Mathematical modeling of bulk and directional crystallization with the moving phase transition layer

This paper is devoted to the mathematical modeling of a combined effect of directional and bulk crystallization in a phase transition layer with allowance for nucleation and evolution of newly born particles. We consider two models with and without fluctuations in crystal growth velocities, which are analytically solved using the saddle-point technique. The particle-size distribution function, solid-phase fraction in a supercooled two-phase layer, its thickness and permeability, solidification velocity, and desupercooling kinetics are defined. This solution enables us to characterize the mushy layer composition. We show that the region adjacent to the liquid phase is almost free of crystals and has a constant temperature gradient. Crystals undergo intense growth leading to fast mushy layer desupercooling in the middle of a two-phase region. The mushy region adjacent to the solid material is filled with the growing solid phase structures and is almost desupercooled.

Local solidification thermal parameters affecting the eutectic extent in Sn-Cu and Sn-Bi solder alloys

Purpose Overall, selection maps about the extent of the eutectic growth projects the solidification velocities leading to given microstructures. This is because of limitations of most of the set of results when obtained for single thermal gradients within the experimental spectrum. In these cases, associations only with the solidification velocity could give the false impression that reaching a given velocity would be enough to reproduce a result. However, that velocity must necessarily be accompanied by a specific thermal gradient during transient solidification. Therefore, the purpose of this paper is to not only project velocity but also include the gradients acting for each velocity. Design/methodology/approach Compilation of solidification velocity, v, thermal gradient, G, and cooling rate, Ṫ, data for Sn-Cu and Sn-Bi solder alloys of interest is presented. These data are placed in the form of coupled growth zones according to the correlated microstructures in the literature. In addition, results generated in this work for Sn-(0.5, 0.7, 2.0, 2.8)% Cu and Sn-(34, 52, 58)% Bi alloys solidified under non-stationary conditions are added. Findings When analyzing the cooling rate (Ṫ = G.v) and velocity separately, in or around the eutectic composition, a consensus cannot be reached on the resulting microstructure. The (v vs. G) + cooling rate diagrams allow comprehensive analyzes of the combined v and G effects on the subsequent microstructure of the Sn-Cu and Sn-Bi alloys. Originality/value The present paper is devoted to the establishment of (v vs. G) + cooling rate diagrams. These plots may allow comprehensive analyses of the combined v and G effects on the subsequent microstructure of the Sn-Cu and Sn-Bi alloys. This microstructure-processing mapping approach is promising to predict phase competition and resulting microstructures in soldering of Sn-Cu and Sn-Bi alloys. These two classes of alloys are of interest to the soldering industry, whereas manipulation of their microstructures is considered of utmost importance for the metallurgical quality of the product.

Grain Refinement and Solidification Velocity of Supercooled Melts

Using a high speed thermal imaging camera, solidification velocity of undercooling is accurately determined for a highly undercooled Ni70Cu30 binary concentrated single phase alloy. It is observed that the velocity of solidification is first continuously and smoothly increasing at the low and mediate undercoolings then increasing discontinuously to a maximum value at the high undercooling range. Thus, the solidifcation velocity-undercooling relation has an abrupt discontinuity, which is caused by nonequilibrium diffusion of solutes in the liquid side near the advancing solid liquid interface. Grain refinement of high undercooling is directly induced by recrystallization, which was in clear contrast with the remelting induced dendrite fragmentation in conventional alloys.

Localized Strain Analysis of Ce- and Mg-Treated Cast Iron under Uniaxial Compression

Cast iron exhibits a wide range of mechanical properties, depending on its microstructural features. The microstructure of cast iron consists of several microconstituents with different elastic-plastic behavior, making the strain non-uniform across the bulk material. To understand the individual effects of these microconstituents on the overall mechanical behavior, local strain analysis using digital image correlation analysis was carried out. Samples with two different compositions (varying cerium, magnesium and silicon) were processed at different solidification velocities in a Bridgman furnace. Sections of the directionally solidified samples were loaded under uniaxial compression to measure global and local strain behavior. Despite the variability of the microstructure, the stress–strain curves obtained by digital image correlation (DIC) were found to react in a well-controlled way to changes in solidification velocity. It was observed that high-strain failure (greater than 15%) was accompanied by local straining of the softer ferritic phase, but during low-strain failure, local straining was not prominent. Higher nodularities, due to higher solidification velocities, raised the compressive strength without affecting the toughness significantly. Higher percentages of carbides led to higher compressive strengths with corresponding losses in ductility. The continuity of the matrix was also found to play an important role in the behavior during compression.

Pore Architectures and Mechanical Properties of Porous α-SiAlON Ceramics Fabricated via Unidirectional Freeze Casting Based on Camphene-Templating

Porous α-SiAlON ceramics were fabricated using the camphene-based unidirectional freeze casting method, in which a gradient porous structure was formed as a result of the decreased solidification velocity in the freezing direction. Microstructure, porosity and pore size distribution of different parts of as-prepared samples were examined and compared, and correlated with their mechanical properties. For a given solid loading, the overall pore size and porosity of the top part were greater than those of the bottom part. Interestingly, despite its higher porosity, the flexural strength and fracture toughness of the top part were both higher than those of the bottom part, suggesting that apart from porosity, pore morphology and size affected mechanical properties of as-prepared porous α-SiAlON ceramics.

Development of an Anti-Trapping Current for Phase Field Models Using Arbitrary CALPHAD Thermodynamics

Unless corrected by so called anti-trapping currents, phase field models of solidification display a dependence upon the diffuse interface width, δ, used in the simulation. This is most commonly manifest as a reduction in solute partitioning, which is both growth velocity and interface width dependent, resulting in a serious impediment to quantitative simulation. However, such anti-trapping currents are often restricted to very simple materials thermodynamics, appropriate only to dilute ideal solutions. Here we propose a form of the anti-trapping current which can be implemented for arbitrary thermodynamics, including both Redlich-Kister solution phases and sub-lattice models for intermetallic growth. The effect of the new anti-trapping current is illustrated with respect to Pb dendrites growing from a Pb-Sn melt containing either 25% or 30% Sn. The new anti-trapping current is shown to render the solutions independent of the diffuse interface width both with regard to solute partitioning and other growth metrics such as solidification velocity and dendrite tip radius.

Fabrication, Properties and Applications of Porous Metals with Directional Pores

Porous metals with long cylindrical pores aligned in one direction are fabricated by unidirectional solidification through pressurized gas method (PGM) and thermal decomposition method of gas compounds (TDM). The pores are evolved from insoluble gas when the molten metal dissolving the gas is solidified in the dissolving gas (PGM) or inert gas (TDM). Three fabrication techniques, mold casting, continuous zone melting and continuous casting techniques, are adopted. The latter two techniques can control the solidification velocity and the last one possesses a merit for mass production of lotus metals. The porosity, pore diameter and its length are able to be controlled by the solidification velocity and ambient gas pressure, while the pore direction can be controlled by the solidification direction. Anisotropy in the elastic and mechanical properties is resulted from anisotropic pore morphology. The anisotropic behaviors of tensile, compressive and fatigue strength are explained in terms of the dependence of stress concentration on the pore orientation. The anisotropic properties of thermal, electrical conduction and magnetization are also found, which are attributed to the scattering of heat flux, electric current and magnetic flux with anisotropic pores, respectively. Several applications of the porous metals to manufacturing products are investigated. The unidirectional pores can be utilized for high performance of heat sinks for electronic devices of cars and computers. Thus, the porous metals are expected to be used for various manufacturing products.