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To investigate aluminum (Al) segregation in industrial-scale Ti-6 wt%Al-4 wt%V (TC4) round ingots produced by electron beam cold hearth remelting (EBCHR), a three-dimensional multiphysics model verified with experimental data in the literature has been established. The numerical predictions qualitatively reveal that the Al concentration distribution in the pool is highly related to the flow pattern. A promising method to restrain Al segregation is to enhance mixing during EBCHR by increasing the casting speed. A series of numerical cases reveal the relation between the casting speed, the dimensionless measure of the stirring intensity (Peclet number, Pe ¯ ), and the corresponding segregation degree (Ф) in the pool. The results suggest that for EBCHR at a pouring temperature 2273 K, as the casting speed increases from 10 to 25 mm/min, the Pe ¯ value increases from 418 to 1820, and the corresponding Ф value increases from 0.681 to 0.871. As a consequence, the intensity of aluminum segregation on the solidified cross-section improves (decreases from 2.77 × 10−3 to 1.76 × 10−4).

Recently, uniformly valid asymptotic solutions of rod eutectic growth for liquid-solid interface slopes at triple phase junction being the normal order have been presented in reference (Li and Xu, 2017). In this work, analytical calculations of rod eutectic growth during directional solidification for liquid-solid interface of small order are performed. The purpose is to study the liquid-solid interfacial shape and average undercooling of rod eutectic growth. We give the mathematical formulation of rod eutectic growth for the general case. The steady solutions of rod eutectic growth are obtained by using asymptotic expansion method and matching method. The relationship of the overall average interfacial undercooling with the rod eutectic spacing is presented. The overall average interfacial undercooling always exists a minimum value at the minimum-undercooling spacing, and the minimum-undercooling spacing is slightly smaller than one given by Jackson and Hunt. We also analyze the effect of pulling speeds and thermal gradients on the interfacial shapes for the case of the minimum-undercooling spacing.

The application of single electron beam cold hearth melting (EBCHM) to the production of large-scale rectangular titanium ingots has the potential to produce high-quality titanium strip coils and a...

A mixed Lagrangian and Eulerian algorithm (MILE) is used to simulate the temperature field during the solidification process of the large-scale Ti-6Al-4V alloy slab ingot in electron beam cold hearth melting (EBCHM). Based on the finite element (FE) method coupled with the cellular automation (CA) model, the microstructure evolution of the ingot is obtained in this paper. The simulated results show that with the pulling speed increasing from 1 × 10 −4 m/s to 3.5 × 10 −4 m/s, the liquidus depth increases from 0.64 cm to 0.70 cm, the length of the transition region increases and the mean grain size is found to increase. With the pouring temperature increasing from 1953 K to 2013 K, the liquidus depth increases from 0.42 cm to 1.34 cm and the length of the transition region increases, whereas the depth of mushy zone decreases. The region near the bottom of the ingot has finer grains for the non-steady solidifying state of TC4 alloy. Moreover, the role of pulling speed is much greater than that of pouring temperature on the microstructure evolution during EBCHM for large-scale TC4 alloy slab ingot.

We consider system of rod eutectic growth under directional solidification for the normal amplitude of the contact angles. The objective of this work is to obtain the uniformly valid asymptotic solutions for steady growth of rod eutectics using the asymptotic expansion method. For the contact angles being the normal order, system of rod eutectic growth will exist a boundary layer at the triple phase junction. According to different length scales, we divide the whole liquid region into three subregions. Solutions in every subregion are derived by asymptotic expansion method. Finally, all the asymptotic expansion solutions are matched in the intermediate regions and the composite solutions are obtained. Results show that the average undercooling in front of both phases are not equal. The dimensional average undercooling exhibits a minimum at the critical eutectic spacing. The critical spacing of SCN-DC is predicted and it is in agreement with the small-spacing stability limit.

The purpose of this work is, based on CAFE method, to study the microstructure evolution and optimize the quality of the large-scale titanium slab ingot during EBCHM. The nucleation parameters of the microstructure simulation of titanium ingot are determined based on one of the actual experimental results. For the determined parameters, our theoretical results are agreement with other experimental results. The effects of pouring temperature and pulling speed on the microstructure are presented based on CAFE method. The quantitative analyses of the simulated results show that with the pulling speed increasing, the number of grains decreases, whereas the mean grain radius increases under identical thermal condition; with the pouring temperature increasing, the mean grain radius increases under the given pulling speed. Our results are very important to obtain the optimal structure of the ingots by controlling pulling speed and pouring temperature.

The phase field model is established for the eutectic growth system in this paper, and the finite difference method is used to solve the model. The evolution of tilted eutectic interface morphology under isothermal solidification and directional solidification conditions, respectively, was investigated. The effects of solid-solid interface anisotropy, solid-liquid interface anisotropy, eutectic spacing and pulling speed on the evolution of the tilted eutectic structure were simulated to reveal the growth mechanism of the tilted eutectic structure. It is found that under isotropic and directional solidification conditions, eutectic growth is influenced by both of the direction of heat flow and the solid-liquid interface anisotropy. When the solid-solid interface anisotropy is small, the direction of heat flow dominates the growth direction of eutectic structure, and as the solid-solid interface anisotropy increases, the growth direction of eutectic structure starts to tilt. Two kinds of instability phenomena, bifurcation or merger and fault line, are also found in the eutectic growth.

This paper focusses on the heterogeneous nucleation on the surface with the non-constant curvature. The formation of a spherical nucleus on the ellipsoid of rotation is considered. Following the classical nucleation theory, the work of formation of a critical nucleus on the ellipsoid of rotation has been given, and the effects of geometry sizes and the material properties of the ellipsoid of rotation on the work of formation of a critical nucleus have been obtained. When the geometry size of the substrate is about value of the critical nucleus radius, there may exist twice nucleation on the ellipsoid of rotation for the case of the smaller value of λ and ϕ π / 2 . As the work of formation of a nucleus has only one extremum (the maximum), the nucleation on the oblate rotational ellipsoid is more easy than on the spherical surface, while nucleation on the prolate ellipsoid of rotation is more difficult than on the spherical surface. Furthermore, if the particles of the ellipsoid are added into the parent phase as nucleation agents or catalysts, for some geometry sizes, they would not have the effects on the heterogeneous nucleation.

A numerical and experimental investigation is performed into the flow characteristics and mixing performance of three microfluidic polydimethylsiloxane blood plasma mixing devices incorporating square-wave, curved and zigzag microchannels, respectively. For each device, the plasma is introduced into the microfluidic channel under the effects of capillary action alone. Of the three devices, that with the square-wave microchannel is found to yield the best mixing performance, and is therefore selected for design optimization. Four microfluidic micromixers incorporating square-wave microchannels with different widths in the x- and y-directions are fabricated using conventional photolithography techniques. The mixing performance of the four microchannels is investigated both numerically and experimentally. The results show that given an appropriate specification of the microchannel geometry, a mixing efficiency of approximately 76 % can be obtained within 4 s. The practical feasibility of the micromixer is demonstrated by performing prothrombin time (PT) tests using a total liquid volume of 4.0 μL (2.0 μL of plasma and 2.0 μL of PT reagent). It is shown that the mean time required to complete the entire PT test (including loading, mixing and coagulation) is less than 30 s.

A cave surface for heterogeneous nucleation is always assumed as a concave spherical or conical substrate. Nucleation in such assumed geometries has been well understood. However, a cave or a groove always has some cusps and certain lateral surface curvature. These geometries of a cave will have important effects on heterogenous nucleation. Here the nucleation in a cave with iso-curvature lateral surface and one apex was investigated in the scope of classical nucleation theory. Nucleation in a cave was described by comparing with nucleation on spherical and conical substrates. Results show that when the contact angle is the acute angle, nucleation in a cave with the convex or concave lateral surface is easier than nucleation on the corresponding spherical surfaces. Furthermore, nucleation in a cave with the concave surface is the easiest and nucleation on the convex surface of a cave is the most difficult, while nucleation in a conical cavity is always in between. However, whether a nucleus is more easily formed in a cave is dependent on the sizes of the cave geometry for the contact angle being the obtuse angle. As the apex angle is close to zero, nucleation in a conical cavity is easier than in a cave with the concave surface but more difficult than in a cave with the convex surface for the contact angle being the obtuse angle. The effect degree of the surface curvature of a cave on nucleation is dependent on the apex angle and the contact angle.

The present paper investigates steady eutectic growth with the isotropic surface tension by using the analytical approach. We consider the case that Peclet number ϵ is small and the segregation coefficient κ is close to the unit, and obtain a family of the global steady state solutions with two free parameters: the Peclet number ϵ and tilt angle φ , which may describe the basic states of both tilted and non-tilted eutectic growth. It is found that due to the singularity of the triple point in the system, there is a thin boundary layer in the vicinity of the triple point, where the curvature and the temperature of interface vary drastically. The quantitative comparisons between the theoretical predictions with recent available experimental data are made with no adjustable parameter. The agreements are very good.

The present paper is concerned with the global instability mechanisms for the basic steady state of lamellar eutectic growth with curved and tilted interface affected by the triple point. We solve the related linear eigenvalue problem (EVP) by using the analytical approach for the case that the Peclet number is small and the segregation coefficient parameter κ is close to the unit. It is found that the system involves two types of global instability mechanisms: the ‘exchange of stability’ invoked by the non-oscillatory, unstable modes and the global wave instabilities invoked by four types of oscillatory unstable modes, namely (AA)-, (SS)-, (AS)- and (SA)-mode. The quantization conditions for these modes are derived, the neutral curves for these global instabilities on the parameters plane are calculated. The stability criterion yields the range of the interlamellar spacing and explains the interfacial pattern transitions observed in the experiments.

This paper deals with the problem of dendritic sidebranches in binary system. The solution of dendritic interface corresponding to a global neutral mode is given. Changing relationships of the distance from dendritic tip to sidebranch-tip, the sidebranch spacing and amplitude with undercooling and impurity concentration are presented using numerical calculation. The results show that all of the distance from dendritic tip to sidebranch-tip, the sidebranch spacing and amplitude scaled by the radius of dendritic tip decrease as undercooling increases. For the fixed undercooling, changes of the scaled distance, spacing and amplitude are more obvious in the region of the small solute concentration. However, the dependence of the scaled distance, spacing and amplitude on both of undercooling and impurity concentration is very weak. The predicted results are agreement with the experimental observation for the pure materials.

Porous preforms were fabricated by cold-pressing process using powder mixture of TiC, TiO2 and dextrin. After pyrolysis and sintering, Al melt was infiltrated into the porous preforms, leading to the formation of Ti3AlC2-Al2O3-TiAl3 composite. Effects of cold-pressing pressure of preforms on microstructures and mechanical properties of the composites were studied. Synthesis mechanism and toughening mechanism of composite were also analyzed. The results shows that TiO2 is reduced into Ti2O3 by carbon, the decomposition product of dextrin, which causes the spontaneous infiltration of Al melt into TiC/Ti2O3 preform. Then, Ti3AlC2-Al2O3-TiAl3 composite is in-situ formed from the simultaneous reaction of Al melt with TiC and Ti2O3. With the increase of cold-pressing pressure from 10 MPa to 40 MPa, the pore size distribution of the preforms becomes increasingly uniform after pre-sintering, which results in the reduction of defects, and the decrease of property discrepancy of composites. Nano-laminated Ti3AlC2 grains and Al2O3 particles make the fracture toughness of TiAl3 increase remarkably by various toughening mechanisms including stress-induced microcrack, crack deflection and crack bridging.