| A numerical investigation of the solidification of a binary alloy (Al-1.0wt.% Cu) around cylindrical fibers with different fiber layouts and physical properties was undertaken to gain insight into the processing of fiber-reinforced metal matrix composites (MMCs). The focus of this study was on mass transfer aspects of the solidification process and a solution of the concentration field within the domain. The cavity boundaries were such that two walls were thermally insulating and the third was set at a constant temperature while the fourth was maintained at a controlled time-dependent temperature to initiate and control the advancement of the solidification front. To treat the phase change in the alloy, a modified version of the temperature-transforming formulation that accounts for the fibrous phase was implemented for the energy equation; the species equation for the solidifying alloy was also solved. A source term that accounts for the solute rejection at the interface was incorporated into the solute concentration equation. The equations were discretized forward in time, with solutions being obtained using the iterative Gauss-Seidel with Successive Over Relaxation scheme both for the energy and species equations.; Detailed results were obtained from the numerical simulations of low-conductivity (alumina) and high-conductivity (copper) fibers in inline and staggered configurations. Effects of fiber pitch (longitudinal spacing) and transverse spacing were investigated. Higher concentrations of solute were seen to accumulate around copper fibers than for alumina fibers. With an initial, uniform concentration of 1.0wt.% Cu in the melt, the maximum-recorded solute concentration in the domain for alumina fibers was 1.26% while that for copper fibers was 3.11%. For inline fibers, increasing the fiber pitch beyond a critical value S c did not change the overall shape of the local solute distribution around the fibers. The critical pitch for alumina fibers was found to be roughly 2.5 fiber diameters while that for copper was 2 fiber diameters. These critical spacings based on solute concentration patterns agree with previously published conclusions based on thermal considerations. In a staggered arrangement of fibers, isolated patches of high concentration (C ≥ 0.80%) in the shapes of “butterflies” were found around copper fibers, while these bands manifested themselves in the form of “bow ties” for alumina fibers.; This study represents a major advance in the understanding of diffusion-dominated solute build up around fibers in metal matrix composites. Even though some simplifying assumptions have been made in the simulations, the results obtained should help improve MMC processing techniques. |
