Volume Fraction Of Dendrites Research Articles

Relationships Between Macrostructure and Microstructure in Lamellar Graphite Iron Castings

AbstractSpherical sheet steel molds filled with gray iron melts of varying chemical compositions and metallurgical conditions were air-cooled until solid, followed directly by austempering to preserve the austenite grain structure. The castings were studied using a combination of cooling curves and quantitative metallography, in order to clarify control of the austenite grain structure and its impact on the local microstructure. A novel method utilizing fast Fourier transform provided visual overview of macroscopic trends in the scale of the flake graphite structure. Castings inoculated with Sr-containing ferrosilicon featured finer eutectic cell structure but coarser equiaxed structure of austenite, emphasizing that melt treatments applied to control the graphite structure may have unintended effects on the austenite grain structure. In most non-inoculated castings, the microstructure was banded, with alternating layers of coarse and fine flake graphite with distance from the casting surface. The extent of the columnar zone of austenite grains showed no correlation with the graphite structure nor the volume fraction of dendrites. The volume-to-surface ratio of dendrites was more uniform in the columnar zone, but increased toward the center in the equiaxed zone. The casting with the highest carbon equivalent (4.34), featured zones containing finer dendrites and graphite. These zones appear to be gaps in the early solidification structure which filled later by secondary dendritic growth from surrounding austenite. This highlights that high carbon equivalent may lead to poor dendrite coherency which can make the microstructure less uniform and less predictable.

Two-Scale Computational Analysis of Deformation and Fracture in an Al-Si Composite Material Fabricated by Electron Beam Wire-Feed Additive Manufacturing

Numerical simulation of deformation and fracture of an AlSi12% alloy additively fabricated by layer-by-layer electron beam melting of a wire is carried out. The microstructure of the alloy is studied by scanning and transmission electron microscopy at different resolutions. The experimental study at a length scale of several dozens of microns reveals a dendritic structure, which can be treated as a composite material consisting of aluminum arms separated by a eutectic network. The volume fraction of dendrites varies with the distance from the base plate in the build direction. The eutectics can also be thought of as a composite with an aluminum matrix reinforced by silicon particles at a scale of a few microns. Particles of different shapes are nearly equally spaced in the matrix. The eutectic and dendritic structures are taken into account explicitly in the calculations. The dynamic boundary-value problems are solved by ABAQUS/Explicit. The isotropic elastic-plastic and elastic models are used to simulate the response of aluminum and silicon. The fracture model includes a maximum distortion energy criterion formulated for the particle and matrix materials in terms of the equivalent stress and plastic strain. A two-scale approach is proposed to investigate deformation and fracture of the AlSi12% alloy. On the eutectic scale, the thermomechanical behavior of the Al matrix-silicon particle two-phase composite is simulated to obtain the homogenized properties of the eutectic composite material, which is then used at a higher scale to investigate the deformation and fracture of a two-phase dendritic structure. Residual stresses formed during cooling of the additively manufactured material were found to decrease the strength of the composite, while the strength increases with the volume fraction of dendrites.

A strategy to design Ti-based in-situ bulk metallic glass composites containing controllable volume fraction and composition of the dendrite phase using conventional titanium alloy Ti–6Al–4V

Up to now, the composition design in the field of Ti-based in-situ dendrite reinforced bulk metallic glass composites (BMGCs) has been a great challenge. In this work, a simple but effective strategy is proposed to tailor the dendrite composition and volume fraction by using conventional Titanium alloy Ti–6Al–4V, and a series of in-situ dendrite reinforced BMGCs (Z1-Z4) are prepared based on it. The dendrite volume fraction can be adjusted by changing the proportion of the Titanium alloy Ti–6Al–4V, while the compositions of the dendrites are highly correlated with Ti–6Al–4V. In these alloys, with the increase of the mass percent of the added Titanium alloy Ti–6Al–4V, the volume fraction of the dendrite phase increases monotonically from Z1 to Z4 alloy. Z1 alloy behaves like a BMG with a high yield strength and limited plasticity due to its small dendrite size. Z2-Z4 alloys show excellent plasticity and significant work-hardening ability, because the dendrite size is appropriate and the dendrites undergo stress-induced martensite transformation during compression. From Z2 to Z4 alloy, with the increase of dendrite volume fraction from 56% to 78%, the yield strength does not decrease, which is due to the gradually enhanced stability of the dendrites. This composition design strategy is effective and universal, which can provide a new perspective for the composition design and development of TiZr-based in-situ dendrite reinforced BMGCs.

In situ synchrotron diffraction and modeling of non-equilibrium solidification of a MnFeCoNiCu alloy

The solidification mechanism and segregation behavior of laser-melted Mn35Fe5Co20Ni20Cu20 was firstly investigated via in situ synchrotron x-ray diffraction at millisecond temporal resolution. The transient composition evolution of the random solid solution during sequential solidification of dendritic and interdendritic regions complicates the analysis of synchrotron diffraction data via any single conventional tool, such as Rietveld refinement. Therefore, a novel approach combining a hard-sphere approximation model, thermodynamic simulation, thermal expansion measurement and microstructural characterization was developed to assist in a fundamental understanding of the evolution of local composition, lattice parameter, and dendrite volume fraction corresponding to the diffraction data. This methodology yields self-consistent results across different methods. Via this approach, four distinct stages were identified, including: (I) FCC dendrite solidification, (II) solidification of FCC interdendritic region, (III) solid-state interdiffusion and (IV) final cooling with marginal diffusion. It was found out that in Stage I, Cu and Mn were rejected into liquid as Mn35Fe5Co20Ni20Cu20 solidified dendritically. During Stage II, the lattice parameter disparity between dendrite and interdendritic region escalated as Cu and Mn continued segregating into the interdendritic region. After complete solidification, during Stage III, the lattice parameter disparity gradually decreases, demonstrating a degree of composition homogenization. The volume fraction of dendrites slightly grew from 58.3 to 65.5%, based on the evolving composition profile across a dendrite/interdendritic interface in diffusion calculations. Postmortem metallography further confirmed that dendrites have a volume fraction of 64.7% ± 5.3% in the final microstructure.

The Effects of Mo and Nb on the Microstructures and Properties of CrFeCoNi(Nb,Mo) Alloys.

The effects of niobium and molybdenum additions on the microstructures, hardness and corrosion behaviors of CrFeCoNi(Nb,Mo) alloys were investigated. All of the CrFeCoNi(Nb,Mo) alloys displayed dendritic microstructures. The dendrites of CrFeCoNiNb and CrFeCoNiNb0.5Mo0.5 alloys were a hexagonal close packing (HCP) phase and the interdendrites were a eutectic structure of HCP and face-centered cubic (FCC) phases. Additionally, the dendrites of CrFeCoNiMo alloys were a simple cubic (SC) phase and the interdendrites were a eutectic structure of SC and FCC phases. The volume fraction of dendrites and interdendrites in these alloys were calculated. The influences of the volume fraction of dendrite in the alloys on the overall hardness were also discussed. The CrFeCoNiNb alloy had the larger volume fraction of dendrite and thus had the highest hardness among these alloys. The CrFeCoNi(Nb,Mo) alloys also showed better corrosion resistances in 1 M H2SO4 and 1 M NaCl solutions by comparing with commercial 304 stainless steel. The CrFeCoNiNb0.5Mo0.5 alloy possessed the best corrosion resistances in these solutions among the CrFeCoNi(Nb,Mo) alloys.

Microstructural characterisation of CuAgZr powder particles produced by argon gas atomisation

ABSTRACTCuAgZr alloy is known for its high strength and high conductivity, which are reasons for its wide application. In this work, CuAgZr powder alloys were produced by high-pressure argon gas atomisation. The results indicate that the surface morphology of the powder is a cellular crystal structure with a pentagonal crystal structure, with a ‘rose-like’ lattice and cross-shaped dendrites. A three-dimensional model of the primary dendritic changes in the CuAgZr alloy powder with different powder diameters was established by studying the surface morphology and internal microstructure of the powder. The relationship between the powder diameter and the powder cooling rate was established as the function of the primary dendritic length (PDL), the primary dendritic volume fraction (PDVF), the secondary dendrite arm spacing (SDAS) and the secondary dendritic volume fraction (SDVF). A confidence validation was performed, and the function fitting error is within 10%. The results establish that the function is meaningful.

Modulating work-hardening behaviors and tensile plasticity of in-situ formed ductile dendrite Ti-based bulk metallic glass composites with tailored dendrite composition

A novel series of in-situ dendrite Ti-based bulk metallic glass composites (BMGCs) were obtained. The Mo content of the dendrites monotonically increases from nil to 10.5at% while the dendrite volume fraction and the composition of the amorphous matrix remain nearly invariant. It was found that the mechanical behaviors varied tremendously simply by changing the Mo content. Thus, the correlation between the composition and the mechanical behaviors under tension has been determined for in-situ dendrite Ti-based BMGCs for the first time.

Tuning plasticity of in-situ dendrite metallic glass composites via the dendrite-volume-fraction-dependent shear banding

This work performs a systematic investigation of identifying how the volume fraction of the in-situ dendrites affects the plasticity of metallic glass composites. The quasi-static uniaxial compressions show that the global plastic strain does not follows a linear rule-of-mixture with the dendrite volume faction, instead, a slow-fast-slow enhancement behaviour is observed with increasing dendrite volume fraction. It is demonstrated that the nucleation and propagation of shear bands in these composites are dependent on the dendrite volume fraction. When the dendrite volume fraction exceeds a critical value, multiple shear bands emerge in a spherical plastic zone around a dendrite. It is further proposed that the percolation of these spherical plastic zones contributes to the fast increase in the plastic strain of the glass composites. Our findings offer important implications for the microstructural optimization of the metallic glass composites with desirable mechanical properties.

Cellular automaton simulation of three-dimensional dendrite growth in Al–7Si–Mg ternary aluminum alloys

Due to the extensive applications in the automotive and aerospace industries of Al–7Si–Mg casting alloys, an understanding of their dendrite microstructural formation in three dimensions is of great importance in order to control the desirable microstructure, so as to modify the performance of castings. For this reason, a three-dimensional cellular automaton model (3-D CA) allowing for the prediction of dendrite growth of ternary alloys is presented. The growth kinetics of the solid/liquid (S/L) interface is calculated based on the solutal equilibrium approach. This proposed model introduces a modified decentered octahedron algorithm for neighborhood tracking, in order to eliminate the effects of mesh dependency on dendrite growth. The thermodynamic and kinetic data needed in the simulations are obtained through coupling with the Pandat software package in combination with thermodynamic/kinetic/equilibrium phase diagram calculation databases. The solute interactions between alloying elements are considered in the model. The model was first used to simulate the Al–7Si dendrite, followed by a validation using theoretical predictions. The influence of Mg content on the dendrite growth dynamics and dendrite morphologies was investigated. Also, the model was applied to Al–7Si–0.5Mg dendrite simulation both with and without a consideration of solute interactions between the Si and Mg alloying elements and the effects on dendrite growth process was analyzed using the simulation results. This model was finally used in order to simulate the dendrite growth in different crystallographic orientations in an Al–7Si–0.36Mg ternary alloy during polycrystalline solidification, resulting in a predicted secondary dendrite arm spacing (SDAS) and dendrite volume fraction data that show a reasonable agreement with experimental results. The single dendrite and polycrystalline growth simulations effectively demonstrate the capability of this model in predicting the three-dimensional dendrite microstructure of ternary alloys.

Effect of cooling rate on solidification parameters and microstructure of Al-7Si-0.3Mg-0.15Fe alloy

The effects of cooling rate on the solidification parameters and microstructure of Al-7Si-0.3Mg-0.15Fe alloy during solidification process were studied. To obtain different cooling rates, the step casting with five different thicknesses was used and the cooling rates and solidification parameters were determined by computer-aided thermal analysis method. The results show that at higher cooling rates, the primary α(Al) dendrite nucleation temperature, eutectic reaction temperature and solidus temperature shift to lower temperatures. Besides, with increasing cooling rate from 0.19 °C/s up to 6.25 °C/s, the secondary dendritic arm spacing decreases from 68 μm to 20 μm, and the primary dendritic volume fraction declines by approximately 5%. In addition, it reduces the length of Fe-bearing phase from 28 μm to 18 μm with a better uniform distribution. It is also found that high cooling rates make for modifying eutectic silicon into fibrous branched morphology, and decreasing block or lamella shape eutectic silicon.

Kinetics of silicon precipitation in a directionally crystallized binary aluminum-silicon alloy

The precipitation of silicon atoms in aluminum in an Al-Si alloy has been studied using differential scanning calorimetry. The alloys containing 8, 13, and 15 wt % silicon were obtained by directional solidification of a ribbon pulled from the melt through a shaper by the Stepanov method at a rate of about 103 μm/s. From the characteristics of the exothermic effects observed in the temperature range 430–650 K, it has been found that the precipitation process leading to the formation of the Guinier-Preston zones occurs with the effective activation energy of 75 kJ/mol, and its intensity decreases with increasing silicon content in the alloy from 8 wt % to the eutectic content. The effect correlates with a decrease in the volume fraction of dendrites of the primary α-Al crystals in the alloy. It can be assumed that the precipitation occurs in the dendrite primary crystals of the solid solution. Based on this assumption, it has been concluded that, during directional solidification of an aluminum-silicon alloy at a rate of 103 μm/s, the metastable solid solution of silicon in aluminum, in which silicon atoms of the metallic lattice are transformed into clusters with covalent bonding forces, is formed during the dendrite growth of the primary crystals.

Ti--BASED AMORPHOUS COMPOSITES WITH QUANTITATIVELY CONTROLLED IN--SITU FORMATION OF DENDRITES

A series of (Ti32.8Zr30.2Ni5.3Cu9Be22.7)100−x (Ti61.5Zr36.4Cu2.1)x (x=10—95) bulk amorphous composites with quantitatively controlled in–situ formation of bcc–dendrites were prepared. The microstructures were analyzed by SEM, XRD and TEM. Thermal behaviors were examined using DSC. The results show that the size and volume fraction of dendrites depend on x in the composites. With increasing x, the volume fraction of dendrites rises monotonically from 20% to 90%. The microstructural transition between the matrix and the dendrites is smooth and successive with no phases observed at the interface. Compression tests show the size and volume fraction of dendrites largely influence the mechanical properties of composites. When the volume fraction is larger than the critical value (approximately 30% in the present work), the plasticity of composites cannot be improved. When the volume fraction is over the critical value, the higher the volume fraction of dendrites, the larger the plastic strain, the stronger the work hardening capacity. It implies that the properties of composite can be mediated by the tunable volume fraction of dendrites. These findings are significant to develop the controllable microstructure and performance materials. When x=90, the plastic strain and the compressive strength of the composites reach 14.4% and 1917 MPa, respectively.

Development of plastic Ti-based bulk-metallic-glass-matrix composites by controlling the microstructures

Lightweight and plastic Ti-based bulk-metallic-glass-matrix composites (BMGMCs) were fabricated by the Bridgman solidification. The β-Ti dendrites were uniformly distributed within the glass matrix. By tailoring the withdrawal velocity, v, the linear dependences of the spanning length, s, and the volume fraction, v f, of dendrites can be determined as: s = −30 v + 139 and v f = −12 v + 50, respectively. The plasticity of Ti-based BMGMCs was extensively studied in terms of the interdendrite spacing and the volume fraction of dendrites. An inverted U-shaped characteristic of the plasticity with the withdrawal velocity has been identified and explained. The present research gave a way for the design of plastic BMGMCs.

Population based quantification of dendrites: evidence for the lack of microtubule-associate protein 2a,b in Purkinje cell spiny dendrites

The high molecular weight isoforms (a and b) of microtubule-associate protein 2 (MAP2a,b) are widely believed to be specific markers for neuronal somata and dendrites. We analyzed and quantified MAP2a,b stained dendrites of the cerebellar molecular layer using a novel approach that segmented and 3D reconstructed them, and the results have been compared with those obtained by other methods, including single-cell reconstruction and analysis of electron micrographs. Our results show that the molecular layer dendritic volume fraction is lower than in the neocortex (10% compared to neocortical 29%). The low total volume fraction of dendrites in the molecular layer is best explained by the majority of the afferents to the dendrites being from the very densely packed parallel fibers, which allows the dendritic fields of individual neurons to be smaller and more compact than in the cerebral cortex. However, the MAP2a,b dendritic volume fraction is even lower (5.2%) than the total volume fraction of dendrites in the molecular layer (10%). Analysis of the material shows that this difference between the two results is due to the unexpected finding that there were few MAP2a,b stained Purkinje cell spiny dendrites.

Deformation and fracture of Ti-base nanostructured composite

Abstract The in-situ formation of nano-eutectic/primary dendrite bulk composites in Ti-base multicomponent alloy systems allows the design of advanced high strength materials, where a nanostructured matrix is combined with ductile β-Ti solid solution dendrites as a toughening phase. This microstructure can be achieved over a wide range of cooling rates. The multicomponent recipe stabilizes the β-Ti phase and helps to reduce the eutectic spacing to the nanometer scale. The superiority in the mechanical properties, i. e. high room temperature ductility (up to 30 %) as well as high strength (up to 2600 MPa), stems from the possibility to tailor the alloy composition leading to the formation of different volume fractions of dendrites in a nanostructured eutectic matrix. All composites with high volume fraction of dendrites offer a high ductility (∊p = 8 – 30 %) and a final failure angle in the range of 46 – 51°. The role of the volume fraction of the dendrites in the composite in enhancing the ductility as well as the fracture angle is critically assessed. The deformation and fracture mechanisms are linked to the macroscopic fracture features as well as to impingement of the shear bands leading to rotation of the shear plane and lattice distortion at the atomic level.

Structure defect prediction of single crystal turbine blade by dendrite envelope tracking model

The structure defects such as stray grains during unidirectional solidification can severely reduce the performance of single crystal turbine blades. A dendrite envelope tracking model is developed for predicting the structure defects of unidirectional solidification turbine blade. The normal vector of dendrite envelope is estimated by the gradient of dendrite volume fraction, and the growth velocity of the dendrite envelope (dendrite tips) is calculated with considering the anisotropy of grain growth. The solute redistribution at dendrite envelope is calculated by introducing an effective solute partition coefficient. Simulation tests show that the solute-build-up due to the rejection at envelope greatly affects grain competition and consequently solidification structure. The model is applied to predict the structure defects (e.g. stray grain) of single crystal turbine blade during unidirectional solidification. The results show that the developed model is reliable and has the following abilities: reproduce the growth competition among the different-preferential-direction grains; predict the stray grain formation; simulate the structure evolution (single crystal or dendrite grains).

Structure simulation in unidirectionally solidified turbine blade by dendrite envelope tracking model(I): numerical modeling

A 3D dendrite envelope tracking model was developed for estimating the solidification structure of unidirectionally solidified turbine blade. The normal vector of dendrite envelope was estimated by the gradient of dendrite volume fraction, and growth velocity of the dendrite envelope (dendrite tips) was calculated with considering the anisotropy of grain growth. The solute redistribution at dendrite envelope was calculated by introducing an effective solute partition coefficient( k e). Simulation results show that the solute-build-up due to the rejection at envelope affects grain competition and consequently the solidification structure. The lower value of k e leads to more waved dendrite growth front and higher solute rejection. The model was applied to predict the structure of turbine-blade-shape samples showing good ability to reproduce the columnar and single grain structures.

Effect of growth rate on microstructure and mechanical properties of directionally solidified multiphase intermetallic Ni–Al–Cr–Ta–Mo–Zr alloy

The effect of growth rate on microstructure and mechanical properties of directionally solidified (DS) multiphase intermetallic alloy with the chemical composition Ni–21.9Al–8.1Cr–4.2Ta–0.9Mo–0.3Zr (at.%) was studied. The DS ingots were prepared at constant growth rates V ranging from 5.56 × 10 −6 to 1.18 × 10 −4 ms −1 and at a constant temperature gradient at the solid–liquid interface of G L = 12 × 10 3 K m −1. Increasing growth rate increases volume fraction of dendrites and decreases primary dendritic arm spacing, mean diameter of α-Cr (Cr-based solid solution) and γ′(Ni 3Al) precipitates within the dendrites. Room-temperature compressive yield strength, ultimate compressive strength, hardness and microhardness of dendrites increase with increasing growth rate. All room-temperature tensile specimens show brittle fracture without yielding. The brittle-to-ductile transition temperature for tensile specimens is determined to be about 1148 K. Minimum creep rate is found to depend strongly on the applied stress and temperature according to the power law with a stress exponent of n = 7 and apparent activation energy for creep of Q a = 401 kJ/mol.

Microstructure and tribological properties of Cu ss-toughened Cr–Cu–Si metal silicide alloys

Wear resistant Cr–Cu–Si metal silicide alloys with different Cu contents were fabricated by the laser melting process. The Cr–Cu–Si alloys have a similar microstructure consisting of the Cr 5Si 3/CrSi dual-phase primary dendrites and the interdendritic Cu-based solid solution (Cu ss). The Cu content has no effect on the phase constitutions of the alloys. The Cr 5Si 3/CrSi dendrite volume fraction and hardness of the Cr–Cu–Si alloys decrease with the increasing Cu content. Wear test results indicate that all the Cu ss-toughened metal silicide alloys have excellent wear resistance and low coefficient of friction. Wear resistance increases and friction coefficient decreases with the decreasing Cu content.

Microstructure control and ductility improvement of La–Al–(Cu, Ni) composites by Bridgman solidification

Microstructure evolutions were experimentally studied as a function of growth velocity and alloy composition in La x Al 14(Cu, Ni) 86 − x alloys ( x = 57–74). The composition–velocity ranges were determined for the formation of eutectic, amorphous, eutectic + compound, amorphous + dendrite, and eutectic + dendrite. A skewed eutectic coupled zone was found towards the compound phase. A composite structure composed of ductile La dendrites in a matrix of either eutectic or amorphous phase can be produced in hypoeutectic alloys. Compressive tests were performed on amorphous/dendrite and eutectic/dendrite composites. As the volume fraction of dendrites increases, fracture strength linearly decreases and obeys a rule-of-mixtures relationship, whereas plastic strain exhibits an exponential increase. Optimised mechanical properties can be realized through both alloy composition design and well-controlled solidification processing.