Issue 24

Ig. S. Konovalenko et alii, Frattura ed Integrità Strutturale, 24 (2013) 75-80; DOI: 10.3221/IGF-ESIS.24.07 80 In the case of quasi-ductile fracture (Fig. 3, a) damage generation and crack growth occurred locally, in several regions of the sample, characterized by the highest value of local porosity (and the least thickness of web between isolated pores). Until a certain moment, some cracks were not merged into main crack, the stage of its growth were somehow elongated. It led to extensive local cracking of the material without losing the integrity of the sample and, consequently, to a substantial dissipation of elastic energy and decreasing of the effective elastic properties of the material (of the whole specimen). Thus, the second criterion of the constructed model verification is fulfilled. To verify the third criterion of the model verification the average value of the effective elastic modulus (<E eff >) and maximum specific resistance force to loading under uniaxial compression were calculated. Then they were compared with the corresponding values found from real experiments. It was shown that the deviation of <σ s_eff > and <E eff > for the model samples from the experimental data did not exceed 30 % and 12 %, respectively. It is a rather good accuracy for simulating highly porous media in plane approximation. This indicates to a good quantitative agreement of the calculations and the experiment and means that the third criterion of the model verification is fulfilled. Thus, a two-scale model of porous ceramics with bimodal pore size distribution function was constructed herein based on a multiscale approach to numerical simulation and validated against available experimental data. C ONCLUSIONS multiscale approach to numerical simulation of porous materials is developed on the basis of movable cellular automaton method. The hierarchical two-scale model constructed using the proposed approach can adequately describe deformation and fracture of the porous zirconia ceramics under mechanical loading. Since the proposed approach is sufficiently general, then, if it is necessary, a heterogeneous material containing more than two structural scales can be also simulated on the basis of this approach. A CKNOWLEDGEMENTS his study was supported by the Russian Foundation for Basic Research, project No. 12-08-00379-а. R EFERENCES [1] Global Roadmap for Ceramics: Proceedings of 2nd International congress on ceramics (ICC2). Alida Belosi and Gian Nicola Babini (Eds.). Institute of Science and Technology for Ceramics, National Research Council, Verona (Italy), (2008). [2] S.P. Buyakova, Han Wei, Li Dunmy et al., Tech. Phys. Lett., 25(9) (1999) 695. [3] S.N. Kulkov, S.P. Buyakova, V.I. Maslovskii, Vestnik TGU, 13 (2003) 34 [in Russian] [4] Ig.S. Konovalenko, A.Yu. Smolin, S.G. Psakhie, Phys. Mesomech., 13(1–2) (2010) 47. [5] S. Psakhie, E. Shilko, A. Smolin, S. Astafurov, V. Ovcharenko, Frattura ed Integrità Strutturale, 24 (2013) 26. [6] Ig.S. Konovalenko, A.Yu. Smolin, In: Proc. of the XXXVI Summer School “Advanced problems in mechanics (APM’ 2008)” D. A. Indeitsev, A. M. Krivtsov (Eds.), Institute for problems in mechanical engineering, St. Petersburg, (2008) 352. [7] A.Yu. Smolin, Ig.S. Konovalenko, S.N. Kul’kov, S.G. Psakhie, Tech. Phys. Lett., 32(9) (2006) 738. [8] A.Yu. Smolin, Ig.S. Konovalenko, S.N. Kulkov, S.G. Psakhie, Izv. vuzov Fizika, 49(3) (2006) 70 [in Russian]. [9] Ig.S. Konovalenko, Theoretical Study of Deformation and Fracture of Porous Materials for Medicine and Biomechanical Structures, Cand. Degree Thesis (Phys&Math), IFPM SO RAN, Tomsk, (2007) [in Russian]. [10] L.M. Kachanov, The Foundations of Fracture Mechanics, Nauka, Moscow, (1974) [in Russian] [11] L.I. Sedov, A Course in Continuum Mechanics, Wolters-Noordhoff, Groningen, (1971). A T