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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">techusgu</journal-id><journal-title-group><journal-title xml:lang="ru">Известия Юго-Западного государственного университета. Серия: Техника и технологии</journal-title><trans-title-group xml:lang="en"><trans-title>Proceedings of the Southwest State University. Series: Engineering and Technology</trans-title></trans-title-group></journal-title-group><issn pub-type="ppub">2223-1528</issn><publisher><publisher-name>Юго-Западный государственный университет</publisher-name></publisher></journal-meta><article-meta><article-id pub-id-type="doi">10.21869/2223-1528-2022-12-3-118-129</article-id><article-id custom-type="elpub" pub-id-type="custom">techusgu-40</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>ФИЗИКА</subject></subj-group><subj-group subj-group-type="section-heading" xml:lang="en"><subject>PHYSICS</subject></subj-group></article-categories><title-group><article-title>Формирование дислокационной структуры зоны аккомодации  в системе двух механических двойников в титане</article-title><trans-title-group xml:lang="en"><trans-title>Formation of a Dislocation Structure of the Accommodation Zone  in a System of Two Mechanical twins in Titanium</trans-title></trans-title-group></title-group><contrib-group><contrib contrib-type="author" corresp="yes"><contrib-id contrib-id-type="orcid">https://orcid.org/0000-0003-1843-0052</contrib-id><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Мишунин</surname><given-names>М. В.</given-names></name><name name-style="western" xml:lang="en"><surname>Mishuni</surname><given-names>M. V.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Мишунин Максим Вадимович, научный сотрудник</p><p>ул. Победы 85, г. Белгород 308015</p></bio><bio xml:lang="en"><p>Maksim V. Mishunin, Researcher</p><p>   85 Pobedy Str., Belgorod 308015</p></bio><email xlink:type="simple">maks_mish@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/0000-0001-6661-3959</contrib-id><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Никуличева</surname><given-names>Т. Б.</given-names></name><name name-style="western" xml:lang="en"><surname>Nikulicheva</surname><given-names>T. B.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Никуличева Татьяна Борисовна, кандидат физико-математических наук, заведующая  лабораторией перспективных материалов  и технологий</p><p>ул. Победы 85, г. Белгород 308015</p></bio><bio xml:lang="en"><p>Tatiana B. Nikulicheva, Cand. of Sci. (Physics and Mathematics), Head of the Laboratory  of Advanced Materials and Technologies</p><p>   85 Pobedy Str., Belgorod 308015</p></bio><email xlink:type="simple">nikulicheva@bsu.edu.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/0000-0001-7055-8243</contrib-id><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Захвалинский</surname><given-names>В. С.</given-names></name><name name-style="western" xml:lang="en"><surname>Zakhvalinskii</surname><given-names>V. S.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Захвалинский Василий Сергеевич, доктор физико-математических наук, профессор  кафедры теоретической и экспериментальной физики</p><p>ул. Победы 85, г. Белгород 308015</p></bio><bio xml:lang="en"><p>Vasilii S. Zakhvalinskii, Dr. of Sci. (Physics  and Mathematics), Professor of the Department  of Theoretical and Experimental Physics</p><p>   85 Pobedy Str., Belgorod 308015</p></bio><email xlink:type="simple">zakhvalinskii@bsu.edu.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/0000-0003-4929-8162</contrib-id><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Никулин</surname><given-names>И. С.</given-names></name><name name-style="western" xml:lang="en"><surname>Nikulin</surname><given-names>I. S.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Никулин Иван Сергеевич, кандидат  физико-математических наук, заведующий  лабораторией физико-химических методов  исследования растений</p><p>ул. Победы 85, г. Белгород 308015</p></bio><bio xml:lang="en"><p>Ivan S. Nikulin, Cand. of Sci. (Physics and  Mathematics), Head of the Laboratory of Physical and Chemical Methods of Plant Research</p><p>   85 Pobedy Str., Belgorod 308015</p></bio><email xlink:type="simple">nikulin@bsu.edu.ru</email><xref ref-type="aff" rid="aff-1"/></contrib></contrib-group><aff-alternatives id="aff-1"><aff xml:lang="ru"><institution>Белгородский государственный национальный исследовательский университет</institution><country>Россия</country></aff><aff xml:lang="en"><institution>Belgorod State National Research University</institution><country>Russian Federation</country></aff></aff-alternatives><pub-date pub-type="collection"><year>2022</year></pub-date><pub-date pub-type="epub"><day>27</day><month>04</month><year>2023</year></pub-date><volume>12</volume><issue>3</issue><fpage>118</fpage><lpage>129</lpage><permissions><copyright-statement>Copyright &amp;#x00A9; Мишунин М.В., Никуличева Т.Б., Захвалинский В.С., Никулин И.С., 2023</copyright-statement><copyright-year>2023</copyright-year><copyright-holder xml:lang="ru">Мишунин М.В., Никуличева Т.Б., Захвалинский В.С., Никулин И.С.</copyright-holder><copyright-holder xml:lang="en">Mishuni M.V., Nikulicheva T.B., Zakhvalinskii V.S., Nikulin I.S.</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://techusgu.elpub.ru/jour/article/view/40">https://techusgu.elpub.ru/jour/article/view/40</self-uri><abstract><sec><title>Цель</title><p>Цель. Экспериментальное исследование и математическое моделирование процессов формирования структуры в аккомодационной зоне системы клиновидных двойников в технически чистом титане. </p></sec><sec><title>Методы</title><p>Методы. Применялись методы микроиндентирования, химического травления, математического моделирования, электронной зондовой микроскопии. </p></sec><sec><title>Результаты</title><p>Результаты. При формировании клинового двойника в поликристаллическом титане образуются условия для формирования дополнительного двойника в его зоне аккомодации. Формирование дополнительного двойника – это в некотором роде способ снятия высоких напряжений на вершинах. Проведенное математическое моделирование распределения напряжений в области прохождения процесса двойникования, учитывающее наличие обнаруженного скопления образованных малоугловых границ, позволяет утверждать о закономерном взаимодействии дефектов структуры с дефектами, образованными в процессе развития двойниковой прослойки. </p><p>Предложенная модель показывает, что образование малоугловых границ в результате взаимодействия существующих дефектов материала и двойникующих дислокаций приводит к изменению эпюры напряжений в зоне аккомодации, что, в свою очередь, порождает множественные малоугловые границы в виде стенок дислокаций. </p><p>Представленный физический механизм и математическая модель дают достаточно ясную картину формирования структуры и эпюры растягивающих напряжений в зоне формирования двух параллельных двойников. Обнаружено скопление малоугловых границ в зоне аккомодации клиновидного двойника закономерно сформированных в процессе ее роста. </p></sec><sec><title>Заключение</title><p>Заключение. В работе представлены результаты экспериментальных исследований и математического моделирования процессов формирования структуры в аккомодационной зоне системы клиновидных двойников в технически чистом титане. Был учтен процесс взаимодействия структурных дефектов с двойникующими дислокациями при образовании клиновидного двойника. Показано, что это взаимодействие изменяет положение максимума напряжений вблизи границ в системе двух клиновидных двойников. </p></sec></abstract><trans-abstract xml:lang="en"><sec><title>Purpose</title><p>Purpose. Experimental study and mathematical modeling of the processes of structure formation in the accommodation zone of a system of wedge-shaped twins in commercially pure titanium. </p></sec><sec><title>Methods</title><p>Methods. Methods of Microindentation, chemical etching, mathematical modeling and electron probe microscopy were user. </p></sec><sec><title>Results</title><p>Results. While forming of wedge twin in poly-crystal of titanium are forming conditions of formation of additional twin in its transition zone. Forming of the extra twin is some way of relaxation of high stresses in the tips. The performed mathematical modeling of the stress distribution in the region of the twinning process, taking into account the presence of the detected accumulation of formed low-angle boundaries, makes it possible to state that the interaction of structural defects with defects formed during the development of the twinning layer is regular. The proposed model indicates that the formation of low-angle boundaries due to the interaction of existing material defects and twinning dislocations leads to a change in the stress diagram in the transition area, which, in turn, generates multiple low-angle borders in the form of the dislocation walls. Shown physical mechanism and mathematic model gives rather clear picture of forming of structure and spreading stresses in zone of forming of two parallel twins.An accumulation of low-angle boundaries was found in the accommodation zone of the wedge-shaped twin, which were regularly formed during its growth. </p></sec><sec><title>Conclusion</title><p>Conclusion. In the work, we have presented the results of experimental studies and mathematical modeling for the processes of the structure formation in a transition zone of wedge-type twins system in commercially pure titanium. The process of interaction of structure defects with twinning dislocations during the formation of a wedge-type twin was taken into consideration. It is shown that the interaction alters the stress maximum in vicinity of boundaries in the system two wedge-type twins. </p></sec></trans-abstract><kwd-group xml:lang="ru"><kwd>углеродные нанотрубки</kwd><kwd>теория функционала плотности</kwd><kwd>сорбционные свойства</kwd><kwd>борирование</kwd><kwd>квантово-химические расчеты</kwd><kwd>экологические фильтры</kwd></kwd-group><kwd-group xml:lang="en"><kwd>twinning</kwd><kwd>dislocation walls</kwd><kwd>grain boundaries</kwd><kwd>stress</kwd><kwd>mathematical modeling</kwd></kwd-group></article-meta></front><back><ref-list><title>References</title><ref id="cit1"><label>1</label><citation-alternatives><mixed-citation xml:lang="ru">Никифоров А. С. Математическое моделирование неупругого деформирования ГЦК поликристаллов с учетом эволюции дислокационных скоплений // XLV Гагаринские чтения. М.: ИПМех РАН, 2019. С. 119–121.</mixed-citation><mixed-citation xml:lang="en">Nikiforov A. S. Matematicheskoe modelirovanie neuprugogo deformirovaniya GTsK polikristallov s uchetom evolyutsii dislokatsionnykh skoplenii  [Mathematical modeling of inelastic deformation of fcc polycrystals taking into account the evolution of dislocation clusters]. XLV Gagarinskie chteniya = XLV Gagarin Readings, Moscow, IPMekh RAN Publ. 2019, pp. 119–121.</mixed-citation></citation-alternatives></ref><ref id="cit2"><label>2</label><citation-alternatives><mixed-citation xml:lang="ru">Классен-Неклюдова М. В. Механическое двойникование кристаллов. М.: Изд-во Акад. наук СССР, 1960. 261 с.</mixed-citation><mixed-citation xml:lang="en">Klassen-Neklyudova M. V. Mekhanicheskoe dvoinikovanie kristallov [Mechanical twinning crystals]. Moscow, Akad. nauk SSSR Publ., 1960.</mixed-citation></citation-alternatives></ref><ref id="cit3"><label>3</label><citation-alternatives><mixed-citation xml:lang="ru">Investigation of twinning dynamics in VT1-0 titanium using acoustic emission / N. V. Kamyshanchenko, I. S. Nikulin, M. S. Kungurtsev [et al.] // Inorganic materials: applied research. 2011. Vol. 2, nо. 2. P. 192–196. https://doi.org/10.1134/S2075113311020109.</mixed-citation><mixed-citation xml:lang="en">Kamyshanchenko N. V., Nikulin I. S., Kungurtsev M. S., eds. Investigation of twinning dynamics in VT1-0 titanium using acoustic emission. Inorganic materials: applied research, 2011, vol. 2, no. 2, pp. 192–196. https://doi.org/10.1134/S2075113311020109.</mixed-citation></citation-alternatives></ref><ref id="cit4"><label>4</label><citation-alternatives><mixed-citation xml:lang="ru">Федоров В. А., Тялин Ю. И., Тялина В. А. Дислокационные механизмы разрушения двойникующихся материалов : монография. М.: Машиностроение-1, 2004. 336 с.</mixed-citation><mixed-citation xml:lang="en">Fedorov V. A., Tyalin Yu. I., Tyalina V. A. Dislokatsionnye mekhanizmy raz-rusheniya dvoinikuyushchikhsya materialov [Dislocation mechanisms of destruction of twinning materials]. Moscow, Mashinostroenie-1 Publ., 2004. 336 p.</mixed-citation></citation-alternatives></ref><ref id="cit5"><label>5</label><citation-alternatives><mixed-citation xml:lang="ru">Влияние распределения дислокаций в границах двойника на зарождение микротрещин в его вершине / В. А. Федоров, В. А. Куранова, Ю. И. Тялин, С. Н. Плужников // Физика твердого тела. 2002. Т. 44, № 6. С. 1057–1059.</mixed-citation><mixed-citation xml:lang="en">Fedorov V. A., Kuranova V. A., Tyalin Yu. I., Pluzhnikov S. N. Vliyanie raspredeleniya dislokatsii v granitsakh dvoinika na zarozhdenie mikrotreshchin v ego vershine [Influence of distribution of dislocations within the boundaries of a twin on the initiation of microcracks in its tip]. Fizika tverdogo tela = Solid State Physics, 2002, vol. 44, no 6, pp. 1057–1059.</mixed-citation></citation-alternatives></ref><ref id="cit6"><label>6</label><citation-alternatives><mixed-citation xml:lang="ru">Курганов А. В. Развитие математического моделирования процесса двойникования в титане // Системный анализ и информационные технологии в науках о природе и обществе. 2017. № 1-2. С. 79–83.</mixed-citation><mixed-citation xml:lang="en">Kurganov A. V. Razvitie matematicheskogo modelirovaniya protsessa dvoinikovaniya v titane  [Development of mathematical modeling of the process of twinning in titanium]. Sistemnyi analiz i informatsionnye tekhnologii v naukakh o prirode i obshchestve = System  analysis and information technology in the sciences of nature and society, 2017, no. 1-2,  pp. 79–83.</mixed-citation></citation-alternatives></ref><ref id="cit7"><label>7</label><citation-alternatives><mixed-citation xml:lang="ru">Ostrikov O. M. Effect of the density of twinning dislocations on the configuration of stress fields near a wedge twin with different shapes of the boundaries // Applied Mechanics and Technical Physics. 2008. Vol. 49, no. 5. P. 872–876.</mixed-citation><mixed-citation xml:lang="en">Ostrikov O. M. Effect of the density of twinning dislocations on the configuration of stress fields near a wedge twin with different shapes of the boundaries. Applied Mechanics and Technical Physics, 2008, vol. 49, no. 5, рр. 872–876.</mixed-citation></citation-alternatives></ref><ref id="cit8"><label>8</label><citation-alternatives><mixed-citation xml:lang="ru">Теребушко О. И. Основы теории упругости и пластичности. М.: Наука, 1984. 320 с.</mixed-citation><mixed-citation xml:lang="en">Terebushko O. I. Osnovy teorii uprugosti i plastichnosti [Fundamentals of the theory of elasticity and plasticity]. Moscow, Nauka Publ., 1984. 320 p.</mixed-citation></citation-alternatives></ref><ref id="cit9"><label>9</label><citation-alternatives><mixed-citation xml:lang="ru">Тялина В. А., Мищенко С. В., Тялин Ю. И. Математическое моделирование развития и взаимодействия упругих двойников // Вестник Тамбовского государственного технического университета. 2014. Т. 20, № 3. С. 579–585.</mixed-citation><mixed-citation xml:lang="en">Tyalina V. A., Mishchenko S. V., Tyalin Yu. I. Matematicheskoe modelirovanie razvitiya i vzaimodeistviya uprugikh dvoinikov [Mathematical modeling of development and interaction of elastic twins]. Vestnik Tambovskogo gosudarstvennogo tekhnicheskogo universiteta = Bulletin of the Tambov State Technical University, 2014, vol. 20, no. 3, pp. 579–585.</mixed-citation></citation-alternatives></ref><ref id="cit10"><label>10</label><citation-alternatives><mixed-citation xml:lang="ru">The role of twinning deformation on the hardening response of polycrystalline magnesium from discrete dislocation dynamics simulations / H. Fan, S. Aubry, A. Arsenlis, J. A. El-Awady // Acta Mater. 2015. Vol. 92. P. 126–139.</mixed-citation><mixed-citation xml:lang="en">Fan H., Aubry S., Arsenlis A., El-Awady J. A. The role of twinning deformation on the hardening response of polycrystalline magnesium from discrete dislocation dynamics simulations. Acta Mater., 2015, vol. 92, pp. 126–139.</mixed-citation></citation-alternatives></ref><ref id="cit11"><label>11</label><citation-alternatives><mixed-citation xml:lang="ru">Бразгина О. В., Трусов П. В. Двухуровневая модель для описания упруговязкопластического деформирования ГПУ-металлов: упрочнение для двойников // Вестник Пермского государственного технического университета. Прикладная математика и механика. 2011. № 9. С. 19–28.</mixed-citation><mixed-citation xml:lang="en">Brazgina O. V., Trusov P. V. Dvukhurovnevaya model' dlya opisaniya uprugovyazkoplasticheskogo deformirovaniya GPU-metallov: uprochnenie dlya dvoinikov  [A two-level model for describing the elastoviscoplastic deformation of hcp metals: hardening for twins]. Vestnik Permskogo gosudarstvennogo tekhnicheskogo universiteta. Prikladnaya matematika i mekhanika = Bulletin of the Perm State Technical University. Applied mathematics and mechanics, 2011, no. 9, pp. 19–28.</mixed-citation></citation-alternatives></ref><ref id="cit12"><label>12</label><citation-alternatives><mixed-citation xml:lang="ru">Numerical analysis of twin-precipitate interactions in magnesium alloys / F. Siska, L. Stratil, J. Cizek, T. Guo, M. Barnett // Acta Materialia. 2020. Vol. 202. P. 80–87.</mixed-citation><mixed-citation xml:lang="en">Siska F., Stratil L., Cizek J., Guo T., Barnett M. Numerical analysis of twin-precipitate interactions in magnesium alloys. Acta Materialia, 2020, vol. 202, pp. 80–87.</mixed-citation></citation-alternatives></ref><ref id="cit13"><label>13</label><citation-alternatives><mixed-citation xml:lang="ru">Formation of low-angle boundaries accompanying the deformation process by twinning in titanium / I. S. Nikulin, N. V. Kamyshanchenko, T. B. Nikulicheva, M. V. Mishunin, K. A. Vokhmyanina // Materials Letters. 2016. Vol. 182. P. 253–256.</mixed-citation><mixed-citation xml:lang="en">Nikulin I. S., Kamyshanchenko N. V., Nikulicheva T. B., Mishunin M. V., Vokhmyanina K. A. Formation of low-angle boundaries accompanying the deformation process by twinning in titanium. Materials Letters, 2016, vol. 182, pp. 253.</mixed-citation></citation-alternatives></ref><ref id="cit14"><label>14</label><citation-alternatives><mixed-citation xml:lang="ru">Bayley C. J., Brekelmans W. A. M., Geers M. G. D. A comparison of dislocation induced back stress formulations in strain gradient crystal plasticity // International Journal of Solids and Structures. 2006. Vol. 43. P. 7268–7286.</mixed-citation><mixed-citation xml:lang="en">Bayley C. J., Brekelmans W. A. M., Geers M. G. D. A comparison of dislocation induced back stress formulations in strain gradient crystal plasticity. International Journal of Solids and Structures, 2006, vol. 43, pp. 7268–7286.</mixed-citation></citation-alternatives></ref><ref id="cit15"><label>15</label><citation-alternatives><mixed-citation xml:lang="ru">Arsenlis A., Parks D. M. Modeling the evolution of crystallographic dislocation density in crystal plasticity // J. Mech. Phys. Solids. 2002. Vol. 50. P. 1979–2009.</mixed-citation><mixed-citation xml:lang="en">Arsenlis A., Parks D. M. Modeling the evolution of crystallographic dislocation density in crystal plasticity. J. Mech. Phys. Solids, 2002, vol. 50, pp. 1979–2009.</mixed-citation></citation-alternatives></ref><ref id="cit16"><label>16</label><citation-alternatives><mixed-citation xml:lang="ru">Mechanism-based strain gradient crystal plasticity. II. Analysis / C. S. Han, H. Gao, Y. Huang, W. D. Nix // J. Mech. Phys. Solids. 2005. Vol. 53. P. 1204–1222.</mixed-citation><mixed-citation xml:lang="en">Han C. S., Gao H., Huang Y., Nix W. D. Mechanism-based strain gradient crystal plasticity. II. Analysis. J. Mech. Phys. Solids, 2005, vol. 53, pp. 1204–1222.</mixed-citation></citation-alternatives></ref><ref id="cit17"><label>17</label><citation-alternatives><mixed-citation xml:lang="ru">Boundary layers in constrained plastic flow: comparison of nonlocal and discrete dis-location plasticity / J. Y. Shu, N. A. Fleck, E. Van der Giessen, A. Needleman // J. Mech. Phys. Solids. 2001. Vol. 49. P. 1361–1395.</mixed-citation><mixed-citation xml:lang="en">Shu J. Y., Fleck N. A., Van der Giessen E., Needleman A. Boundary layers in constrained plastic flow: comparison of nonlocal and discrete dislocation plasticity. J. Mech. Phys. Solids, 2001, vol. 49, pp. 1361–1395.</mixed-citation></citation-alternatives></ref><ref id="cit18"><label>18</label><citation-alternatives><mixed-citation xml:lang="ru">Yaghoobi M., Allison J. E., Sundararaghavan V. Multiscale modeling of twinning and detwinning behavior of HCP polycrystals // Int. J. Plast. 2020. Vol. 127. P. 102653.</mixed-citation><mixed-citation xml:lang="en">Yaghoobi M., Allison J. E., Sundararaghavan V., Multiscale modeling of twinning and detwinning behavior of HCP polycrystals. Int. J. Plast., 2020, vol. 127, pp. 102653.</mixed-citation></citation-alternatives></ref><ref id="cit19"><label>19</label><citation-alternatives><mixed-citation xml:lang="ru">Мацюк К. В., Трусов П. В. Модель неупругого деформирования ГПУполикристаллов: несимметричные меры напряженно-деформированного состояния, законы упрочнения, ротация решетки // Математическое моделирование в естественных науках. 2013. Т. 1. С. 105–107.</mixed-citation><mixed-citation xml:lang="en">Matsyuk K. V., Trusov P. V. Model' neuprugogo deformirovaniya GPUpolikristallov: nesimmetrichnye mery napryazhenno-deformirovannogo sostoyaniya, zakony uprochneniya, rotatsiya reshetki  [A model of inelastic deformation of hcp polycrystals: asymmetric measures of the stress-strain state, hardening laws, lattice rotation]. Matematicheskoe modelirovanie v estestvennykh naukakh = Mathematical modeling in natural sciences, 2013, vol. 1, pp. 105–107.</mixed-citation></citation-alternatives></ref><ref id="cit20"><label>20</label><citation-alternatives><mixed-citation xml:lang="ru">Zhang R. Y., Daymond M. R., Holt R. A. A finite element model of deformation twinning in zirconium // Materials Science and Engineering: A. 2008. Vol. 473, no. 1-2. P. 139.</mixed-citation><mixed-citation xml:lang="en">Zhang R. Y., Daymond M. R., Holt R. A. A finite element model of deformation twinning in zirconium. Materials Science and Engineering: A, 2008, vol. 473, no. 1–2,  pp. 139.</mixed-citation></citation-alternatives></ref><ref id="cit21"><label>21</label><citation-alternatives><mixed-citation xml:lang="ru">Yefimov S., Groma I., Van der Giessen E. A comparison of a statistical-mechanics based plasticity model with discrete dislocation plasticity calculations // J. Mech. Phys. Solids. 2004. Vol. 52. P. 279–300.</mixed-citation><mixed-citation xml:lang="en">Yefimov S., Groma I., Van der Giessen E. A comparison of a statistical-mechanics based plasticity model with discrete dislocation plasticity calculations. J. Mech. Phys. Solids, 2004, vol. 52, pp. 279–300.</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>
