The paper presents applications of a new theory of the representative volume element (RVE) based on the MityushevEisenstein-Rayleigh sums (M-sums) to describe particle-reinforced composites. This theory is applied to study F3K.10S metal matrix composites reinforced SiC particles. The most important M-sum e 2 is calculated for the initial state as e 2 = -0.00206281. This shows considerable heterogeneity of distribution of reinforcing particles and its anisotropic properties. Further, the results are compared with the results obtained by the FSP. It is established that the use of a single FSP process causes a significant change in the distribution of particles reinforcing phase when the value e 2 becomes 3.19488. It follows from Mityushev's theory that e 2= π corresponds to isotropic distributions. The article confirms that the new RVE theory resolves the problem of the constructive pure geometrical description of the properties of composites. Further work requires the optimization and extension of the theory to three-dimensional models.Keywords: Representative volume element, Mityushev-Eisenstein-Rayleigh sums, Metal Matrix Composites W artykule przedstawiono nową teorię RVE bazującą sumach Mityushev-Eisenstein-Rayleigh (M-sums) oraz ich wykorzystanie do opisu niektórych właściwości kompozytów wzmacnianych cząstkami. Praktyczne zastosowanie prezentowanej teorii pokazano na przykładzie kompozytu na osnowie metalowej wzmacnianego cząstkami SiC (F3K.10S). Bazując na analizowanych mikrostrukturach kompozytu, obliczono wartości sum Mityushev-Eisenstein-Rayleigh'a dla stanu wyjściowego, otrzymując wartość sumy e 2 równą -0.00206281, co świadczy o dużej niejednorodności rozmieszczenia cząstek fazy wzmacniającej. Otrzymane wyniki porównano z danymi obliczonymi dla kompozytu po obróbce friction stir processing (FSP). Zaobserwowano istotny wpływ zastosowanego procesu na zmianę dystrybucji cząstek fazy wzmacniającej, co potwierdzono obliczeniowo, uzyskując wartość sumy Mityushev-Eisenstein-Rayleigh'a e 2 równą 3,19488. Obserwowana tendencja zmierzania wartości sumy Mityushev-Eisenstein-Rayleigh'a e 2 do liczby π świadczy o znacznej poprawie dystrybucji cząstek fazy wzmacniającej po procesie FSP.W pracy pokazano, że nowa teoria RVE bazująca na sumach Mityushev-Eisenstein-Rayleigh 'a pozwala na określanie wybranych właściwości kompozytów na podstawie czysto geometrycznych czynników. Stwierdzono jednak, że konieczne są dalsze prace nad optymalizacją i rozszerzeniem teorii w celu pełnego trójwymiarowego analizowania struktur kompozytowych.
In order to increase wear resistance cast steel casting the TiC-Fe-Cr type composite zones were fabricated. These zones were obtained by means of in situ synthesis of substrates of the reaction TiC with a moderator of a chemical composition of white cast iron with nickel of the Ni-Hard type 4. The synthesis was carried out directly in the mould cavity. The moderator was applied to control the reactive infiltration occurring during the TiC synthesis. The microstructure of composite zones was investigated by electron scanning microscopy, using the backscattered electron mode. The structure of composite zones was verified by the X-ray diffraction method. The hardness of composite zones, cast steel base alloy and the reference samples such as white chromium cast iron with 14 % Cr and 20 % Cr, manganese cast steel 18 % Mn was measured by Vickers test. The wear resistance of the composite zone and the reference samples examined by ballon-disc wear test. Dimensionally stable composite zones were obtained containing submicron sizes TiC particles uniformly distributed in the matrix. The macro and microstructure of the composite zone ensured three times hardness increase in comparison to the cast steel base alloy and one and a half times increase in comparison to the white chromium cast iron 20 % Cr. Finally ball-on-disc wear rate of the composite zone was five times lower than chromium white cast iron containing 20 % Cr.
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