Comparison of the Yield Functions for Micropolar Media Using a Cylindrical Sample Model

K. P. Frolova; E. N. Vilchevskaya

doi:10.17804/2410-9908.2019.5.006-022

K. P. Frolova, E. N. Vilchevskaya

COMPARISON OF THE YIELD FUNCTIONS FOR MICROPOLAR MEDIA USING A CYLINDRICAL SAMPLE MODEL

DOI: 10.17804/2410-9908.2019.5.006-022

The article discusses different yield functions extended to the case of micropolar media in order to investigate the effect of local plasticity in metals. The paper is concerned with the inhomogeneous stress-strain state obtained within the frame of the micropolar continuum approach for a cylindrical specimen under distributed couple stress on its lateral surface. The case corresponding to specimen tension is considered. Plastic strains prove to arise near the border of the specimen, while the material continues to behave elastically. According to the results, it is necessary to take into account couple stresses to clarify what happens in the area near the border when the size of this area is comparable to the size of the structure inhomogeneity.

Keywords: yield function for a micropolar medium, size effects, pseudo-Cosserat continuum, couple stress

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К. П. Фролова, Е. Н. Вильчевская

СРАВНЕНИЕ УСЛОВИЙ ПЛАСТИЧНОСТИ ДЛЯ МИКРОПОЛЯРНЫХ СРЕД НА ПРИМЕРЕ МОДЕЛИ ЦИЛИНДРИЧЕСКОГО ОБРАЗЦА

В статье рассматриваются условия пластичности, обобщенные различными способами на случай микрополярных сред, с целью исследования эффекта локализации пластических деформаций в металлах. В качестве примера в статье рассматривается полученное в рамках микрополярной теории сплошных сред неоднородное напряженно-деформированное состояние цилиндрического образца, на боковой поверхности которого задан распределенный момент и к торцам которого приложено растягивающее усилие. Оказывается, что пластическое течение инициируется непосредственно у границы образца, в то время как материал в целом продолжает вести себя упруго. Результаты свидетельствуют о необходимости учета моментных взаимодействий между частицами среды при рассмотрении приграничной области, размеры которой сопоставимы с характерным размером структурной неоднородности материала.

Ключевые слова: критерий текучести для микрополярной среды, размерный эффект, псевдоконтинуум Коссера, моментное взаимодействие

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Библиографическая ссылка на статью

Frolova K. P., Vilchevskaya E. N. Comparison of the Yield Functions for Micropolar Media Using a Cylindrical Sample Model // Diagnostics, Resource and Mechanics of materials and structures. - 2019. - Iss. 5. - P. 6-22. -
DOI: 10.17804/2410-9908.2019.5.006-022. -
URL: http://dream-journal.org/issues/2019-5/2019-5_270.html
(accessed: 21.11.2024).