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ScienceDirect JOURNAL OF IRON AND STEEL RESEARCH, INTERNATIONAL. 2009, 16(5): 43-49

Application of FEM to Hot Continuous Rolling Process for Inconel 718 Alloy Round Rod SUI Feng-li':" ,

CHEN Li-qing",

LIU Xiang-hua' ,

XU Li-xia"

O. School of Materials Science and Engineering, Anhui University of Technology, Ma' anshan 243002, Anhui , China; 2. The State Key Laboratory of Rolling and Automation, Northeastern University, Shenyang 110004, Liaoning, China; 3. Fushun Special Steel Co Ltd, Fushun 113001, Liaoning, China) Abstract: A finite element model for coupled thermo-mechanical analysis has been developed in hot continuous rolling process for Inconel 718 alloy round rod with diameter of 45 mm, The stability of this alloy is discussed by integration of FEM and processing map reported in literatures. The result shows that the stability of Inconel 718 alloy is analyzed effectively during that process and good stability appears as the initial temperature is 960 'C and the initial velocity is from O. 15 to O. 45 rn > S-1 or the initial temperature is 980 'C and the initial velocity is from O. 15 to O. 25 m > S-I. Key words: hot continuous rolling; elastic-plastic FEM; coupled thermo-mechanical analysis; processing map; Inconel 718

Compared with the traditional hot rolling in open-train mill, hot continuous rolling of Inconel 718 alloy has higher productivity, higher production yield and accurate control. Therefore, it has been taking place of the traditional one. As a useful approach in optimizing the workability, processing maps have been used in forging process of Inconel 718 alloy[I-4]. The processing map[4] of Inconel 718 alloy made by Jonas instability criterion during hot compression is verified by microstructure observation of compressed samples, and microstructure observational points that exhibited stable microstructure reported in the literatures[I.S-7] marked in this processing map are all involved in the stable region. However, the analysis about hot continuous rolling of Inconel 718 alloy using processing maps has not been reported due to strain rate and temperature variation for different points in the cross-section of the workpiece at different time during rolling process. Recently, FEM for analyzing temperature, strain, strain rate and stress distribution in transverse section has been widely used during hot strip continuous rolling-'". In this study, a finite element

model for eighth-pass hot continuous rolling of Inconel 718 alloy round rod is built, and the stability of this alloy during that process is discussed by integration of elastic-plastic FEM and processing map. The original billet is square one with square cross section of 80 mm X 80 mm (the edge radius is 14 mm) and its length is 210 mm. The finished product is the round rod with diameter of 45 mrn,

1

Establishment of Finite Element Model

Finite element method has higher calculation accuracy for complex boundary conditions as used to calculate temperature, strain, strain rate and stress fields of the workpiece during hot continuous rolling. A coupled thermo-mechanical analysis model is built for an eight-pass hot continuous rolling process of Inconel 718 alloy using elastic-plastic finite element method. Some necessary assumptions are made in the model as follows: (a) due to high temperature and large deformation in hot continuous rolling, the roll is considered as rigid material and has no elastic deformation; (b) considering the shape change of passes during hot continuous rolling, 3D FEM IS

Foundation Item: Item Sponsored by National Natural Science Foundation of China (50634030); the Program of Education Ministry for New Century Excellent Talents in University (NECT-06-0285) Blography:SUI Feng-li

• 44 •

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Journal of Iron and Steel Research. International

used to build the analysis model; (c) considering the rolling symmetry in the cross-section. only a quarter of the geometric model is selected in simulation; (d) since the billet is reheated in a tunnel reheating furnace installed at the entrance of the hot continuous rolling mills, uniform temperature distribution is assumed throughout the original billet; (e) the process of hot continuous rolling can be assumed to be steady state except for the head and the tail of the workpiece. Hence, the middle part of the workpiece in the rolling direction is used for analysis at each pass. Some parameters about the workpiece and the roll Table 1

regarding FE simulation are given In Table 119 - JI J. Among them, the variation curves of flow stress with strain. strain rate and temperature are used in metal flow model. The heat conduction equation during continuous rolling is used in temperature field model.

e: . rJ T = I rJz Tz + a T + a T'I +!L z 2

2

( 1)

at a.r ay2 rJz , k where, p (kg > m-:1 ) is the mass density, c (] • kg- J • K- I ) is the specific heat, k (W· m- I • K- J) is the

k

thermal conductivity, and generation term.

q(W

• m- a ) is the heat

Parameters of workpiece and roll for FEM analysis Workpiece

Roll (cast steel)

Mass densi ty / (kg' m -:, )

8210

7800

Young's modulus/CPa

47.19-112.24

175

Poisson's ratio

0.34 -0.45

0.27

Stress-strain curve

Obtained from Cleeble-3800 simulator

Rigid

1.81X10

o

24.02

43. 00

Items Mechanical property

Thermal property Thermal expansion coefficient/ K -, Thermal conductivity/f W> m-' • K Heat capacity/j N • m

1)

2 • K-I)

Emissivity

5. 7X 10'

3.666 X 106

O. 7

O. 7

Eqn, (1) can be calculated once the initial condi-

tion and the boundary condition are determined. When the boundary is the third kind boundari Jz:. it can be expressed as:

aT aTt, '] =h(T-T.) -k aT -al'+-JlV+-J

(2) [ .r (y' a z: where, h (W· m" • K- I ) is the heat exchange coefficient, T. (K) is the ambient temperature, lI' ly' l, are the normal directional cosines on the boundaries. Heat transfer mode during hot continuous rolling consists of the following three parts: (a) interval heat loss through radiation and convection between the workpiece and the ambient air; (b) heat generation due to the plastic deformation and friction at the contact surface after the workpiece enters into the deformation region; (c) heat loss resulted from sudden temperature drop due to the contact of the workpiece to the roll. When the workpiece is air cooled between stands, the convective heat transfer mode is natural convection, and the heat loss caused by which is only a certain percentage of that caused by radiation as rolling temperature is no higher than 800 "C. The rolling speed is lower and the interval cooling condition is air cooling'!", As a result, the heat

loss caused by convection is omitted. Parameters and calculation methods for different heat transfer process [q,(W • m- 2 ) , h,(W· m " • K- J) are separately heat flux and heat exchange coefficient for radiation, S is Stefan-Boltzmann constant (5. 669 9 X 10- 8 W· rn" • K- J ) , e: is emissivity, T (K) is temperature of workpiece, To (K) is ambient air temperature. qR(W· m- Z ) . hR(W· m- z• K- J ) are separately heat flux and heat exchange coefficient between workpiece and roll, As (W • m -J • K- 1 ) is thermal conductivity, as(m 2 • s-J) is thermal diffusivity of workpiece, t (s) is contact time between workpiece and roll, T R (K) is temperature of roll. r; is conversional efficiency of plastic work into heat, ir( MPa) is equivalent stress; ~ (s -I) is equivalent strain rate. ] are shown in Table 2. The metal flow model and the temperature field model constitute the coupled thermo-mechanical analysis model. The element division method of the workpiece and the roll for the first pass rolling is shown in Fig. 1. The element of eight-node. isoparameter and arbitrary hexahedron is used in this model. The total element amount is 1 050 for the quarter workpiece and about 3 000 for the half roll.

Application of FEM

Issue 5 Table 2

to

Basic equations and methods used in heat transfer models

Phenomena of heat transfer Air cooling (radiation)

Contact heat transfer

currence of the above defects. Of course, the function of (j phase must be considered during that process for Inconel 718 alloy.

Main equations and parameters

(3) a=ck/dd~>5 where a is the workability parameter, and e is the strain rate. The rolling process is simulated using the model described above. As known, the existence of (j phase will restrict the grain growth during hot deformation'<" . The peak precipitation temperature of (j phase of Inconel 718 alloy is about 900 'C[I7] , and the temperature for starting dissolution is about 980 'C, but a certain amount of (j phase still exist after being reheated at 980 and 1 000 'C for more than 6 h respectively during dissolution process'J'", So the initial temperature of square billet by (j phase precipitation treatment should be less than 1 000 'C, and is separately designed as 960 and 980 ·C. The initial velocity of square billet is separately designed as O. 15, 0.25, 0.45 and O. 55 m • S-I according to the rolling capability of the continuous rolling mill, and corresponding rolling schedule is shown in Table 3. The elerxent I located in the half radius at diagonal line (Fig. 2) is selected to analyze the stability of hot continuous rolling process, by inputting the points in the curves of temperature-log strain rate obtained from coupled thermo-mechanical analysis into processing maps. Fig. 3 displays the variation of effective strain rate (a) and temperature (b) during the first pass rolling process, as the initial temperature of square billet is 960 'C and the initial velocity of square billet is 0.25 m > S-I. It is different from the compression experiments carried out at constant strain rate and constant temperature that the strain rate and temperature are changeable during rolling process. The relation between effective strain rate and temperature during the first pass can be obtained from Fig. 3 and is shown in Fig. 4. The temperature-log strain rate curves of element I for the whole rolling process can be obtained

q,=E'S'(T4_T~)

h,=q,/(T-T.) qR = 2As • (T - T R )

!t/(as • ,,) hR=qR/(T-TR)

Heat generation due to deformation

Fig. 1

2

• 45 •

Hot Continuous Rolling Process for Inconel 718 Alloy Round Rod

FE model for the first pass

Results and Discussion

Processing maps developed at different strains for Ni-based alloy[J4] and titanium alloy['5] show that the general feature of maps does not change significantly with strain. So the processing map can be applied to the deformation during hot continuous rolling at different stages. The processing map made by Eqn. (3) can really reflect the microstructure observations available in the open literature and is selected to analyze the stability of the hot continuous rolling process. There are three unstable regions in this map. the first one in the top left corner exhibits adiabatic shear bands. the second one in the top right corner exhibits intergranular cracking-!", and the last one is near the down-right corner. The aim of stability analysis for the rolling process is to avoid the ocTable 3

Rolling schedule of eight continuous rolling mills

Stand

lR

Roll diameter/mm Rolling speed at different initial velocity / (rn • s

I)

2L

3R

4L

5R

6L

7R

8L

530

530

460

460

460

460

380

380

0.15

0.19

0.22

0.27

0.34

0.44

O. 54

0.68

0.82

0.25

0.29

0.34

O. 43

0.51

O. 62

0.69

0.77

O. 90

0.35

0.43

O. S2

0.63

O. 78

I. 02

I. 25

I. 58

I. 92

0.45

0.56

O. 67

0.81

I. 01

I. 32

I. 61

2.03

2.47

0.55

0.68

0.81

I. 00

I. 23

I. 61

I. 97

2.49

3.02

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Journal of Iron and Steel Research. International

from the coupled thermo-mechanical analysis. The rolling process of element I can be considered to be stable when temperature-log strain rate curves inserted in processing map are all located in the stable region, or else the rolling process will lead to the defects described in Ref. [1]. The change history of strain rate and temperature for element I at initial temperature of 960C and initial velocity of O. 25 m • S-I for the square billet is presented in Fig. 5, and the curves of temperature-log strain rate can be obtained from it. Fig. 6 displays the curves of temperature-log strain rate for element I during the eighth-pass rolling process at initial temperature of 960 'C and dif-

\ \ ------.

I

------.

Fig. 2

Vol. 16

Analysis element in intermediate section of the billet 1.80 (a)

962.50 (b)

/\

~ 1.35

~

.~

\

!:l 0.90 til

~

:::l

~ 0.45 ....

\..

~

......./ 0'--

-'--

15.00

15.25

--1

960.00

15.50

L.....=-----''-.---

15.20

--'-

15.40

...........J

15.60

Time/s

Fig.3

Variation of effective strain rate

0.3 . . . . . - - - - - - - - - - - - - - . ,

o -0.3

.g: .....

.£ -0.6 -0.9 -1.2

L...o...

960.00

Fig. 4

~

961.25 Temperature/T'

.......

962.50

Relation between effective strain rate and temperature for element I

ferent initial velocities, and the corresponding processing map is integrated with them. All (log strain rate, temperature) points in the curves can be seen in the stable region. That means the defects described above is avoided during the whole rolling process for Inconel 718 alloy as the initial temperature

(a)

and temperature (b) for element I

is from 960 to 980 'C and the initial velocity is from 15 to O. 55 m > S-I for the square billet. It should be noted that high temperature should be accompanied with high solid solubility of Nb atoms in matrix, so the () phase can fully dissolve at 1 020 'C[18 J • Obviously, the grain will grow rapidly due to high temperature holding and no constraint of () phase as the temperature of some region in the finished product is more than 1 020 ·C. That appears as the initial temperature of square billet is 980 'C and the initial velocity of square billet is higher than 0.25 m > S-I, or the initial temperature of square billet is 960 'C and the initial velocity of square billet is higher than 0.45 m > S-l (Fig. T), The actual hot continuous rolling process for Inconel 718 alloy round rod with diameter of 45 mm is operated as the initial velocity is 0.25 m • S-I and the initial temperature is 960 'C for the square billet. The surface temperature of the workpiece is measured at the exit of pass 2, pass 4 and pass 8, and comparison between the measured values and the

o.

Application of FEM

Issue 5

1000

to

8

(a)

990

(l;

0-

E (l;

(b)

6

Y

1

• 47 •

Hot Continuous Rolling Process for Inconel 718 Alloy Round Rod

l

980

4

.~

970

~

[/.l

E-<

2

960 950 10

0

20

40

30

50

70

60

0

10

I

30

20

40

50

60

70

Time/s Fig. 5

2 (a)

Variation of temperature (a) and strain rate (b) for element I

Unstable

(b)

Unstable

0

-1 Stable -2 ..!!! .", eo .9

2

960

Stable

976

992

Unstable

(c)

960

972

984

996

Unstable

(d)

o -1

Stable -2

'--~

--'-

960

976

Stable ",-992

"""",,---, 1 008

986

1003

1020

Temperaturel'C .~Passl; (a)

Fig. 6

D-Pass2; %0 ·C. 0.15 m· S-I;

A-Pass 3; ,6,-Pass4; (b) 960 C. 0.25 rn > s-';

+-Pass5; O-Pass6; (e) 960 ·C. 0.55 rn > 5- 1;

.-Pass7; Q-Pass8 (d) 980 ·C. 0.55 m· S-I

Process chart and distribution of effective strain rate-temperature curves of element I for each roIling pass

calculated ones is demonstrated in Table 4. The deviation is no more than 1. 89 % between them, and the actual temperature variation is well predicted in this model. At the same time, the microstructure at the position equal to element I of the finished product is shown in Fig. 8, which exhibits fine equiaxed

grains and straight-even boundaries. This indicates that the deformation process for element I is stable in actual rolling process, so it is an effective way to analyze the stability of Inconel 718 during hot continuous rolling process by integration of FEM and processing maps.

Vol. 16

Journal of Iron and Steel Research. International

• 48 •

(a) 960 C. O. 45 m • s -

Fig. 7 Table 4

1;

(b) 960 C, O. 55 m • s - I

;

(c)

980

r. o. 25 m • s - \ ;

(d) 980 C. O. 35 m • s-\

Temperature distribution of a quarter of cross-section at the end of the eight-pass rolling process

Comparison of calculated surface temperature with measured one Temperature/ C

Classification Pass 2

Pass 4

Pass 8

Calculated value

964

968

976

976

Measured value

960

950

979

980

Deviations/ %

O. 42

1. 89

0.3\

0.4\

3

Conclusions

The stability of hot continuous rolling process IS analyzed by integration of FEM and processing map. The analysis result indicates that the rolling process of Inconel 718 alloy round rod with diameter of 45 mm is stable as the initial temperature is 960 'C and the initial velocity is from O. 15 to O. 45 m • s - I , or the initial temperature is 980 'C and the initial velocity is from O. 15 to O. 25 m > S-I. The actual rolling process is operated at the initial velocity of O. 25 m • s - I and the initial temperature of 960 ·C. The actual temperature variation is well predicted in this model, and good stability for the element I at the 1/2 radius along diagonal line in a quarter of crosssection appears in Inconel 718 alloy round rod. References;

[\ J Fig.8

Microstructure at 1/2 radius in the profile of finished rod with diameter of 4S mm

[2J

Srinivasan :-I. Prasad Y V R K. Microstructural Control in Hot Working of IN-718 Supperalloy Using Processing Map [JJ. Metallurgical and Materials Transactions. 1994. 25A( 10): 2275. Luo Z

J. Liu D. Evaluation of IN718 Disk-Forging Process

Issue 5

[3J

[4J

[5J

[6J

[7J

[8J

[9J

Application of FEM to Hot Continuous Rolling Process for Inconel 718 Alloy Round Rod

Using the Quality-Loss Function [J]. Journal of Materials Processing Technology. 1995. 59(4): 381. Narayana Murty S V S. Nageswara Rao, On the Development of Instability Criteria During Hotworking With Reference to IN 718 [J]. Materials Science and Engineering. 1998. 254A(1-2): 76. Narayana Murty S V S. Nageswara Rao B. On the Flow Localization Concepts in the Processing Maps of IN 718 [J]. Materials Science and Engineering. 1999. 267AO): 159. Howson T E. Couts W H Jr. Progress Toward a Deformation Map for Fine Grain Alloy 718 Billet [A]. Loria E A. eds. Metallurgy and Applications of Superalloy 718 [C]. Warrandale , TMS-AMIE. 1989. 685. Zhou LX. Baker T N. Effects of Strain Rate and Temperature on Deformation Behaviour of IN 718 During High Temperature Deformation [J]. Materials Science and Engineering. 1994. 177AO-2): I. Medeiros S C. Prasad Y V R K. Frazier W G. et al. Microstructural Modeling of Metadynamic Recrystallization in Hot Working of IN 718 Superalloy [J]. Materials Science and Engineering. 2000. 293AO-2): 198. LI Xue-tong , WANG Min-ting. DU Feng-shan. A Coupling Thermal Mechanical and Microstructural FE Model for Hot Strip Continuous Rolling Process and Verification [J]. Material Science and Engineering. 2005. 408AO-2): 33. Weiss V. Sessler J G. Aerospace Structure Metals Handbook. Vol II • Non-Ferrous [MJ. New York: Syracuse University Press. 1963.

[10J

[IlJ [12J

[13J [14J

[15J

[16J

[17J

[18J

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Wolf J. Aerospace Structure Metals Handbook. Vol 4 [MJ. Traverse City: Mechanical Properties Data Center. Belfour Stulen Inc. 1974. Frank Kreith , William Z Black. Basic Heat Transfer [MJ. New York: Harper and Row Publishers. 1980. LIU Xiang-hua. Rigid-Plastic FEM and Its Application in Rolling [M]. Beijing: Metallurgical Industry Press. 1994 (in Chinese). Vladimir B Ginzburg. Steel-Rolling Technology: Theory and Practice [MJ. New York: Marcel Decker Inc. 1989. CAl Da-yong , XIONG Liang-yin. LIU Wen-chang. et al. Development of Processing Maps for aNi-Based Superalloy [J]. Materials Characterization. 2007. 58( 10): 941. Park N K •. Yeom J T. Na Y S. Characterization of Deformation Stability in Hot Forging of Conventional Ti-6AI-4V Using Processing Maps [J]. Journal of Materials Processing Technology. 2002. 130-131(2): 540. Dedvallees Y. Bouzidi M. Bois F. et al, Delt Phase in Inconel 718 Mechanical Properties and Forging Process Requirements [AJ. Superalloys 718. 706 and Various Derivatives [CJ. Warrendale: TMS. 1994. 281. Sundararaman M. Mukhopadhyay P. Banerjee S. Precipitation of the o--NisNb Phase in Two Nickel Base Superalloys [J]. Metallurgical Transactions. 1988. 19A(3): 453. CAl Da-yong , ZHANG Wei-hong. NIE Pu-Iin , et al. Dissolution Kinetics and Behavior of 8 phase in Inconel 718 [J]. Transactions of Nonferrous Metals Society of China. 2003. 13 (6): 1338 (in Chinese).