By Jerzy Sobczak; Ludmil Drenchev
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Additional info for Metal based functionally graded materials : engineering and modeling
In the applications discussed below these partially differential equations are solved numerically. The method of lines, which transforms the partial differential equations into a large system of ordinary differential equations, is applied. To find a solution of the obtained system of ordinary differential equation a standard software implementation of Adam’s method is used. A variety of numerical simulations, which show the model features and explain many particular usual and unusual MMC structures obtained by centrifugal casting of Cu alloy/graphite, Al alloy/graphite and Al alloy/SiCP composites, are commented on in [9,10].
A2) as functions of time in the case Vf(0) = 25%. 6 4 2 0 0 10 20 time, s 30 40 0 50 100 150 200 time, s Dynamics of SiC volume fraction at H = 110 mm. % Fig. A4. Dynamics of SiC volume fraction at H = 92 mm. % 20 12 10 8 Vol. % SiC Vol. % SiC 4 2 0 Fig. A3. 6 6 4 2 0 15 10 5 0 0 100 200 300 400 time, s Fig. A5. Dynamics of SiC volume fraction at H = 73 mm. % 0 20 40 60 80 time, s Fig. A6. Dynamics of SiC volume fraction at H = 110 mm. % The curves in all the figures shown the dynamics of particle concentration Vf have a 30 Metal Based Functionally Graded Materials Sobczak and Drenchev relatively slow decrease in Vf, but not as sharp as could be expected.
05 and = 0. In order to find more adequate expression of the adapted viscosity, the coefficients , and in the function V were determined using the experimental results, described above. More details about the procedure can be found in . Taking into account the experimental results in Fig. e. 465. 5V f2 + 170V f3 (A8) This formula is used in calculation of the thickness of the particle free zone as function of time in the experiments above. The same calculations are repeated applying formula (A6) and the results are compared in Table A1.