi.org/10.1016/j.crhy.2007.09.015</mixed-citation><mixed-citation xml:lang="en">Withers P.J. Mapping residual and internal stress in materials by neutron diffraction. Comptes Rendus Physique. 2007; 8(7-8):806–820. https://doi.org/10.1016/j.crhy.2007.09.015</mixed-citation></citation-alternatives></ref><ref id="cit32"><label>32</label><citation-alternatives><mixed-citation xml:lang="ru">Withers P.J., Turski M., Edwards L., Bouchard P.J., Buttle D.J. Recent advances in residual stress measurement. International Journal of Pressure Vessels and Piping. 2008; 85(3):118–127. https://doi.org/10.1016/j.ijpvp.2007.10.007</mixed-citation><mixed-citation xml:lang="en">Withers P.J., Turski M., Edwards L., Bouchard P.J., Buttle D.J. Recent advances in residual stress measurement. International Journal of Pressure Vessels and Piping. 2008; 85(3):118–127. https://doi.org/10.1016/j.ijpvp.2007.10.007</mixed-citation></citation-alternatives></ref><ref id="cit33"><label>33</label><citation-alternatives><mixed-citation xml:lang="ru">Sekimoto K. Internal stress as a link between macroscale and mesoscale mechanics. In: Chemomechanical Instabilities in Responsive Materials. 2009:241–250. https://doi.org/10.1007/978-90-481-2993-5_10</mixed-citation><mixed-citation xml:lang="en">Sekimoto K. Internal stress as a link between macroscale and mesoscale mechanics. In: Chemomechanical Instabilities in Responsive Materials. 2009:241–250. https://doi.org/10.1007/978-90-481-2993-5_10</mixed-citation></citation-alternatives></ref><ref id="cit34"><label>34</label><citation-alternatives><mixed-citation xml:lang="ru">Wong S.L., Dawson P.R. Evolution of the crystal stress distributions in face-centered polycrystals subjected to cyclic loading. Acta Materialia. 2011;59(18):6901–6916. https://doi.org/10.1016/j.actamat.2011.07.042</mixed-citation><mixed-citation xml:lang="en">Wong S.L., Dawson P.R. Evolution of the crystal stress distributions in face-centered polycrystals subjected to cyclic loading. Acta Materialia. 2011;59(18):6901–6916. https://doi.org/10.1016/j.actamat.2011.07.042</mixed-citation></citation-alternatives></ref><ref id="cit35"><label>35</label><citation-alternatives><mixed-citation xml:lang="ru">McNelis K.P., Dawson P.R., Miller M.P. A two-scale metho­dology for determining the residual stresses in polycrystalline solids using high energy X-ray diffraction data. Journal of the Mechanics and Physics of Solids. 2013;61(2):428–449. https://doi.org/10.1016/j.jmps.2012.09.015</mixed-citation><mixed-citation xml:lang="en">McNelis K.P., Dawson P.R., Miller M.P. A two-scale metho­dology for determining the residual stresses in polycrystalline solids using high energy X-ray diffraction data. Journal of the Mechanics and Physics of Solids. 2013;61(2):428–449. https://doi.org/10.1016/j.jmps.2012.09.015</mixed-citation></citation-alternatives></ref><ref id="cit36"><label>36</label><citation-alternatives><mixed-citation xml:lang="ru">Demir E., Park J.-S., Miller M.P., Dawson P.R. A computational framework for evaluating residual stress distributions from diffraction-based lattice strain data. Computer Methods in Applied Mechanics and Engineering. 2013;265:120–135. https://doi.org/10.1016/j.cma.2013.06.002</mixed-citation><mixed-citation xml:lang="en">Demir E., Park J.-S., Miller M.P., Dawson P.R. A computational framework for evaluating residual stress distributions from diffraction-based lattice strain data. Computer Methods in Applied Mechanics and Engineering. 2013;265:120–135. https://doi.org/10.1016/j.cma.2013.06.002</mixed-citation></citation-alternatives></ref><ref id="cit37"><label>37</label><citation-alternatives><mixed-citation xml:lang="ru">Skrotzki W. Deformation heterogeneities in equal channel an­­gular pressing. Materials Transactions. 2019;60(7): 1331–1343. https://doi.org/10.2320/matertrans.MF201926</mixed-citation><mixed-citation xml:lang="en">Skrotzki W. Deformation heterogeneities in equal channel an­­gular pressing. Materials Transactions. 2019;60(7): 1331–1343. https://doi.org/10.2320/matertrans.MF201926</mixed-citation></citation-alternatives></ref><ref id="cit38"><label>38</label><citation-alternatives><mixed-citation xml:lang="ru">Yildirim C., Jessop C., Ahlström J., Detlefs C., Zhang Y. 3D mapping of orientation variation and local residual stress within individual grains of pearlitic steel using synchrotron dark field X-ray microscopy. Scripta Materialia. 2021;197:113783. https://doi.org/10.1016/j.scriptamat.2021.113783</mixed-citation><mixed-citation xml:lang="en">Yildirim C., Jessop C., Ahlström J., Detlefs C., Zhang Y. 3D mapping of orientation variation and local residual stress within individual grains of pearlitic steel using synchrotron dark field X-ray microscopy. Scripta Materialia. 2021;197:113783. https://doi.org/10.1016/j.scriptamat.2021.113783</mixed-citation></citation-alternatives></ref><ref id="cit39"><label>39</label><citation-alternatives><mixed-citation xml:lang="ru">Hirsch P.B., Howrie A., Nicholson R.B., Pashley D.W., Whelan M.J. Electron Microscopy of Thin Crystals. London: Butterworths; 1965:549.</mixed-citation><mixed-citation xml:lang="en">Hirsch P.B., Howrie A., Nicholson R.B., Pashley D.W., Whelan M.J. Electron Microscopy of Thin Crystals. London: Butterworths; 1965:549.</mixed-citation></citation-alternatives></ref><ref id="cit40"><label>40</label><citation-alternatives><mixed-citation xml:lang="ru">Мадер С., Зеегер А., Лейтц К. Деформационное упрочнение и распределение дислокаций в ГЦК металлах. В кн.: Материалы конференции «Структура и механические свойства металлов», Теддингтон, Мидлсекс, 7 – 9 января 1963 г. Москва: Металлургия; 1967;384.</mixed-citation><mixed-citation xml:lang="en">Mader S., Zeeger A., Leitts K. Deformation hardening and dislocation distribution in HCC metals. In: Proceedings of the Conf. “Structure and Mechanical Properties of Me­tals”, Teddington, Middlesex, January 7 – 9, 1963. Moscow: Metal­lurgiya; 1967:9–41. (In Russ.).</mixed-citation></citation-alternatives></ref><ref id="cit41"><label>41</label><citation-alternatives><mixed-citation xml:lang="ru">Конева Н.А., Тришкина Л.И., Жданов А.Н., Перевалова О.Б., Попова Н.А., Козлова Э.В. Источники полей напряжений в деформированных поликристаллах. Физическая мезомеханика. 2006;9(3):93–102.</mixed-citation><mixed-citation xml:lang="en">Koneva N.A., Trishkina L.I., Zhdanov A.N., Pereva­lova O.B., Popova N.A., Kozlova E.V. Sources of stress fields in deformed polycrystals. Fizicheskaya mezomekha­nika. 2006;9(3):93–102. (In Russ.).</mixed-citation></citation-alternatives></ref><ref id="cit42"><label>42</label><citation-alternatives><mixed-citation xml:lang="ru">Громова А.В., Юрьев А.Б., Иванов Ю.Ф., Чинока­­лов В.Я. Формирование дальнодействующих полей напряжений при волочении проволоки. Известия вузов. Черная металлургия. 2006;49(2):27–31.</mixed-citation><mixed-citation xml:lang="en">Gromova A.V., Yur’ev A.B., Ivanov Yu.F., Chinokalov V.Ya. Formation of long-range stress fields during wire drawing. Izvestiya. Ferrous Metallurgy. 2006;49(2):27–31. (In Russ.).</mixed-citation></citation-alternatives></ref><ref id="cit43"><label>43</label><citation-alternatives><mixed-citation xml:lang="ru">Рыбин В.В. Закономерности формирования мезоструктур в ходе развития пластической деформации. Вопросы материаловедения. 2002;29(1):11–33.</mixed-citation><mixed-citation xml:lang="en">Rybin V.V. Patterns of mesostructure formation during deve­lopment of plastic deformation. Voprosy materialovedeniya. 2002;29(1):11–33. (In Russ.).</mixed-citation></citation-alternatives></ref><ref id="cit44"><label>44</label><citation-alternatives><mixed-citation xml:lang="ru">Calcaynotto M., Ponge D., Demir E., Raabe D. Orientation gradients and geometrically necessary dislocations in ultrafine grained dual-phase steels studied by 2D and 3D EBSD. Materials Science and Engineering: A. 2010;527(10-11): 2738–2746. https://doi.org/10.1016/j.msea.2010.01.004</mixed-citation><mixed-citation xml:lang="en">Calcaynotto M., Ponge D., Demir E., Raabe D. Orientation gradients and geometrically necessary dislocations in ultrafine grained dual-phase steels studied by 2D and 3D EBSD. Materials Science and Engineering: A. 2010;527(10-11): 2738–2746. https://doi.org/10.1016/j.msea.2010.01.004</mixed-citation></citation-alternatives></ref><ref id="cit45"><label>45</label><citation-alternatives><mixed-citation xml:lang="ru">Kundu A., Field D.P. Influence of plastic deformation hete­rogeneity on development of geometrically necessary dislocation density in dual phase steel. Materials Science and Engineering: A. 2016;667:435–443. https://doi.org/10.1016/j.msea.2016.05.022</mixed-citation><mixed-citation xml:lang="en">Kundu A., Field D.P. Influence of plastic deformation hete­rogeneity on development of geometrically necessary dislocation density in dual phase steel. Materials Science and Engineering: A. 2016;667:435–443. https://doi.org/10.1016/j.msea.2016.05.022</mixed-citation></citation-alternatives></ref><ref id="cit46"><label>46</label><citation-alternatives><mixed-citation xml:lang="ru"></mixed-citation><mixed-citation xml:lang="en"></mixed-citation></citation-alternatives></ref><ref id="cit47"><label>47</label><citation-alternatives><mixed-citation xml:lang="ru"></mixed-citation><mixed-citation xml:lang="en"></mixed-citation></citation-alternatives></ref></ref-list><fn-group><fn fn-type="conflict"><p>The authors declare that there are no conflicts of interest present.</p></fn></fn-group></back></article>
