Obrabotka Metallov 2014 No. 4

ОБРАБОТКА МЕТАЛЛОВ № 4 (65) 2014 83 ТРУДЫ КОНФЕРЕНЦИИ OBRABOTKAMETALLOV (METAL WORKING AND MATERIAL SCIENCE) N 4(65), October – December 2014, Pages 78–84 Influence of range of compositions elements characteristics on the effective thermal expansion coefficients for microheterogeneous materials Reznikov B.S. , D.Sc. (Engineering), Professor, e-mail: reznikov@corp.nstu.ru Gobysh A.V. , Ph.D. (Physics and Mathematics), e-mail: agobysh@mail.ru Novosibirsk State Technical University, 20 Prospect K. Marksa, Novosibirsk, 630073, Russian Federation Abstract The approach for the numerical analysis of the averaged thermal expansion coefficients of multiphase composites based on the method of statistical testing is proposed. This approach allows to take into account the stochastic nature of the composite. The influence of the variation of physical and mathematical characteristics of the substructural elements: Young modulus, Poisson ratios and linear thermal expansion coefficients is investigated. The mathematical model of the composite is based on the principle of effective homogeneity, structural analysis and correctly formulated interference conditions (for deformation, stress and temperature) at the interphase boundary. The numerical results are presented for the effective coefficients of linear thermal expansion of the composite for various structures of three- phase environments. The confidence intervals with given confidence probability for various structures are found. The influence of the stochastic nature of various characteristics of substructural elements on mathematical expectation of thermal expansion coefficients of the composite is estimated. Keywords: structure-heterogeneous mediums, stochastic nature of composite, Monte-Carlo technique, effective coefficients, thermal expansion, statistical characteristics, confidence interval. References 1. Reznikov B.S., Nikitenko A.F., Kucherenko I.V. Prognozirovanie makroskopicheskikh svoistv strukturno- neodnorodnykh sred. Soobshchenie 1 [Determination Technique of Macroscopic Properties of Structurally Nonhomogeneous Environments. Information 1]. Izvestiya vysshikh uchebnykh zavedenii. Stroitel'stvo – News of higher educational institutions. Construction , 2008, no. 2, pp. 10–17. 2. Reznikov B.S., Gobysh A.V. Raschet effektivnykh koeffitsientov teplovogo rasshireniya mikroneodnorodnykh kompozitov [Calculation of the effective thermal expansion coefficients for microheterogeneous composites]. Doklady Akademii nauk vysshei shkoly Rossiiskoi Federatsii – Proceedings of the Russian Higher School Academy of Sciences , 2013, no. 2 (21), pp. 139–149. 3. Reznikov B.S., GobyshA.V. [Prediction of the structure of multi-phase composites dimensionally at temperature influence]. Doklady 3 Vserossiiskoi konferentsii “Problemy optimal'nogo proektirovaniya sooruzhenii” [Reports of the 3rd All-Russian conference "Problems of optimal design of structures"]. Novosibirsk, NGASU Publ., 2014, pp. 345–352. 4. Buslenko N.P., Golenko D.I., Sobol' I.M., Sragovich V.G., Shreider Yu.A. Metod statisticheskikh ispytanii (metod Monte-Karlo) [Method of statistical tests (Monte Carlo method)]. Moscow, Fizmatgiz Publ., 1962. 332 p. 5. Reznikov B.S. [Prediction of fracture annular plates with the real structure and the stochastic nature of fiber reinforced materials]. Mezhvuzovskii sbornik nauchnykh trudov “Kraevye zadachi i ikh prilozheniya” [Interuniversity collected articles “Boundary value problems and their applications”], 1989, pp. 89–99. 6. Reznikov B.S. Raschet na prochnost’ konstruktsii iz armirovannykh materialov metodom Monte-Karlo [Calculation of the strength of structures of reinforcedmaterials by theMonte Carlomethod]. Mekhanika kompozitnykh materialov – Mechanics of Composite Materials , 1986, no. 6, pp. 1059–1063. (In Russian) 7. Venttsel’ E.S. Teoriya veroyatnostei [Probability theory]. 3 rd ed. Moscow, Nauka Publ., 1964. 576 p. 8. Ivanova V.M., Kalinina V.N., Neshumova L.A., Reshetnikova I.O. Matematicheskaya statistika [Mathematical Statistics]. 2 nd ed. Moscow, Vysshaya shkola Publ., 1981. 371 p.