Columnar-to-equiaxed Transition Research Articles

Multi-scale investigation of A356 alloy with trace Ce addition processed by laser surface remelting

Laser surface remelting (LSR) has shown great application potential in Al-Si alloy parts (e.g., surface strengthening, surface repairing). However, the microstructural details and properties of LSR-treated hypoeutectic Al-Si alloy remains to be investigated. In this work, the microstructure of an Al-7Si alloy with adding 0.05 wt% Ce fabricated by LSR was studied through multi-scale characterization. Three regions with distinct morphologies after LSR were obtained: i) the remelting zone (RMZ) including an equiaxed grain region and a columnar to equiaxed transition (CET) region; ii) the heat-affected zone (HAZ) with segregation of Si; iii) substrate zone (SZ). Nanoscale eutectic Si particles were observed in RMZ and HAZ. Moreover, it is confirmed for the first time that the Ce atom can absorb on the {111}Si planes and leads to high density of twins and stacking faults. After LSR, the increased microhardness of RMZ is mainly attributed to the precipitation and dislocation strengthening. By further T6 heat treatment, the microhardness of RMZ increases to 126 HV. Dispersed small Si particles decrease the critical stress of crack propagation. Additionally, the high density of twins, stacking faults and Al-rich clusters within Si particle plays a significant role in toughness improvement.

Cross-Scale Simulation Research on the Macro/Microstructure of TC4 Alloy Wire Laser Additive Manufacturing

A cross-scale model of macro-micro coupling is established for the wire laser additive manufacturing process of the TC4 titanium alloy. The model reproduces the dynamic evolution process of the molten pool shape, reveals the temperature change law in the molten pool, and simulates the microstructure and morphology of different regions of the molten pool. Finally, the model is used to quantitatively analyze the effects of process parameters (laser power, scanning speed) on the growth morphology of dendrites during solidification. The research shows that with the increase in laser power and the decrease in scanning speed, the peak temperature of the molten pool increases rapidly, and the size of the molten pool increases gradually. When the laser scanning speed is greater than 5 mm/s, the molten pool length decreases significantly. After solidification, an asymmetrically distributed equiaxed grain structure is formed at the upper part of the molten pool, the bottom of the molten pool is made up of slender columnar crystals, and the columnar-to-equiaxed transition (CET) occurs in the middle of the molten pool. With the decrease in laser power and the increase in scanning speed, the growth rate of dendrites becomes faster, the arm spacing and the overall morphology of dendrites become smaller, and the arrangement of columnar crystals have a tighter microstructure.

The microstructure evolution and precipitation behavior of TiB2/Inconel 718 composites manufactured by selective laser melting

Additive Manufacturing is an advanced material processing technology emerging in recent years. However, coarse columnar grain structure of additive manufactured metals reduces the performance of the material. Facilitating the columnar to equiaxed transition (CET) has become a research hotspot. In this paper, the equiaxed grain of additive manufactured Inconel 718 was achieved by adding TiB2 particles. Simultaneously, the microstructure evolution and precipitation behavior with nano-TiB2 particles addition were studied. The results show that the grain morphology of Inconel 718 exhibited coarse columnar grains with epitaxial growth and strong <100> texture. When 3 wt% TiB2 was added, the columnar grains became finer, further increased the content of TiB2 to 5 wt%, the equiaxed grains were obtained and the texture intensity decreased significantly. In addition, TiB2 partially melted under the high laser energy changed the phase precipitation behavior of Inconel 718 from chain-like Laves phase to reticulated (γ + M3B2) eutectics, which lead to the hardness increased from 276 HV to 578 HV when 5 wt% TiB2 was added. After heat treatment, the precipitation of high density γ′ and γ″ strengthening phase were promoted the hardness increased by 87% to 516 HV in Inconel 718. However, the hardness of TiB2 reinforced samples showed a little change, which could be attributed to the partial dissolution of M3B2 boride during the heat treatment.

Microstructure and mechanical properties of directionally solidified Al-rich Ni3Al-based alloy under static magnetic field

The influence of a longitudinal static magnetic field on microstructures and mechanical properties of Ni3Al-based alloy during directional solidification at the growth speed of 25 µm/s and 100 µm/s has been experimentally investigated. Results reflected that the utilization of a 0.5 T magnetic field refines the NiAl dendrites at both speeds of growth. When applying a high magnetic field, the columnar-to-equiaxed transition (CET) occurred at growth speed of 25 µm/s and dendrite networks formed at growth speed of 100 µm/s. Tensile property results indicated that the refinement of dendrites enhanced both plasticity and ultimate tensile strength of Ni-Al alloy. The change of microstructures and mechanical properties should be attributed to the combined action of the thermoelectric magnetic convection (TEMC) in mushy zone together with the thermoelectric magnetic force (TEMF) acting on the solid. When applying a low magnetic field (0.5 T), the TEMF is too small to fragment the dendrites, and the refined dendrites is mainly due to the TEMC in the interdendritic regions. At a lower growth speed, the TEMF is supposed to strong enough to fragment the dendrites and induce the occurrence of CET under 2 or 4 T. When the growth speed increased to 100 µm/s, no obvious CET was observed, but a vertical secondary convection is induced by the circulation in the parallel plane, which promotes the growth of secondary and tertiary branches, leading to the formation of abnormally developed high order dendrites. The hierarchical dendritic structure was suggested to provide a channel for rapid crack propagation and thus degraded the mechanical properties.

Concurrent model for sharp and progressive columnar to equiaxed transitions validated by directional solidification experiments processed in microgravity conditions

Columnar and equiaxed structures, which occur during solidification of metallic alloys, influence the texture and properties of castings, welded joints and additively manufactured components. During transient solidification, where grain refiner particles provide the predominant nucleation mechanism, a Columnar to Equiaxed Transition (CET) occurs when conditions that had originally favoured directional columnar growth change to those favouring equiaxed. Constitutional undercooling ahead of the columnar front can permit equiaxed nucleation and growth. By carrying out experiments in microgravity conditions, liquid flows due to thermal and solutal buoyancy effects are suppressed. In these diffusion-controlled conditions, we have observed examples of both sharp (clear) and progressive (gradual) CET. The experimental outcomes, especially the observation of a progressive CET, has highlighted the need for a continuum model that allows for competitive columnar and equiaxed structure development; hence, the Concurrent Columnar to Equiaxed Transition (C2ET) model is proposed. The C2ET is thermally transient and relies on the well-known concept of extended growth for impingement mechanics; thereby, greatly reducing numerical complexity. Importantly, the proposed approach removes the need for a specific equiaxed-blocking criterion, which is often proposed as an essential requirement in other CET models. The C2ET model is validated by four experimental solidification scenarios: two velocity jumps and two thermal-gradient decreases. The velocity jumps induced sharp CETs; whereas, thermal-gradient decreases gave progressive CETs. The C2ET model gave good agreement for the columnar and equiaxed transition zones for both sharp and progressive CET. Results are compared with the classic Hunt model. Unlike Hunt’s model, the C2ET model predicted all macrostructure transitions faithfully using a single (or consistent) set of nucleation input parameters across all four scenarios. Since, the same level of grain refinement was used in each experiment, a consistent set of nucleation parameters was expected. The validated approach can enable effective simulation at lower computational cost for industrial processes that rely on a solidification processing step.

Dynamic solidification process during laser cladding of IN718: Multi-physics model, solute suppressed nucleation and microstructure evolution

The solidification microstructures directly determine the mechanical properties of the laser cladding. At present, the investigation of the dynamic evolution of the microstructures during the laser cladding process is still limited. In this study, a multi-physics model was established to analyze the complex microstructure evolution process during the laser cladding of IN718. The model consists of heat and mass transfer process, polycrystalline solidification process, heterogeneous nucleation process with solute suppressed nucleation. The accuracy of the model was verified by comparing the profile of the molten pool calculated by the heat and mass transfer model and the solidification microstructures of the molten pool calculated by the polycrystalline solidification model with the experimental results. The results show that thermal convection is the main heat transfer mode in the molten pool. The decrease of the line energy decreases the flow velocity pool and weakens the thermal convection in the molten pool. Columnar grains are composed of epitaxial growth grains and elongated grains nucleated between the primary branches. The columnar-to-equiaxed transition (CET) is affected by the size of "active nucleation zone (ANZ)", and the size of equiaxed grain is affected by the size of "inhibited nucleation zone (INZ)". The decrease of line energy leads to the decrease of the area of both the ANZ and INZ, which leads to the increase of the area of the columnar grain zone, but the decrease of the equiaxed grain size.

Effect of Transient Thermal Conditions on Columnar-to-Equiaxed Transition during Laser Welding: A Phase-Field Study

The columnar-to-equiaxed transition (CET) is commonly observed in laser welds. It is able to prevent the growth of large columnar grains and consequently improve the mechanical properties of welded joints. In this paper, the CET behaviors at different locations in the laser weld of an Al–Mg alloy are observed experimentally and studied systematically. In order to describe the dynamic CET behaviors, an integrated phase-field (PF) model coupled with transient thermal conditions and a Gaussian heterogeneous nucleation model is developed. Investigations on columnar growth under steady conditions are performed first. In particular, the effects of thermal conditions, i.e., solidification rate and temperature gradient, on the constitutionally undercooled degree and region ahead of the solidification front are quantitatively studied. In a laser weld, it is found that the CET behaviors vary significantly along the thickness direction. Our PF simulation results indicate that the CET depends strongly on the locally transient thermal conditions in the fusion zone. The transient thermal conditions affect CET behaviors by dynamically adjusting the constitutionally undercooled degree and region during the solidification process. The predicted CET behaviors under transient conditions exhibit reasonably good agreements with corresponding experimental results.

Effect of laser additive manufacturing on the microstructure and mechanical properties of TiB2 reinforced Al-Cu matrix composite

Understanding the effect of reinforcements on microstructure evolution and strengthening mechanism in aluminum matrix is crucial for development of good performance aluminum matrix composites (AMCs) prepared by laser additive manufacturing (LAM). In this work, the roles of submicron-TiB2 particles in the grain morphological evolution, mechanical properties and corresponding strengthening mechanism of the 2024Al matrix processed by laser directed energy deposition (L-DED) and laser powder bed fusion (L-PBF) were comparable investigated. The microstructure of L-DED processed TiB2p/2024Al composite consists of equiaxed grains, instead of the coarse columnar grains in L-DED prepared 2024Al alloy. While only the refinement of columnar grains was observed in the L-PBF processed similar composite sample. Combining with the thermal simulation results and Hunt criterion, the solidification conditions of the molten pool during L-DED process facilitate the formation of Al-Ti layer between TiB2 and Al matrix, which promotes the columnar to equiaxed transition (CET) of α-Al grains by increasing the nuclei density (N0). The as-fabricated 3 wt %-TiB2p/2024Al composites, no matter prepared by L-DED or L-PBF, exhibited simultaneously enhanced strength and plasticity (elongation) due to the grain refinement. The grain boundary strengthening, dislocation strengthening and load transfer strengthening should be responsible for the increase of 79% in yield strength (YS) of L-DEDed TiB2p/2024Al sample. While the increment of YS for L-PBFed composite sample is 15%.

A method to manipulate non-steady-state columnar-to-equiaxed transition in powder bed fusion additive manufacturing using an electron beam

Site-specific control of solidification grain structure is one of the largest attractiveness of manufacturing metallic parts with powder bed fusion additive manufacturing. In this study, we manufacture non-weldable superalloy Alloy713ELC with powder bed fusion additive manufacturing using an electron beam (PBF-EB) and achieve various bulk solidification grain structures, i.e. near fully equiaxed structure, interlocked zigzag structure, and columnar structures with various grain widths, through controlling process parameters under a line order scan strategy. An analytical transient model, which is capable of simulating heat transfer in PBF-EB single-layer melting under the experimental conditions, is established and validated by compared to numerical models of computational fluid dynamics and finite element method in PBF-EB single-track melting. The evolutions of solidification grain structure are rationalized using microstructural characterization and simulations based on various models. It is found that the mechanisms of columnar grain refinement and columnar-to-equiaxed transition (CET) are related to the Walton and Chalmers selection effect, which is governed by the spatial and temporal variations of solidification direction, and to the effect of convection within mushy zone. Based on the grain structure evolution mechanisms, we propose a method to manipulate CET or to achieve a novel interlocked zigzag grain structure in PBF-EB.

Multi-phase field lattice Boltzmann model of columnar-to-equiaxed transition in entire welding molten pool

Columnar-to-equiaxed transition (CET) often occurs during the solidification of the weld. Moving molten pool and strong fluidity are two notable characteristics in this process. The former causes the deflective epitaxial growth of columnar dendrites, while the latter makes the equiaxed dendrites grow asymmetrically and continuously move, collide and coalesce in the melt. This paper proposed a multi-phase field lattice Boltzmann model to simulate the CET in the entire molten pool. The model can characterize the polycrystalline growth, compute the fluid flow, and simulate the solid motion, collision, and coalescence. It also combined the transient growth condition model and the continuous nucleation model to reproduce the moving molten pool and define heterogeneous nucleation respectively. It further combined the initial grain structure of the base metal to provide a more realistic condition for epitaxial growth. The proposed model was verified by simulating the pure motion of dendrite in lid-driven flow, the free fall of single dendrite in static flow, and the single-dendrite growths in lid-driven and channel flow. The CET in the entire molten pool was simulated under different conditions, including considering or ignoring the fluid flow and gravity, the columnar and equiaxed dendrites growing simultaneously or sequentially. In these simulations, settlement, collision, and coalescence of equiaxed dendrites were reproduced successfully. Clear asymmetric growth, dendrite aggregation effect, and solute vortex were found. Significant differences in the size, symmetry, dendrite spacing, dendrite morphology, and solute distribution were found when the melt flow was considered or ignored. The dense equiaxed dendrite belt was found in the later stage of CET. They gathered in front of columnar dendrites and dominated the following solidification. The typical mixed structure that consists of columnar and equiaxed grains was obtained after complete solidification.

Effects of Static Magnetic Field on the Microstructure of Selective Laser Melted Inconel 625 Superalloy: Numerical and Experiment Investigations

A number of researchers have reported that a static magnetic field (SMF) will affect the process of selective laser melting (SLM), which is achieved mainly through affecting molten pool evolution and microstructure growth. However, its underlying mechanism has not been fully understood. In this work, we conducted a comprehensive investigation of the influence of SMF on the SLM Inconel 625 superalloy through experiments and multi-scale numerical simulation. The multi-scale numerical models of the SLM process include the molten pool and the dendrite in the mushy zone. For the molten pool simulation, the simulation results are in good agreement with the experimental results regarding the pool size. Under the influence of the Lorentz force, the dimension of the molten pool, the flow field, and the temperature field do not have an obvious change. For the dendrite simulation, the dendrite size obtained in the experiment is employed for setting up the dendrite geometry in the dendrite numerical simulation, and our findings show that the applied magnetic field mainly influences the dendrite growth owing to thermoelectric magnetic force (TEMF) on the solid–liquid interface rather than the Lorentz force inside the molten pool. Since the TEMF on the solid–liquid interface is affected by the interaction between the SMF and thermal gradient at different locations, we changed the SLM parameters and SMF to investigate the effect on the TEMF. The simulation shows that the thermoelectric current is highest at the solid–liquid interface, resulting in a maximum TEMF at the solid–liquid interface and, as a result, affecting the dendrite morphology and promoting the columnar to equiaxed transition (CET), which is also shown in the experiment results under 0.1 T. Furthermore, it is known that the thermoelectric magnetic convection (TEMC) around the dendrite can homogenize the laves phase distribution. This agrees well with the experimental results, which show reduced Nb precipitation from 8.65% to 4.34% under the SMF of 0.1 T. The present work can provide potential guidance for microstructure control in the SLM process using an external SMF.

β Grain refinement by yttrium addition in Ti-6Al-4V Wire-Arc Additive Manufacturing

Wire-Arc Additive Manufacturing (WAAM) of large near-net-shape titanium parts has the potential to reduce costs in aerospace applications. However, with titanium alloys, such as Ti-6Al-4V, conventional WAAM processing conditions generally result in epitaxial solidification from the melt pool fusion boundary, which over many layers can generate coarse cm-scale,<001>//ND fibre textured, columnar β grain structures within the deposited metal. The mechanical anisotropy caused by this coarse primary grain structure cannot be eliminated by subsequent solid-state phase transformations. In order to attempt to refine the size of the solidified β-grains and reduce their strong texture, the growth restriction efficiency of low addition levels of the strongly partitioning element (k = 0.1) yttrium (Y) has been investigated. Less than 0.8 wt.% Y was sufficient to reduce the widths of the solidified columnar β grains from 1 to 2 mm to 100–300 µm. Y was also found to induce a columnar-to-equiaxed transition (CET) in the latter stages of melt pool solidification, which benefits from a lower liquid thermal gradient and higher solidification velocity. Inter-dendritic segregation of Y was also found to be significant and oxygen scavenging led to the formation of Y2O3 particles in the inter-dendritic liquid, with a previously unreported irregular eutectic morphology. High-resolution EBSD analysis showed these particles exhibited specific orientation relationships with the solidified β grains, which were confirmed experimentally.

Use of Alloying to Effect an Equiaxed Microstructure in Additive Manufacturing and Subsequent Heat Treatment of High-Strength Titanium Alloys

This paper addresses the use of alloying additions to titanium alloys for additive manufacturing (AM) with the specific objective of producing equiaxed microstructures. The additions are among those that increase freezing ranges such that significant solutal undercooling results when combined with the rapid cooling rates associated with AM, and so be effective in inducing a columnar-to-equiaxed transition (CET). Firstly, computational thermodynamics has been used to provide a simple graphical means of predicting these additions; this method has been used to explore additions of Ni and Fe to the alloy Ti–6Al–4V (Ti64). Secondly, an experimental means of determining the minimum concentration of these alloying elements required to effect the CET has been developed involving gradient builds. Thirdly, it has been found that additions of Fe to Ti64 cause the alloy to change from an α/β Ti alloy to being a metastable β-Ti alloy, whereas additions of Ni do not produce the same result. This change in type of Ti alloy results in a marked difference in the development of microstructures of these compositionally modified alloys using heat treatments. Finally, hardness measurements have been used to provide a preliminary assessment of the mechanical response of these modified alloys.

In situ investigation of the Columnar-to-Equiaxed Transition during directional solidification of Al–20 wt.%Cu alloys on Earth and in microgravity

Solidification experiments on Al–20 wt.%Cu alloys with grain refiner were performed in a Bridgman-type furnace to investigate the impact of gravity-driven phenomena on the Columnar-to-Equiaxed Transition (CET) during directional solidification (i) in microgravity, on board the sounding rocket MASER-14 and (ii) on Earth in three growth directions, namely horizontal, vertical upward (counter-gravity direction) and vertical downward (in-gravity direction). The CET was provoked by a step increase of the cooling rate and was visualised in situ and in real-time using X-radiography. This paper reports direct observations of dendritic columnar growth, CET and the subsequent equiaxed regime, and quantitative characterisation of the microstructures. The increase in constitutional undercooling that induces the nucleation of the first grains ahead of the columnar front can be related to the rapid thermal change following the increase in cooling rate. The nucleation distance of equiaxed grains ahead of the columnar front is larger in microgravity than on Earth and possible origins for this difference are discussed. Both mechanical and solutal blocking mechanisms were observed at CET. Mechanical blocking is attributed to the occurrence of solidification-induced shrinkage flow. The relative importance of each blocking mechanism is detailed for each growth configuration. In particular, mechanical blocking is shown to be the principal type of impingement in the microgravity experiment. The final equiaxed grain structure was characterised, and the results confirm that gravity effects become less significant at high growth rates.

Multi-GPU implementation of a cellular automaton model for dendritic growth of binary alloy

A parallel three-dimensional (3D) cellular automaton (CA) model is developed for dendritic growth simulation during solidification of binary alloy. The CA model is implemented using the graphic processing unit (GPU). Compute Unified Device Architecture (CUDA) is combined with Message Passing Interface (MPI) to perform large-scale simulation on the multi-GPU architecture. A CUDA-Aware OpenMPI is used to reduce the communication cost between different GPU cards. The accuracy and the speedup ratio of the CA model are investigated. First, the simulated steady-state tip velocity under different undercooling is compared with the LGK analytical solution. Then, dendritic growth during directional solidification and equiaxed multi-dendrite growth are simulated. Dendritic growth simulation with a domain size up to 453 million grids is performed. Finally, the speedup ratio of the CA model using four GPUs is compared with that using four CPU processes via MPI, which leads to a maximal speedup ratio of 152.19. The developed CA model achieves high parallel performance compared with the MPI-based parallel model. The developed CA model is capable of predicting the columnar to equiaxed transition (CET) event during directional solidification. The results indicate that increasing cooling rate promotes the occurrence of the equiaxed dendrites in the melt ahead of the solidification front, and equiaxed dendrites are prone to nucleate in the columnar dendrite groove zone when a middle cooling rate is applied.

Grain morphology evolution mechanism of titanium alloy by the combination of pulsed arc and solution element during wire arc additive manufacturing

Coarse columnar grains formed during titanium alloy additive manufacturing (AM) are generally regarded as unfavorable, which trend to cause solidification defects and mechanical property anisotropy. Achieving the columnar to equiaxed transition (CET) of grain structures has been a great challenge, especially for wire arc additive manufacturing (WAAM) with the highly localized heat input and large temperature gradient. The interdependence model is widely used to explain and predict the grain size and evolution during the welding or AM process. However, the thermal undercooling and the molten pool flow which were neglect in its assumption have been found to have obvious effects on the grain morphology evolution. In this work, different deposition experiments with the combination of growth restricting solutes (boron), nucleant particles (La2O3), and pulsed arc were employed to investigate these intrinsic factors which are often neglected how to influence the grain morphology.

Inverse Columnar-Equiaxed Transition (CET) in 304 and 316L Stainless Steels Melt by Electron Beam for Additive Manufacturing (AM)

According to Hunt’s columnar-to-equiaxed transition (CET) criterion, which is generally accepted, a high-temperature gradient (G) in the solidification front is preferable to a low G for forming columnar grains. Here, we report the opposite tendency found in the solidification microstructure of stainless steels partially melted by scanning electron beam for powder bed fusion (PBF)-type additive manufacturing. Equiaxed grains were observed more frequently in the region of high G rather than in the region of low G, contrary to the trend of the CET criterion. Computational thermal-fluid dynamics (CtFD) simulation has revealed that the fluid velocity is significantly higher in the case of smaller melt regions. The G on the solidification front of a small melt pool tends to be high, but at the same, the temperature gradient along the melt pool surface also tends to be high. The high melt surface temperature gradient can enhance Marangoni flow, which can apparently reverse the trend of equiaxed grain formation.

Effect of Pressure on Second Dendrite Arm Spacing and Columnar to Equiaxed Transition of 30Cr15Mo1N Ingot

In order to clarify the effects of pressure on the second dendrite arm spacing (SDAS) and columnar to equiaxed transition (CET) of 30Cr15Mo1N ingot, changes in solidification parameters, cooling rate and columnar dendrite tip growth rate with pressure have been investigated. A formula is proposed to obtain the quantitative correlation between pressure (≤ 2 MPa) and interfacial heat transfer coefficient: . And then, A formula is proposed to calculate SDAS with cooling rate: , which is applicable for low pressure (≤2 MPa) and low cooling rate (0.4–1.4 K · s−1). There are tiny changes in solidification mode and equilibrium partition coefficient with increasing pressure from 0.5 to 2 MPa. Therefore, increasing pressure refines SDAS mainly by enlarging cooling rate. Pressurization can increase columnar dendrite tip growth rate by enhancing undercooling, and inhibit nucleation and growth of equiaxed dendrite by decreasing constitutional undercooling. It results that the distance between the center of ingot and CET position decreased with increasing pressure from 0.5 to 2 MPa. And a formula is proposed to calculate columnar dendrite tip growth rate with undercooling: , which is suitable for low pressure (≤2 MPa).

Columnar to equiaxed transition during β heat treatment in a near β alloy by laser additive manufacture

Abstract Columnar β grains are widely present in titanium alloys fabricated by Additive Manufacturing (AM), which leads to significant anisotropy in mechanical properties. An outstanding challenge is to facilitate the columnar to equiaxed transition (CET) of the prior β grains. In this research, CET and the underlying grain growth mechanism during β heat treatment in Ti–5Al–5Mo–5V–1Cr–1Fe (Ti55511) alloy manufactured by selected laser melting (SLM) and laser metal deposition (LMD) were investigated. For the first time, the quasi-in-situ observation was employed in the AM near β titanium alloys by the electron backscatter diffraction technique to analyze morphology, crystal orientation and substructure evolution, especially in the situation of bamboo-like microstructure with columnar grains and equiaxed grains distributed layer by layer. It was found that the prior β grains enriched low-angle grain boundaries (LAGB) are in a high stored strain energy state in as-deposited SLM Ti55511 leading to a recrystallized nucleation-and-growth process during heat treatment, while the prior β grains containing a small amount or even no LAGB are in a relatively lower stored strain energy state in as-deposited LMD Ti55511 resulting in recrystallization and grain growth processes.

Heterogeneous nucleation models to predict grain size in solidification

Heterogeneous nucleation models in solidification have been developed to predict grain size over several decades. Up to now, the models are divided into three categories. The first is a well-known spherical cap nucleus model, where the effectiveness of nucleant, i.e. contact angle, is mainly focused on characterising the nucleants. In this model, the kinetics is determined by activation energy of embryos formation and the adsorption rate of atoms into the embryos. The second is a free growth model, in which active nucleants are determined by the size distribution of nucleants, and the heterogeneous nucleation is considered as an athermal process. The third is a constitutional supercooling model in which active nucleants are triggered by the constitutional undercooling at the front of growing crystals. All models remain uncertain to describe constitutionally the kinetics of heterogenous nucleation. In addition, the crystal growth rate affects significantly the heterogeneous nucleation events since growing crystals release solute atoms and heat. Therefore it is very important to approximate a flux of solute at the solid–liquid interface. In practical aspect, how to predict the grain size in the equiaxed zone is of interest. Equiaxed grains in front of growing columnar block the growth when the volume of equiaxed grains reaches a critical value, and eventually equiaxed zones are formed, i.e. columnar to equiaxed transition (CET). It is believed that the grain size in the equiaxed zone can be predicted using the cooling rate of remained melt at the time when CET occurs. In addition, further investigations on the efficiency variation of grain refiner are also required, although it is agreed that the efficiency decreases significantly with increasing amounts of nucleant.