Growth of interdendritic eutectic in directionally solidified Al-Si alloys

Interdendritic eutectic microstructures in Al-Si (6 to 12.6 wt pct Si) alloys have been investigated as a function of growth velocity and temperature gradient. The interface morphology, as well as the behavior of the eutectic spacing and undercooling, suggest that the resultant microstructure is governed by two different growth processes. That is, at low growth rates, steady-state columnar eutectic growth is found and obeys the relationship, λ²V = constant, where λ is the eutectic spacing andV is the growth rate. At higher growth rates, the nucleation of equiaxed eutectic grains occurs in the interdendritic liquid. The experimental findings are interpreted in the light of recently developed models for the columnar to equiaxed transition and for irregular eutectic growth.     

The Effect of Fluid Flow on the Eutectic Lamellar Spacing

The effect of fluid flow on the lamellar spacing of unidirectionally solidified Al-CuAl₂ eutectic alloy has been investigated experimentally. It was found that the practical condition for the modification of lamellar spacing can conveniently be given byPe > 1(Pe = Uλ/2D, whereU: flow rate, λ : lamellar spacing,D : solute diffusion coefficient in the melt), when the value ofU at the characteristic distance λ/8 ahead of the solid-liquid interface is used. The theoretical prediction of the relation between λ andv, given by Quenisset and Naslain, λ²v = A/(1 − BG_uλ²/D) where G_u is the flow velocity gradient at the solid-liquid interface and v is the solidification rate, was confirmed to be valid. The numerical constantsA andB are determined to be 8.46 x 10^-17 m³ per second and 1.56 × 10^-2, respectively. Associate Professor, on leave from the Department of Metallic Materials and Technology, Dalian Institute of Technology, Dalian, China.     

A new analytical approach to predict spacing selection in lamellar and rod eutectic systems

The Jackson and Hunt (JH) theory has been modified to relax the assumption of isothermal solid/liquid interface used in their treatment. Based on the predictions of this modified theory, the traditional definitions of regular and irregular eutectics are revised. For regular eutectics, the new model identifies a range of spacing within the limits defined by the minimum undercooling of the α and β phases. For the irregular Al-Si eutectic system, two different spacing selection mechanisms were identified: (1) for a particular growth rate, a nearly isothermal interface can be achieved at a unique minimum spacing λ _I ; (2) the average spacing (λ _av >λ _I ) is essentially dictated by the undercooling of the faceted phase. Based on the modified theoretical model, a semiempirical expression has been developed to account for the influence of the temperature gradient, which is dominant in the irregular Al-Si system. The behavior of the Fe-Fe₃C eutectic is also discussed. The theoretical calculations have been found to be in good agreement with the published experimental measurements.     

Ordering and the strength of an aligned Ag3Mg-AgMg eutectic

A fine lamellar structure with interlamellar spacings from 1 to 7μ has been produced by directional solidification of an Ag₃Mg-AgMg eutectic alloy. The tensile properties were measured as a function of test temperature, interlamellar spacing,λ, and degree of order in the Ag₃Mg phase. The dependence of flow stress onλ ^-1/2 increased sharply with ordering of Ag₃Mg and this strengthening persisted at elevated temperatures. Work hardening rate and ductility of the eutectic at low temperatures also were affected, leading to the conclusion that ordering changes the compatibility of slip across interphase boundaries.     

The effect of matrix strength on void nucleation and growth in an alpha-beta titanium alloy,CORONA-5

This work was undertaken to examine the effect of increasing matrix strength at constant equiaxed microstructure on void nucleation and growth in the titanium alloy, CORONA-5, Ti-4.5Al-5Mo-1.5Cr. A martensite and a beta matrix were used in the as-quenched and the heat treated conditions. For each matrix, fine and coarse alpha sizes were produced and a third size of alpha was used for the as-quenched condition of the martensite series. The processing procedures produced an aligned alpha structure which was most pronounced in the fine structure. Void nucleation occurred in an aligned fashion and took place predominantly atα /martensite orα/β interfaces. An explanation is offered for the aligned nucleation in terms of nonuniform deformation of the banded structure which appeared most prominently after heat treatment to produce the coarser microstructure. An incubation strain was found for both types of matrices. The incubation strain increased for the interface in the following order: martensite/martensite,α /martensite, andα/ β. The incubation strain for martensite/martensite interfaces was relatively independent of the matrix strength. Void growth as a function of true strain was generally found to occur in two stages, a slow stage I and a more rapid stage II. Stage II growth occurred as a result of coalescence of voids growing toward one another from nearby particles. Stage II growth was more rapid for the martensite matrix than for theβ matrix. For the martensite matrix void growth rates could not be accounted for either on the basis of strength or strain hardening rates. However, the longest void growth rate was found to increase as the function λ ^N /d _α ^L increased. λ^N is the interparticle spacing normal to the tensile axis and _α ^L is the alpha particle size parallel to the tensile axis. For the beta matrix void growth rates increased with increasing yield s trength and decreased with increasing strain hardening. It was not possible to relate fracture strength to an extrapolated longest void at fracture as was done in earlier studies. This is explained in terms of the nonuniformity of fracture paths observed in the alloy.     

Modeling structure parameters of irregular eutectic growth: Modification of Magnin-Kurz theory

A new approach to irregular eutectic growth (faceted/nonfaceted crystallization) in Fe-C and Al-Si alloys has been presented in this article. The results of unidirectional crystallization of the irregular eutectic in the Fe-C, Al-Si, and Al-Fe systems were used for the experimental verification of the resulting model. For the oriented graphite, α(Al)-Si and α(Al)-Al₃Fe eutectics, a decrease of the interlamellar spacing λ and in protrusion δ_β of the nonfaceted phase (austenite, α(Al)) by the leading faceted phase (graphite, silicon, and Al₃Fe), the increase of growth rate v was observed. The Magnin-Kurz theory of irregular eutectic growth has been modified in order to better understand the physical mechanisms driving the crystallization process. A comparison of the measured and calculated average λ values has revealed good agreement for the (γ)Fe-graphite, α(Al)-Si, and α(Al)-Al₃Fe eutectics. The developed model also considered the influence of the material constants of the examined alloys on the interlamellar spacing and protrusion of the leading phase—graphite, silicon, and Al₃Fe. It has been found that material constants such as the wetting angle, diffusion coefficient, and Gibbs-Thomson coefficient are of great importance in this eutectic growth.     

Overstability of lamellar eutectic growth below the minimum-undercooling spacing

We investigate the stability of lamellar eutectic growth by thin-sample directional solidification experiments and two-dimensional phase-field simulations. We find that lamellar patterns can be morphologically stable for spacings smaller than the minimum undercooling spacing λ _m . Key to this finding is the direct experimental measurement of the relationship between the front undercooling and spacing, which identifies λ _m independently of the Jackson and Hunt (JH) theory and of uncertainties of alloy parameters. This finding conflicts with the common belief that patterns with λ<λ _m should be unstable, which is based on the Jackson-Hunt-Cahn assumption that lamellae grow normal to the envelope of the front. Our simulation results reveal that lamellae also move parallel to this envelope to reduce spacing gradients, thereby weakly violating this assumption but strongly overstabilizing patterns for a range of spacing below λ _m that increases with G/V (temperature gradient to growth rate ratio). This range is much larger than predicted by previous stability analyses and can be significant for standard experimental conditions. An analytical expression is obtained phenomenologically, which predicts well the variation of the smallest stable spacing with G/V. We also present results that shed light on the history-dependent selection and long-time evolution of the experimentally observed range of spacings.     

Structure and mechanical properties of unidirectionally solidified Fe-Cr-C and Fe-Cr-X-C alloys

In this work four different microstructures were obtained by unidirectional solidification of Fe-Cr-C eutectic alloys. Conditions for zone coupled growth were determined in alloys containing approximately 30 wt pct chromium. Furthermore, mechanical testing indicated that the maximum strength was exhibited by Fe-30Cr-C alloys with cerium or titanium additions. These alloys had the largest volume fraction of eutectic fibers and their ultimate tensile strength was of the order of 3250 MPa. Correlations between the rate of crystal growth(u) and fiber spacing (λ) or tensile strength(Rm) were found and an expression of the typeRm = Aλ^-b2 was obtained whereb ₂ varied between 0.283 and 0.685. Finally, manganese or chromium (35 wt pct Cr) additions did not lead to appreciable improvements in composite strength for this alloy system.     

Unidirectional transformation of Fe-0.8C-Co alloys: Part II. Kinetics of the eutectoid reaction

Unidirectional transformation techniques have been applied to a study of the kinetics of eutectoid growth in Fe-0.8C-Co alloys. The technique readily yielded kinetic data which it is shown could be used to indicate the rate controlling process for pearlitic growth. Accurate measurements of interlamellar spacing (λ) could be made at controlled growth rates (V) and analyzed in terms of the expressionVλⁿ, where the exponentn can indicate the rate controlling process. The results obtained by unidirectional transformation were compared with those achieved by conventional isothermal transformation, both to aid in the initial interpretation of the more unfamiliarV:λ data and also to show that the two different experimental routes lead to equivalent kinetic data. Analysis of the results obtained for Fe-0.8C-Co alloys suggested control by interfacial diffusion of carbon at high growth rates (n=3) changing towards volume diffusion of carbon at lower growth rates (n=2), but also revealed an unexpected region at very slow growth rates (n=4). This anomalous region could be explained in terms of the partitioning of cobalt as the growth rate decreased. It was also shown that cobalt additions decreased the pearlite interlamellar spacing at constant undercooling or growth rate. B. G. MELLOR, formerly Research Student, Department of Metallurgy and Materials Science, University of Cambridge, U. K., is now     

The influence of interparticle spacing on cyclic deformation and fatigue crack propagation in an aluminum-4 Pct copper alloy

A high purity Al-4 pct Cu alloy has been overaged for two different times at 400°C giving interparticle spacings (λ) of about 0.53 and 1.37 μm. Cyclic plasticity of the alloy with the smaller interparticle spacing can be explained in terms of plastic deformation behavior controlled by the structure whereas that for the alloy with the larger interparticle spacing is controlled by the matrix. The fatigue lives of the weaker alloy (λ = 1.37 μm) may be accurately predicted using the models of Coffin-Manson and Tomkins, however, these models are not applicable to the stronger alloy (λ = 0.53 μm). It was found that the crack tip opening displacement at the threshold stress intensity range (ΔK_th) was equivalent to the interparticle spacing. ΔK_th is related to the cyclic yield stress, σ_cy and the interparticle spacing in the following manner: ΔK_th ≈ (2 Eλσ_cy)^1/2, whereE is the modulus of elasticity. In the present case, the term λσ_cy is constant, giving the impression that ΔK_th is independent of the mechanical properties and microstructure. At very low growth rates, however, the fatigue crack growth is independent of these parameters and also the method of cyclic deformation. A transition to higher crack growth rates occurs when the plastic zone size reaches approximately one-seventh of the specimen thickness, allowing a nonplanar crack front to be developed. The value of the stress intensity range (ΔK_T) at this transition was found to be dependent upon the interparticle spacing according to the relation: ΔK_Tλ = 9.6 Pa-m^3/2. Formerly Lecturer and Research Associate, Department of Mechanical Engineering, University of Waterloo     

On the contribution of concurrent grain growth to strain

Flow behavior and microstructural evolution in an Al-Cu eutectic alloy of equiaxed grains were investigated over ε ≃ 2× 10⁻⁶ to 2 × 10⁻² s⁻¹ andT = 400° to 540 °C. Depending on the test conditions, there appeared either strain hardening or strain softening predominantly in the early part of the σ-ε curves. The microstructural observations showed evidence for grain growth, development of zig-zag boundaries, dislocation interactions, and cavitation. The grain growth adequately accounts for the observed strain hardening at higher temperatures and lower strain rates. However, at lower temperatures the strain hardening can be only partly accounted for by the observed grain growth; under this condition, some dislocation interactions also contribute to the strain hardening. The presence of cavitation causes strain softening predominantly at higher strain rates. Therefore, to develop a proper understanding of the superplastic behavior of the Al-Cu eutectic alloy, it is necessary to take into account the influence of dislocation interactions and cavitation along with that of grain growth.     

The dendrite arm spacings of aluminum-copper alloys solidified under steady-state conditions

Aluminum-copper alloys of different composition have been solidified under steady-state conditions with known growth velocities and temperature gradients. Specimens were quenched during solidification to reveal the dendrite growth morphology and to allow the solute content at dendrite tips to be analyzed. Primary and secondary arm spacings have been measured as a function of the distanced behind the growing dendrite tips, the tip velocityR the temperature gradient in the liquid G_l and the solute content. The primary arm spacing λ₁ is described for each alloy by the empirical relation: λ₁ = kG_L ^-aR^-b wherek is a constant, and both a and b are close to 1/2; λ₁ is also found to increase with solute content. The secondary arm spacing λ₂ for each alloy increases with timeθ spent in the liquid/solid region, being directly proportional to θⁿ where n is close to 1/3; increasing solute content however causes a reduction in λ₂. It is suggested that the observed “coarsening” of the secondary arms is primarily a coalescence phenomenon. Formerly at Sheffield University     

Fatigue crack propagation in two classes of directionally solidified eutectic alloys

Fatigue crack propagation rates were measured in two classes of directionally solidified eutectic alloys under isothermal, stress-controlled cycling at temperatures of 298 to 1311 K. Alloy 73C, a cobalt-base material reinforced by fibers of Cr₇C₃, and γ/γ′ + δ, a nickel-base alloy reinforced by lamellae (platelets) of Ni₃Cb, were grown at solidification rates of 1 and 25 cm/h to achieve significant differences in interfiber and interlamellar spacing (λ). No influence of the spacing of the reinforcing phase on crack growth rates were found for either alloy. In addition, chromium level and perfection of the microstructure had a minimal effect on propagation rates for γ/γ′ + δ. The independence of the fatigue crack growth rates on λ may be associated with the ratio of the cyclic plastic zone diameter at the crack tip to λ. In all instances, this ratio was estimated to be greater than one for the test conditions employed. At the lower temperatures, crack propagation rates in γ/γ′ + δ were up to two orders of magnitude lower than those in Alloy 73C due to crack deflection at interlamellar interfaces and grain boundaries which lowered the effective stress intensity range for opening mode cracking. Formerly of Pratt & Whitney Aircraft     

The effect of microstructure on fracture toughness and fatigue crack growth behavior in γ-titanium aluminide based intermetallics

Ambient-temperature fracture toughness and fatigue crack propagation behavior are investigated in a wide range of (γ+α ₂) TiAl microstructures, including single-phase γ, duplex, coarse lamellar (1 to 2 mm colony size (D) and 2.0 μm lamellar spacing (λ)), fine lamellar (D ∼ 150 μm, λ=1.3 to 2.0 μm), and a powder metallurgy (P/M) lamellar microstructure (D=65 μm, λ=0.2 μm). The influences of colony size, lamellar spacing, and volume fraction of equiaxed γ grains are analyzed in terms of their effects on resistance to the growth of large (>5 mm) cracks. Specifically, coarse lamellar microstructures are found to exhibit the best cyclic and monotonic crack-growth properties, while duplex and single-phase γ microstructures exhibit the worst, trends which are rationalized in terms of the salient micromechanisms affecting growth. These mechanisms primarily involve cracktip shielding processes and include crack closure and uncracked ligament bridging. However, since the potency of these mechanisms is severely restricted for cracks with limited wake, in the presence of small (<300 μm) cracks, the distinction in the fatigue crack growth resistance of the lamellar and duplex microstructures becomes far less significant.     

Tensile properties of directionally solidified Al-4 wt pct Cu alloys with columnar and equiaxed grains

The tensile properties of directionally solidified Al-4 wt pct Cu-0.15-0.2 wt pct Ti alloys with equiaxed grains were determined and compared with the properties of directionally solidified Al-4 wt pct Cu columnar structures. The tensile properties of the equiaxed structure were isotropic, but varied with the distance from the chill face. The mechanical properties of the equiaxed structure were generally between those of the longitudinal and transverse columnar structures. The 0.2 pct offset yield stress(σ _y, MPa) is represented as a function of the grain size,d (mm), the average concentration, C_o (wt pct), and the local concentration, C (wt pct), by σ_y = [(15.7 + 22.6 C_o) + (1.24 + 1.04 C_o)d ^-1/2] + [15.7 △C], where △C = C - C_o. The equiaxed structure exhibits inverse segregation similar to that in the columnar structure.     

The thermal expansion of the directionally solidified AI-CuAI2 eutectic

Alloys of Al-CuAl₂ eutectic composition were prepared from 99.999 pct pure materials and directionally solidified in a temperature gradient of about 45 °C/cm at different growth ratesR. The λ²R= constant relation was verified and lamellar spacings of 7.5, 3.5, 2.6, 1.8 and 1.4 μm were obtained. Dilatometer specimens were machined with axes aligned in the principal lamellae coordinate directions. Thermal expansion was measured by standard dilatometry (Cu standard) using a set point program cycling between room temperature and 500 °C. Thermal expansion of the directionally solidified Al-CuAl eutectic is greatest in the growth direction (in the plane of the lamellae), least in the tranverse direction (orthogonal to the growth direction in the plane of the lamellae) and intermediate in the direction normal to the lamellae. The most significant finding of the study is that the thermal expansion increases with decreasing lamellar spacing between limits defined approximately by the thermal expansion of the CuAl₂ phase alone and the predicted thermal expansion of an isotropic elastic model of the composite.     

Response of primary dendrite spacing to varying temperature gradient during directional solidification

The response of primary dendrite spacing λ to a change in solidification condition is examined through the directional solidification of a succinonitrile-acetone alloy. While the growth velocity was kept constant, the thermal gradient G was altermately varied between two extreme values. The measured average dendrite spacing is compared to a calculation involving a previously proposed model, revealing good correlation. The investigation results enable us to characterize some important features about dendrite spacing evolution: during alternately changing G, dendrite spacing λ varies along different paths; after changing G-variation direction at turning points, the incubation periods required for the initiation of λ variation are much longer than those at the initial stage; as G changes back to its initial state, λ cannot return to its original value, revealing an unclosed hysteresis loop for the λ-G diagram; and continuing the process of alternately changing G will result in the formation of a closed loop. This kind of hysteresis loop is repeatable and roughly the same for varying G in reverse sequences. Thus, becoming free of the effect of the initial state, λ varies in nearly the same way for the same change in process condition, regardless of the difference in previous history.     

The transition from columnar to equiaxed dendritic growth in proeutectic,low-volume fraction copper,Pb−Cu alloys

Lead, 17.1, 11.2, and 5 volume fraction copper (14, 9, and 4 wt pct Cu) alloys have been directionally solidified at constant growth velocities ranging from 1 to 100 μm s⁻¹. Serially increasing the growth velocity within this range results in a graded microstructural transition from fully columnar, albeit segregated, copper dendrites in a lead matrix to one consisting only of equiaxed grains. The imposed velocity necessary to effect fully equiaxed growth is found to drop rapidly as the volume fraction of copper is decreased. Factors which complicate the controlled, directional solidification of these alloys are discussed and the experimental results are interpreted in view of, and seen to be in qualitative agreement with, Hunt’s theory on the transition from columnar to equiaxed growth of dendrites.     

The direct observation of solidification as a function of gravity level

The solidification of a metal-model material, NH₄Cl−H₂O, was directly observed on Earth at 1 g and at 10⁻⁵ g on a suborbital rocket flight. In the 1 g experiments, nucleation started at the cold walls and then dendrites and dendritic debris were swept into the central region by fluid flow. The numerous crystals in the central zone created an equiaxed zone. Secondary dendrite arms were oriented toward the cold wall with suppressed arm growth in the direction of the flow pattern. The necking and fragmentation of secondary arms were observed. The variation in secondary and tertiary arm spacing ranged from 27 to 38 pct. Individual dendrites grew at similar rates to interface fronts. When solidified in low g, only four nuclei grew to form the complete casting. There were no free floating crystals or visible dendrite remelting. Symmetrical dendrite growth into the fluid and some necking of secondary arms occurred but no coarsening or fragmentation resulted. The growth rate of interfaces was less than that of individual dendrites. Total growth was columnar with no equiaxed zone being formed.     

Directional solidification of white cast iron

Several studies of the ledeburite eutectic (Fe-Fe₃C), in pure Fe-C alloys have shown that it has a lamellar morphology under plane front growth conditions. The structure of ledeburite in white cast irons, Fe-C-Si, consists of a rod morphology. It is generally not possible to produce plane front growth of Fe-C-Si eutectic alloys in the Fe-Fe₃C form, because at the slow growth rates required for plane front growth, the Fe₃C phase is replaced by graphite. By using small additions of Te, the growth of graphite was suppressed, and the plane front growth of the ledeburite eutectic in Fe-C-Si alloys was carried out with Si levels up to 1 wt pct. It was found that the growth morphology became a faceted rod morphology at 1 wt pct Si, but in contrast to the usual rod morphology of white cast irons, the rod phase was Fe₃C rather than iron. It was shown that the usual rod morphology only forms at the sides of the two-phase cellular or dendritic growth fronts in Fe-C-Si alloys. Possible reasons for the inability of plane front directional solidification to produce the usual rod morphology in Fe-C-Si alloys are discussed. Also, data are presented on the spacing of the lamellar eutectic in pure Fe-C ledeburite, which indicates that this system does not follow the usual λ² V = constant relation of regular eutectics. Formerly Graduate Student, Department of Materials Science and Engineering, Iowa State University.