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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">zldm</journal-id><journal-title-group><journal-title xml:lang="ru">Заводская лаборатория. Диагностика материалов</journal-title><trans-title-group xml:lang="en"><trans-title>Industrial laboratory. Diagnostics of materials</trans-title></trans-title-group></journal-title-group><issn pub-type="ppub">1028-6861</issn><issn pub-type="epub">2588-0187</issn><publisher><publisher-name>ООО «Издательство «ТЕСТ-ЗЛ»</publisher-name></publisher></journal-meta><article-meta><article-id pub-id-type="doi">10.26896/1028-6861-2024-90-1-72-81</article-id><article-id custom-type="elpub" pub-id-type="custom">zldm-2100</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>ИССЛЕДОВАНИЕ СТРУКТУРЫ И СВОЙСТВ. МЕХАНИКА МАТЕРИАЛОВ: ПРОЧНОСТЬ, РЕСУРС, БЕЗОПАСНОСТЬ</subject></subj-group><subj-group subj-group-type="section-heading" xml:lang="en"><subject>TESTING OF STRUCTURE AND PARAMETERS. MECHANICAL TESTING METHODS</subject></subj-group></article-categories><title-group><article-title>Уравнения состояния вязкоупругости полиметилметакрилата</article-title><trans-title-group xml:lang="en"><trans-title>Equations of state of the viscoelasticity of polymethyl methacrylate</trans-title></trans-title-group></title-group><contrib-group><contrib contrib-type="author" corresp="yes"><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Куркин</surname><given-names>А. С.</given-names></name><name name-style="western" xml:lang="en"><surname>Kurkin</surname><given-names>A. S.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Алексей Сергеевич Куркин</p><p>105005, Москва, 2-я Бауманская ул., д. 5</p></bio><bio xml:lang="en"><p>Alexey S. Kurkin</p><p>5, 2-ya Baumanskaya ul., Moscow, 105005</p></bio><xref ref-type="aff" rid="aff-1"/></contrib><contrib contrib-type="author" corresp="yes"><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Киселев</surname><given-names>А. С.</given-names></name><name name-style="western" xml:lang="en"><surname>Kiselev</surname><given-names>A. S.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Александр Сергеевич Киселев</p><p>123182, Москва, пл. Академика Курчатова, д. 1</p></bio><bio xml:lang="en"><p>Alexander S. Kiselev</p><p>1, Akad. Kurchatova pl., Moscow, 123182</p></bio><xref ref-type="aff" rid="aff-2"/></contrib><contrib contrib-type="author" corresp="yes"><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Устинов</surname><given-names>В. С.</given-names></name><name name-style="western" xml:lang="en"><surname>Ustinov</surname><given-names>V. S.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Василий Сергеевич Устинов</p><p>123182, Москва, пл. Академика Курчатова, д. 1</p></bio><bio xml:lang="en"><p>Vasily S. Ustinov</p><p>1, Akad. Kurchatova pl., Moscow, 123182</p></bio><xref ref-type="aff" rid="aff-2"/></contrib><contrib contrib-type="author" corresp="yes"><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Богданов</surname><given-names>А. А.</given-names></name><name name-style="western" xml:lang="en"><surname>Bogdanov</surname><given-names>A. A.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Алексей Александрович Богданов</p><p>123182, Москва, пл. Академика Курчатова, д. 1</p></bio><bio xml:lang="en"><p>Aleksey A. Bogdanov</p><p>1, Akad. Kurchatova pl., Moscow, 123182</p></bio><xref ref-type="aff" rid="aff-2"/></contrib></contrib-group><aff-alternatives id="aff-1"><aff xml:lang="ru"><institution>Московский государственный технический университет имени Н. Э. Баумана</institution><country>Россия</country></aff><aff xml:lang="en"><institution>Bauman Moscow State Technical University</institution><country>Russian Federation</country></aff></aff-alternatives><aff-alternatives id="aff-2"><aff xml:lang="ru"><institution>Национальный исследовательский центр «Курчатовский институт»</institution><country>Россия</country></aff><aff xml:lang="en"><institution>National Research Centre «Kurchatov Institute»</institution><country>Russian Federation</country></aff></aff-alternatives><pub-date pub-type="collection"><year>2024</year></pub-date><pub-date pub-type="epub"><day>22</day><month>01</month><year>2024</year></pub-date><volume>90</volume><issue>1</issue><fpage>72</fpage><lpage>81</lpage><permissions><copyright-statement>Copyright &amp;#x00A9; Куркин А.С., Киселев А.С., Устинов В.С., Богданов А.А., 2024</copyright-statement><copyright-year>2024</copyright-year><copyright-holder xml:lang="ru">Куркин А.С., Киселев А.С., Устинов В.С., Богданов А.А.</copyright-holder><copyright-holder xml:lang="en">Kurkin A.S., Kiselev A.S., Ustinov V.S., Bogdanov A.A.</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://www.zldm.ru/jour/article/view/2100">https://www.zldm.ru/jour/article/view/2100</self-uri><abstract><p>Представлены результаты исследования ползучести полиметилметакрилата (ПММА) в температурном интервале от 0 до +30 °C при скоростях деформирования от 0,02 до 2 % в минуту и напряжениях выдержки от 48 до 72 МПа продолжительностью до 100 ч. Рассмотрено вязкоупругое поведение ПММА при нормальных условиях эксплуатации, до начала процессов повреждения материала. Для этих условий получена единая степенная зависимость деформации ползучести от времени для всего периода выдержки, без разделения на стадии неустановившейся и установившейся ползучести. Предложены формулы для аппроксимации результатов изотермических испытаний образцов при постоянной скорости деформации и при выдержке под постоянной нагрузкой. Получены зависимости параметров аппроксимации от скорости деформации, уровня напряжения и температуры испытаний ПММА. Сопоставление диаграмм деформации ползучести при одинаковых напряжениях выдержки после деформирования с различными скоростями показало, что эти диаграммы располагаются со смещением по времени на единой кривой. Это указывает на возможность описания совокупности полученных экспериментальных данных единым уравнением состояния, связывающим скорость ползучести с напряжением и температурой. Дифференцирование аппроксимирующих формул позволило выявить закономерности изменения скорости ползучести в процессе испытаний, а повторное дифференцирование — получить уравнение ускорения ползучести при деформировании с постоянной скоростью и исключить из него переменную времени. Аналогично получено уравнение замедления ползучести для условий выдержки под постоянным напряжением, из которого также исключена переменная времени. В таком виде эти два уравнения можно рассматривать как частные случаи уравнения состояния вязкоупругого материала, поведение которого не зависит от предыстории нагружения. Ползучесть при непрерывном деформировании представляет собой суперпозицию двух процессов: ускорения ползучести вследствие роста напряжения и ее замедления с течением времени. На этой основе сформулировано единое уравнение состояния вязкоупругого материала для процесса с произвольным законом роста деформации и напряжения. Параметрами уравнения состояния являются температура, скорость и ускорение ползучести, напряжение и скорость его изменения. Накопленная деформация ползучести не входит в число параметров. Применимость этого уравнения при более сложных условиях немонотонного термосилового нагружения материала требует дополнительного экспериментального обоснования, а также идентификации параметров уравнения.</p></abstract><trans-abstract xml:lang="en"><p>The results of studying creep of polymethyl methacrylate (PMMA) in the temperature range from 0 to +30°C at a strain rate from 0.02 to 2% per minute and holding for up to 100 h under stress values within a range of 48 – 72 MPa are presented. The viscoelastic behavior of PMMA is analyzed under normal operating conditions before the onset of the material damage. A unified power dependence of the creep deformation on time was obtained for the entire holding period, without any division into the stages of the unsteady and steady creep. Formulas to be used for approximating the results of isothermal tests of samples at a constant strain rate and holding under a constant load are proposed. The dependences of the approximation parameters on the strain rate, stress level, and temperature of PMMA tests are obtained. A comparison of the creep strain diagrams for the same holding stress after deformation at different rates showed that the diagrams lie on a single curve with a time shift. This indicates the possibility of describing the totality of the experimental data obtained by a single equation of state linking the creep rate, stress and temperature. Differentiation of the approximating formulas made it possible to reveal the regularities of changes in the creep rate during testing and repeated differentiation allowed us to obtain an equation for the creep acceleration upon deformation at a constant rate and to exclude the time variable from it. Similarly, the time variable was also excluded from the creep deceleration equation obtained for holding under constant stress. In this form, these two equations can be considered special cases of the equation of state of a viscoelastic material which behavior is independent on the loading prehistory. Creep under continuous deformation is a superposition of two processes: creep acceleration due to the stress growth and creep deceleration with time. On this basis, a unified equation of state for a viscoelastic material was derived for a process with an arbitrary law of the strain and stress growth. The parameters of this equation are the temperature, creep velocity and acceleration, stress and the rate of stress change. The accumulated creep strain is not a parameter of equation. The applicability of this equation under more complex conditions of a nonmonotonic thermopower loading of materials requires additional experimental justification, as well as identification of the equation parameters.</p></trans-abstract><kwd-group xml:lang="ru"><kwd>вязкоупругость</kwd><kwd>полиметилметакрилат</kwd><kwd>ПММА</kwd><kwd>непрерывная деформация</kwd><kwd>выдержка под нагрузкой</kwd><kwd>уравнение состояния</kwd><kwd>скорость ползучести</kwd><kwd>ускорение ползучести</kwd></kwd-group><kwd-group xml:lang="en"><kwd>viscoelasticity</kwd><kwd>polymethyl methacrylate (PMMA)</kwd><kwd>continuous deformation</kwd><kwd>holding under load</kwd><kwd>equation of state</kwd><kwd>creep rate</kwd><kwd>creep acceleration</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">Christoefl P. et al. 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