Solidification Growth Rate Research Articles

Dimensionless numbers in additive manufacturing

The effects of many process variables and alloy properties on the structure and properties of additively manufactured parts are examined using four dimensionless numbers. The structure and properties of components made from 316 Stainless steel, Ti-6Al-4V, and Inconel 718 powders for various dimensionless heat inputs, Peclet numbers, Marangoni numbers, and Fourier numbers are studied. Temperature fields, cooling rates, solidification parameters, lack of fusion defects, and thermal strains are examined using a well-tested three-dimensional transient heat transfer and fluid flow model. The results show that lack of fusion defects in the fabricated parts can be minimized by strengthening interlayer bonding using high values of dimensionless heat input. The formation of harmful intermetallics such as laves phases in Inconel 718 can be suppressed using low heat input that results in a small molten pool, a steep temperature gradient, and a fast cooling rate. Improved interlayer bonding can be achieved at high Marangoni numbers, which results in vigorous circulation of liquid metal, larger pool dimensions, and greater depth of penetration. A high Fourier number ensures rapid cooling, low thermal distortion, and a high ratio of temperature gradient to the solidification growth rate with a greater tendency of plane front solidification.

Numerical simulation of thermal behavior and multicomponent mass transfer in direct laser deposition of Co-base alloy on steel

During direct laser deposition process, rapid melting–solidification and addition of multicomponent powder lead to complex transport phenomena in the melt pool. The thermal behavior and mass transport significantly affect the solidified microstructure and properties of fabricated layer. In this paper, an improved 3D numerical model is proposed to simulate the heat transfer, fluid flow, solidification and multicomponent mass transport in direct laser deposition of Co-base alloy on steel. The solidification characteristics, including temperature gradient (G), solidification growth rate (R) and cooing rate (G×R), can be obtained by transient thermal distribution to predict the morphology and scale of the solidification microstructure. Multicomponent transport equation based on a mixture-averaged approach is combined with other conservation equations. The calculated melt pool geometry and the composition profiles of iron (Fe), carbon (C), cobalt (Co) and chromium (Cr) are compared with the experimental results. The results show that in the initial stage of direct laser deposition, the rapidly mixture of substrate material and added material occur in the melt pool and conduct plays an important role in heat transfer due to the low Peclet number. As the melt pool is developed, the heat and mass transfer in the melt pool are dominated by strong Marangoni convection. An unmixed zone is observed near the bottom of melt pool where the convection is frictionally dissipated due to the presence of solidified dendrites. Since the G/R decreases and G×R increases from the bottom to the top of the solidified track, the morphology of the microstructure changes from planar front to columnar dendrites to equiaxed dendrites and the grain size decreases.

Existence of Universal Phase Diagrams for Describing General Pore Shape Resulting From an Entrapped Bubble During Solidification

This study shows that there exist a pair of universal and unique phase diagrams to describe general development of the pore shape in solid, resulting from a bubble captured by a solidification front. Like thermodynamics, phase diagrams have advantages to generally identify the states and design processes of a system. Pore formation and its shape in solids influence not only microstructure of materials but also contemporary issues of biology, engineering, foods, geophysics, and climate change, etc. In this study, a pair of phase diagrams is thus found to be under dimensionless coordinate systems of dimensionless apex radius, contact angle, and base radius of the bubble cap, as well as solidification rate, contact angle, and growth rate of base radius. The computed results of the development of the pore shape agree with experimental data. The pore shape in solid thus can be optimistically predicted and controlled by choosing a desired path on phase diagrams.

Thermal Parameters and Microstructural Development in Directionally Solidified Zn-Rich Zn-Mg Alloys

Transient directional solidification experiments have been carried out with Zn-Mg hypoeutectic alloys under an extensive range of cooling rates with a view to analyzing the evolution of microstructure. It is shown that the microstructure is formed by a Zn-rich matrix of different morphologies and competitive eutectic mixtures (Zn-Zn11Mg2 and Zn-Zn2Mg). For 0.3 wt-pct Mg and 0.5 wt-pct Mg alloys, the Zn-rich matrix is shown to be characterized by high-cooling rates plate-like cells (cooling rates >9.5 and 24 K/s, respectively), followed by a granular–dendritic morphological transition for lower cooling rates. In contrast, a directionally solidified Zn1.2 wt-pct Mg alloy casting is shown to have the Zn-rich matrix formed only by dendritic equiaxed grains. Experimental growth laws are proposed relating the plate-like cellular interphase, the secondary dendritic arm spacing, and the eutectic interphase spacings to solidification thermal parameters, i.e., cooling rate and growth rate. The experimental law for the growth of secondary dendritic spacings under unsteady-state solidifications is also shown to encompass results of hypoeutectic Zn-Mg alloys subjected to steady-state Bridgman growth.

Numerical investigations of drop solidification on a cold plate in the presence of volume change

We present a front-tracking/finite difference method for simulation of drop solidification on a cold plate. The problem includes temporal evolution of three interfaces, i.e. solid–liquid, solid–gas, and liquid–gas, that are explicitly tracked under the assumption of axisymmetry. Method validation is carried out by comparing computational results with exact solutions for a two-dimensional Stefan problem, and with related experiments. We then use the method to investigate a drop solidifying on a cold plate in which there exists volume change due to density difference between the solid and liquid phases. Numerical results show that the shape of the solidified drop is profoundly different from the initial liquid one due to the effects of volume change and the tri-junction in terms of growth angles ϕgr on the solidification process. A decrease in the density ratio of solid to liquid ρsl or an increase in the growth angle results in an increase in the height of the solidified drop. The solidification process is also affected by the Stefan number St, the Bond number Bo, the Prandtl number Pr, the Weber number We, the ratios of the thermal properties of the solid to liquid phases ksl and Cpsl. Increasing St, Bo, Pr, We, or ksl decreases the solidified drop height and the time to complete solidification. Moreover, the solidification growth rate is strongly affected by St, ksl and Cpsl. An increase in any of these parameters hastens the growth rate of the solidification interface. Contrarily, increasing ρsl decreases the growth rate. However, other parameters such as ϕgr, Bo, Pr and We have minor effects on the solidification growth rate.

Understanding grain refinement in aluminium welding

Grain refinement is an important opportunity to improve mechanical properties of fusion welds and the weldability (susceptibility to solidification cracking) of the base metal. In this study, grain refinement was achieved in aluminium welds through additions of grain refiner to the weld metal. Increasing grain refiner additions led to a decrease of the weld metal mean grain size (down to −86 %). The grain refinement efficiency was the highest in commercial pure Al (Alloy 1050A, Al 99.5), followed by Alloy 6082 (Al Si1MgMn) and Alloy 5083 (Al Mg4.5Mn0.7). To investigate this clear influence of alloy content on grain size, the undercooling parameters P and Q were calculated. Temperature measurements revealed that solidification parameters such as solidification growth rate or cooling rate vary significantly along the solidification front, dependent upon torch speed and alloy. On the basis of this comparison, an analytical approach was used to model the columnar to equiaxed transition (CET). Moreover, wavelength dispersive X-ray spectroscopy (WDS) and transmission electron microscopy (TEM) analyses revealed particles rich in Ti and B that are probably TiB2 particles coated by Al3Ti nucleating Al grains during solidification. Also, Ti/B contents needed in commercial filler wires to allow optimum weld metal grain refinement were calculated dependent upon base alloy and welding process.

Remelting and interface dynamics during solidification of a eutectic solution in a top-cooled rectangular cavity: A numerical study

The present work is a numerical investigation on the occurrence of remelting phenomenon during solidification of a eutectic aqueous ammonium chloride solution in a top-cooled rectangular cavity. The analysis is performed following a fixed-grid single-domain approach. Accordingly, the solidification process is represented by a set of mass, momentum and energy conservation equations, where the enthalpy update scheme is used to trace the solid–liquid interface during solidification. The set of governing differential equations is solved using semi-implicit finite volume method, based on SIMPLER algorithm, applying line-by-line TDMA solver. The present simulation predicts the distribution of temperature and streamline along with fraction of solid in the computational domain, and evolution of the solidified layer during solidification. The simulation shows remelting of solidified layer at the solid–liquid interface during later stages of solidification due to irregular superheat of the bulk solution convected towards the solid–liquid interface. Hence, the occurrence of the remelting phenomenon during solidification is studied by evaluating the interface growth history as a function of the process parameters, namely, cavity height and thermal gradient imposed across the cavity. It is found that there is a small increase in the solidification growth rate with increase in cavity height, where the possibility of remelting is high. With the increase in imposed thermal gradient, the solidification growth rate increases significantly and the occurrence of remelting disappears.

Effects of CNTs on microstructure and hardness of laser welds of the CNT-reinforced magnesium composite

A magnesium composite reinforced with 1.3wt.% multiwall carbon nanotubes (MWCNTs) was welded using a CO2 laser. Abundant nanoscale and submicron carbon particles formed in the laser welds, owing to the coalescence of the reinforcing CNTs as the result of conjoint effect of laser irradiation and welding thermal annealing. Dense intra- and inter-granular carbon particles and carbon particle-enveloped equiaxed dendrites in the magnesium matrix constituted the characteristic weld microstructure. Lateral-irregular cellular growth originated from the weld fusion boundary and the carbon particle-enveloped equiaxed dendrites with substructure formed in the weld center. It is inferred that the CNTs affected the weld solidification mainly via retarding solidification growth rate. The gained weld hardening is primarily attributed to the local refined weld microstructure and locally denser carbon particles and MWCNTs. Lower laser fluence facilitated finer weld structure and less laser irradiation on the CNTs hence more hardening effect.

Mechanical properties of Sn–Zn lead-free solder alloys based on the microstructure array

The aim of this study is to develop a comparative experimental study interrelating mechanical properties, solidification thermal parameters and microstructure characteristics of a hypoeutectic Sn–4 wt.% Zn, a hypereutectic Sn–12 wt.% Zn and a eutectic Sn–9 wt.% Zn solder alloys. A water-cooled vertical upward unidirectional solidification system was used to obtain the samples. It was found that a more homogeneous distribution of the eutectic mixture, which occurs for smaller dendritic spacings in hypoeutectic and hypereutectic alloys, increases the ultimate tensile strength. The resulting microstructure of the eutectic Sn-9 wt.% Zn alloy has induced higher mechanical strength than those of the Sn–4 wt.% Zn and Sn–12 wt.% Zn alloys. It was found that the eutectic alloy experiences a microstructural transition from globular-to-needle-like Zn-rich morphologies which depend on the solidification growth rate. It is also shown that a globular-like Zn-rich morphology provides higher ultimate tensile strength than a needle-like Zn-rich eutectic morphology.

Phase-field simulation of weld solidification microstructure in an Al–Cu alloy

Since the mechanical properties and the integrity of the weld metal depend on the solidification behaviour and the resulting microstructural characteristics, understanding weld pool solidification is of importance to engineers and scientists. Thermal and fluid flow conditions affect the weld pool geometry and solidification parameters. During solidification of the weld pool, a columnar grain structure develops in the weld metal. Prediction of the formation of the microstructure during welding may be an important and supporting factor for technology optimization. Nowadays, increasing computing power allows direct simulations of the dendritic and cell morphology of columnar grains in the molten zone for specific temperature conditions. In this study, the solidification microstructures of the weld pool at different locations along the fusion boundary are simulated during gas tungsten arc welding of Al–3wt%Cu alloy using the phase-field model for the directional solidification of dilute binary alloys. A macroscopic heat transfer and fluid flow model was developed to assess the solidification parameters, notably the temperature gradient and solidification growth rate. The effect of the welding speed is investigated. Computer simulations of the solidification conditions and the formation of a cellular morphology during the directional solidification in gas tungsten arc welding are described. Moreover, the simulation results are compared with existing theoretical models and experimental findings.

Y 2BaCuO 5-free melt textured YBa 2Cu 3O 7: a search for the reference sample

Melt textured YBa 2Cu 3O 7 (MTG YBCO) composites free of Y 2BaCuO 5 (211) precipitates have been grown by the top seeding method by adding a Zr-oxide to the starting precursor mixture. This addition has induced a pushing effect of the Zr-oxide and 211 inclusions out of the YBCO single domain. The effect on the growth process and modification of the microstructure has been analyzed. Growth parameters like particle size of the precursors, initial content of 211, BaZrO 3, and CeO 2 and solidification growth rate have been tuned in order to enhance the pushing effect and be able to grow 211-free MTG YBCO composites to be used as reference sample, for physical and microstructural studies of MTG YBCO composites. The superconducting properties like critical current density, irreversibility line (IL), and anisotropy of the resulting material, have been determined and compared to YBCO single crystals and standard MTG YBCO.

Microstructure of unidirectionally solidified Fe-V-C alloy and interface temperature measurement of γ+VC eutectic carbide

Alloying elements such as Cr, W, V, Mo of the high speed cast iron for hot rolling have been added to improve fracture toughness and wearing resistance. It is important to control solidification structures of these cast irons including eutectic carbides, M3C, M7C3, M6C and MC. Therefore, it is required to predict which carbide will solidify at certain composition and solidification condition. This prediction criteria will be gained by measuring the interface temperature of each carbide in various samples with different solute elements, composition and growth rate. In this report, the solidification temperature of γ+VC eutectic in Fe-V-C ternary system was measured during the directional solidification process. The relationship between solidification temperature and growth rate was obtained. In eutectic solidification along γ+VC monovariant lines, coefficient of undercooling, according to equation ΔT = k√V was obtained. At 1 μm/sec growth rate, γ+VC/γ+M3C banded structure was observed. The paper also discussed about γ+VC/γ+M3C banded structure formation at low growth rate, where the conditions under which the γ+VC+M3C ternary eutectic was expected to solidify.

Computer model of unidirectional solidification of single crystals of high temperature alloys

AbstractI t has been common practice to use mould withdrawal unidirectional solidification to produce single crystal castings. To grow single crystals successfully, it is important to control several solidification parameters, such as the morphology of the solidification front (solid/liquid interface), thermal gradient, and growth rate during solidification. It is the aim of this study to develop a solidification model that can predict such solidification parameters for various design and operating conditions. The solidification phenomena in the process modelled are basically controlled by two heat transfer mechanisms: conduction and radiation. A set of heat transfer equations and boundary conditions were employed to describe mathematically the heat transfer phenomena. Then the finite difference method was used numerically to solve these equations for specified boundary conditions to obtain the temperature distribution and temperature variation in the casting. The solidification parameters can subsequentl...

A Nonlinear Stability Analysis of a Model Equation for Liquid Phase Electro-Epitaxial Growth of a Dilute Binary Substance

An investigation is made of the weakly nonlinear morphological stability of a uniformly moving planar solid-liquid interface during the controlled unidirectional solidification of a dilute binary substance by the process of liquid phase electro-epitaxy (LPEE). A prototype model equation for LPEE is considered which postulates two-dimensional diffusion and electromigration of solute under a fixed temperature gradient and electric current. The results of this nonlinear analysis, which can be represented in a plot of temperature gradient versus the component of solidification growth rate due to diffusion for a particular imposed electric field, are then compared with those obtained in the absence of that electric current, the latter being a model for thermal liquid phase epitaxy (LPE). If the electric current is increased beyond a certain critical value for a solid substrate such that the electric field enhances the overall solidification growth rate, then the subcritical instability always present during LP...

Coarsening of eutectic fiber composites during cooling from the eutectic temperature

Coarsening and microstructural changes, which occur on cooling from the eutectic temperature, were experimentally studied in Al-Al3Ni eutectic fiber composites solidified at rates of 0.8, 5.0 and 32.5 cm per h. At the two higher growth rates, changes in fiber density on the order of 10 pct were observed between the solid-liquid interface and positions 2.0 cm from the interface. At the low growth rate the surface roughness of the as-grown fiber was noticeably decreased during cooling from the eutectic temperature. Theoretical expressions relating the change in average fiber radius or fiber density as a function of position were developed in terms of the solidification conditions, growth rate and temperature gradient, as well as the usual kinetic and thermodynamic factors influencing coarsening. The model was combined with independently obtained isothermal coarsening data to compare the experimentally observed extent of coarsening with that predicted. The pre-dictions of the model agreed qualitatively with the data on the effect of growth rate on coarsening, but the absolute extent of coarsening was greater than that predicted from the isothermal studies.