V. A. Zimina, I. Yu. Smolin

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

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.

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

References:

1. Voigt W. Lehrbuch der Kristallphysik, Berlin, Teubner, 1928, 962 p.
2. Reuss A. Berechung der fliessgrenze von mischkristallen auf grund der plastizitatsbedingund für einkristalle. ZAMM – Zeitschrift für Angewandte Mathematik und Mechanik, 1929, vol. 9 (1), pp. 49–58. DOI: 10.1002/zamm.19290090104.
3. 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, pp. 3125. DOI: 10.1063/1.1728579.
4. Maxwell J.C. A Treatise on Electricity and Magnetis, Oxford, Clarendon Press., 1873, 577 p.
5. 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, pp. 23–36. DOI: 10.1016/j.ijengsci.2012.12.004.
6. Chen F., Sevostianov I., Giraud A., Grgic D. Combined effect of pores concavity and aspect ratio on the elastic properties of a porous material. International Journal of Solids and Structures, 2018, vol. 134, pp. 161–172. DOI: 10.1016/j.ijsolstr.2017.10.016.
7. Trofimov A., Abaimov S. G., Akhatov I. S., Sevostianov I. On the bounds of applicability of two-step homogenization technique for porous materials. International Journal of Engineering Science, 2018, vol. 123, pp. 117–126. DOI: 10.1016/j.ijengsci.2017.11.017.
8. Roberts A., Garboczi E. Elastic properties of model porous ceramics. Journal of the American Ceramic Society, 2000, vol. 83, No. 12, pp. 3041–3048. DOI:10.1111/J.1151-2916.2000.TB01680.X.
9. Cannillo V., Leonelli C., Manfredini T., Montorsi M., Boccaccini A. R. Computational simulations for the assessment of the mechanical properties of glass with controlled porosity. Journal of Porous Materials, 2003, vol. 10, pp. 189–200. DOI: 10.1023/A:1027490502044.
10. Sadowski T., Samborski S. Prediction of the mechanical behaviour of porous ceramics using mesomechanical modeling. Computational Materials Science, 2003, vol. 28, iss 3–4, pp. 512–517. DOI: 10.1016/j.commatsci.2003.08.008.
11. Pabst W., Gregorová E., Tichá G. Effective properties of suspensions, composites and porous materials. Journal of the European Ceramic Society, 2007, vol. 27, pp. 479–482. DOI: 10.1016/j.jeurceramsoc.2006.04.169.
12. Pabst W., Gregorová E. Young’s modulus of isotropic porous materials with spheroidal pores. Journal of the European Ceramic Society, 2014, vol. 34 (13), pp. 3195–3207. DOI: 10.1016/j.jeurceramsoc.2014.04.009.
13. Knudsen F.P. Effect of Porosity on Young's Modulus of Alumina. Journal of the European Ceramic Society, 1962, vol. 45, iss. 2, pp. 94–95. DOI: 10.1111/j.1151-2916.1962.tb11089.x.
14. 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, pp. 366–370. DOI: 10.1111/j.1151-2916.1983.tb10051.x.
15. Munro R.G. Effective Medium Theory of the Porosity Dependence of Bulk Moduli. Journal of the European Ceramic Society, 2001, vol. 84, iss. 5, pp. 1190–1192. DOI: 10.1111/j.1151-2916.2001.tb00815.x.
16. Rodrigues J.A., Ortega F.S., Paiva A.E. M., Villaboim E.L. G., Pandolfelli V.C. The relation between porosity and elastic moduli of gelcast ceramic foams. Cerâmica, 2004, vol. 50, pp. 209–216. DOI: 10.1590/S0366-69132004000300007.
17. 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, pp. 020162. DOI: 10.1063/1.5083405.
18. Morrell R. Handbook of properties of technical & engineering ceramics. Part 2. Data reviews, Section I. High-alumina ceramic, London, HMSO, 1987, 255 p.
19. Zimina V.A. Determination of the mechanical characteristics of brittle porous materials based on numerical simulation. Ph.D. thesis, Tomsk, 2021. (In Russian).
20. 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, pp. 012016. DOI: 10.1088/1742-6596/1214/1/012016.

Article reference