Cold and Hot Forging: Fundamentals and Applications / Edited by Taylan Altan, Gracious Ngaile, Gangshu Shen

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Process Modeling in Cold Forging Using Finite-Element Analysis / 245

Fig. 18.13

Three-dimensional ﬁnite-element model for or-

bital forming simulation [Cho et al., 2003]

metal forming processes can assist the designers

in establishing and optimizing process variables

and die design. As a result, process development

effort and cost can be reduced.

18.4.7 Advanced Orbital Forming

Simulations [Cho et al., 2003]

Orbital forging is an incremental forging pro-

cess with a complicated die movement that can

be used to reduce axial load requirements for

axisymmetric or near-axisymmetric forging

operations. At the ERC/NSM, orbital forging

simulations were conducted to study and de-

velop a robust assembly process of an automo-

bile spindle. Orbital forming requires a number

of revolutions to form a part. Therefore, in FEM

simulation, a relatively large number of simu-

lation steps are required to minimize the errors

in solution accuracy. Also, a full 3-D modeling

is required, due to an asymmetric rotational tool

movement. Figure 18.13 shows the FE model.

Figure 18.14 shows the predicted metal ﬂow at

intermediate stages of forming. Solution accu-

racy was veriﬁed by comparing the predicted

forces and tab outer diameters with experimental

measurements, and good agreement was ob-

tained.

REFERENCES

[Altan et al., 1990]: Altan, T., Oh, S.I., “Appli-

cation of FEM to 2-D Metal Flow Simulation:

Practical Examples,” Advanced Technology of

Plasticity, Vol 4, p 1779, 1990.

[Altan et al., 2001]: Dixit, R., Ngaile, G., Altan,

T., “Measurement of Flow Stress for Cold

Forging,” ERC/NSM-01-R-05, Engineering

Research Center for Net Shape Manufactur-

ing.

[Altan et al., 2003]: Cho, H., Ngaile, G., Altan,

T., “Simultaneous Determination of Flow

Stress and Interface Friction by Finite Ele-

ment Based Inverse Analysis Technique,” En-

gineering Research Center for Net Shape

Manufacturing, submitted for publication to

CIRP.

[Cho et al., 2003]: Cho, H., Kim, N., Altan, T.,

“Simulation of Orbital Forming Process Us-

ing 3-D FEM and Inverse Analysis for Deter-

mination of Reliable Flow Stress,” submitted

Fig. 18.14 Predicted metal ﬂow at intermediate stages of simulation [Cho et al., 2003]

246 / Cold and Hot Forging: Fundamentals and Applications

to Third International Seminar for Precision

Forging, Japan Society for Technology of

Plasticity (Nagoya, Japan), 2003.

[Hannan et al., 1999]: Hannan, D., Vazquez, V.,

Altan, T., “Precision Forging of Golf Ball

Mold Cavities,” Report No. PF/ERC/NSM-

99-R-12A, Engineering Reseach Center for

Net Shape Manufacturing.

[Hannan et al., 2000]: Hannan, D., and Altan,

T., “Prediction and Elimination of Defects in

Cold Forging Using Process Simulation,”

Tenth International Cold Forging Congress,

International Cold Forging Group, Sept 13–

15, 2000 (Stuttgart).

[Kim et al., 1996]: Kim, H., and Altan, T.,

“Cold Forging of Steel—Practical Examples

of Computerized Part and Process Design,”

Journal of Materials Processing Technology,

Vol 59, 1996, p 122.

[Messner et al., 1994]: Messner, A., Engel, U.,

Kals, R., Vollertsen, F., “Size effect in the FE

simulation of microforming processes,”

JMPT, Vol 45, p 374, 1994

[Palaniswamy et al., 2001]: Palaniswamy, H.,

Ngaile, G., Altan, T., “Coining of Surgical Slit

Knife,” F/ERC/NSM-01-R-26, Engineering

Research Center for Net Shape Manufactur-

ing.

[Tiesler et al., 1999]: Tiesler, N., Engel, U.,

Geiger, M., “Forming of Microparts—Effects

of Miniaturization on Friction,” Advanced

Technology of Plasticity, Vol. 2, Proceedings

of the Sixth ICTP, Sept. 19–24, 1999.

[Vazquez et al., 1996]: Vazquez, V., Sweeney,

K., Wallace, D., Wolff, C., Ober, M., Altan,

T., ”Tooling and Process Design to Cold

Forge a Cross Groove Inner Race for a Con-

stant Velocity Joint—Physical Modeling and

FEM Process Simulation,” JMPT, Vol 59, p

144–157.

[Yamanaka et al., 2002]: Yamanaka, M., and

Sunami, F., “Tool Design for Precision Forg-

ing,” Cold and Warm Precision Forging

Workshop, Schuler Inc., Yamanaka Engineer-

ing, Scientiﬁc Forming Technologies Corp.,

and ERC/NSM, Nov 14, 2002 (Canton, MI).

SELECTED REFERENCE

●

[Hayama, 1969]: Hayama, M., Plasticity

and Plastic Working, Ohmusha, 1969, p 125.

CHAPTER 19

Microstructure

Modeling in Superalloy Forging

Gangshu Shen

19.1 Introduction

In aerospace forging, in addition to meeting

the geometry requirements, meeting microstruc-

ture and mechanical property requirements of

components plays a major role in the develop-

ment of the forging processes and sequences.

The understanding and prediction of microstruc-

tures that develop during the hot deformation

processing has long been the “art” of forging

metallurgists. Many tools, such as wedge tests,

were used in the past to understand the impact

of temperature, strain, and strain rate on micro-

structures and properties and to guide metallur-

gists in process development [Deridder and

Koch, 1979]. These methods were good, but

quantitative extraction of various processing pa-

rameters on the resulting microstructures and

properties was not effectively accomplished.

The application of ﬁnite-element modeling

(FEM) to forging made it possible to obtain the

detailed thermomechanical histories at each in-

dividual location of the forged components. Mi-

crostructure modeling procedures were devel-

oped to make use of this information for grain

size and property predictions for steels [Sellars,

1979] and superalloys [Shen et al., 1995, and

Shen and Hardwicke, 2000].

In this chapter, the experimental procedure,

microstructure model formulation, and the ap-

plication of the microstructure model in super-

alloy forgings are discussed.

19.2 Experiments for Microstructure

Model Development

Hot forging involves preheating, deformation,

transfer, and dwell (resting) between operations

and ﬁnal postforging cooldown. Small-scale ex-

periments were run to simulate these operations

and to establish the relationship between vari-

ables and microstructures and to generate data

for the development of a microstructure model.

Real-scale tests were run to compare the model

prediction with reality. Three sets of experi-

ments were used in the model development.

19.2.1 Preheating Tests

Heat treatment studies were conducted with

different temperatures and hold times to produce

the as-preheated grain size for a forging opera-

tion. From these tests, the grain growth model

for preheating of a particular billet pedigree was

developed. This model was then used to estab-

lish the preheated grain size (d

) just prior to

subsequent forging operations.

19.2.2 Compression Tests

Laboratory upset tests were conducted with

different temperatures, strains, strain rates, as-

preheated grain sizes, and postdeformation hold

times to characterize dynamic recrystallization

during forging and meta-dynamic recrystalliza-

tion and static grain growth during postforging

Cold and Hot Forging Fundamentals and Applications

Taylan Altan, Gracious Ngaile, and Gangshu Shen, editors, p247-255

DOI:10.1361/chff2005p247

www.asminternational.org

248 / Cold and Hot Forging: Fundamentals and Applications

cooldown. Both the MTS Systems Corporation

compression stand and Gleeble test unit were

used to perform these compression tests. The ad-

vantage of the MTS test stand is that it can pro-

vide more uniform temperature of the work-

piece. The advantage of the Gleeble test is that

it can perform a fast postforging cooling with a

controlled manner. From these compression

tests with rapid postdeformation cooling, infor-

mation related to dynamic recrystallization ki-

netics was obtained. The kinetics information in-

cluded: peak strain for dynamic recrystallization

which is related to the critical strain for(¯e ),

dynamic recrystallization the strain that(¯e );

corresponds to 50% (0.5 fraction) dynamic re-

crystallization the fraction of dynamic re-(¯e );

0.5

crystallization (X

dyn

); and the size of dynami-

cally recrystallized grains (d

dyn

). Information

regarding meta-dynamic recrystallization and

postforging grain growth was also obtained from

compression tests with controlled postforge hold

times. This information included: time for 50%

meta-dynamic recrystallization (t

0.5

), fraction of

meta-dynamic recrystallization (X

m-dyn

), meta-

dynamically recrystallized grain size (d

m-dyn

and grain growth at a given temperature and

time after the completion of meta-dynamic re-

crystallization.

19.2.3 Pancake and Generic Forgings

In addition to laboratory tests, large pancakes

and generic component conﬁgurations were pro-

duced on production equipment under various

forging conditions and methods to assess the mi-

crostructure model.

Finite-element analysis was used for each ex-

periment to provide detailed information for

each test. Thus, accurate thermal-mechanical

histories of local points of forged samples were

used to develop the models for the microstruc-

ture evolution of Waspaloy during the forging

process.

19.3 Microstructure

Model Formulation

The processes that control grain structure evo-

lution during hot working of superalloys were

found to be dynamic recrystallization, meta-dy-

namic recrystallization, and static grain growth.

Microstructure model formulation is discussed

in these three categories. Waspaloy formulas are

used as examples here [Shen et al, 1995].

19.3.1 Dynamic Recrystallization

Dynamic recrystallization happens instanta-

neously during high-temperature deformation.

The fraction of dynamic recrystallization can be

obtained by examining micrographs obtained

from samples quenched after the deformation.

Under production conditions, pure dynamic re-

crystallization is difﬁcult to achieve. This is be-

cause meta-dynamic recrystallization often fol-

lows immediately. The amount of dynamic

recrystallization is related to the as-preheated

grain size (d

), effective strain temperature(¯e),

(T), and effective strain rate in a hot defor-

(¯e)

mation process. There are four important param-

eters related to dynamic recrystallization: the

peak strain the strain for 50% dynamic re-(¯e ),

crystallization the fraction of dynamic re-(¯e ),

0.5

crystallization (X

dyn

), and the size of dynami-

cally recrystallized grains (d

dyn

Peak Strain. The strain corresponding to the

peak stress in the ﬂow stress curve is an(¯e )

important measure for the onset of dynamic re-

crystallization. The occurrence of dynamic re-

crystallization modiﬁes the appearance of ﬂow

curves. At the strain rates typical for forging of

Waspaloy, single-peak stress-strain curves are

most common. As a result of dynamic recrys-

tallization, the stress diminishes to a value in-

termediate between the yield stress and the peak

stress once past the peak strain. The reason for

this curve following a single peak is that under

the condition of high Z (Zener-Hollomon pa-

rameter, Z ⳱ for Waspaloy),

¯e exp[468000/RT]

the dislocation density can be built up very fast.

Before recrystallization is complete, the dislo-

cation densities at the center of recrystallized

grains have increased sufﬁciently that another

cycle of nucleation occurs, and new grains begin

to grow again. Thus, average ﬂow stress inter-

mediate between the yield stress and the peak

stress is maintained. The equations developed

for the peak strain for Waspaloy are:

ⳮ4 0.54 0.106

¯e ⳱ 5.375 ⳯ 10 d Z

(sub- and in-c⬘ solvus) (Eq 19.1)

ⳮ4 0.54 0.106

¯e ⳱ 1.685 ⳯ 10 d Z (super-c⬘ solvus)

(Eq 19.2)

Strain for 50% Dynamic Recrystallization.

Micrographs taken from quenched compression

samples show that dynamic recrystallization

progresses in a sigmoidal manner with respect

Microstructure Modeling in Superalloy Forging / 249

Fig. 19.1

Schematic of strain corresponding to 50% (0.5

fraction) dynamic recrystallization (DRX) for a

given condition of temperature, strain rate, and as-preheated

grain size

to strain. The Avrami equation can be used to

describe a sigmoidal curve for the fraction of

dynamic recrystallization versus strain:

X ⳱ 1 ⳮ exp{ⳮln2[¯e/¯e ] } (Eq 19.3)

dyn 0.5

When the constants and n are determined,¯e

0.5

the relation for the fraction of dynamic recrys-

tallization is determined. The strain for 50% re-

crystallization, can be obtained from com-¯e ,

0.5

pression tests with different magnitudes of strain

for a given condition of temperature, strain rate,

and as-preheated grain size, as shown in Fig.

19.1. The exponent can be obtained by taking

the logarithm of Eq 19.3. is related to as-¯e

0.5

preheated grain size, d

, and Z by:

0.32 0.03

¯e ⳱ 0.145 d Z (sub-c⬘ solvus) (Eq 19.4)

0.5 0

0.32 0.03

¯e ⳱ 0.056 d Z (in-c⬘ solvus) (Eq 19.5)

0.5 0

0.29 0.04

¯e ⳱ 0.035 d Z (super-c⬘ solvus)

0.5 0

(Eq 19.6)

Fraction of Dynamic Recrystallization. Af-

ter the strain for 50% dynamic recrystallization

and the exponent n for Eq 19.3 are determined,

equations for the fraction of dynamically re-

crystallized grains can be formulated for Was-

paloy as below:

3.0

X ⳱ 1 ⳮ exp{ⳮln2[¯e/¯e ] } (sub-c⬘ solvus)

dyn 0.5

(Eq 19.7)

2.0

X ⳱ 1 ⳮ exp{ⳮln2[¯e/¯e ] } (in-c⬘ solvus)

dyn 0.5

(Eq 19.8)

1.8

X ⳱ 1 ⳮ exp{ⳮln2[¯e/¯e ] } (super-c⬘ solvus)

dyn 0.5

(Eq 19.9)

Figures 19.2(a) and (b) summarize the exper-

imental data and the ﬁtted model for Waspaloy

dynamic recrystallization at 1850 and 1951 F

(1010 and 1066 C), respectively.

The critical strain for the start of dynamic re-

crystallization usually follows the relationship

[Sellars, 1979]:

¯e ⳱ 0.8 ¯e (Eq 19.10)

The Size of Dynamically Recrystallized

Grain. The dynamically recrystallized grain size

is the function of the Zener-Hollomon parame-

ter, Z, only. This is because Z deﬁnes the density

of the subgrains and the nuclei. Though the dy-

namically recrystallized grain size is not related

to strain, the strain has to reach the value of

steady-state strain to result in full dynamic re-

crystallization. The relationship between dy-

namically recrystallized grain, d

dyn

, and Z is

shown as follows:

ⳮ0.16

d ⳱ 8103 Z (sub- and in-c⬘ solvus)

dyn

(Eq 19.11)

ⳮ0.0456

d ⳱ 108.85 Z (super-c⬘ solvus)

dyn

(Eq 19.12)

Figure 19.3 shows the correlation between the

experimental data and Eq 19.11 and 19.12. It is

seen that there is a difference between subsolvus

forging and supersolvus forging in terms of the

sizes of the dynamically recrystallized grains.

The subsolvus forging results in ﬁner grain

sizes, while supersolvus forging results in coarse

grain sizes. However, subsolvus forging needs

large strains to ﬁnish dynamic recrystallization,

as shown in Eq 19.4 and 19.7.

19.3.2 Meta-Dynamic Recrystallization

Meta-dynamic recrystallization is important

in the determination of the grain size obtained

under practical forging conditions. Meta-dy-

namic recrystallization occurs when a deforma-

tion stops at a strain that passes the critical strain

for dynamic recrystallization but does not reach

the steady-state strain for dynamic recrystalli-

zation [McQueen and Jonas, 1975], which is the

case for most regions in a forged part. Under

meta-dynamic recrystallization conditions, the

250 / Cold and Hot Forging: Fundamentals and Applications

Fig. 19.2

Measured (data points) dynamic recrystallization (DRX) kinetics for hot deformation of Waspaloy at (a) 1850 F (1010 C)

and (b) 1951 F (1066 C) and ﬁtted curves

Fig. 19.3

Logarithm of dynamically recrystallized grain size

(in lm) versus ln Z obtained from compression

tests

partially recrystallized grain structure that is ob-

served right after deformation (Fig. 19.4a)

changes to a fully recrystallized grain structure

(Fig. 19.4b) by continuous growth of the dynam-

ically recrystallized nuclei at a high temperature.

The meta-dynamically recrystallized grains are

coarser than the dynamically recrystallized

grains. However, they can often provide the uni-

formity of the grains under a production condi-

tion. The amount of meta-dynamic recrystalli-

zation is related to the as-preheated grain size,

the strain, the temperature, the strain rate, and

the holding time in a hot deformation process.

Microstructure Modeling in Superalloy Forging / 251

Fig. 19.4

Micrographs obtained from Waspaloy samples with different cooling histories after forging. (a) Rapidly cooled immedi-

ately after deformation. (b) Rapidly cooled after a 5 s hold at deformation temperature (1951 F, or 1066 C)

Important parameters related to meta-dynamic

recrystallization are the time for 50% meta-dy-

namic recrystallization (t

0.5

), the fraction of

meta-dynamic recrystallization (X

m-dyn

), and the

size of the meta-dynamically recrystallized grain

m-dyn

Time for 50% Meta-Dynamic Recrystalli-

zation. Meta-dynamic recrystallization is time

dependent. For a given strain, strain rate, and as-

preheated grain size, meta-dynamic recrystalli-

zation progresses in the following manner with

respect to time:

X ⳱ 1 ⳮ exp{ⳮln2[t/t ] } (Eq 19.13)

m-dyn 0.5

The t

0.5

can be obtained from compression

tests with different holding times for a given

temperature, strain, strain rate, and as-heated

grain size. The empirical t

0.5

for meta-dynamic

recrystallization follows:

ⳮ50.51ⳮ1.28 ⳮ0.073

t ⳱ 4.54 ⳯ 10 d ¯e ¯e exp(9705/T)

0.5 0

(Eq 19.14)

The exponent, n, for meta-dynamic recrystal-

lization is found to be 1 for Waspaloy. This num-

ber is typical for meta-dynamic recrystallization

[Jonas, 1976, and Devadas et al., 1991].

Fraction of Metadynamic Recrystalliza-

tion. The fraction of meta-dynamic recrystalli-

zation progresses according to:

1.0

X ⳱ 1 ⳮ exp{ⳮln2[t/t ] } (Eq 19.15)

m-dyn 0.5

Figures 19.5(a) and (b) show the fraction of

meta-dynamic recrystallization versus time ob-

tained from the experiments and the predictions

at 1951 F (1066 C) with different as-preheated

grain size, strain, and strain-rate conditions. The

meta-dynamic recrystallization ﬁnishes sooner

for cases of larger strains, ﬁner as-preheated

grain sizes, higher strain rates, and higher tem-

peratures.

Meta-Dynamic Recrystallized Grain Size.

The grain size obtained at the end of meta-dy-

namic recrystallization is found to have the fol-

lowing relationship with the strain, the as-pre-

heated grain size, and the Zener-Hollomon

parameter, Z:

0.33 ⳮ0.44 ⳮ0.026

d ⳱ 14.56d ¯e Z (Eq 19.16)

m-dyn 0

The meta-dynamic recrystallized grain size in

ASTM number versus strain under conditions

with different as-preheated grain sizes, tempera-

tures, and strain rates is shown in Fig. 19.6.

19.3.3 Grain Growth

Under high-temperature deformation condi-

tions, grain growth happens rapidly after the

completion of meta-dynamic recrystallization.

Grain-boundary energy is the driving force caus-

ing grain-boundary motion at high temperature.

Grain-boundary energy is comparable to the sur-

face energy; i.e., it tends to minimize itself

whenever possible by decreasing the grain-

boundary area. In general, grain growth will

continue to occur at elevated temperatures until

252 / Cold and Hot Forging: Fundamentals and Applications

Fig. 19.5

Fraction of meta-dynamic recrystallization (DRX) versus time at 1951 F (1066 C) with a strain of (a) 0.22 and (b) 0.6

to 1.3

the balance between the grain-boundary energy

and the pinning effects of precipitates (precipi-

tate size and spacing) is reached.

Grain growth is characterized by compression

tests with different postforging hold times. From

the micrographs obtained from these tests, the

microstructural evolution from partial dynamic

recrystallization to full meta-dynamic recrystal-

lization and to grain growth was observed. The

change in grain size versus time after the com-

pletion of meta-dynamic recrystallization is

found to follow:

33 26

d ⳮ d ⳱ 2 ⳯ 10 t exp(ⳮ595000/[RT])

m-dyn

(Eq 19.17)

The form of Eq 19.17 is well known for the

characterization of grain growth. The reason for

emphasizing that the d

m-dyn

is the grain size after

complete meta-dynamic recrystallization is that

after the completion of meta-dynamic recrystal-

lization, the dislocations have essentially disap-

peared, and the driving force for grain size

changes is the grain-boundary energy only.

The experimentally obtained data and the

model prediction for the short-time grain growth

are shown in Fig. 19.7. It is seen from this ﬁgure

that the grain growth at a temperature of ap-

proximately 2050 F (1121 C) is very fast.

There was not much difference in grain size after

the completion of meta-dynamic recrystalliza-

tion between the two samples obtained from

compression tests at 1951 and 2050 F (1066 and

1121 C) (Fig. 19.3 and 19.7). However, the

grain growth results in a large difference in the

ﬁnal grain size between the two sets of tests.

Microstructure Modeling in Superalloy Forging / 253

Fig. 19.7

Grain growth versus time after the completion

of meta-dynamic recrystallization in Waspaloy

forging

Fig. 19.6 Meta-dynamic recrystallized grain size versus strain for various process conditions

19.3.4 Model Summary

It is seen from these equations that the major

factors in the control of the grain size in the forg-

ing of Waspaloy are strain, temperature-com-

pensated strain rate, and the as-preheated grain

size.

Strains create localized high densities of dis-

locations. To reduce their energy, dislocations

rearrange into subgrains. When the subgrains

reach a certain size, the nuclei of new grains

form. The higher the strain, the greater the

amount of dislocations and the greater the num-

ber of cycles of recrystallization. Hence, larger

strains result in a higher percentage of recrys-

tallization.

The reason that deformation under high-Z

conditions gives ﬁner grain size is that an in-

crease in Z results in the increase in the subgrain

density, which gives a higher density of nuclei.

There are also more cycles of recrystallization

present under high values of Z. Thus, the size of

the recrystallized grains decreases [McQueen

and Jonas, 1975].

At a given strain, the as-preheated grain size

plays an important role in the determination of

the fraction of recrystallization and recrystalli-

zed grain size, because when polycrystalline

metal is deformed, the grain boundaries interrupt

the slip processes. Thus, the lattice adjacent to

grain boundaries distorts more than the center of

the grain. The smaller the as-preheated grain, the

larger the grain-boundary area and the volume

of distorted metal. As a consequence, the num-

ber of possible sites of nucleation increases, the

rate of nucleation increases, and the size of the

recrystallized grains decreases. Moreover, the

uniformity of distortion increases with the de-

crease in as-preheated grain size. Therefore,

having a ﬁne as-preheated initial grain size is

very important for obtaining a ﬁne recrystallized

ﬁnal grain size.

The equations developed for the quantitative

prediction of these phenomena for Waspaloy are

summarized in Table 19.1.

254 / Cold and Hot Forging: Fundamentals and Applications

Fig. 19.8

Comparison of model prediction and experimen-

tal results. Fraction of recrystallization of a 718

developmental forging

Table 19.1 Mathematical model for

microstructure development in Waspaloy

forging

Dynamic recrystallization

Z ⳱ exp(468000/RT)

¯e

⳱¯e 0.8¯e

Subsolvus forging

⳱ 5.375 ⳯ 10

ⳮ4

0.54

0.106

¯e

⳱ 0.145 d

0.32

0.03

¯e

0.5

dyn

⳱ 1 ⳮ exp{ⳮln2

3.0

[¯e/¯e ]}

0.5

dyn

⳱ 8103 Z

ⳮ0.16

In-solvus forging

⳱ 5.375 ⳯ 10

ⳮ4

0.54

0.106

¯e

⳱ 0.056 d

0.32

0.03

¯e

0.5

dyn

⳱ 1 ⳮ exp{ⳮln2

2.0

[¯e/¯e ]}

0.5

dyn

⳱ 8103 Z

ⳮ0.16

Supersolvus forging

⳱ 1.685 ⳯ 10

ⳮ4

0.54

0.106

¯e

⳱ 0.035 d

0.29

0.04

¯e

0.5

dyn

⳱ 1 ⳮ exp{ⳮln2

1.8

[¯e/¯e ]}

0.5

dyn

⳱ 108.85 Z

ⳮ0.0456

Meta-dynamic recrystallization

0.5

⳱ 4.54 ⳯ 10

ⳮ5

0.51

exp(9705/T)

ⳮ1.28 ˙ⳮ0.073

¯e ¯e

m-dyn

⳱ 1 ⳮ exp{ⳮln2[t/t

0.5

]

1.0

}

m-dyn

⳱ 14.56d

0.33 ⳮ0.44 ⳮ0.026

¯e Z

Grain Growth

ⳮ d

m-dyn

⳱ 2 ⳯ 10

t exp(ⳮ595000/[RT])

19.4 Prediction of Microstructure in

Superalloy Forging

The methodology used in Waspaloy micro-

structure model development has also been used

for superalloy 718 [Shen, 2000]. The models

are integrated into ﬁnite-element software

DEFORM (Scientiﬁc Forming Technologies

Corp.) to predict microstructures developed for

different forging processes [Wu and Oh, 1985,

and Scientiﬁc Forming Technologies Corp.,

2002].

Figures 19.8 and 19.9 are the comparison of

model prediction and experimentally obtained

values (numbers shown on the contours) of re-

crystallization and average ASTM grain size of

a hammer-forged 718 disk [Shen et al., 2001].

Multiple dies were used in this hammer forging.

The blow-by-blow simulation was run for the

hammer forging in the FEM code DEFORM that

allows the entire thermal-mechanical history of

the hammer forging to be stored in the computer.

The microstructure model uses the thermal-me-

chanical history of the hammer forging to pre-

dict the recrystallization and grain size of the

hammer-forged 718 disk. Figures 19.8 and 19.9

show that the fraction of recrystallization and the

ASTM average grain size predicted by the

model agree well with the experimentally mea-

sured values.

Figure 19.10 shows the model-predicted

ASTM grain sizes and the experimentally mea-

sured ASTM grain sizes for an experimental

Waspaloy disk. The forging process involved a

hydraulic press isothermal forging followed by

a hammer forging [Stewart, 1988]. Again, the

model predicted well the average grain size of

the forged Waspaloy disk. These examples show

that the microstructure model is capable of pre-

dicting the recrystallization and grain size for

quite complex processes, such as hammer forg-

ing with multiple blows and die sets and the

combination of press and hammer forgings.

19.5 Nomenclature of

Microstructure Model

d ﬁnal grain size, lm

as-preheated grain size, lm

Fig. 19.9

Comparison of model prediction and experimen-

tal results. Average ASTM grain size of a 718 de-

velopmental forging