Features of the Stress State of Porous Brittle Materials under Tensile Conditions

V. A. Zimina; I. Yu. Smolin

doi:10.17804/2410-9908.2022.2.035-044

V. A. Zimina, I. Yu. Smolin

FEATURES OF THE STRESS STATE OF POROUS BRITTLE MATERIALS UNDER TENSILE CONDITIONS

DOI: 10.17804/2410-9908.2022.2.035-044

The paper discusses the problem of taking into account the influence of the heterogeneous structure of a material on its effective characteristics and mechanical behavior. To evaluate the effective properties and features of the stress and strain analysis of porous materials, it is proposed to use a combined method that includes experimental data (an SEM image of a porous material surface) and numerical methods of solids mechanics. Numerical simulation of the mechanical behavior of porous ceramics is performed on the basis of experimental data on its pore structure. As a result of the performed research, it is shown that this method makes it possible to determine the features of the stress and strain state of porous ceramics. The stress analysis reveals both tensile and compressive local stresses in porous ceramics mesovolumes under uniaxial tension. At the same time, the values of these local stresses exceed the mesovolume-average values by an order of magnitude.

Acknowledgement: The work was performed under the state assignment to the Institute of Strength Physics and Materials Science SB RAS, theme No. FWRW-2022-0003.

Keywords: effective properties, microstructure, ceramics, modeling, stress and strain state, stress-strain curve

References:

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В. А. Зимина, И. Ю. Смолин

ОСОБЕННОСТИ НАПРЯЖЕННОГО СОСТОЯНИЯ ПОРИСТЫХ ХРУПКИХ МАТЕРИАЛОВ В УСЛОВИЯХ РАСТЯЖЕНИЯ

Работа посвящена проблеме учета влияния неоднородной структуры материала на его эффективные характеристики и механическое поведение. Для оценки эффективных свойств и особенностей напряженно-деформированного состояния пористых материалов было предложено использовать комбинированный метод, включающий экспериментальные данные (РЭМ-изображение поверхностей образцов пористых материалов) и численные методы механики деформируемого твердого тела. Выполнено численное моделирование механического поведения пористой керамики на основе экспериментальных данных о ее поровой структуре. В результате проведенного исследования сделан вывод, что этот метод позволяет определить особенности напряженно-деформированного состояния исследуемого материала. Анализ напряжений в пористой керамике подтвердил, что при одноосном растяжении ее мезообъемов в них присутствуют как растягивающие, так и сжимающие локальные напряжения. При этом значения этих напряжений на порядок превышают средние значения по мезообъему.

Благодарность: Работа выполнена в рамках государственного задания Института физики прочно-сти и материаловедения СО РАН, тема номер FWRW-2022-0003.

Ключевые слова: эффективные свойства, микроструктура, керамика, моделирование, напряженно-деформированное состояние, диаграмма нагружения

Библиография:

Voigt W. Lehrbuch der Kristallphysik. – Berlin : Teubner, 1928. – 962 p.
Reuss A. Berechung der fliessgrenze von mischkristallen auf grund der plastizitatsbedingund für einkristalle // ZAMM – Zeitschrift für Angewandte Mathematik und Mechanik. – 1929. – Vol. 9 (1). – P. 49–58. – DOI: 10.1002/zamm.19290090104.
Hashin Z., Shtrikman S. A variational approach to the theory of the effective magnetic permeability of multiphase materials // Journal of Applied Physics. – 1962. – Vol. 33. – P. 3125. – DOI: 10.1063/1.1728579.
Maxwell J. C. A treatise on electricity and magnetism. – Oxford : Clarendon Press, 1873. – 577 p.
Sevostianov I., Giraud A. Generalization of Maxwell homogenization scheme for elastic material containing inhomogeneities of diverse shape // International Journal of Engineering Science. – 2013. – Vol. 64. – P. 23–36. – DOI: 10.1016/j.ijengsci.2012.12.004.
Combined effect of pores concavity and aspect ratio on the elastic properties of a porous material / F. Chen, I. Sevostianov, A. Giraud, D. Grgic // International Journal of Solids and Structures. – 2018. – Vol. 134. – P. 161–172. – DOI: 10.1016/j.ijsolstr.2017.10.016.
On the bounds of applicability of two-step homogenization technique for porous materials / A. Trofimov, S. G. Abaimov, I. S. Akhatov, I. Sevostianov // International Journal of Engineering Science. – 2018. – Vol. 123. – P. 117–126. – DOI: 10.1016/j.ijengsci.2017.11.017.
Roberts A., Garboczi E. Elastic properties of model porous ceramics // Journal of the American Ceramic Society. – 2000. – Vol. 83, No. 12. – P. 3041–3048. – DOI: 10.1111/J.1151-2916.2000.TB01680.X.
Computational simulations for the assessment of the mechanical properties of glass with controlled porosity / V. Cannillo, C. Leonelli, T. Manfredini, M. Montorsi, A. R. Boccaccini // Journal of Porous Materials. – 2003. – Vol. 10. – P. 189–200. – DOI: 10.1023/A:1027490502044.
Sadowski T., Samborski S. Prediction of the mechanical behaviour of porous ceramics using mesomechanical modeling // Computational Materials Science. – 2003. – Vol. 28, iss 3–4. – P. 512–517. – DOI: 10.1016/j.commatsci.2003.08.008.
Pabst W., Gregorová E., Tichá G. Effective properties of suspensions, composites and porous materials // Journal of the European Ceramic Society. – 2007. – Vol. 27. – P. 479–482. – DOI: 10.1016/j.jeurceramsoc.2006.04.169.
Pabst W., Gregorová E. Young’s modulus of isotropic porous materials with spheroidal pores // Journal of the European Ceramic Society. – 2014. – Vol. 34 (13). – P. 3195–3207. – DOI: 10.1016/j.jeurceramsoc.2014.04.009.
Knudsen F. P. Effect of Porosity on Young's Modulus of Alumina // Journal of the European Ceramic Society. – 1962. – Vol. 45, iss. 2. – P. 94–95. – DOI: 10.1111/j.1151-2916.1962.tb11089.x.
Dean E. A., Lopez J. A. Empirical Dependence of Elastic Moduli on Porosity for Ceramic Materials // Journal of the European Ceramic Society. – 1983. – Vol. 66, iss. 5. – P. 366–370. – DOI: 10.1111/j.1151-2916.1983.tb10051.x.
Munro R. G. Effective Medium Theory of the Porosity Dependence of Bulk Moduli // Journal of the European Ceramic Society. – 2001. – Vol. 84, iss. 5. – P. 1190–1192. – DOI: 10.1111/j.1151-2916.2001.tb00815.x.
The relation between porosity and elastic moduli of gelcast ceramic foams / J. A. Rodrigues, F. S. Ortega, A. E. M. Paiva, E. L. G. Villaboim, V. C. Pandolfelli // Cerâmica. – 2004. – Vol. 50. – P. 209–216. – DOI: 10.1590/S0366-69132004000300007.
Kulkov A. S., Smolin I. Yu., Mikushina V. A. Investigation of mechanical response of Al2O3 ceramic specimens to loading with consideration for their structural features // AIP Conference Proceedings. – 2018. – Vol. 2051. – P. 020162. – DOI: 10.1063/1.5083405.
Morrell R. Handbook of properties of technical & engineering ceramics : part 2: Data reviews. – Section I : High-alumina ceramic. – London : HMSO, 1987. – 255 p.
Зимина В. А. Определение механических характеристик хрупких пористых материалов на основе численного моделирования: дис. ... канд. физ. - мат. наук: 1.1.8. – Томск, 2021. – 141 с.
Mikushina V. A., Smolin I. Yu. Numerical analysis of the stress state and fracture of porous ceramics at the mesolevel // Journal of Physics: Conference Series. – 2019. – Vol. 1214. – P. 012016. – DOI: 10.1088/1742-6596/1214/1/012016.

Библиографическая ссылка на статью

Zimina V. A., Smolin I. Yu. Features of the Stress State of Porous Brittle Materials under Tensile Conditions // Diagnostics, Resource and Mechanics of materials and structures. - 2022. - Iss. 2. - P. 35-44. -
DOI: 10.17804/2410-9908.2022.2.035-044. -
URL: http://dream-journal.org/issues/2022-2/2022-2_357.html
(accessed: 21.12.2024).