From digital image of microstructure to the size of representative volume element: B4C/Al composite

• Autorzy: Różański, A. , Łydżba, D.
• Języki publikacji: EN

Abstrakty

EN

In the field of micromechanics, the notion of representative volume element (RVE) and its quantitative definition are of the paramount importance. The definitions of RVE, used by scientists for different purposes, are mathematically strict but do not quantify its size. Furthermore, all the methods of RVE size determination (available in a voluminous literature) require a large number of numerical calculations like, for instance, those of finite element or other numerical techniques. In this paper, it is shown that the size of RVE can be evaluated based only on the morphology of microstructure that is involved in the statistical microstructure descriptor, namely the two-point correlation function. A methodology is applied to the digital image of the reconstructed 2D realization of the boron-carbide/aluminum (B4C/Al) composite. The condition for the minimum size of RVE used in the numerical procedure has been formulated in previous work of authors. The size of RVE is determined for different values of estimation error and the contrast in phase properties. The method is verified by performing numerical calculations of effective thermal conductivity coefficient.

Słowa kluczowe

PL

reprezentatywna elementarna objętość (RVE); węglik boru/aluminium; kompozyt B4C/Al

EN

representative volume element; RVE; boron carbide/aluminum composit

• Czasopismo: Studia Geotechnica et Mechanica
• Rocznik: 2011
• Tom: Vol. 33, nr 1
• Strony: 55-68
• Opis fizyczny: Bibliogr. 22 poz.

Twórcy

autor

Różański, A.

autor

Łydżba, D.

• Institute of Geotechnics and Hydrotechnics, Wrocław University of Technology, Wybrzeże Wyspiańskiego 27, 50-370 Wrocław,

Bibliografia

• [1] DU X., OSTOJA-STARZEWSKI M., On the size of representative volume element for Darcy law in random media, Proc. R. Soc. London A, 2006, Vol. 462, 2949–2963.
• [2] FELLER W., An Introduction to Probability Theory and its Applications, Vol. I, 2nd Edition, John Wiley and Sons, N.Y., 1961.
• [3] GITMAN I.M., ASKES H., SLUYS L.J., Representative volume: existence and size determination, Engineering Fracture Mechanics, 2007, Vol. 74, 2518–2534.
• [4] GRAHAM S., YANG N., Representative volumes of materials based on microstructural statistics, Scripta Materialia, 2003, Vol. 48, 269–274.
• [5] GRUFMAN C., FERNAND E., Determining a representative volume element capturing the morphology of fibre reinforced polymer composites, Compos. Sci. Technol., 2007, Vol. 67, 766–775.
• [6] GUSEV A., Representative volume element size for elastic composites: a numerical study, J. Mech. Phys. Solids., 1997, Vol. 45, 1449–1459.
• [7] JANKE W., Pseudo random number: generation and quality checks, Lecture Notes John von Neumann Institute for Computing, 2002, Vol. 10, 447.
• [8] JIAO Y., STILLINGER F.H., TORQUATO S., Modeling heterogeneous material via two-point correlation functions. II. Algorithmic details and applications, Phys. Rev. E, 2008, Vol. 77(3).
• [9] KANIT T., FOREST S., GALLIET I., MOUNOURY V., JEULIN D., Determination of the size of the representative volume element for random composites: statistical and numerical approach, Int. J. Solids. Struct., 2003, Vol. 40, 3647.
• [10] KANIT T., N’GUYEN F., FOREST S., JEULIN D., REED M., SINGLETON S., Apparent and effective physical properties of heterogeneous materials: representativity of samples of two materials from food industry, Comput. Methods Appl. Mech. Engrg., 2006, 195 (33–36), 3960–3982.
• [11] KIRKPATRICK S., GELATT C.D., VECCHI M.P., Optimization by simulated annealing, Science, 1983, Vol. 220, 671–680.
• [12] LANTUÉJOUL C., Geostatistical Simulation Models and Algorithms, Springer, Berlin, 2002.
• [13] POVIRK G.L., Incorporation of microstructural information into model of two-phase materials, Acta Metal. Mater., 1995, Vol. 43 (8), 3199–3206.
• [14] RÓŻAŃSKI A., Random composites: representativity, minimum RVE size, effective transport properties, PhD dissertation, Universite Lille 1, LML (UMR CNRS 8107), No. 40444, 2010.
• [15] RÓŻAŃSKI A., ŁYDŻBA D., SHAO J.F., Numerical determination of minimum size of RVE for random composite materials: two-point probability approach, Proceedings of the First International Symposium on Computational Geomechanics, COMGEO I, Juan les Pins, 2009.
• [16] RÓŻAŃSKI A., ŁYDŻBA D., SOBÓTKA M., Numerical determination of effective transport properties on the basis of microstructure digital images, Górnictwo i Geoinżynieria, 2010, Vol. 34 (2), 537– 552 (in Polish).
• [17] STROEVEN M., ASKES H., SLUYS L.J., Numerical determination of representative volumes for granular materials, Comput. Methods Appl. Mech. Engrg., 2004, Vol. 193, 3221–3238.
• [18] THOMAS M., BOYARD N., PEREZ L., JARNY Y., DELAUNAY D., Representative volume element of anisotropic unidirectional carbon-epoxy composite with high-fibre volume fraction, Compos. Sci. Technol., 2008, Vol. 68, 3184.
• [19] TORQUATO S., Random Heterogeneous Materials. Microstructure and Macroscopic Properties, Springer-Verlag, New York, 2002.
• [20] YEONG C.L.Y., TORQUATO S., Reconstructing random media, Phys. Rev. E, 1998, Vol. 57, 495.
• [21] YEONG C.L.Y., TORQUATO S., Reconstructing random media. II. Three-dimensional media from two-dimensional cuts, Phys. Rev. E, 1998, Vol. 58, 224.
• [22] ZEMAN J., SEJNOHA M., Numerical evaluation of effective elastic properties of graphite fiber tow impregnated by polymer matrix, J. Mech. Phys. Solids., 2001, Vol. 49, 69.