On the Mechanism of Macrosegregation Formation in Continuously Cast Steels

Macrosegregation

C. Beckermann , in Encyclopedia of Materials: Science and Technology, 2001

4 Conclusions

Modeling of macrosegregation in castings and ingots has made considerable progress since the early 1960s. It is clear that realistic models must take into account the intricate interactions between melt flow, solid movement, microstructure formation, and multicomponent phase transformations. Macrosegregation owing to interdendritic fluid flow alone can now be simulated for complex, three-dimensional castings, although the resolution of small-scale features such as freckles is still beyond computational capabilities. Much less progress has been made in those cases where grain structure transitions (e.g., columnar-to-equiaxed), movement of free solid, or deformation of mush are significant. As a result, the prediction of macrosegregation in ingot or continuous casting of steel, for example, is still not satisfactory.

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Casting, Semi-Solid Forming and Hot Metal Forming

T.S. Prasanna Kumar , in Comprehensive Materials Processing, 2014

5.12.5.5 Micro–Macro Segregation

Macrosegregation is a phenomenon that affects the quality of industrial castings and therefore attracted many research groups for several decades. It is caused by relative movement of solid–liquid flow during solidification. Of the many causes of segregation, the feeding of solidification shrinkage, thermal and solutal gradients in the liquid, buoyancy-driven force, flow during pouring, magnetic stirring, rotation, vibration, movement of equiaxed grains due to heterogeneous nucleation, etc. may be cited.

Modeling of macrosegregation has focused on the basic flow mechanism involved considering heat transfer and solute transport, fluid flow, solid movement, and solid deformation. In addition, phase equilibrium, nucleation at microscopic level will have to be considered. For a detailed review of macrosegregation models, readers are referred to Ref. (1). The initial effort began by Flemings and coworkers in 1960 who considered interdendritic flow of liquid as flow through a fixed solid dendritic network. They arrived at local solute redistribution equation basically starting from Scheil's equation. Their equation can explain the conditions under which macrosegregation occurs as in the case of Al alloys (inverse segregation). The LSRE equation could explain inverse segregation in aluminum alloys, negative macrosegregation, positive macrosegregation in steel castings, freckling, etc.

Simultaneously, experiments were performed to measure the permeability of mushy zone. Ridder et al. (81) solved the coupled set of equations given by Darcy's law, the energy equation and the LSRE in the mushy zone, and the momentum and energy equation in the fully liquid region. The single-domain model based on mixture theory (82,83) was based on mass, momentum, solute segregation, and convection equations that are valid in all the regions of the alloy during solidification.

Fixed grid single-domain numerical models were developed for steel ingot, continuous casting of steel, aluminum direct chill casting, nickel base superalloy casting, and shape metal casting (1).

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Defect formation mechanisms and preventive procedures in laser welding

S. Katayama , in Handbook of Laser Welding Technologies, 2013

Macrosegregation

Macrosegregation is present in the weld fusion zone in the case of laser welding of dissimilar materials ²⁰ or using a filler wire different in chemical composition from the base metal. ²³ Mixing or steering of melt in the molten pool can reduce macrosegregation. The cross section and schematic of a laser weld, EDX analysis results of Fe and Ni elements and line analysis results of Fe and Ni along the bead centerline are shown in Fig. 12.5, where laser welding was performed for a butt-joint of 0.4   mm gap between cast iron and low carbon steel plates using a 97%Ni filler wire. ²³ In laser welding, sufficient mixing of a filler wire into the base metal is difficult, and consequently the compositions of the bottom part of the weld fusion zone are approaching those of the base metal. ²³ ' ³⁴ The wider the gap in the butt-joint, the more deeply the compositions of the filler wire reach. ²³

12.5. Cross section and schematic of laser weld made in butt-joint of cast iron and low carbon steel plate with 0.4   mm gap using 97%Ni filler wire, EDX analysis results of Fe and Ni elements and line analysis results of Fe and Ni along bead centerline, showing enrichment of Ni in upper part of weld fusion zone.

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Welding and Bonding Technologies

J.L. Caron , J.W. Sowards , in Comprehensive Materials Processing, 2014

6.09.6.2.1 WM Dendrite Coring

Microsegregation and macrosegregation during weld solidification results in localized variations in composition in the WM. Chromium and molybdenum, two alloying elements that typically promote corrosion passivity to the Ni-base alloys, have a tendency to segregate to interdendritic regions during solidification of the WM. The dendrite cores can see a significant reduction in chromium and molybdenum concentration, thereby decreasing their corrosion resistance. PWHT is performed on the weldments to reduce the concentration gradients and restore corrosion resistance. An index of residual concentration (δ) is useful for predicting the PWHT temperatures and times necessary to restore uniformity of the WM composition (4). This index is defined below where D is alloying element diffusivity in the matrix (and is a function of temperature), t is time, and λ is the dendrite spacing:

$\delta =\exp \left(-\frac{4{\mathrm{\pi }}^{2}Dt}{{\lambda }^2}\right)$

The index δ begins at unity and decreases toward zero with homogenization time. Increasing the temperature, and time at temperature, tend to accelerate homogenization, and smaller dendrite spacing tends to also reduce time for homogenization. However, these may not be practical from a welding process standpoint. This equation merely illustrates a simple method for considering a PWHT to enhance the corrosion resistance.

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Solute Segregation

M.C. Flemings , in Encyclopedia of Materials: Science and Technology, 2001

2 Macrosegregation

The cause of macrosegregation in castings and ingots is the physical movement of liquid or solid phases during solidification. The diffusional transport that leads to microsegregation can be significant only over very small distances. One way in which the physical displacement can occur is by floating or settling of precipitated phases early in solidification (e.g. flotation of inclusions or settling of fine grains early in the solidification process). Most macrosegregation, however, is caused by a different mechanism—the flow of liquid through the interdendritic spaces in the liquid–solid zone. Causes of this flow include solidification shrinkage, gravity induced convection, and solid movement (e.g., "bulging").

Figure 3 is a schematic diagram of a "volume element" in the liquid–solid region of a solidifying casting. The element is permeable to liquid flow. Because liquid composition varies spatially within the liquid–solid zone, any interdendritic flow other than that parallel to an isotherm must alter the composition of the volume element. Conservation of solute requires modification of the Scheil equation to a new "local solute redistribution equation" (Flemings and Nereo 1967, Flemings et al. 1970a):

Figure 3. Fluid flow through a solidifying "volume element."

(3) $\frac{\partial g_{\text{L}}}{\partial C_{\text{L}}}=\left(\frac{1-\beta }{1-k}\right)\left(1+\frac{\upsilon \cdot \nabla T}{\varepsilon }\right)\frac{G_{\text{L}}}{C_{\text{L}}}$

where b is solidification contraction and e is rate of temperature change. The physical significance of Eqn. (3) can be seen by considering steady state solidification with planar isotherms moving with velocity R in the x direction. Eqn. (3) then becomes

(4) $\frac{\partial g_{\text{L}}}{\partial C_{\text{L}}}=\left(\frac{1-\beta }{1-k}\right)\left(1-\frac{{\upsilon }_{\text{x}}}{R}\right)\frac{G_{\text{L}}}{C_{\text{L}}}$

where υ _x is isotherm velocity perpendicular to isotherms. Equation (4) reduces to the Scheil equation when υ _x and b both equal to zero. It also reduces to the Scheil equation (written in terms of volume fraction) when

(5) ${\upsilon }_{\text{x}}=-\left(\frac{\beta }{1-\beta }\right)R$

This flow is just that required to feed solidification shrinkage, and in steady state solidification the result is no macrosegregation. Flow with a speed greater (down the temperature gradient) from that of Eqn. (5) results in negative segregation; a speed that is less, or in the opposite direction, results in positive macrosegregation.

A schematic illustration of application of these principles to continuous casting is shown in Fig. 4. No segregation results if interdendritic flow lines are all vertical. Negative segregation at mid-radius would result from flow lines such as those of Fig. 4(a), and positive segregation at the centerline would result from flow lines such as those of Fig. 4(b). It can easily be visualized that "bulging" will result in greater downward flow, and in particular, greater downward flow toward the centerline (as illustrated in Fig. 4(c)), thus enhancing centerline segregation. In continuous casting of aluminum alloys, solute-rich interdendritic liquid sometimes "exudes" from within the dendrite arms outward into the space between the casting and the mold wall, resulting in a form of surface segregation known as "exudation."

Figure 4. Interdendritic fluid flow in a continuous casting: (a) no segregation; (b) negative segregation at mid-radius; (c) positive segregation at centerline.

A limiting condition of Eqn. (4) occurs when

(6) $\frac{{\upsilon }_{\text{x}}}{R}>1$

that is, when flow is in the same direction as, and is greater than, isotherm velocity. In this case, as temperature continues to fall (and so local liquid composition increases), local melting occurs, rather than solidification. It is this local melting that results in the channel segregates known in their various manifestations as "freckles," "A" segregates, and "V" segregates (Flemings 1970b, Fellicelli et al. 1991).

Quantitative analyses of segregation phenomena given above are applicable for solidification rates found in usual castings and ingots. At the very high rates found in some newer "rapid solidification" processes, microsegregation may be altered by liquid undercooling, limited interface kinetics, or metastable phase selection.

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SOLIDIFICATION

H. BILONI , W.J. BOETTINGER , in Physical Metallurgy (Fourth Edition), 1996

9.3.2. Interdendritic fluid flow and macrosegregation

The first attempt to create models for macrosegregation due to flow of solute rich material was by Kirkaldy and Youdelis [1958]. Later the subject was treated extensively at MIT by Flemings and Nereo [1967]) and Mehrabian et al. [1970] and has been summarized by Flemings [1974], [1976]. Using a volume element similar to that chosen in fig. 41, a mass balance is performed under the additional possibility that flow of liquid in or out of the volume elements can occur and that the liquid and solid can have different densities. Thus the necessity for flow to feed solidification shrinkage is treated. The result is a modified form of the solute redistribution equation used to describe microsegregation in § 7,

(113) $\frac{\mathrm{d}{f}_{\mathrm{L}}}{\mathrm{d}{C}_{\mathrm{L}}}=-\frac{(1-\beta )}{(1-k_0)}\left[1+\frac{\overline{v}\cdot \nabla T}{\varepsilon }\right]\frac{f_{\mathrm{L}}}{{\mathrm{C}}_{\mathrm{L}}},$

where: f _L is the fraction of liquid; β = (ρ_s–ρ_L)/ρ_s = solidification shrinkage; ν ≈ velocity vector of interdendritic liquid; ∇T = local temperature gradient vector; ɛ = local rate of temperature change.

This expression assumes: i) local equilibrium without curvature correction, ii) uniform liquid composition in the small volume of interest, iii) no solid diffusion, iv) constant solid density, v) no solid motion, and vi) absence of voids. In this approach, the appropriate values for $\overline{\text{v}}$ and ɛ at each location must be determined from a separate calculation involving thermal analysis and flow in the mushy zone, which will be outlined below. However given these values for each small volume element, C _L and hence C _s as a function of f _s can be determined along with the fraction of eutectic. The average value of C _s from f _s = 0 to 1 gives the average composition at each location in the casting. The average composition will not in general be equal to the nominal alloy composition.

Several cases can be distinguished. If the interdendritic flow velocity just equals the flow required to feed local shrinkage,

(114) $\overline{n}•\overline{v}=-\frac{\beta }{1-\beta }\overline{n}•\overline{V}.$

Then eq. (113) reverts to the Scheil equation and the average composition is equal to the nominal. Here $\overline{n}$ is the unit normal to the local isotherms and $\overline{\text{V}}$ is the isotherm velocity. If on the other hand $\overline{n}•\overline{v}$ is greater than or less than this value, negative or positive macrosegregation occurs, respectively. A particularly simple case ocurs at the chill face of a casting. Here $\overline{n}•\overline{v}$ must be zero because there can be no flow into to the chill face. This clearly produces positive macrosegregation (for normal alloys where β > 0 and k ₀< 1. This is commonly observed in ingots and is termed inverse segregation (Kirkaldy and Youdelis [1958]) because it is reversed from what one would expect based on the initial transient of plane front growth.

In order to compute the fluid velocity of the liquid, the mushy zone is treated as a porous media and D'Arcy's Law is used. The pressure gradient and the body force due to gravity control the fluid velocity according to

(115) $\overline{v}=\frac{K_{\rho }}{\eta f_{\mathrm{L}}}(\nabla P+{\rho }_{\mathrm{L}}\overline{g}),$

where:

K _p = specific permeability; η = viscosity of the interdendritic liquid; ∇P = pressure gradient; $\overline{g}=\text{acceleration}$ vector due to gravity.

Often, heat and fluid flow in the interdendritic region have been computed by ignoring the fact that the fraction of liquid at each point in the casting depends on the flow itself through eq. (115). This decoupling is thought to cause little error if the macrosegregation is not too severe. Flemings [1974] and Ridder et al. [1981] solved the coupled problem using an iterative numerical scheme for an axisymmetric ingot. In their work the flow in the bulk ingot was also coupled to that in the interdendritic region. Experiments on a model system showed good agreement.

Determining an accurate expression for the permeability of a mushy zone is a difficult problem since the value of K _p depends on interdendritic channel size and geometry. In the case of the mushy zone it has been proposed (Piwonka and Flemings [1966]) that

(116) $K_{\mathrm{p}}={\lambda }_{\mathrm{c}}{f}_{\mathrm{L}}^2,$

where λ_c is a constant depending on dendritic arm spacing. Recently, Poirier [1987] analysed permeability data available for the flow of interdendritic liquid in Pb–Sn and borneol–paraffin. The data were used in a regression analysis of simple flow models to arrive at relationships between permeability and the morphology of the solid dendrites. When flow is parallel to the primary dendritic arms the permeability depends upon λ₁ (primary arm spacing) but not λ₂ (secondary arm spacing). When flow is normal to the primary arms the permeability depends upon both λ₁ and λ₂. These correlations are only valid over an intermediate range of f _L, roughly between 0.2 and 0.5.

With this model of macrosegregation, Flemings [1974], [1976] was able to explain different types of macrosegregation present in industrial ingots (fig. 63): a). Gradual variations in composition from surface to center and from bottom to top are due to the interdendritic fluid flow with respect to isotherm movement, b) Inverse segregation as described above. If a gap is formed between the mould and the solidifying casting surface, a severe surface segregation or exudation can arise, c) Banding or abrupt variations in composition that result from either unsteady bulk liquid or interdendritic flow, or from sudden changes in heat transfer rate. d) "A" segregates or "frecke". These are abrupt and large variations in composition consisting of chains of solute-rich grains. They result from movement of interdendritic liquid that opens channels in the liquid–solid region. Recent work by Hellawell [1990] seems to prove that, at least in some cases, the initiation of the channels is at the growth front itself, e) "V" segregates. As the fraction solid in the central zone increases in the range of 0.2 to 0.4, the solid network that has formed is not yet sufficiently strong to resist the metallostatic head and fissures sometimes occur. These internal hot tears open up and are filled with solute rich-liquid. f) Positive segregation under the hot top: Probably occurs during the final stages of solidification when the ingot feeding takes place only by interdendritic flow.

More recently Kato and Cahoon [1985] concluded that void formation can affect inverse segregation. They studied inverse segregation of directionally solidified Al–Cu–Ti alloys with equiaxed grains. Minakawa et al. [1985] employed a finite difference model of inverse segregation. This model allowed for volume changes due to microsegregation and thermal contractions as well as the phase change.

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Macroscopic Modeling

R.M. McDavid , in Encyclopedia of Materials: Science and Technology, 2001

(c) Species balance

This balance equation is used to predict important processes like macrosegregation. A balance equation for the behavior of chemical species is very similar to the energy balance equation. In the former, Fick's law replaces Fourier's law as a constitutive equation. Fick's law relates the mass flux of a species to the gradient in concentration of that element. In simplified form, the species balance equation may be written as:

(13) $\frac{\partial c_{\text{A}}}{\partial t}+\mathbf{u}\cdot \nabla c_{\text{A}}={\mathcal{D}}_{\text{AB}}{\nabla }^2{c}_{\text{A}}+{\stackrel{.}{r}}_{\text{A}}$

where c _A is the molar concentration of species A, ${\mathcal{D}}_{\text{AB}}$ is the mass or molecular diffusivity of species A in species B, and $\stackrel{.}{r}$ _A is the molar rate of production of species A. Chemical reactions would be the most likely species generation source.

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Metal Matrix Composites

BING LI , ENRIQUE J. LAVERNIA , in Comprehensive Composite Materials, 2000

3.23.3.4 Distribution of Reinforcement in the Deposit

Except for the layered MMCs, spray-formed MMCs are normally macrosegregation free. Such a feature may be traced back to the same origins which lead to eliminated macro-segregation and minimized microsegregation in spray-formed monolithic alloys. They include disintegration of the molten material into a spray of micron-sized droplets and deformation of the semisolid/fully liquid droplets upon their impingement onto the substrate. These are inherent for all spray forming methods. For the spray forming and co-injection method as well as its variants, symmetrically co-injecting the reinforcements into the matrix spray also contributes to the elimination of macrosegregation of reinforcements in the deposit. Finally, for layered MMCs, the segregation is introduced in a controlled pattern (alternate reinforcement segregated layers) and is limited to the mesoscopic level. This is intrinsically different from macrosegregation in its conventional sense.

Microscopically, distribution of the reinforcement may not be completely uniform. It is occasionally reported that many reinforcements are observed located at the grain boundary regions. This is most likely to be related to the reinforcement pinning effect on the grain boundary during grain growth. According to the grain boundary pinning mechanism, the grain boundary will be the preferential location of reinforcements. The applicability of this mechanism to spray forming techniques is justified by the experimental and numerical studies which suggested that a certain extent of grain growth did occur during the deposition stage (Liang et al., 1992a). Notice that this mechanism is applicable to all spray forming methods. In the spray forming and co-injection method, another mechanism may lead to microscopically nonuniform distribution of the reinforcement: incomplete penetration of the reinforcement into the matrix droplets (Li and Lavernia, 1997b).Accordingly, in the deposited MMCs, the reinforcement will be either located preferentially at the prior-droplet boundaries when the droplet is completely solidified at the moment of their impingement onto the substrate or segregated along the deformed droplets, leading to the formation of microscopic layered characteristics. This type of nonuniform distribution of reinforcements may be minimized by optimizing the processing conditions, as discussed in detail in several studies (Lawrynowicz et al., 1997; Li and Lavernia, 1997b; Wu and Lavernia, 1992; Wu et al., 1994; Zhang et al., 1994b). Among the different options, shortening the atomizer-to-injector distance seems to be the most viable choice. However, such a change might have some effects on the interfacial reaction between the matrix and the reinforcement.

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Production and casting of aerospace metals

In Introduction to Aerospace Materials, 2012

Segregation of alloying elements

Segregation of the alloying elements is another problem with castings. There are two types of segregation, macrosegregation and microsegregation, which occur at different levels in the casting. Macrosegregation is where the average alloy composition varies over a large distance through the casting. Macrosegregation often occurs between the surface and core of the casting, with the alloy composition of the surface (which freezes first) being different from the centre owing to diffusion of alloy elements ahead of the solid/liquid interface. Alloying elements can either diffuse from the liquid into the solid, which raises the alloy content near the surface, or the elements can migrate from the solid into the liquid which enriches the central region of the casting. The mechanical properties vary from the surface to centre of the cast metal owing to the change in alloy content. The effect of macrosegregation on the properties can be minimised by hot working the cast metal; this involves plastically deforming the casting at high temperature and redistributing the alloying elements. The hot working of cast metal is described in chapter 7.

Microsegregation is the local variation in alloy composition on a scale smaller than the grain size. Microsegregation occurs over short distances, often between the dendrite arms which are typically spaced several micrometres apart. The dendrite core, which is the first solid to freeze, is richer in the alloying elements with higher melting temperatures.

Segregation can be removed by a heat treatment process known as homogenising anneal, which involves heating the solid metal to just below the melting temperature for an extended period of time to allow the alloying elements to disperse throughout the casting. Homogenisation treatments are generally effective in producing a levelling of micro-scale concentration differences in alloying elements, although some residual minor differences may remain.

Section 6.8 presents a case study of casting defects causing engine disc failure on United Airlines flight 232.

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Solidification Structure

John Campbell , in Complete Casting Handbook (Second Edition), 2015

5.3.3 Dendritic Segregation

Figure 5.43 shows how microsegregation, the sideways displacement of solute as the dendrite advances, can lead to a form of macrosegregation. As freezing occurs in the dendrites, the general flow of liquid that is necessary to feed solidification shrinkage in the depths of the pasty zone carries the progressively concentrating segregate towards the roots of the dendrites.

Figure 5.43. Normal dendritic segregation (usually misleadingly called inverse segregation) arising as a result of the combined actions of solute rejection and shrinkage during solidification in a temperature gradient.

In the case of a freely floating dendrite in the centre of the ingot that may eventually form an equiaxed grain, there will be some flow of concentrated liquid towards the centre of the dendrite if in fact any solidification is occurring at all. This may be happening if the liquid is somewhat undercooled. However, the effect will be small, and will be separate for each equiaxed grain. Thus the build-up of long-range segregation in this situation will be negligible.

For the case of dendritic growth against the wall of the mould, however, the temperature gradient will ensure that all the flow is in the direction towards the wall, concentrating the segregation here. Thus the presence of a temperature gradient is necessary for a significant build-up of segregation.

It will by now be clear that this type of segregation is in fact the usual type of segregation to be expected in dendritic solidification. The phenomenon has in the past suffered the injustice of being misleadingly named 'inverse segregation' on account of it appearing anomalous in comparison to planar front segregation and the normal pattern of positive segregation seen in the centres of large ingots. In this book we shall refer to it simply as 'dendritic segregation'. It is perfectly normal and to be expected in the normal conditions of dendritic freezing.

Dendritic segregation is observable but is not normally severe in sand castings because the relatively low temperature gradients allow freezing to occur rather evenly over the cross-section of the casting; little directional freezing exists to concentrate segregates in the direction of heat flow.

In castings that have been made in metal moulds, however, the effect is clear and makes the chill casting of specimens for chemical analysis a seriously questionable procedure. Chemists should beware! The effect of positively segregating solutes such as carbon, sulphur and phosphorus in steel is clearly seen in Figure 5.44 as the high concentration around the edges and the base of the ingot; all those surfaces in contact with the mould.

Figure 5.44. Segregation of (a) solutes and (b) inclusions in a 3000 kg sand cast ingot.

Information mainly from Nakagawa and Momose (1967).

In some alloys with very long freezing ranges, such as tin bronze (liquidus temperature below 1000°C and solidus close to 800°C), the contraction of the casting in the solid state and/or the pressure in the liquid from the metallostatic head, plus perhaps the evolution of dissolved gases in the interior of the casting causes eutectic liquid to be squeezed out on to the surface of the casting. This exudation is known as tin sweat. It was described by Biringuccio in the year 1540 as a feature of the manufacture of bronze cannon. Similar effects can be seen in many other materials; for instance when making sand castings in the commonly-used Al-7Si-0.3Mg alloy, eutectic (Al-11Si) is often seen to exude against the surface of external chills (Figure 5.13). The surface exudation of eutectic liquid gives problems during the manufacture of Ni-base superalloy single crystal turbine blades as is discussed in the section on Ni-based alloys.

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