Competitive Growth Of Dendrites Research Articles

High wear resistance and strength of Hastelloy X reinforced with TiC fabricated by laser powder bed fusion additive manufacturing

Hastelloy X (HX) alloy as a typical solid solution strengthened nickel-based superalloy, has been widely used in the preparation of hot end components. The microstructure evolution and properties of HX alloy and nano-TiC reinforced HX alloy (TiC/HX) formed by laser powder bed fusion (LPBF) were studied. The results show that adding 3 wt% nano-TiC particles can not only inhibit the formation of cracks, but also effectively improve the dry sliding friction, wear properties and room temperature tensile properties. Nano-TiC particles can significantly promote the competitive growth of dendrites, refine the grains, and reduce the residual thermal stress. In addition, it can significantly improve the shear modulus and tensile strength. Under the same forming parameters, the wear rate of the nano-TiC/HX composite material is 51 % lower than that of the pure HX alloy, only 174.49 μm3/(N·mm). At the same time, the tensile strength of the alloy increased from 708 MPa to 1131 MPa, the yield strength increased from 619 MPa to 842 MPa, and the elongation doubled to 16 %.

Differential analysis of the influence mechanism of ultrasonic vibrations on laser cladding

Although the laser cladding technology is widely used in various fields, the laser cladding layer is prone to pores, inclusions and microcracks, severely limiting the popularization and application of this technology. High-frequency mechanical vibration can effectively reduce the micro defects in the cladding layer and strengthen the solidification structure of the cladding layer. In this paper, a laser cladding system for a disc laser assisted by ultrasonic vibration is built, and the dynamic response of ultrasonic vibration of the cladding experiment platform is tested. A finite element model of the dynamic response of the cladding experiment platform under ultrasonic vibration was established, and the difference of the vibration of the experimental platform substrate at different positions under the ultrasonic vibration was calculated. The internal amplitude of the substrate is differentiated in a hemispherical shape with the vibration source as the center and is distributed under the influence of ultrasonic vibration. On this basis, the phase field method was used to establish the ultrasonic-assisted disc laser cladding solidification model to obtain the dendrite growth state during the solidification process. The calculation reveals the change law of single crystal and polycrystalline solidification growth under the influence of ultrasonic amplitude at different substrate positions. Calculations show that ultrasonic vibration can effectively increase the growth rate of dendrites and promote the formation of secondary dendrite arms. The polycrystalline solidification growth model is closer to reality. The competitive growth of dendrites suppresses the growth of primary dendrites to a certain extent and affects the selective growth of dendrites. The results show that the larger the ultrasonic amplitude, the more rapid the formation of secondary dendrite arms.

Field variable diffusion cellular automaton model for dendritic growth with multifold symmetry for the solidification of alloys

The substantial mesh dependency caused by the discrete properties of cells and limitations of the sharp interface model are the inherent disadvantages of the cellular automaton (CA) model, which leads to difficulties in simulating dendritic growth with multifold symmetry and random preferred orientations for the solidification of alloys. A novel field variable diffusion CA (FCA) model is proposed by referring to the concept of the gradient energy term for diffuse interfaces in the phase field method. The diffusion equation for the field variable based on the constructed gradient functional is derived using the gradient descent method and is introduced into the CA model to reduce the mesh dependency. The FCA model deals with the solidification/remelting growth kinetics of the solid–liquid interface according to the lever rule and by considering the constitutional supercooling and Gibbs–Thomson effect. Free dendritic growth from undercooled melts and competitive dendritic growth during the directional solidification of Al–4 wt% Cu and Mg–5.26 wt% Al alloys were calculated to validate the accuracy of the FCA model for four-fold, six-fold symmetric dendritic morphologies and growth kinetics. The FCA model can efficiently reproduce multi-equiaxed and columnar dendrites with multifold symmetry and random preferred orientations as well as graphically reveal essential dendritic growth information, such as coarsening of secondary arms and side branch fusion.

Formation of Heterostructure with Appearance of α-Al Phase in Hyper- and Eutectic Al-Si Alloys by Solidification at High Rate

Normally, the microstructure of eutectic and hypereutectic Al-Si alloys consists of Al-Si eutectic or Al-Si eutectic + SiI, that is why they have good wear-resistance properties, but their ductility decreases somewhat, which can be improved by the appearance of non-equilibrium α-aluminum grains. In present work, a recrystallization and partial melting (RAP) technique was applied in the preliminary research to investigate the solidification behavior of the eutectics at high cooling rate. The results show that numerous α-Al dendrites appeared instead of the eutectic structure. In the followed researches, the combination of some technological procedures, based on the competitive growth of dendrites and eutectics, such as heterogeneous nucleation and high cooling rate, were applied: A413.0 and A390.0 alloys were melted in resistant furnace and poured into a mold, made of copper at one side and of steel at another, which is connected to the temperature measuring device via four K-class thermocouples. The various pouring regimes: gravity, via 450 tilt cooling slope and injection with Argon gas for 2 min. before pouring, were applied at different temperatures of 680, 650, 6300 C. The results show that the hetero-structure of eutectic and hyper-eutectic Al-Si alloys, consists of non-equilibrium α-Al grains, primary silicon and eutectics was obtained. Grain size varies with cooling rate, with minimum value of 10 μm when the specimen thickness is 5 mm. Non-dendritic grains were achieved with semi-solid treatment (pouring via cooling slope). The elongation of alloy is expected to be enhanced due to the appearance of α-Al grains.

Two-dimensional phase-field simulations of competitive dendritic growth during laser welding

A phase-field model is applied to study competitive dendritic growth between different grains with different crystalline orientations during laser welding of Al-Cu alloy. An unfavorable oriented (UO) grain is set to locate between two favorable oriented (FO) grains to study the dendritic growth behaviors at not only converging grain boundary (GB) but also diverging GB. It is found that the cellular dendrites appear firstly nearby the GBs at initial instability stage. At early competitive growth stage, the UO misalignment angle influences the competitive dendritic growth at both GBs. After completely entering competitive growth stage, the leading dendrites that are much faster than other dendrites at GBs firstly grow in lateral direction. The side branches growing from leading dendrites block growth path of nearby dendrites and change the UO/FO grain widths. The converging GB deflection angle and the side branch development at diverging GB as characteristic competitive dendritic growth behavior at relatively steady growth stage also significantly affect UO and FO grain widths. The numerical results are basically consistent with microstructure obtained by experiment.

Numerical simulation of dendrite growth in Ni-based superalloy casting during directional solidification process

Abstract An understanding of dendrite growth is required in order to improve the properties of castings. For this reason, cellular automaton−finite difference (CA−FD) method was used to investigate the dendrite growth during directional solidification (DS) process. The solute diffusion model combined with macro temperature field model was established for predicting the dendrite growth behavior. Model validation was performed by the DS experiment, and the cooling curves and grain structures obtained by the experiment presented a reasonable agreement with the simulation results. The competitive growth of dendrites was also simulated by the proposed model, and the competitive behavior of dendrites with different misalignment angles was also discussed in detail. Subsequently, 3D dendrites growth was also investigated by experiment and simulation, and both were in good accordance. The influence on dendrites growth of initial nucleus was investigated by three simulation cases, and the results showed that the initial nuclei just had an effect on the initial growth stage of columnar dendrites, but had little influence on the final dendritic morphology and the primary dendrite arm spacing.

In situ observation and phase-field simulation on the influence of pressure rate on dendritic growth kinetics in the solidification of succinonitrile

The influence of pressure rate on dendritic growth kinetics in solidification of succinonitrile was studied via in situ observation based on a novel apparatus established in our previous work and using phase-field modeling where a pressure term associated with pressure rate was introduced. The experimental and simulation results revealed that dendrites grew much faster at higher pressure rate, resulting in dendrites characterized by more developed secondary arms and larger secondary dendrite arm spacing (SDAS), while dendrites growing at lower pressure rate was more cellular-like with small secondary arms. Higher pressure rate facilitated the competitive growth of dendrites, which led to fewer but larger dominate primary dendrites and larger primary dendrite arm spacing (PDAS) in the final microstructure. The cellular-to-dendrite transition (CDT) was more advanced at higher pressure rate, and it was demonstrated that it was the higher pressure rate not the high value of pressure that motivated CDT, via elevating effective undercooling and thus growth velocity at CDT moment. Furthermore, the growth kinetics was analyzed quantitatively, and the variation of tip velocity at different pressure rates was consistent with that of the corresponding undercooling induced by pressure and thermal condition. Moreover, the slope of growth and re-melting velocity—the tip acceleration—increased with pressure-rising rate and pressure-declining rate, respectively, even in a complicated periodic pattern, which was qualitatively consistent with the theoretical relationship of tip acceleration and pressure rate.

Competitive growth of dendrites and eutectic in Al2O3/Y3Al5O12 eutectic ceramics

Great insight so far have been gained into the eutectic structure of the non-faceted/non-faceted and non-faceted/faceted eutectics. However, little studies were devoted to the competitive growth of the dendrites and eutectic in faceted/faceted eutectics. Here, Y3Al5O12 dendrites were discovered in the Al2O3/Y3Al5O12 eutectic ceramics having an exactly eutectic composition. The growth direction of the Y3Al5O12 dendrite is < 001 > . The tips of the Y3Al5O12 dendrites are pyramid-like because of its high melting entropy and cubic structure. A skewed couple zone was proposed to explain the reason for the Y3Al5O12 dendrites appearing.

Phase-field simulation of competitive growth of grains in a binary alloy during directional solidification

Taking Al-2%mole-Cu binary alloy as an example, the influence of grain orientation on competitive growth of dendrites under different competitive modes was investigated by using the three-dimensional (3-D) phase-field method. The result of phase-field simulation was verified by applying cold spray and directional remelting. In the simulation process, two competitive modes were designed: in Scheme 1, the monolayer columnar grains in multilayer columnar crystals had different orientations; while in Scheme 2, they had the same orientation. The simulation result showed that in Scheme 1, the growth of the dendrites, whose orientation had a certain included angle with the direction of temperature gradient, was restrained by the growth of other dendrites whose direction was parallel to the direction of temperature gradient. Moreover, the larger the included angle between the grain orientation and temperature gradient, the earlier the cessation of dendrite growth. The secondary dendrites of dendrites whose grain orientation was parallel to the temperature gradient flourished with increasing included angles between the grain orientation and temperature gradient. In Scheme 2, the greater the included angle between grain orientation and temperature gradient, the easier the dendrites whose orientation showed a certain included angle with temperature gradient inserted between those grew parallel to the temperature gradient, and the better the growth condition thereafter. Some growing dendrites after intercalation were deflected to the temperature gradient, and the greater the included angle, the lower the deflection. The morphologies of the competitive growth dendrites obtained through simulation can also be found in metallographs of practical solidification experiments. This implies that the two modes of competitive growth of dendrites characterized in the simulation do exist and frequently appear in practical solidification processes.

Advent of Cross‐Scale Modeling: High‐Performance Computing of Solidification and Grain Growth

AbstractThe application range of computational metallurgy is rapidly expanding thanks to the recent progress in high‐performance computing. In this Progress Report, state‐of‐the‐art collections of large‐scale simulations of solidification and grain growth, performed on the GPU supercomputer, are introduced. One of the notable achievements in this direction is a billion‐atom molecular dynamics simulation for nucleation and solidification, which revealed the heterogeneity in homogeneous nucleation. Moreover, a series of large‐scale phase‐field simulations shed light on the topics at issue including competitive growth of dendrites during the directional solidification, the effect of forced and natural convections on the solidification, and so on. Based on simulation results bridging the gap between atomistic and continuum‐based simulations, a new criterion of multi‐scale modeling is proposed in the age to come. We are now standing at the new era of cross‐scale modeling, in which the overlap between atomistic and continuum simulations creates new research concepts and fields.

Phase-field numerical simulation of three-dimensional competitive growth of dendrites in a binary alloy

The normal vector of migration direction in the solid-liquid interface of dendrites was used to describe the phase-field governing equation. By using the three angles formed by the normal vector for the migration direction of the dendritic growth interface and the coordinate axes of the simulation region, the authors expressed the interfacial anisotropy equation, and built a phase-field model for the competitive growth of multiple grains. Taking a Al-2%mole-Cu binary alloy as an example, the competitive growth of multiple grains during isothermal solidification was simulated by applying parallel computing techniques. In addition, the phase field simulation results were verified by the experimental method. The simulation results show that the competitive growth of equiaxed dendrite is divided into two types: the first occurs during the process of competitive growth, the tips of primary dendrite on different grains taking part in the competition stop growing in their optimal growth direction; the second also occurs during competitive growth, the tips of primary dendrite which participate in the competition on different grains never stop growing in their optimal growth direction. The dendritic morphologies of the first competition growth type are divided into two types. Primary dendrites of grains taking part in the competition stop growing in their optimal growth direction and the competition plane enlarges when neither one wins the competition. However, when one wins the competition, the primary dendrites of grains with superiority go through the blocking grains and continue to grow in their optimal growth direction. The primary dendrites of inferior grains stop growing in their optimal growth direction and then instead grow in those areas without obstacles. The dendritic morphology of the second competition-growth type is shown to be the deformation of primary dendrites, which are mainly represented as the deflection and bending observed from different views. Compared with the metallographic picture, the simulation results can show the morphology of the competitive growth in all directions, so this simulation method can better characterize the competitive growth process.

Modeling of microporosity formation during solidification of aluminum alloys

A two-dimensional (2D) multi-phase cellular automaton (MCA) model is adopted to simulate the dendrite and microporosity formation during solidification of aluminium alloys. The model involves three phases of liquid, gas, and solid. The effect of liquid-solid phase transformation on the nucleation and growth of porosity, the redistribution and diffusion of solute and hydrogen, and the effects of surface tension and environmental pressure are taken into account. The growth of both dendrite and porosity is simulated using a CA approach. The diffusion of solute and hydrogen is calculated using the finite difference (FD) method. The simulations can reveal the interactive and competitive growth of dendrites and micropores, and the microsegregationof solute and hydrogen. The porosity nuclei with large size are able to grow preferentially, while the growth of the small porosity nuclei is inhibited. Gas pores grow spherically when it is enveloped by liquid. After touching with dendrites, the shapes of pores become irregular. An increased initial hydrogen concentration reduces the incubation time of porosity nucleation, but increases the final percentage of porosity and the average porosity size at the eutectic temperature. With cooling rate decreasing, the competitive growth between gas pores becomes more evident, leading to non-uniform porosity sizes, and more irregular morphology of the porosities with larger size. The simulation results are compared reasonably well with the experimental data reported in literature.

Two-dimensional phase-field simulations of dendrite competitive growth during the directional solidification of a binary alloy bicrystal

We investigated the competitive growth of dendrites at the converging grain boundaries (GBs) of bicrystals during the directional solidification of an Al–Cu alloy by means of two-dimensional phase-field simulations. In particular, the focus was on the recently observed phenomenon of unusual overgrowth during the directional solidification of a Ni-based superalloy, where the favorably oriented (FO) dendrites are overgrown by the unfavorably oriented (UO) ones. The phase-field simulations were accelerated by parallel computations on graphics processing units. The simulation results showed that unusual overgrowth occurs in Al–Cu alloys, indicating that this phenomenon is a common one in metallic materials. It was also concluded that the differences in the diffusion layers in front of the FO and UO dendrites had a dominant effect on the competitive growth of dendrites at the converging GB as well as on the unusual overgrowth. In addition, unusual overgrowth was observed in all the FO dendrites with a spacing that allowed the dendrite array to grow stably without necessitating a change in the number of dendrites. The FO dendrite at the GB is overgrown by the UO dendrite when the spacing between the FO dendrite at the GB and the next FO dendrite is approximately equal to the critical minimum spacing. However, the unusual overgrowth was not observed for UO dendrites with a large inclination angle. In this case, all the UO dendrites are blocked by the FO dendrite at the GB, and the FO dendrites migrate toward the UO dendrites.

A two-dimensional model for the quantitative simulation of the dendritic growth with cellular automaton method

A two-dimensional cellular automaton model was developed for simulating the diffusion-controlled dendritic growth in the low Péclet regime. The growth velocity of the solid/liquid interface was determined by the local solute diffusion, and the modified decentered square growth was improved to capture the first eight neighboring cells of the interface cell. In order to quantitatively validate the developed model, the free dendritic growth from an undercooled melt was simulated and compared with the classic Lipton–Glicksman–Kurz (LGK) analytical model. The results show that the predicted steady state tip velocity is in a reasonable agreement with the analytical value, and the dendritic growth can be quantitatively determined by the present model. Meanwhile, the simulation of the dendritic growth with random crystallographic orientation shows that the effects of the mesh dependency of the model on the growth kinetics and crystallographic orientation can be reduced to an accepted level. Moreover, the single dendritic growth and the multi-dendritic growth from an undercooled melt and the competitive dendritic growth in a unidirectional solidification were simulated and the dendritic growth features, such as crystallographic orientation, dendrite arm growing and coarsening, side branching, and arms fusion were graphically revealed.

MODELING OF MICROPOROSITY FORMATION IN ANAl-7%Si ALLOY

The performance of castings is primarily dependent on the solidification microstruc- tures and defects. Gas porosity is one of the major casting defects existing in the castings of aluminium and magnesium alloys. In this work, a two-dimensional (2D) cellular automaton (CA) model is pro- posed to simulate dendrite and microporosity formation during solidification of alloys. The model involves three phases of liquid, gas and solid. The effect of liquid-solid phase transformation on the nucleation and growth of porosity, the redistribution and diffusion of solute and hydrogen, and the effects of surface tension and environmental pressure are taken into account. The growth of both den- drite and porosity is simulated using a CA approach. The diffusion of solute and hydrogen is calculated using the finite difference method (FDM). The simulations can reveal the coupling and competitive growth of dendrites and microporosities, as well as the microsegregation of solute and hydrogen. The model is applied to simulate the microporosity formation during solidification of an Al-7%Si (mass fraction) alloy. The effects of initial hydrogen concentration and cooling rate on microporosity forma- tion are investigated. The results show that the simulated pressure difference between the inside and outside of a porosity as a function of the reciprocal of porosity radius obeys the Laplace law. With the increase of initial hydrogen concentration, porosity volume fraction increases, and the incubation time of microporosity nucleation and growth decreases, while the porosity density does not increase obvi- ously. With cooling rate decreasing, porosity volume fraction and maximum porosity radius increase, as well as porosity nucleates and starts to grow at higher temperatures. However, the porosity density shows a decreasing trend with the decrease of cooling rate. The competitive growth between different microporosity and dendrites is observed. The porosity nuclei with larger size are able to grow prefer-

Competitive grain growth in directional solidification investigated by phase field simulation

During directional solidification, the competitive dendritic growth between various oriented grains is a key factor to obtain desirable texture. In order to understand the mechanism of competitive dendritic growth, the phase field method was adopted to simulate the microstructure evolution of bicrystal samples. The simulation has well reproduced the whole competitive growth process for both diverging and converging dendrites. In converging case, besides the block of the unfavorably oriented dendrite by the favorably oriented one, the unfavorably oriented dendrite is also able to overgrow the favorable one under the condition of relatively low pulling velocity. This unusual overgrowth is dictated by the solute interaction of the converging dendrite tips. In diverging case, it was found that the grain boundary can be either inclined or parallel to the favorably oriented grain depending on the disposition of two grains.

Phase-field study of competitive dendritic growth of converging grains during directional solidification

The microstructure evolution of grains with different orientations during directional solidification is investigated by the phase-field method. For converging dendrites, in addition to the usually accepted overgrowth pattern wherein the favorably oriented dendrites block the unfavorably oriented ones, the opposite pattern of overgrowth observed in some recent experiments is also found in our simulations. The factors which may induce this unusual overgrowth are analyzed. It is found that in addition to the difference in tip undercooling, the solute interaction of converging dendrites, which has been ignored in the classical theoretical model, also has a significant effect on the nature of the overgrowth at low pulling velocities. Solute interaction can retard the growth of dendrites at the grain boundary (GB) and induce a lag of these dendrites relative to their immediate neighbors, which gives the unfavorably oriented dendrite the possibility to overgrow the favorably oriented one. However, this unusual overgrowth only occurs when the spacing between the favorably oriented GB dendrite and its immediate favorably oriented neighbor decreases to a certain level through lateral motion. These findings can broaden our understanding of the overgrowth mechanism of converging dendrites.

A Three Dimensional Modified Cellular Automaton Model for the Prediction of Solidification Microstructures.

A three dimensional modified cellular automaton model (3-D MCA) was developed in order to simulate the evolution of microstructures in solidification of alloys. Different from the classical cellular automata in which only the temperature field was calculated, this model included the solute redistribution both in liquid and solid during solidification. The relationship between the growth velocity of a dendrite tip and the local undercooling, which consists of thermal, constitutional and curvature undercooling terms, was calculated according to the KGT (Kurz-Giovanola-Trivedi) and LKT (Lipton-Kurz-Trivedi) models. The finite volume method, which was coupled with the cellular automaton model, was used to calculate the temperature and solute fields in the calculation domain. The present 3-D MCA model was applied to predict the microstructures, such as the free dendritic growth from an undercooled melt, the competitive dendritic growth in practical casting solidification. Some of the simulated results were compared with those obtained experimentally.

A Modified Cellular Automaton Model for the Simulation of Dendritic Growth in Solidification of Alloys.

A modified cellular automaton model (MCA) was developed in order to simulate the evolution of dendritic microstructures in solidification of alloys. Different from the classical cellular automata in which only the temperature field was calculated, this model also included the solute redistribution both in liquid and solid during solidification. The finite volume method, which was coupled with the cellular automaton model, was used to calculate the temperature and solute fields in the domain. The relationship between the growth velocity of a dendrite tip and the local undercooling was calculated according to the KGT (Kurz–Giovanola– Trivedi) model. The effects of constitutional undercooling and curvature undercooling on the equilibrium interface temperature were also considered in the present model. The MCA model was applied to predict thedendritic microstructures, such as the free dendritic growth from an undercooled melt and competitive dendritic growth in practical casting solidification. The simulated results were compared with those obtained experimentally.