33328241 micro structures

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Version 2006.0 Page 458

MICROSTRUCTURES

The Microstructure models were improved in version 2006.0. In particular, the

treatment of the thermal algorithm was significantly improved. This allows to

have much larger timesteps than before. Please note that due to this change the

maximum timestep should be kept to reasonable values (i.e. one should make sure

that the solidification range is crossed in several timesteps).

Concerning the prediction of the Casting strength, previously it was only a

function of the grain size. It has been improved in order to be also a function of

the ferrite-perlite fractions. As a consequence, the Casting strength will not beonly dependent upon the thermal history near the solidification, but also upon the

further cooling (i.e. it will depend upon the cooling rates between 700 and 900C).

INTRODUCTION

The microstructure module of ProCAST is now able to calculate automatically the

microstructures, based upon the composition of the alloy. This can be achieved

with the link of the module with thermodynamic databases.

Depending upon the chemical composition, the microstructure module

automatically detects the phases which will appear and the type of microstructure

which should be computed (dendritic, eutectic, nodular, ...).

For instance, if an Al-7%Si-0.3%Mg alloy is specified (A356), automatically, the

software will detect that primary dendrites will form, followed by an interdendritic

eutectic. On the other hands, if the composition of a Nodular Cast Iron (SGI) is

defined, the nodule counts, the austenite radius, the pearlite and ferrite fractions

will be computed, together with the corresponding mechanical properties (such as

hardness, yield and tensile strength). The software will also automatically detect

that if there is no Magnesium in the cast iron, the structure will be lamellar rather

than spheroidal. In the same way, if the composition is hypo-eutectic, primary

dendrites of austenite will form first before the eutectic precipitation.

The only parameters that the user may need to specify are the nucleation

parameters (see below). This is due to the fact that this is not an intrinsic property

and that it may depend upon the metal treatment. Moreover, it may be necessary

to define the growth kinetics of the eutectic phase (see below)


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As the microstructure module is linked with the thermodynamic databases, it is

necessary to have the corresponding database license, for the desired base

material.

Nucleation of the primary dendritic grains

The primary dendritic phase (if any) will nucleate and grow as equiaxed grains.

The nucleation of these grains strongly depends upon the alloy treatment and thus

the nucleation parameters should be defined.

The model which is used is based upon the "Gaussian distribution" model

proposed in 1987 by Rappaz et al.(Acta Metall., 35, (1987), 1487 and 2929). This

model defines the relationship between the number of nuclei and the

undercooling. The distribution of the nuclei with undercooling has the form of a

Gaussian distribution and thus, the integral of this curve is an "S-shape" function(see graphs below).

The mathematical description of this "S-shape" curve is as follows :

with the following definitions :


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Thus, the nucleation behavior of the primary dendritic phase is fully defined by

the three above parameters.

Nucleation of the eutectic grains

The nucleation of the eutectic grains is based upon the model proposed in 1966 by

Oldfield (ASM Transaction, 598, (1966), 945). The number of nuclei is a

powerlaw (Oldfield proposed a quadratic law) of the undercooling.

The model is described by the following equations :

Thus, the nucleation behavior of the eutectic phase is fully defined by the two

above parameters.

Growth kinetics of the eutectic grains

The eutectic is growing with a quadratic power of the undercooling :

Thus, the above constant fully defines the growth characteristics of the eutectic

growth.

Default values

The following table is showing the default values which are used in the

microstructure module for the models described above and for the different alloys.

Of course, the nucleation data may change from one alloy to the other, due to

different metal treatment. These default values corresponds to values proposed in

the literature.


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CASE SET-UP AND RESULTS

Set-up

The set-up of a microstructure calculation is very simple as the model is based

upon the chemical composition.

Firstly, the problem should be defined as a usual thermal case.

Then, the chemical composition of the alloy should be specified in the

corresponding material properties tab (see below).

For the thermal properties, only the thermal conductivity and the density should be

defined in addition to the chemical composition. Then, the enthalpy needs to be

calculated in PreCAST, with the Thermodynamic database (based upon the

specified chemical composition), using the Lever model for Fe alloys and the

Scheil model for the other systems. Thus, at the end, the thermal conductivity, the


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density, the enthalpy, the fraction of solid, the liquidus and solidus temperatures

are defined.

Finally, the Run Parameter MICRO should be set to 1 (for the users of previous

versions, one should not anymore use values different from 1, as the selection ofthe micro model is now automatic). A value of 0 will disable the microstructure

calculation.

If the nucleation or growth parameters have to be changed from the default values

(see Table below), the corresponding Run parameters can be modified (see the

Microstructure Run Parameters section for more details).

Results

Depending upon the alloy composition, the type of microstructure will be

different. As a consequence, the type of results which are computed will also be

different. All the microstructure results can be visualized in the post-processing, inthe "Contour/Micro" menu.

a) Dendritic primary phase and eutectic secondary phase

Most alloys are solidifying with a primary phase of dendrites, followed by inter-

dendritic eutectic. In this case, the following quantities are calculated :


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The "Primary Dendrite Radius" corresponds to the primary grain size. The

"Secondary Dendrite Arm Spacing" (also called SDAS) is the distance between

the secondary dendrite arms of the primary phase.

The "Primary Solid Fraction" corresponds to the fraction of primary phase,

whereas the rest corresponds to the "Fraction of Eutectic".

The "Eutectic Grain Radius" corresponds to the radius of equiaxed eutectic grains

which are nucleating in between the dendrites of the primary phase. Finally, the

"Eutectic Inter-lamellar Spacing" is the characteristic distance of the eutectic

structure.

b) Special case of Fe-C alloys - grey iron (lamellar eutectic)

In the case of grey iron (lamellar eutectic), in addition to the quantities described

above, other quantities can be calculated :

Metastable phases ("Fraction of Metastable Eutectic" and "Metastable Eutectic

Grain Radius"), may appear depending upon the chemical composition and the

local cooling conditions.

The solid state transformations of austenite decomposition into Ferrite and Pearlite

is calculated ("Fraction of Ferrite" and "Fraction of Pearlite", "Pearlite Spacing"),


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as well as the corresponding final mechanical properties ("Tensile Strength",

"Yield Strength" and "Brinell Hardness").

c) Special case of Fe-C alloys - nodular cast iron (eutectic composition)

In the case of Nodular cast iron, nodules of graphite, surrounded by austenite are

formed, instead of eutectic grains. Thus, the "Nodule count" (which corresponds

to the density of graphite nodules), as well as the "Austenite Radius" and

"Graphite Radius" are calculated. The solid state transformations, as well as the

mechanical properties are calculated, as described above. In addition, the

"Elongation" is calculated from the microstructure results.

The Nodular cast iron (SGI) model is activated as soon as there is a non zeroamount of Mg in the chemical composition. Please note that Mg is not an element

which is present in the Computherm thermodynamic database as it will have a

negilible effect on the computed material properties. However, it should be

specified in order to trigger the SGI model.

d) Special case of Fe-C alloys - nodular cast iron (hypo-eutectic composition)

In the case of a hypo-eutectic nodular cast-iron, the same properties as described

above are obtained, in addition to the primary phase calculation of the austenite

dendrites.


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The Nodular cast iron (SGI) model is activated as soon as there is a non zero

amount of Mg in the chemical composition. Please note that Mg is not an element

which is present in the Computherm thermodynamic database as it will have a

negilible effect on the computed material properties. However, it should be

specified in order to trigger the SGI model.

e) Special case of Fe-C alloys - steel

In the case of a steel with the composition of carbon equivalent less than 0.53 , the

following properties are obtained.

The fraction of peritectic is the solid fraction formed from the reaction of liquid

and the existing primary solid phase. The fraction of proeutectoid refers to the

fraction of proeutectoid ferrite or cementite formed from the austenite phase as a

function of time during the solid phase transformation. The carbon equivalent

value controls which type of the proeutectoid phase will form (the "carbon

equivalent" corresponds to %C + (%Si + %P)/3 ).

References

For cast iron, the mechanical properties calculations are based upon the

microstructure, according to two following papers :

Stefanescu et al, Proceedings of the 4th Decennial International Conference on

Solidification Processing, Sheffield, (July 1997), 609.

Goettsch et al, Metallurgical and Materials Transactions, 25A:5, (1994), 1063.


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EXAMPLES

In order to illustrate the application of the microstructure module on thesolidification of nodular cast iron, two calculations were performed with two

different chemical compositions.

To do so, a very simple geometry was used, as shown below. The casting is

cooled from the right with a chill, whereas the rest is in a sand mold.

This set-up produces a full range of cooling rates, as shown in the cooling curves

hereafter.


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The following figure is showing the two alloys which were used, with the

corresponding chemical compositions. The only difference between the two

calculations is the amount of Carbon (from 3.2% to 3.5%).


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The above figure is showing the different kind of results which are automatically

computed for the two alloys. One can see that for the Alloy B, there is no

"Primary phase", as the alloy is lying on the eutectic composition.

The following figures are showing the comparison of the different results. On the

left, the Alloy 1 is shown (3.2% C - Hypo-eutectic) and the Alloy 2 is shown on

the right (3.5% C - Eutectic).

Eutectic phase fraction

Nodule counts


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Austenite Radius

Ferrite fraction


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Pearlite fraction

Brinell Hardness

Elongation


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Tensile strength

Yield strength

Secondary Dendrite Arm Spacing (SDAS)


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One can see that the SDAS is only available for Alloy 1, as there is no dendrites

(i.e. no primary phase) in Alloy 2.


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IRON AND STEEL

In order to run iron micro modeling, the following set-ups are needed in PreCAST andin the p.dat file :

a. Run Parameters/Micro:

i. MICRO=1

ii. Select Default Values (Gray Iron or Ductile Iron)

iii. Based on the inoculation level change the values accordingly

1. EUNUCL (For ductile iron, default value is 2000 )

2. EUPOWER (For ductile iron, default value is 2.5 )

3.

b. Run Parameters/Thermal

i. MACROFSii. PIPEFS

iii. FEEDLEN

c. p.dat file (for SGI only)

i. MOLDRIG (0~1, change it according to the hardness of mold)

ii. GRAPHITE (0~1, default=1.0)

Introduction to Iron and Steel

The study of the micro structure of steels and irons must start with the iron-carbon

equilibrium diagram. Many of the basic features of this system (Fig. 1) influence

the behavior of even the most complex iron alloys. For example, the phases found

in the simple binary Fe-C system persist in complex steels. The iron-carbon

diagram provides a valuable foundation on which to build knowledge of both

plain carbon and alloy steels in their immense variety.


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Figure 1. The iron-carbon diagram.

It should first be pointed out that the normal equilibrium diagram really represents

the metastable equilibrium between iron and iron carbide (cementite). Cementite

is metastable, and the true equilibrium should be between iron and graphite.

Graphite occurs extensively in cast irons (2-4 wt % C), but it is usually difficult to

obtain this equilibrium phase in steels (0.03-1.5 wt %C). Therefore, the metastable

equilibrium between iron and iron carbide should be considered for steel, because

it is relevant to the behavior of most steels in practice.

It is convenient to combine the effect of the silicon with that of the carbon into a

single factor which is called the carbon equivalent (CE):

CE=%C+%Si/3

It is called iron if CE is greater than 2, otherwise it is called steel.

Steel

When the weight percent sum of all elements other than Fe is more than 5% (such

as some alloy steel or stainless steel), only equiaxed dendrite model will be

activated.


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1) Carbon content less than 0.53% (such as Alloy A in Fig. 1)

When the melt alloy cools from an initial temperature higher than the liquidus

temperature down to a temperature slightly below it, the primary delta dendrite

phase begins to nucleate in the liquid until a recalescence occurs due to the heatreleased from the growing nuclei. During the recalescence, the nucleation ceases

and the nuclei grow rapidly into dendritic grains and soon impinge on each other

at the end of recalescence. Then the growth of delta dendritic grains is replaced by

the coarsening of delta dendritic arms. When the temperature reaches to the

peritectic temperature, the peritectic transformation starts if there is still liquid

available. Otherwise, the austenite phase precipitates from the delta phase until all

of the delta phase is transformed into the austenite phase. Lastly, when the

temperature of the casting is cooled down to the alpha phase transformation

temperature, the alpha phase precipitates from the austenite phase to the eutectoid

temperature. Below the eutectoid temperature, the graphite of Fe3C phase

nucleates initially on the boundary of the austenite grains and then the coupledgrowth of alpha and Fe3C phases leads to the formation of pearlite phase.

2) Carbon content is greater than 0.53% (such as Alloy B in Fig. 1)

When the melt alloy cools from an initial temperature higher than the liquidus

temperature down to a temperature slightly below it, the primary austenite

dendrite phase begins to nucleate in the liquid. The austenite phase will grow until

the end of solidification. There is no peritectic reaction here. When the

temperature of the casting is cooled down to the alpha phase(C0.8%) transformation temperature, the alpha phase or

cementite phase precipitates from the austenite phase to the eutectoid temperature.

Below the eutectoid temperature, the coupled growth of alpha and Fe3C phases

leads to the formation of pearlite phase.

The eutectoid temperature is around 723C while the eutectoid composition is

0.80% C. Slowly cooling alloys containing less than 0.80% C, hypo-eutectoid

ferrite is formed from austenite in the range 910-723C with enrichment of the

residual austenite in carbon, until at 723C the remaining austenite, now

containing 0.8% carbon transforms to pearlite, a lamellar mixture of ferrite and

iron carbide (cementite). In austenite with 0.80 to 2.06% carbon, cooling in the

temperature interval 1147C to 723C, cementite first forms progressivelydepleting the austenite in carbon, until at 723C, the austenite contains 0.8%

carbon and transforms to pearlite.

Steels with less than about 0.8% carbon are thus hypo-eutectoid alloys with ferrite

and pearlite as the prime constituents, the relative volume fractions being

determined by the lever rule which states that as the carbon content is increased,

the volume percentage of pearlite increases, until it is 100% at the eutectoid

composition. Above 0.8% C, cementite becomes the hyper-eutectoid phase, and a

similar variation in volume fraction of cementite and pearlite occurs on this side of

the eutectoid composition.


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Cast Iron

The term cast iron, like the term steel, identifies a large family of ferrous alloys.

Cast irons are multicomponent ferrous alloys. They contain major (iron, carbon,

silicon), minor (0.01%) elements.

Cast iron has higher carbon and silicon contents than steel. Because of the higher

carbon content, the structure of cast iron, as opposed to that of steel, exhibits a

rich carbon phase. Depending primarily on composition, cooling rate and melt

treatment, cast iron can solidify according to the thermodynamically metastable

Fe-Fe3C system or the stable Fe-graphite system.

When the metastable path is followed, the rich carbon phase in the eutectic is the

iron carbide; when the stable solidification path is followed, the rich carbon phase

is graphite. Referring only to the binary Fe-Fe3C or Fe-C system, cast iron can be

defined as an iron-carbon alloy with more than 2% C. Important notice is that

silicon and other alloying elements may considerably change the maximum

solubility of carbon in austenite. The formation of stable or metastable eutectic is

a function of many factors including the nucleation potential of the liquid,

chemical composition, and cooling rate. The first two factors determine the

graphitization potential of the iron. A high graphitization potential will result in

irons with graphite as the rich carbon phase, while a low graphitization potential

will result in irons with iron carbide. The metastable phase amount has both direct

and indirect effects on the properties of ductile iron castings. Increasing the

volume percent of hard, brittle carbide increases the yield strength, but reduces the

tensile strength and elongation, of ductile iron castings. Because there is nographite expansion for the metastable phase, the formation of carbide increases the

likelihood of internal casting porosity.

The two basic types of eutectics - the stable austenite-graphite or the metastable

austenite-iron carbide (Fe3C) - have wide differences in their mechanical

properties, such as strength, hardness, toughness, and ductility. Therefore, the

basic scope of the metallurgical processing of cast iron is to manipulate the type,

amount, and morphology of the eutectic in order to achieve the desired mechanical

properties.

The structure of the matrix is essentially determined by the cooling rate through

the eutectoid temperature range. Slow cooling rates prevalent in heavy sectionspromote the transformation of ferrite.

Classification

Historically, the first classification of cast iron was based on its fracture. Two

types of iron were initially recognized:


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White iron: Exhibits a white, crystalline fracture surface because fractureoccurs along the iron carbide plates; it is the result of metastable solidification

(Fe3C eutectic)

Gray iron: Exhibits a gray fracture surface because fracture occurs along the

graphite plates (flakes); it is the result of stable solidification (Graphiteeutectic).

With the advent of metallography, and as the body of knowledge pertinent to cast

iron increased, other classifications based on microstructural features became

possible:

Graphite shape: Lamellar (flake) graphite (FG) as shown in Fig. 4.1 and 4.2,spheroidal (nodular) graphite (SG) as shown in Fig. 5.1 and 5.2, compacted

(vermicular) graphite (CG), and temper graphite (TG); temper graphite results

from a solid-state reaction (malleabilization.)

Matrix: Ferritic, pearlitic, austenitic, martensitic, bainitic (austempered).

The correspondence between commercial and microstructural classification, as

well as the final processing stage in obtaining common cast irons, is given in Fig.

2.

Fig.2. Basic microstructures and processing for obtaining common commercial

cast irons


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Graphite is a hexagonal-close pack form of carbon that can grow in both the liquid

and solid forms of iron. In theory, in irons above the eutectic composition of

carbon, the graphite first nucleates in the liquid, and then continues to grow in the

solid. In irons below the eutectic composition, the carbon does not start to growuntil the iron reaches eutectic temperature. As seen in a micro, the larger nodules

are from growth initiated in the liquid, and the smaller nodules are from growth

that does not start until solidification temperatures are reached. The graphite

nodules continue to grow as the iron cools, so the amount of growth that occurs in

the liquid is smaller than what would be assumed by the micro.

The expansion from the graphite that grows in the liquid pushes liquid back into

the riser, and does not offset shrinkage. So in order to minimize shrinkage, it is

necessary to maximize the late formation of graphite without having to reduce the

actual amount of graphite. Understanding what happens in a non-steady state

solidification of Ductile Iron suggests a way that this can be done.

In a hypoeutectic mode of solidification, austenite forms as a solid with a lower

than average carbon content. This increases the carbon content of the remaining

liquid until it reaches the eutectic composition. Likewise, in a hypereutectic mode

of solidification, graphite nodules form in the liquid, removing carbon from the

liquid until it is reduced to the eutectic composition

Fig. 3 Phase diagram showing movement of carbon concentration in liquid metalas iron solidifies.

It can be seen from the diagram on the previous page, which the maximum

amount of carbon that can be formed in late graphite is determined by the eutectic

composition, and as long as the iron is at eutectic or above, the amount of late

graphite will be the same.


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Iron and Steel models

The following micro models are available in ProCAST:

1. Equiaxed Dendrite Model

The model is based upon the model proposed in 1987 by Rappaz et al. This model

defines the relationship between the number of nuclei and the undercooling. The

distribution of the nuclei with undercooling has the form of a Gaussian

distribution and thus, the integral of this curve is an "S-shape" function. Following

nucleation, the dendrite tip growth is controlled by the supersaturation at the

dendrite tip. This means that the tip growth is based on the total undercooling at

the tip. As the tip grows, the solid fraction in each grain is not known from the tip

position. In fact, the fraction solid is less than the fraction of the grain obtainedfrom the tip position. At each time, the new tip concentration and fraction solid

are known from a thermal and solute balance at the scale of the grain. The tip

growth velocity is obtained from the Lipton-Glicksman-Kurz model, which

simulates the growth of an isolated dendrite tip. The tip continues to grow until it

reaches the end of the grain. At this point, solid fraction is still less than unity.

However, mixing of the solute is complete at this stage. Therefore, a back

diffusion type equation can be used to calculate solid fraction. If the phase

diagram has a terminal reaction, e.g., eutectic, the remaining liquid gets rapidly

transformed into a solid structure. It is assumed that the temperature of the grain is

uniform and curvature undercooling is neglected. Also it is considered that the


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thermal undercooling is negligible. The growth of the dendrite tip is controlled

mainly by solute diffusion. Therefore, only solutal undercooling is considered.

2. Eutectic ModelThis model can be applicable to both regular and irregular eutectics. In the case of

regular eutectics, growth of both phases of the eutectic structure is non-faceted in

nature. For irregular eutectic, the growth process of one of the phases is faceted.

Growth of the faceting phase requires considerably higher entropy of fusion.

Examples of faceted growth are graphite growth in stable austenite/graphite

eutectic and Silicon in Al-Si eutectic. The metastable austenite/cementite eutectic

is an example of non-faceted/non-faceted type eutectic growth. Growth of both the

stable and metastable eutectic are addressed here. Growth of the stable eutectic

usually proceeds at a higher temperature. A higher cooling rate results in the

formation of a metastable eutectic. This model assumes bulk heterogeneous

nucleation at foreign sites which are already present within melt or intentionallyadded to the melt by inoculation.

The nucleation of the eutectic grains is based upon the model proposed in 1966 by

Oldfield (ASM Transaction, 598, (1966), 945). The number of nuclei is a power

law (Oldfield proposed a quadratic law) of the undercooling. The growth of the

grains is controlled by thermal undercooling at the solid/liquid interface. Solutal

undercooling is neglected here since solute diffusion during eutectic solidification

is negligible. The thermal undercooling is given by the difference between the

eutectic temperature and the actual solid/liquid interface temperature.

3. Ductile Iron Eutectic Model

The eutectic growth process in ductile iron is a divorced growth of austenite and

graphite, which do not grow concomitantly. At the beginning of the liquid/solid

transformation, graphite nodules nucleate in the liquid and grow in the liquid to a

small extent. The formation of graphite nodules and their limited growth in liquid

depletes the melt locally of carbon in the vicinity of the nodules. This facilitates

the nucleation of austenite around the nodules, forming a shell. Further growth of

these nodules is possible by diffusion of carbon from the melt through the

austenite shell. Once the austenite shell is formed around each nodule, thediffusion equation for carbon through the austenitic shell is solved in 1--D

spherical coordinates. The boundary conditions are known from the phase diagram

because thermodynamic equilibrium is maintained locally. Conservation of mass

and solute is maintained in each grain. Because of the density variation resulting

from the growth of austenite and graphite, the expansion/contraction of the grain

is taken into account by allowing the final grain size to vary. Toward the end of

solidification, the grains impinge on each other. This is taken into consideration

by using the Johnson-Mehl approximation.

4. Gray/White Iron Eutectic Model


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This model is a special case of eutectic growth model and is applicable to cast

gray/white iron only. In cast iron, one may obtain both gray and white iron

depending on the melt composition and cooling conditions. Given a controlled

melt composition, the most important factor that will determine whether a givenregion will solidify as white or gray is the cooling rate. It has been observed that

for a specific melt composition and solidification condition, there exists a

parameter called a critical cooling rate. If a region of a casting solidifies with a

cooling rate higher than the critical cooling rate, then it will be white. The reverse

is the case for gray iron.

5. Ductile Iron Eutectoid Model

This model can be used during the eutectoid transformation while describing the

phase transformation of ductile iron to room temperature after solidification. Theeutectoid reaction leads to the decomposition of austenite into ferrite and graphite

for the case of the stable eutectoid and to pearlite for the metastable eutectoid

transformation. Usually, the metastable eutectoid temperature is lower than the

stable eutectoid temperature. Slower cooling rates result in more stable eutectoid

structure. If the complete transformation of austenite is not achieved when the

metastable temperature is reached, pearlite forms and grows in competition with

ferrite.

Growth of Ferrite:

Even though ferrite can form either from the breakdown of pearlite or from thedirect decomposition of austenite, it is assumed here that ferrite results only from

the latter source. The following assumptions are made for modeling the growth of

ferrite:

1) The austenite to ferrite transformation occurs at steady state and is controlled

by carbon diffusion.

2) The ferrite grains grow as spherical shells within austenite grains and the

number of ferrite grains is equal to the number of graphite nodules.

3) Thermodynamic equilibrium exists at graphite/ferrite and ferrite/austenite

interfaces. These are defined by equilibrium solvus lines extended below the

equilibrium eutectoid temperatures.4) Diffusion from the ferrite/austenite interface towards austenite is neglected as

diffusion coefficients and concentration gradients in austenite are small compared

to those in ferrite.

Nucleation and Growth of Pearlite:

The nucleation of pearlite usually occurs at austenite grain boundaries. It has been

demonstrated that pearlite colonies grow either as spheres or hemispheres

following nucleation. By the movement of high mobility (i.e., low interface

energy) incoherent interfaces, these colonies can grow edgewise or sidewise into

the austenite. This means that pearlite grows in competition with ferrite until

austenite is completely transformed.


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Transformation of austenite into pearlite is usually modeled with an Avrami

equation because the study of nucleation of pearlite is difficult, especially under

continuous cooling conditions. Also, pearlite grains impinge on each other at an

early stage, especially at a relatively high cooling rate.

6. Gray Iron Eutectoid Model

The gray iron eutectoid transformation model is based on the approach used for

gray iron eutectic. Nucleation and growth of ferrite takes place once the

temperature drops below the stable eutectoid temperature. If the transformation of

austenite is not complete when the metastable eutectoid temperature is reached,

then nucleation and growth of pearlite takes place. The nucleation and growth rate

expressions for pearlite are the same as those for the ductile iron eutectoid model.

7. Peritectic Transformation Model

In a peritectic transformation, liquid reacts with an existing solid phase to form a

new solid phase. In conventional models, the new solid is assumed to form at the

interface between the parent liquid and solid phases. Once the new solid phase is

formed, further reaction between the parent phases is limited by the layer of solid

formed. Hence the rate of reaction is controlled by the diffusion of solute through

the shell of the transformed product. It has been suggested by some researchers

that the peritectic transformation may be achieved through a liquid layer inbetween the parent and the product solid phases. This mechanism has been

adopted in the present model. For example, in the case of steel, the austenite phase

forms initially at the root of the dendrite arms of the delta phase and grows along

the delta/liquid interface. The speed of this growth is the same as that with which

liquid moves toward the delta phase. The diffusion problem can be simplified as

the liquid layer is very thin and the diffusion of carbon in the liquid is very rapid

so that the carbon concentration gradient in the liquid is negligible.

8. Solid Transformation Models

This model is only applicable to the Fe-C system and is used for tracking the

fraction transformed for the cases of gamma to ferrite and gamma to cementite.

Prior to reaching the eutectoid temperature, some of the austenite phase may

transform into alpha phase as part of a pro-eutectoid transformation. If you started

with a hypereutectoid composition, the pro-eutectoid transformation will be from

austenite (gamma) to cementite. Both of these pro-eutectoid transformations are

addressed by the current model. The wt% carbon equivalent determines whether

the gamma to ferrite or gamma to cementite transformation will be used. Both of

these models require that the equiaxed dendrite model be chosen for the initial

liquid/solid phase transformation.


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Density calculation during iron alloys solidification:

During gray or ductile solidification, the densities of the different phases are

computed according to the composition of the phase at that particular temperature.In the calculation, the graphite expansion is included. The densities are updated at

each time based on the temperature. The porosity calculation is based upon the

calculated density (see the "SGI Porosity model" section for more details). The

input density curve in PreCAST will not affect the calculated porosity formation if

micro model is activated.

Iron micro model inoculation setup:

In ProCAST, you can modify the phase nucleation depending on the inoculation

practice in the foundry for iron alloys solidification simulation. The inoculation

will be good if it is in-mold or in-stream with additional melt pretreatment. It is

not as good if the inoculation is only in-ladle. You can change the run parameters

to represent the practice of different inoculation. The higher value of EUNUCL (a

micro run parameter) represents better inoculation. The default value is set to 2000

which should represent pretty good inoculation. Metastable phase can form in the

faster cooling area if the inoculation is not good enough.

Graphite precipitation:

One more micro run parameter for iron alloys solidification simulation is added

called graphite precipitation (GRAPHITE in p.dat) which tells the degree of

graphite precipitation during solidification. It varies from 0 to 1. 1 means that the

graphite expansion potential is completely considered in the simulation so the

casting will have a relatively low tendency of shrinkage. 0 means that the graphite

expansion does not occur hence there is no compensation for the shrinkage of the

liquid during solidification by graphite expansion. During the micro calculation,

the computed expansion part of the density (as a function of the phases present) is

multiplied by GRAPHITE. If GRAPHITE = 0, there will be no expansion,

whereas with a value of 1, the full expansion contribution will be taken into

account in the density. This density is only used if a porosity calculation (POROS= 1) is made during the microstructure calculation (see the "SGI Porosity model"

section for more details). The value of GRAPHITE will not affect at all the

computed microstructure.

The default value is set to 1.0. This parameter is used to adjust the porosity

formation to the real foundry condition.

Case studies


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A simple geometry casting is used to illustrate the application of the

microstructure module on the solidification of different alloys. The casting is

cooled from the right with a chill (higher heat transfer coefficient). The two bigger

surfaces (back and front) are symmetry. All the other faces are adiabatic.

1. Al 4.9wt%Si

For this alloy, as the temperature cools down, the primary phase forms first. The

possibility to have and the amount of eutectic phase depends on the cooling rate.

With faster cooling rate, there is less amount of primary phase but more eutectic

phase. Fig. 6 shows the comparison of current calculation with some experiment

and other modeling results for the solidification of this alloy.

Fig. 6 Fraction of Eutectic

1) Primary dendrite radius

The PRIMARY DENDRITE RADIUS provides the current position of the

dendrite tip and volume fraction of the dendritic grain as it varies with time. At the

end of the primary solidification, this parameter will equal the final grain radius.


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Primary dendrite radius

2) Primary solid fraction

This reflects the volume fraction of the primary phase formed during

solidification. As stated above, there is more primary phase for lower cooling.

3) Eutectic grain radius (grain radius of the eutectic phase)


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4) Fraction of eutectic

5) Eutectic interlamellar spacing

The INTER-LAMELLAR SPACING parameter determines the fineness of the

eutectic. Smaller values of this parameter provide better mechanical properties.


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2. Ductile Iron (GGG 60)

This is a eutectic ductile iron. There is no primary austenite phase but only

eutectic phase during solidification. If the Carbon Equivalent is less then the

eutectic composition, the first phase comes out would be primary austenite phase

then eutectic.

The AUSTENITE RADIUS and GRAPHITE RADIUS provide the instantaneous

values of the solidified grain size and nodule size respectively. At the end of

solidification, they provide a correct description of the final grain size and nodule

size. AUSTENITE RADIUS AND GRAPHITE RADIUS can be related to the

mechanical

properties of castings. Density is calculated from the local fraction of graphite,

austenite, and liquid, thus capturing the contraction and expansion behavior of

ductile iron. As explained earlier, the stable eutectoid growth refers to the

decomposition of austenite into ferrite and graphite and the metastable eutectoid

growth refers to the decomposition of austenite into pearlite, which is a coupled

growth of ferrite and cementite.The properties of the iron depend strongly on the relative amounts of ferrite and

pearlite in the matrix. As the pearlite content increases, tensile and yield strengths

also increase, but at the cost of ductility. Ferrite content controls fracture

toughness and dynamic properties of iron. The FRACTION OF FERRITE and

FRACTION OF PEARLITE give the relative amount of stable and metastable

eutectoid structures. The pearlite/ferrite ratio can be related to tensile strength

through its effect on matrix microhardness. Usually, a finer pearlite grain size is

associated with a finer interlamellar spacing with better mechanical properties.

The following run parameters are used.

EUNUCL=1000 EUPOWER=2.5


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1) Nodule counts

2) Austenite radius

3) Graphite radius


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4) Pearlite Spacing

5) Fraction of Ferrite


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6) Fraction of Pearlite

7) Fraction of Eutectic


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8) Fraction of Metastable Phase

9) Tensile Strength


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10) Yield Strength

11) Elongation


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12) Hardness

We can see that it is not 100% stable phase (Eutectic) every where for this casting

after solidification. On the higher cooling area (right side), the metastable phase

(ledeburite) formed. The fraction of stable phase plus the fraction of metastable

phase is 1. The hard brittle metastable phase can form at higher cooling area

when the inoculation is not good enough. The metastable phase can increase the

yield strength but reduce the tensile strength of the ductile iron castings.

3. Gray Iron (GG 20)


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Mechanical properties of the cast grey iron part are a function of the stable and

metastable eutectic volume fractions and grain sizes. FRACTION OF EUTECTIC

gives the amount of the gray eutectic, whereas FRACTION OF METASTABLE

EUTECTIC gives the amount of the white eutectic. In most cases, the graystructure is more desirable as it gives improved tensile strength and ductility. The

EUTECTIC GRAIN RADIUS parameter gives the gray eutectic grain radius. The

INTER LAMELLAR SPACING parameter calculates the spacing of the gray

eutectic.

1) Fraction of Primary phase

2) Fraction of Eutectic


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3) Fraction of Metastable Eutectic

4) Eutectic grain Radius


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5) Eutectic Interlamelar Spacing

6) Fraction of Ferrite


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7) Fraction of Pearlite

8) Pearlite Spacing


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9) Tensile Strength

10) Yield Strength


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11) Brinell Hardness

Metastable phase can form if the cooling is high enough.

4) Carbon Steel (Plain Carbon AISI 1008 steel)

From the phase diagram, we know that the first phase formed during solidification

is primary austenite. The peritectic reaction happens when the temperature drops

to the peritectic temperature. Usually, peritectic growth is limited by the formation

of the solid transformed product at the reacting liquid/solid phase boundary. The

PERITECTIC FR. OF SOLID parameter gives the volume fraction of solid


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resulting from this reaction. It is important to know the amount of the phase

formed through this reaction, as it usually forms as a surface layer on the primary

dendritic solid phase. As temperature cools down, pro-eutectoid ferrite or

cementite will form depends on the composition until when the temperature

reaches to the eutectoid temperature. Below the eutectoid temperature, thepearlite forms. FRACTION OF PROEUTECTOID PHASE refers to the fraction

of proeutectoid ferrite or cementite formed from the austenite phase as a function

of time. The carbon equivalent value controls which type of the proeutectoid

phase (ferrite or cementite) will form. If the carbon content is less than the

eutectoid composition 0.8%, the proeutectoid phase would be ferrite phase,

otherwise would be cementite phase.

1) Primary dendrite arms

2) Primary solid fraction


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3) Secondary dendrite arm spacing

4) Fraction of peritectic


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5) Fraction of eutectoid

6) Fraction of proeutectoid


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33328241 micro structures

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