Directional Solidification Of Alloys Research Articles

Microstructure and room temperature fracture toughness of Nb ss/Nb 5Si 3 in situ composites

The microstructure and room temperature fracture toughness of binary Nb ss/Nb 5Si 3 and ternary Nb ss/Nb 5Si 3 in situ composites alloyed with Mo are investigated at hypo- and hypereutectic compositions, where Nb ss denotes the niobium solid solution. The binary and ternary alloys consist of coarse primary Nb ss particles and fine eutectic at a hypoeutectic composition, while they are composed of fine eutectic at near-eutectic compositions. The room temperature fracture toughness of binary arc-melted alloys is 12 MPa m 1/2 at the hypoeutectic composition and decreases rapidly to about 4.5 MPa m 1/2 at near-eutectic compositions. In the arc-melted alloys, 5%Mo addition increases the fracture toughness up to 9–15 MPa m 1/2 depending on Si content. The fracture toughness of the arc-melted alloys with eutectic microstructure is higher than that of the directionally solidified (DS) alloys with fine microstructure mostly aligned perpendicular to the direction of crack propagation. No significant influence of Mo addition on the toughness is observed for the DS alloys. Scanning electron micrographic observations confirm that the fracture toughness is increased by large scale bridging of thick primary Nb ss particles in the hypoeutectic composition for the binary alloys, and by complicated bridging of Nb ss with maze-like structure at near-eutectic compositions for the ternary alloys. The low fracture toughness of the DS alloys is discussed on the basis of unfavorable interface decohesion.

Effect of growth rate on macrosegregation during directional solidification of a Pb-Sb alloy

Directional solidification experiments on Pb-5.8 wt% Sb alloy have been carried out over growth rates varying from 0.8 to 20 μm s−1 in a positive temperature gradient of 140 Kcm−1. The microstructural examination of this alloy composition indicated cellular to dendritic transition at a growth rate of 1.5 μm s−1. The primary arm spacing was observed to decrease with growth rate in dendritic solidification regime. The maximum primary arm spacing occurred at the growth rate corresponding to the cellular to dendritic transition. Chemical analysis data revealed large amounts of macrosegregation in the longitudinal section of the alloy. A decrease in growth rate resulted in an increased degree of macrosegregation. These effects are discussed in light of thermo-solutal convection in the melt ahead of the solid-liquid interface during directional solidification of this alloy. A parameter ke is used to represent the extent of convection in the melt and the consequent degree of macrosegregation of the alloy with varying growth rates for solidification with a cellular-dendritic interface in the same way as it has been earlier used for the planar-front solidification condition.

Flow-induced patterns in directional solidification: localized morphologies in three-dimensional flows

We consider the effect of steady, three-dimensional cellular convective fields impressed upon the moving front of a dilute binary alloy in directional solidification. The flows have length scales longer than the characteristic lengths of the morphological instability. A Floquet problem with multiple degrees of freedom in space governs the interfacial dynamics and determines the morphological patterns and marginal stability boundaries. In the cases of weak flows the induced patterns are superpositions of rolls modulated by the forced flows. When the flows are strong, the instability becomes spatially localized and confined at inward flow-stagnation regions on the front. Numerical computations and the WKB method are used to solve the eigenvalue problems, showing various localized states depending on the structures of the imposed flows.

Phase transformation studies at the solid/liquid interface by directional solidification of Alloy 718

The phase transformation temperatures are especially important in alloy 718 because it requires careful heattreatment cycles. The DTA method is generally used to estimate the characteristic temperatures of phase transformations. However, DTA is an indirect method to confirm phase transformations, and there are always discrepancies in analyzing the DTA thermograms. In this study, the directional solidification and quenching technique has been applied to estimate the phase transformation temperatures near the solid/liquid interface temperatures by measuring temperatures directly during directional solidification. These phase transformation temperatures were confirmed in the quenched solid/liquid interface. Solidification behavior at the solid/liquid interface with solidification rate and temperature gradient were also discussed.

Directional solidification of TiAl–Si alloys using a polycrystalline seed

Directional solidification (DS) process of Ti–43Al–3Si alloys has been studied. Successful DS ingots having not only fully lamellar microstructure parallel to longitudinal axis but also rotated columnar grains with respect to longitudinal axis were obtained using a polycrystalline seed material. Successful seeding and growing require plane-front solidification condition during the entire DS process. Fracture toughness of the DS alloys were superior to the PST alloys, with a value of K Q=21.7–31.7 MPa (m) 1/2 for the crack arrest/divide mode and K Q=7.4–19.0 MPa (m) 1/2 for the short transverse mode. The orientation dependence of fracture toughness for the crack arrest/divide mode was improved in the DS alloy compared to the PST alloy.

Microstructural stability, hardness and compressive behaviour of directionally solidified intermetallic Ni 3Al-based alloy with γ/γ′-β structure

Microstructural stability, hardness and compressive behaviour were investigated in directionally solidified (DS) Ni–20.2Al–8.2 Cr–2.44 Fe (at.%) alloy. The as-grown lamellar γ(Al)/γ′(Ll 2)-β(B2) structure of DS alloy is found to transform to a γ/γ′-α(A2) structure during annealing in the temperature range 1023–1173 K. This annealing is connected with precipitation of spherical α-Cr particles within the lamellae and lath-shaped α-Cr particles in the interlamellar γ/γ′-region. The size of the lath-shaped α-Cr precipitates depends on the annealing temperature. However, these precipitates are found to be relatively stable with respect to their size and morphology during annealing for 100–600 h at given temperature. Annealing at temperatures higher than 1210 K stabilises β-lamellae in the microstructure. The volume fraction of transformed lamellae is found to follow ΔV l ∝ t 1/ n law with n=4 and the activation energy for lamellae transformation is determined to be Q=236 kJ/mol. The kinetics of lamella transformation is proposed to be governed by diffusion along disordered regions bounding growing ordered domains of γ′-phase around the lamellae. The peak hardness and γ/γ′-region microhardness values are reached after 100 h annealing at 1023 K. The compressive yield stress increases with increasing temperature, reaching a peak value at about 1000 K, and rapidly decreases at higher temperatures. The quasi-steady strain-hardening rate decreases with increasing temperature in the temperature range 773–1273 K. Both yield stress and strain-hardening rate depend on strain rate.

The relationship between dendrite tip characteristics and dendrite spacings in alloy directional solidification

We summarize and discuss a new theoretical model for the directional solidification of alloys in the form of dendrite arrays. Slender body theory is used to obtain an integral equation for the dendrite shape in the asymptotic limit of the dendrite tip radius being much smaller than the solute diffusion length. This equation has a solvability condition that selects the shape and tip undercooling for prescribed solidification conditions and array spacings. A consequence of our results is that we obtain a unique solution to the well-known indeterminacy for the single-dendrite [2] similarity solution by considering the interaction between individual members of an array of dendrites. Further, the dependence of the solutions on the dendrite spacing gives a family of “array solutions,” in which the tip radius is related directly to the dendrite spacing. These solutions agree well with experiments in parameter ranges where the slender dendrite theory is expected to be valid. Finally, we discuss how these array solutions, together with surface energy and stability considerations, can describe the selection of dendrite spacings during directional solidification.

Composition and growth rate effects in directionally solidified TiAl alloys

Abstract Effects of alloy compositions and growth rates on the microstructure and the deformation behavior of fully lamellar TiAl alloys were systematically investigated by directional solidification (DS) techniques. Some β stabilizing elements, such as Mo, Nb and Cr, have been added in order to increase the β phase field in the binary system. It was found that the lamellar orientation was aligned nearly 0–45° to the growth direction in Ti–46Al–2Nb and Ti–46Al–2Cr(at.%) DS ingots grown at the growth rate of 90 mm h −1 . Therefore, it could be concluded that there is a good possibility to control the lamellar orientation by adding some β stabilizing elements, such as Mo, Nb and Cr, in the TiAl system. In the Ti–47.5Al–2.5Mo DS alloy, the lamellar boundary was nearly perpendicular to the growth direction at growth rates of 180 and 360 mm h −1 , however, it was nearly parallel to the growth direction at the growth rate of 90 mm h −1 . These results indicate that the lamellar boundary orientation of DS ingot has been affected by the growth rate as well as the alloy composition.

Effect of ageing on the microstructure and mechanical behaviour of a directionally solidified Ni3Al-based alloy

Abstract The effect of ageing in the temperature range from 1023 to 1373 K on the micro-structure and mechanical behaviour of a directionally solidified (DS) Ni3Al-based alloy modified with additions of chromium and iron was investigated. The microstructure of the as-grown alloy consisted of well-aligned and equally spaced lamellas composed of β(B2) intermetallic compound NiAl (Cr, Fe), some β′(L10) martensite and spherical α-Cr precipitates. The matrix consisted of γ′(L12) intermetallic compound Ni3Al (Cr, Fe), γ-phase (Ni-based solid solution) and lath-shaped α-Cr precipitates. Ageing at 1123 and at 1173 K was found to be the most effective in transforming the unstable lamellae to γ′-phase and α-Cr precipitates. The change of microstructural characteristics such as volume fraction of lamellae, size, morphology and distribution of γ′-phase, γ-phase and α-Cr precipitates significantly influenced the room-temperature yield strength and elongation of DS alloy after ageing. The strain-hardening exponent varied with the ageing temperature between 0.30 and 0.46 and the quasi-steady work-hardening rate between 2710 and 5340 MPa. In the specimens with the lowest amount of disordered regions, the strain-hardening exponent was found to be 0.46 and the quasisteady work hardening rate was determined to be 3340 MPa.

Ｎｉ基超合金の微小疲労き裂進展に及ぼす温度の影響

Based on the measurement of crack opening-closing behavior, the effect of temperature on small fatigue crack growth behavior was investigated in three kinds of Ni-base superalloys at the temperature range of 873K to 1123K, in comparison with the physically long crack properties; a polycrystalline alloy (CM247LC-CC), a directionally-solidified alloy (CM247LC-DS) and a single crystal alloy (CMSX-2) at temperatures of 873K, 1023K and 1123K. It was found that the propagation resistance and the fatigue threshold of long crack increased with temperature in all of the materials on an appearance. However, the long crack growth rates at three different temperatures were approximately represented by an unique curve, by taking account of temperature dependences not only of crack closure level but also of elastic modulus. On the other hand, the small fatigue crack growth resistance decreased with temperature even when the crack closure phenomenon was taken into account. In addition, the small fatigue crack exhibited considerably higher growth rate than the long crack at a given effective stress initensity factor range, and grew even at the lower effective stress intensity factor range than the long crack threshold. Based on the results thus obtained and the chemical analysis near crack propagation plane, the factors which lead to the lack of similitude in propagation law between small and long cracks were also discussed.

き裂開閉口測定に基づくＮｉ基超合金の高温における微小疲労き裂進展の調査

Fatigue small crack growth behavior was studied in three kinds of Ni-base superalloys at high temperature and was compared with the physically long crack behavior; a single crystal alloy, CMSX-2, a directionally-solidified alloy, CM247LC-DS and a polycrystalline alloy, CM247LC-CC. The crack opening-closing behavior was also measured by means of a new device originally developed and improved. The experimental results indicated that the small cracks exhibited a higher growth rate than the long cracks at the same stress intensity factor range in all of the materials. However, the rates of small crack growth in the CMSX-2 and CM247LC-DS agreed with those of the long crack, when they were correlated with the effective stress intensity factor. This shows that the crack opening-closing effect is mainly responsible for difference of small and long crack growth rates. In contrast to these two materias, the lack of similitude between small and long crack propagation rates was still found in CM247LC-CC, even if the crack closure effect was taken into account.

Interface dynamics and coupled growth in directional solidification in presence of bubbles

The formation and dynamics of gas bubbles in Bridgman growth of succinonitrile-acetone alloys is examined. The experimental results show for the first time the rich dynamics that are associated with the formation and propagation of bubbles during directional solidification of alloys. The strong coupling of bubbles with the solid-liquid interface is found to result in the growth of elongated bubbles, either attached to a flat solidification front or forming localized cellular as well as dendritic duplexes (bubbles wrapped by a solid envelope). The coupling of the bubble with the solidification front is shown to cause oscillations in the bubble, which are characterized by fast Fourier transforms. When several duplexes are formed, coupled growth and screening may occur. The basic factors that give rise to oscillations, namely competition between source and sink of acetone assisted by capillary convection at the bubble cap, are discussed qualitatively through the development of an internal oscillator model. Coherent sidebranching observed on dendritic duplexes is shown to be due to resonant modes between the bubble cap and the solid envelope.

Nonlinear local dynamics of the melt/crystal interface of a binary alloy in directional solidification.

Numerical simulations of large-amplitude cellular dynamics during thin-film, directional solidification of a succinonitrile-acetone alloy demonstrate strongly nonlinear local dynamics that involve oscillations of the deep grooves between the cells. The oscillations begin as breathing modes of the grooves and become more complex, showing period doubling, when the simultaneous dynamics of more than one groove is considered. These oscillations are not predicted by amplitude equations derived for cells near the planar interface. Simulations of the onset of cellular solidification demonstrate the importance of this mechanism to explain the scattered finite-amplitude cells that are observed in experiments near the onset of cellular solidification.

Array of doublets: A branch of cellular solutions in directional solidification.

In directional solidification of alloys, the interface pattern assumes a cellular structure, with a periodic array of cells, when the velocity is increased beyond the threshold of planar interface instability. A detailed experimental study in the succinonitrile-acetone system has revealed a branch of cellular structure in which the interface pattern consists of a periodic array of coupled cells or doublets. This doublet interface evolves with two characteristic length scales at the advancing front: a small intraspacing between the cells in a doublet, whose selection is sharp, and a larger interspacing corresponding to the distance between cells in adjoining doublets, whose selection is weak. The dynamics of the time-dependent evolution of a doublet interface is investigated by statistical analysis of tip spacings, by using a Fourier transform of the interface shape and through the study of the variation of shape parameters with time. These dynamical studies have confirmed the selection of doublet interface as a stable solution of the cellular pattern formation. A range of stable regime for an array with doublets is determined and the key factor that controls the formation of regular cells or doublets in an array is discussed. When doublets are unstable, time dependency may follow due to a source mechanism at grain boundaries, which induces strong spatiotemporal chaos.

Phase quasi-integral for stimulated Raman scattering initiated by quantum fluctuations and statistics of solitonlike random pulses in a depleted pump.

In directional solidification of alloys, the interface pattern assumes a cellular structure, with a periodic array of cells, when the velocity is increased beyond the threshold of planar interface instability. A detailed experimental study in the succinonitrile-acetone system has revealed a branch of cellular structure in which the interface pattern consists of a periodic array of coupled cells or doublets. This doublet interface evolves with two characteristic length scales at the advancing front: a small intraspacing between the cells in a doublet, whose selection is sharp, and a larger interspacing corresponding to the distance between cells in adjoining doublets, whose selection is weak

Experimental results on the analogy between Saffman-Taylor fingers and the cellular pattern in directional solidification of an alloy.

Precise undercooling measurements at the cell tips of solid-liquid cellular interfaces in directional solidification of a dilute succinonitrile alloy in a rectangular channel are made in a metastable regime that is unstable relative to a longer-wavelength pattern seen at larger undercooling. As the pattern coarsens, its wavenumber scales with undercooling. The data are consistent with an unstable cellular pattern predicted for the Saffman-Taylor analogy of directional solidification.

Primary dendrite spacing in constrained solidification

A theory of primary dendrite spacing γ 1 in directional solidification of alloys is developed based on thermodynamic and geometric arguments. The results for a cubic material is γ 1 = ( πΔTR/ G) 0.5), where ΔT is the unit undercooling, R is the tip radius and G is the temperature gradient. This prediction is in quantitative agreement with experimental data.

Vertical solidification of dendritic binary alloys

Three numerical techniques are employed to analyze the influence of thermosolutal convection on defect formation in directionally solidified (DS) alloys. The finite-element models are based on the Boussinesq approximation and include the plane-front model and two plane-front models incorporating special dendritic regions. In the second model the dendritic region has a time-independent volume fraction of liquid, and in the last model the dendritic region evolves as local conditions dictate. The finite-element models permit the description of nonlinear thermosolutal convection by treating the dendritic regions as porous media with variable porosities. The models are applied to lead-tin alloys including DS alloys, and severe segregation phenomena such as freckles and channels are found to develop in the DS alloys. The present calculations and the permeability functions selected are shown to predict behavior in the dendritic regions that qualitatively matches that observed experimentally.

Stability of dendritic arrays.

An approximate method for studying steady-state properties and linear stability of the dendritic arrays that are formed in directional solidification of alloys is proposed. This analysis is valid at high growth rates where the primary spacing between dendrites is larger than the velocity-dependent solutal diffusion length. A neutral stability boundary is computed and it is found that, in the situations where the results should be valid, the experimental data of Somboonsuk, et al. (1984) lie in the stable region, well away from the boundary.

一方向凝固Ａｌ‐Ｌｉ合金を用いた高温高サイクル疲労における第１段階き裂進展挙動の観察

High-cycle fatigue tests were carried out using directionally-solidified Al-Li alloy at 453K, and the first stage fatigue crack growth behavior was investigated by employing an elaborate replication technique. It was shown that the directionally-solidified alloy predominantly revealed the typical stage I fatigue fracture; that is, the fracture occurred on the crystallographic {111} slip planes and preferentially in <101> directions, which are the most important slip system in f.c.c. materials. It was also found that the rate of the stage I crack growth, whose crack tip was far apart enough from neighbouring grain boundaries, proportionally increased with crack length, and that it rapidly decreased as the crack tip approached to neighbouring grain boundaries. Such a stage I crack growth behavior was compared with Tanaka model, which was proposed based on the phenomenon that the crack tip plastic deformation at small crack tip was blocked by neighbouring grain boundaries. The stage I crack growth behavior not only far apart from but also near grain boundaries obtained in this work could be successfully evaluated by Tanaka model. The above results suggested that the crack tip sliding displacement played an important role in the stage I crack growth.