NAT'L INST. OF STAND & TECH R.I.C

AlllOS 353153

NIST

PUBLICATIONS

r\jisr United States Department of Commerce

Technology Administration

National Institute of Standards and Technology

NIST Technical Note 1393

Modeling of the Microstructure

and Mechancial Properties

of Steels during

Thermomechanical Processing

Roman Kuziak

Yi-Wen Cheng

Miroslaw Glowacki

Maciej Pietrzyk

QC

100

U5753

NO. 1393

1997

NIST Technical Note 1393

Modeling of the Microstructure and

Mechancial Properties of Steels

during Thermomechanical Processing

Roman Kuziak*

Yi-Wen Cheng

Miroslaw Glowacki**

Maciej Pietrzyk**

Materials Reliability Division

Materials Science Engineering Laboratory

National Institute of Standards and Technology

325 Broadway

Boulder, Colorado 80303-3328

* Materials Science Department

Institute of Ferrous Metallurgy

Gliwice, Poland

**Materials Engineering Department

Academy of Mining and Metallurgy

Cracow, Poland

Supported by

The United States-Poland Maria Sklodowska-Curie Joint Fund

November 1997

U.S. DEPARTMENT OF COMMERCE, William M. Daley, Secretary

TECHNOLOGY ADMINISTRATION, Gary R. Bachula, Acting Under Secretary for Technology

NATIONAL INSTITUTE OF STANDARDS AND TECHNOLOGY, Raymond G Kammer. Director
National Institute of Standards and Technology Technical Note

Natl. Inst. Stand. Technol., Tech. Note 1393, 80 pages (November 1997)

CODEN:NTNOEF

U.S. GOVERNMENT PRINTING OFFICE

WASHINGTON: 1997

For sale by the Superintendent of Documents, U.S. Government Printing Office, Washington, DC 20402-9325
Contents

Nomenclature v Foreword vii Abstract 1

1. Introduction 2

2. Structure of the Research Project 4

3. Experiments 5

4. Microstructural Evolution Models 7

4.1 Microstructural Evolution during Hot Working 8

4.1.1 Static Recrystallization Model 8 4.1.2 Dynamic Recrystallization Model 14

4.1.3 Metadynamic Recrystallization Model 17

4.1.4 Grain Growth of the Austenite after Recrystallization 19 4.2 Phase Transformations on Cooling after Hot Working 20

4.2.1 Ferrite-Pearlite Steels 20

4.2.2 900A Eutectoid Steel 24

5. Microstructure-Mechanical-Property Relationships 27

5.1 Ferrite-Pearlite Steels 27

5.2 900A Eutectoid Steel 31

6. Laboratory Experimental Validation of the Microstructural Evolution Models 32

6.1 Laboratory Experiments and the Linkage to the Finite-Element Codes 32

6.2 Press Compression of Carbon-Manganese Steel 35

6.2.1 Experimental Procedures 35

6.2.2 Thermomechanical Behavior during Compression 37

6.2.3 Effect of Processing Conditions on the Mechanical Properties 39

6.2.4 Effect of Processing Conditions on Microstructure 41

6.3 Forging of Vanadium-Treated Microalloyed Medium-Carbon Steel 46

6.3.1 Experimental Procedures 46

6.3.2 Mathematical Modeling 47

6.4 Flat Rolling of 900A Eutectoid Steel 51

7. Industrial Experiments 53

7.1 Plate Rolling 53

7.2 Rod Rolling 56

7.2.1 Experimental Procedures 56

7.2.2 Validation of the Model 57

7.3 Rail Rolling 62

8. Summary 68

8.1 Mathematical Modeling 68

8.2 Industrial Experiments 69

8.2.Plate Rolling 69

8.2.2 Rod Rolling 69

8.2.3 Rail Rolling 70

9. Acknowledgments 70

10. References 70

in

Nomenclature

Abbreviations

FDT finish deformation temperature

FEM finite-element method

FRT finish rolling temperature

HV5 Vickers microhardness (load = 5 N)

ITT impact transition temperature

tot total VT vanadium treated

Symbols

8 strain

s strain rate

e

a strain retained in the microstructure after cooling to ambient temperature

e

c critical strain for dynamic recrystallization

s

; total strain imposed on a specimen during the z'th deformation

8 strain to peak stress in the flow curve

z

lr retained strain

k thermal conductivity

A. penalty coefficient

p material density

p initial dislocation density

pd dislocation density

p forest-dislocation density a saturation stress in the flow curve ad yield strength component due to dislocation

o~

; /th component of stress tensor oy vector of boundary traction as structure-related yield strength otot total yield strength au ultimate tensile strength av yield strength

t incubation time

x* vector of boundary traction

A^ austenite-to-ferrite transformation temperature

b Burgers vector Cp

specific heat

C cooling rate over the transformation temperature range
D initial grain size

Da

ferrite grain size

D austenite grain size Dc pearlite colony size

Z)dvn dynamically recrystallized grain size

Dmd metadynamically recrystallized grain size

Drex statically recrystallized grain size D(t) effective grain size during static recrystallization

f volume fraction of ferrite after equilibrium transformation

fa volume fraction of ferrite after nonequilibrium transformation

fw

nonequiaxed ferrite volume fraction

G shear modulus

M mean distance for slip in pearlite ferrite Nd

pearlite nodule diameter

Q heat generated during deformation

Qd

activation energy for deformation

R gas constant S boundary surface

Sq mean true interlamellar spacing of cementite in pearlite

{ time

/05 time for 50 percent of recrystallization

t c carbide thickness

T absolute temperature

Tn equilibrium transformation temperature

T austenitization temperature

Td temperature of deformation

T pearlite transformation temperature

TR reheating temperature

|v| relative velocity at the tool-material interface

V control volume

W real velocity field X volume fraction

X(t) total volume fraction of recrystallized material by all mechanisms

X(tj dyn volume fraction of dynamically recrystallized material

X(t) md volume fraction of metadynamically recrystallized material

X{t)s volume fraction of statically recrystallized material

X(t) changes in pearlite volume fraction as a function of time

Z Zener-Hollomon parameter

VI
Foreword

The Materials Reliability Series of NIST Technical Notes are reports covering

significant research accomplishments of the Materials Reliability Division. The division

develops measurement technologies that enable the producers and users of materials to improve the quality and reliability of their products. Measurement technologies are developed for process control to improve the quality and consistency of materials, for nondestructive evaluation to ensure the quality of finished materials and products, and

for materials evaluation to ensure reliable performance. Within these broad areas of

measurement technology, the division has focused its resources on three research themes:

• Intelligent Processing of Materials: To develop on-line sensors for measuring the

materials characteristics and/or processing conditions needed for real-time process

control.

• Ultrasonic Characterization of Materials: To develop ultrasonic measurements for characterizing internal geometries of materials, such as defects, microstructures, and

lattice distortions.

• Micrometer-Scale Measurements for Materials Evaluation: To develop measurement

techniques for evaluating the mechanical, thermal, and magnetic behavior of thin films

and coatings at the appropriate scale.

Research on microstructural evolution in steel is one of the projects in our research on Intelligent Processing of Materials. This report is a result of cooperative research

between the Institute for Ferrous Metallurgy (IFM), Gliwice, Poland and NIST. The re- search was supported by the United States-Poland Maria Sklodowska-Curie Joint Fund II. and the research was conducted mainly at IFM. The research plan was formulated while

the principal author. Dr. Roman Kuziak, was a guest researcher in the Materials Reliability Division during 1990 and 1991.

Harry I. McHenry

Chief

Materials Reliability Division

\n

Modeling of the

Micrestructure and Mechanical Properties of Steels

during Thermomechanical Processing

Roman Kuziak

Materials Science Department

Institute of Ferrous Metallurgy

Gliwice, Poland

Yi-Wen Cheng

Materials Reliability Division

National Institute of Standards and Technology

Boulder, Colorado, USA

Miroslaw Glowacki and Maciej Pietrzyk

Materials Engineering Department

Academy of Mining and Metallurgy

Cracow, Poland

Models have been developed for the microstructural changes in C-Mn, vanadiumtreated, and eutectoid steels during thermomechanical processing. They relate processing parameters, such as strain, strain rate, and temperature, to microstructural features,

such as volume fraction of the recrystallized material and austenite grain size, with

emphasis on the effect of microstructural changes on the mechanical properties of the

final product. Model-predicted mechanical properties were compared with values measured in laboratory and industrial experiments. The models gave an accurate, quantitative characterization of the plates, rods, and rails subjected to rolling processes. The

results of this study provide a basis for future optimization of the chemical composition and processing of steels.

Key words: C-Mn steel; computer modeling; eutectoid steel; finite-element method:

mechanical properties; microstructure; thermomechanical processing;

vanadium-treated steel.
1. Introduction

Recent research in computer modeling of the microstructural evolution of steels during

thermomechanical processing has increased our understanding of the austenite microstructural

restoration processes occurring during and after plastic deformation. Computer modeling can

accurately characterize the sequences and interactions of the mechanisms that change the austenite microstructure. Thus, we can predict the effects of chemical composition and processing

parameters on the final microstructure and mechanical properties of a steel. Since modeling is an efficient tool for the development of new steel grades and for optimizing production technologies, it has great potential for improving the manufacturing processes and reducing the cost of steel products.

The ultimate goal of modeling industrial processes is to predict the mechanical properties of

commercial products. Quantitative relationships between the microstructural parameters and the

mechanical properties are frequently based upon a Hall-Petch type of relationship. To date,

many relationships have been developed for the yield strength, ultimate tensile strength, and

impact transition temperature in a variety of steels. One of the most successful approaches to the

prediction of mechanical properties was developed by Gladman et al. [1]. However, our critical assessment of the equations deveoped by Gladman and coworkers has shown that their accuracy

of prediction may be insufficient for a particular application. Therefore, we developed some new

relationships for the steels investigated in this study.

The objectives of this research project were

1. to develop and validate models of microstructural evolution and mechanical properties for plain-carbon (C-Mn), vanadium-treated (VT), and eutectoid steels and

2. to couple these models with finite-element-method (FEM) calculations to predict the microstructures and mechanical properties of these steels following industrial rolling of plates, rods,

and rails.

The microstructural evolution models developed in this study are composed of equations

that relate parameters characterizing the state of austenite microstructure during and after plastic

deformation at elevated temperatures to the deformation parameters, which include strain, strain

rate, and temperature. To demonstrate the practical application of the models, the effects of

microstructural changes on the mechanical properties of the final industrial products were also

examined. Although models can predict the development of austenite microstructure during all stages of thermomechanical processing, their accuracy depends on precise knowledge of the

deformation parameters of the workpiece. For simplicity, flat-rolling parameters are often as- sumed to be constant through the thickness direction. However, for bar- and rail-rolling processes and for more complete analysis of the flat-rolling process, these parameters must be

obtained with numerical analyses, such as FEM.

Generally, two types of behavior occur during hot working of steels, and they are reflected

in the shape of the flow curve (fig. 1). Dynamic recrystallization initiates easily in materials

with low stacking-fault energy that are deformed at low and moderate strain rates at elevated

temperatures (fig. la). Following initiation of dynamic recrystallization, the flow stress decreases

continually until the entire material is recrystallized. Upon completion of dynamic recrystallization, steady flow is established in the deformed material. After deformation, postdynamic processes predominate in the deformed material: metadynamic recrystallization, static recrystallization, and static recovery. Low-temperature deformation employing high strain rates does not lead
150

(a)

03 Q_

c/) CD

CD

13

100

t r 0.2 0.3

True strain

0.5

(b)

ca Q.

CO

CO

CD

CO

250

200

150 -

100 -

50 -

0.2 0.3

True strain

0.5

Figure 1. Flow curves of the VT steel deformed by compression in the dilatometer

(s = 3 s~ ; Dq = 65 p.m). (a) Dynamic recrystallization initiates once the critical strain

is reached (7^ = 1 180°C). (b) Recovery offsets work hardening before the critical strain for dynamic recrystallization is reached (7^= 950°C).
to dynamic recrystallization; instead, the work hardening is counterbalanced by recovery that leads to the steady flow shown in the flow curve in figure lb.

The conventional approach to microstructural evolution modeling is based upon the effects of strain, strain rate, temperature, and the austenite grain size before deformation. Some fundamental effects of these parameters on the plastic flow and resulting microstructural evolution are discussed by Sellars [2]. The major difficulty in the application of the conventional approach to computer modeling of industrial processes is that the models do not incorporate the inhomogeneity of plastic flow and temperature fields in the workpiece during processes such as shape

rolling. To remedy the deficiency in the conventional approach, thermomechanical FEM computer codes developed at the Academy of Mining and Metallurgy in Cracow, Poland were used

in the present investigation to calculate the deformation and temperature fields in the workpiece

during the various industrial processes.

Computer simulations of the microstructural evolution of austenite during thermomechanical

processing make it possible to calculate phase transformations (and thus the microstructure that develops in final products) after processing and cooling. This step is prerequisite for predicting

the mechanical properties of steel products. The transformation models can be based upon

sophisticated classical theories [3], but this approach is not very productive because the trans- formation models would require substantial adjustments to specific conditions prevailing in industrial practice. Therefore, in the present study, mostly empirical models were developed to quantitatively relate the microstructure of the final product to the parameters characterizing the

state of the austenite microstructure before transformations, the processing parameters, and the

cooling conditions after plastic deformation.

2. Structure of the Research Project

The primary objective of this research project was to develop models to characterize the

microstructural evolution occurring during thermomechanical processing of C-Mn, VT mediumcarbon, and 900A eutectoid steels. To complete this task, submodels for the following phenomena were developed:

work hardening and dynamic recovery

static recrystallization

dynamic recrystallization

metadynamic recrystallization

grain growth following recrystallization

phase transformations on cooling after thermomechanical processing

Finally, we developed relationships linking strength properties to the microstructural parameters

and the chemical compositions of the experimental steels. After completing the development of

the microstructural evolution models, we incorporated constitutive equations into the thermomechanical FEM codes for some industrial plate- and shape-rolling simulations.
3. Experiments

The chemical compositions of the steels used in our model-development experiments are

listed in table 1. The steels were produced in continuously cast industrial heats. We developed

the predictive equations from averaged measurements of 30 to 40 specimens. Although the

microstructural evolution models in the research program were developed essentially for the

thermomechanical processing of these basic steels, some submodels were substantially extended

to cover a wider range of steels.

The submodels were developed from experiments conducted with a dilatometer that is equipped with a hot-deformation attachment that conducts very precise simulations of thermomechanical processing. Specimen deformation in the dilatometer was imposed by compression.

The two simulation schedules used in the development and validation of the microstructuralevolution models are shown in figures 2 and 3, respectively. All reheating, deformation, and

cooling parameters were precisely controlled during the experiment. The models were validated

further in laboratory press-forging and plate-rolling experiments; the details of these experiments

are given below. The verified models were used to simulate industrial processes.

Typically, we used an optical microscope to study microstructural evolution in deformed

specimens as a function of strain s, strain rate 8, temperature T, and time t after deformation.

Saturated picric acid was used to delineate austenite grain boundaries, and the mean-linearintercept method was adopted to measure the austenite grain size. To examine the microstructures in greater detail, we used a transmission electron microscope and a scanning electron

microscope.

The major difficulty in relating the state of the austenite microstructure to hot-deformation

conditions is the nonuniformity of the plastic flow during compression. To alleviate this problem, a commercial FEM program was used to calculate the deformation parameters in the

deformed specimens [4]. An example of the calculation for specific deformation conditions

is shown in figure 4. The results demonstrate that the deformation parameters are relatively

homogeneous in the central region of the specimen. In figure 4c, the lower temperature at the

top is due to heat loss to the anvil, and the higher temperature at the bottom (center of specimen) is due to heat generated by plastic deformation.

Table 1. Chemical composition (mass percent) of the experimental steels.

Steel C Mn Si P S V A1

tot N

C-Mn 0.18 1.40 0.23 0.024 0.021 — 0.002 0.007

VT 0.20 1.36 0.26 0.022 0.020 0.09 0.002 0.009

eutectoid 0.72 1.20 0.28 0.023 0.018 — 0.001 0.006
Time

Figure 2. One-step deformation experiment conducted in the dilatometer to develop

constitutive equations for the microstructural evolution models: (1) reheating at a constant rate; (2) soaking at a predefined temperature and duration; (3) cooling to the deformation temperature and deformation at predefined parameters: (4) holding

for a specified time after deformation; (5) quenching.

CDE

Time

Figure 3. Two-step deformation experiment conducted in the dilatometer to validate

microstructural evolution models: (1) reheating; (2) soaking; (3) first deformation;

(4) cooling to second deformation temperature; (5) second deformation; (6) quenchinj
0.0 0.5 1.5 2.0 2.5 3.0 3.5

X, m m

Figure 4. Results of an FEM calculation for the deformation (Tj= 950°C) of a cylindrical spe- cimen 10 mm high and 8 mm in diameter: (a) strain field; (b) strain-rate field; (c) temperature

field. The specimen was reduced from 10 to 4.9 mm. Since the specimen was symmetrical with

respect to its center, only one quarter of the specimen is shown in this figure.

4. Microstructural Evolution Models

Depending on the deformation conditions and the state of the austenite microstructure

before deformation, different processes are involved in the restoration of the work-hardened

microstructure. The most important are dynamic recovery and recrystallization. metadynamic

recrystallization, static recovery and recrystallization, and grain growth after recrystallization.

The conventional approach to the microstructural evolution modeling, adopted for this study, is based upon relating the state of the austenite microstructure during and after deformation to the

state of the austenite microstructure before the deformation and to the deformation parameters.

The set of consecutive equations of the microstructural evolution model can be used to develop

a computational procedure for computer modeling of microstructural evolution during thermomechanical processing.

For deformation experiments conducted in the dilatometer, the general strategy was to select deformation conditions to simulate either one process or a sequence of consecutive
processes. The austenite-microstructure restoration processes were identified by flow-curve

analysis (fig. 1); they were characterized by measuring microstructural changes as a function

of time.

4.1 Microstructural Evolution during Hot Working

4.1.1 Static Recrystallization Model

Typically, static recrystallization nuclei are formed throughout the deformed material when

the deformation conditions during processing are not favorable for initiation of dynamic recrystallization and when the critical strain for static recrystallization initiation is exceeded. Most

research on static recrystallization kinetics uses the fractional-softening method [5], but for our

study, this method was not suitable because the plastic flow in the specimens deformed by compression in the dilatometer was not homogeneous.

Therefore, a new method based upon analysis of the average austenite grain-size changes

during recrystallization was proposed. It employs an equation cited by Beynon and Sellars [6] relating effective grain size during static recrystallization D{t) to the recrystallized grain size

Drex

, initial grain size Dq, and volume fraction of recrystallized material X(t)

s

:

D(t) = X(tYs Drex + [i -x{t)s]D;

(i)

Equation (1) gives a good characterization of the average variation in austenite grain size during

static recrystallization. By combining this relationship with the Avrami-type equation

m= i-exP

0.693

'0.5

(2)

commonly used for characterizing the kinetics of static recrystallization [6], we obtained DYQX , n, and /Q 5 (time for 50 percent of recrystallization). As an example, figure 5 presents a best-fit curve obtained from eqs (1) and (2) with respect to the measured average changes in austenite

grain size during static recrystallization of the VT steel. By changing the deformation conditions

and the austenite grain size before the deformation, we obtained general equations relating Z)

rex and (q 5 to s, e, and Dq. Selected data related to static recrystallization in the experimental VT

steel are listed in table 2. The set of equations for the static recrystallization model for the VT

steel developed from these data is given in table 3. A comparison of the model-predicted and

measured dependences of the statically recrystallized grain size on strain in the VT steel is shown in figure 6. Based upon the results shown in figures 5 and 6, we postulate that the equations of the static recrystallization model give a good characterization of this process in the

experimental steel. The form of the equation for (q 5 used for the VT steel is adopted from the

model developed by Beynon and Sellars [6]. According to this model, the effect of Dq on /Q 5

is expressed by the term Dq, which can be rationalized on the basis of the effect of the grain size on nucleation-site density.

The static recrystallization process in the experimental C-Mn steel can be adequately described by the equations of Roberts et al. [7] (see table 4). An example of their capability for predicting the austenite grain-size changes during static recrystallization in the experimental

8
E

COCD

CD

CD

CO

100

90 H

80

70 -

60 -

50 -

40

30

20 -

10 -

measured

calculated

10 20 30 40

Time, s

50 60

Figure 5. Average austenite grain size as a function of time during static recrystallization in the VT steel (DQ = 65 urn; Td = 950°C; s = 0.22; e = 3 s"

1 ). Calculations using eq (1) agree well with the experimental data.

C-Mn steel is shown in figure 7. These equations do not account for the effect of strain rate on

the static recrystallization kinetics, which is relatively small in the case of plate rolling. In the

rod-rolling process, however, the strain rate is very high (as high as 1000 s~ ), and its effect should not be neglected in the calculation. Therefore, an equation (T-8) developed by Medina

and Lopez [8] for tQ 5 was used for the rod-rolling process instead of eq (T-7) of Roberts and

coworkers.

Results of another investigation by Kuziak [9] on microstructural evolution in eutectoid

steels have shown that the equations developed by Beynon and Sellars [6] poorly substantiate

the experimental results of static recrystallization in these steels. The best fit of the experimental

results in this case is obtained by employing equations of Choquet et al. [10]. The set of constants of this model, adjusted to the behavior of the experimental 900A steel, is given in table 5. The effect of the austenite grain size on recrystallization kinetics in the model of Choquet and

coworkers is much more complicated than that in the model of Sellars; it cannot be explained

simply by rational assumptions. The capability of the model of Choquet and coworkers to predict effective austenite grain-size evolution during static recrystallization in the 900A eutectoid

steel is demonstrated in figure 8.

The models described in this section adequately predict the influence of the processing

parameters and austenite grain size on the kinetics of static recrystallization and the overall

changes of the grain size during the recrystallization. By employing eq (1), some results obtained earlier by Kuziak and Cheng [11] were correlated quantitatively with the model. For
example, they observed that the deformation of a fine-grain austenite in Ti-V-N steels at elevated temperatures led to extensive grain growth during static recrystallization. These characteristics of the recrystallization process were predicted by the model (see fig. 9); they can be

associated with the vast mobility of small recrystallization nuclei at elevated temperatures. The

result of this simulation shows that static recrystallization does not necessarily lead to austenite

grain refinement at the high temperatures of hot working.

Table 2. Experimental data related to static recrystallization in the VT steel. DQ, f.im T, °C s e,sj r0.5' s Drex

, urn

163 930 0.15 2.2 480 80

163 930 0.18 2.2 240 68

163 930 0.22 2.2 100 60

94 980 0.15 2.0 63 50

94 980 0.18 2.0 40 57

94 980 0.22 2.0 13 48

122 950 0.22 4.0 43 54

122 1000 0.22 3.0 14 56

122 1050 0.22 2.5 9 60

72 980 0.27 4.0 3.2 30

72 1050 0.25 3.2 1.3 34

72 1180 0.23 2.0 — 43

72 950 0.16 1.8 48.0 48

72 950 0.27 3.6 5.0 33

72 950 0.38 3.8 1.2 29

72 950 0.46 4.4 — 21

53 930 0.31 3.0 3.2 28

53 980 0.31 3.0 — 22

53 1130 0.31 3.0 — 31

10
Table 3. Equations in the static recrystallization model for the VT steel.

Equation Description

Drex

. c . „0.67 -0 53 • -0.1 4.54Dn

8 e exp

-15 000

RT

(T-l) recrystallized grain size

m = l-exp -0.693

'0.5

0.95 (T-2) recrystallization kinetics

/05 = (9.3xl0~ 13 )£> V4 exp

230 000

RT

(T-3)

time for 50 percent of

recrystallization

D(t) =X(t) ;Z)rex+ \-X{t)

s rex Dr (T-4)

effective grain size

during recrystallization

1 uu

90 -

80 - E= 70-

CD

rsi co 60 -

2 50 - 03 >v

A measured

calculated

2 40-

cr

CD ^ 30 -

Z2 20 -

10 -

- 1 i ' i 0.1 0.2 0.3

Strain

0.4 0.5

Figure 6. Statically recrystallized austenite grain size as a function of strain (D() =72 urn; Td = 950°C). Calculations using eq (T-l) agree well with experimental data.

II
Table 4. Equations in the static-recrystallization model for the C-Mn steel adopted

from Roberts et al. [7] [eqs (T-5-T-7)] and Medina and Lopez [8] [eq (T-8)].

Equation Description

Z)

rex =6.2 + 55.7Z)

01 V^

X(t)s = 1-exp 0.693

'0.5

exp

1.7

350 000

RT

-0.11

t05 = (S.lxlO^^^s^exp 330 000

RT

t05 = (1.03xl0- 10 )8-2 - 6 8-°-44

Z)

58 000

RT

(T-5)

(T-6)

(T-7)

(T-8)

recrystallized grain size

recrystallization kinetics

time for 50 percent of

recrystallization

time for 50 percent of recrystal- lization (rod-rolling process)

100

CDM

'.co 60 -

2 40

cz

CD

CO

20 - calculated

measured —i

1

1

1

1

1

1 1

1

1

1

12 3 4 5 6 Time, s

Figure 7. Average austenite grain-size changes during static recrystallization in the

experimental C-Mn steel (DQ = 76 u.m; Td = 950°C; 8 = 0.2) compared with the

model predictions of Roberts et al. [7] (table 4).

12
Table 5. Equations in the static-recrystallization model for the eutectoid steel [10].

Equation Description

n x =9.91Dr

4 B- 65 s01

exp

-17 540

RT

(T-9) recrystallized grain size

X{t), = 1 -exp -0.693

'0.5

0.95 (T-10) recrystallization kinetics

t05 = (2.403 x 10 "*) exp

160 420

RT

p, -0.29 n

-02

e^e

(T-ll)

p = -\.006Dq0.22

time for 50 percent of

recrystallization

300

CDN

COD5

CD

czCD

CO

ZJ <

250 -

200 -

150 -

100 -

50 "—

r

20

calculated

measured

40 60

Time, s

"" 1 r 80 100 120

Figure 8. Average austenite grain-size evolution during static recrystallization in the

experimental eutectoid steel (D = 270 u.m; Td = 900°C; e = 0.2) compared with the

model predictions of Choquet et al. [10] (table 5).

13
0.00 0.02 0.04 0.06 0.08 0.10 0.12

Time, s

Figure 9. Calculated average austenite grain-size evolution in the VT steel with the

assumption of small initial grain size and high deformation temperature (Dq = 20 p.m;

T,= 1180°C; s = 0.13; e = 1 s"

1 ).

4.1.2 Dynamic Recrystallization Model

The conventional concept of dynamic recrystallization is based upon the assumption that the critical strain must be reached before the process initiates (fig. la). The critical strain depends on the Zener-Hollomon parameter and the initial austenite grain size [6]. The relationships were determined by analysis of the flow curves employing a generalized Voce equation

proposed by Beynon and Sellers [6] and by taking into consideration that the decrease in the

flow stress, which takes place after recrystallization has initiated, indicates the creation of

dislocation-free nuclei. Thus, the effect of dynamic recrystallization on the flow curves relates directly to the volume fraction of recrystallized material.

For the VT steel, selected results of the Zener-Hollomon parameter Zand the initial austenite grain-size effects on the critical strain are listed in table 6, along with measurements

of dynamically recrystallized grain size. The relationships for the critical strain and dynamically recrystallized grain size were obtained from all the experimental data for dynamic re- crystallization. A complete model for dynamic recrystallization in the VT steel is given in table 7. Similar relationships for the C-Mn and eutectoid steels are given in tables 8 and 9,

respectively. Dynamically recrystallized grain size depends solely on the Zener-Hollomon

parameter (fig. 10).

14
Table 6. Selected data showing the influence of the deformation parameters and

the initial austenite grain size on the critical strain for dynamic recrystallization

and dynamically recrystallized grain size in the VT steel. D , urn T, °C M-1 £

c Ddyn, urn

25 950 0.3 0.194 13.2

28 1050 0.3 0.145 20.2

30 1150 0.3 0.132 26.2

50 950 2.0 0.321 8.10

50 1050 2.0 0.231 15.1

50 1150 2.0 0.198 20.1

110 1150 3.0 0.291 19.3

Table 7. Equations in the dynamic-recrystallization model for the VT steel.

Equation Description

Z=texp(Qd /RT)

Qd =3\2 kJ/mol

(T-13) critical strain

Ddyn = (1.4xl03 )Z-°- 16 (T-14) dynamically recrystallized grain size (p.m)

^(Odyn = ] - exp

ep

= 1.12sc

1.5

(T-15) recrystallization kinetics

15
Table 8. Equations in the dynamic-recrystallization model for the C-Mn steel. Equation (T-17) is from Hodgson [12].

Equation Description

s

c = (4xlO- 4

)

JD

°- 5 Z

- 15

Z = 8 exp (Qd/RT)

Qd =3\2 kJ/mol

Ddyn = (1.6xl04)Z-°-23

(T-16) critical strain

(T-17) dynamically recrystallized grain size (u,m)

X(t)dyn = 1-exp

zp

= 1.23sc

-0.8

1 1-4

(T-18) recrystallization kinetics

Table 9. Equations in the dynamic-recrystallization model for the eutectoid steel.

Equation Description

s

c = (4.3x10 - 4

)Z>

0,3 Z

011

Z = e exp (QdIRT)

^ = 315 kJ/mol

Ddyn = (1.6xl04 )Z-°-2

(T-19) critical strain

(T-20) dynamically recrystallized grain size (u.m)

^(Odyn = 1_exP

B -1.058c

(T-21) recrystallization kinetics

16
E

CDM

</} _C

caCD

a>

CD

60-

40-

A

-____D md

20- DdH________^

o- '1 ' i ' i ' i > i -\ 0E+0 1E+12 2E+12 3E+12 4E+12 5E+12 6E+12 7E+12

Z,s1

Figure 10. Dependence of dynamically and metadynamically recrystallized grain size

in the VT steel (table 7) on the Zener-Hollomon parameter.

4.1.3 Metadynamic Recrystallization Model

Once dynamic recrystallization has been initiated during deformation, postdynamic

microstructure-restoration processes operate after deformation. The major process leading to the softening of the material during postdynamic processes is static recrystallization, according

to Sakai [13], and metadynamic recrystallization, according to Hodgson [12]. Our analysis of

the dependence of the postdynamic microstructure-restoration process kinetics on deformation

parameters supports Hodgson's view: The kinetics of microstructure-restoration processes in Hodgson's study were strongly dependent on strain rate, weakly dependent on temperature,

and apparently not dependent on strain. In contrast, during static recrystallization, the kinetics

depend strongly on strain and temperature and weakly on strain rate.

Hodgson's viewpoint on the postdynamic process mechanisms was adopted in this study.

Further refinement of the metadynamic recrystallization process was done by Pietrzyk and

Kuziak [14], who showed that the grain size during metadynamic recrystallization in Hodgson's

experiments [12] varied linearly with the volume fraction recrystallized [eq (T-26) in table 10]. This finding was confirmed by Kuziak [9] for 900A eutectoid steel.

For illustration, predicted and measured changes in the austenite grain size during metadynamic recrystallization of 900A eutectoid steel are shown in figure 1 1 [9]. The set of equations for the metadynamic recrystallization model is given in table 10. The kinetics equation for metadynamic recrystallization has the same form for all the experimental steels; it is adopted

from the research conducted by Hodgson [12], and the model incorporates the same type of

17
dependence of dynamically and metadynamically recrystallized grain size on the ZenerHollomon parameter. However, metadynamically recrystallized grain size is greater than

dynamically recrystallized grain size, as shown in figure 10 for the VT steel.

CD

C/5 CZocCO

enc

CD

</> Z3 <

Figure 11. Austenite grain-size evolution during metadynamic recrystallization of the 900A

eutectoid steel (Dq = 60 u.m; Td = 950°C; e = 0.2 s ). For the calculation (curve), a linear dependence of the average grain size on the volume fraction of metadynamically recrystallized

material was assumed [see eq (T-26) in table 10].

Table 10. Equations in the metadynamic-recrystallization model for the experimental steels.

Metadynamically recrystallized grain size, fim

Recrystallization kinetics

for all steels (Hodgson [12])

C-Mn /) , = (2.6x1 4 )Z 4w-0.23

VT

Eutectoid £>md = (2.5 x 10

4 )Z "° 23

(T-22)

Z)md =(2.3xl04 )Z- • ,6 (T-23) X{t)

(T-24)

All steels D(t) = Ddyn (T-25)

+ (And-^dyn^Omd

md exp 0.693

I

'0.5 .12Z" 08

exp

'0.5

230 000

RT

1.3

. (T-26)

18
4.1.4 Grain Growth of the Austenite after Recrystallization

A characteristic feature of the grain growth after recrystallization is an abrupt decrease in the growth rate sometime after the completion of recrystallization. In this study, the approach

developed by Roberts et al. [7] was adopted to characterize this behavior quantitatively. In the

model of Roberts and coworkers, a parabolic type of equation describes the grain-growth kinetics with two parameter sets, depending on the stage of grain growth.

The best fit of the data on the kinetics of grain growth for the VT steel obtained during the course of this investigation gave the set of constants in the parabolic equation. These constants

are listed in table 11 together with the constants for the C-Mn and 900A eutectoid steel. Following the approach of Roberts and coworkers, we used a 20-s breakpoint to separate the rapidand slow-growth kinetics ranges. An example of our prediction of the austenite grain growth

in the VT steel is given in figure 12. For simplicity, we did not distinguish between the grain

growth after static and metadynamic recrystallization. Kuziak had found this approach to be

satisfactory for a 900A eutectoid steel [9].

Another approach to grain-growth modeling after static recrystallization, described by

Sellars [2], is based on the use of a larger exponent in the equation for the early stage of grain

growth; for plain-carbon and microalloyed steels, the exponents are typically in the range 7 to

10. However, the experience gained in this research on recrystallized grain-growth kinetics

shows that Sellars's approach leads to overestimation of the final grain size, especially when

large interpass times are involved.

Table 11. Constants in the austenite-recrystallized grain-growth model for the experimental steels.

Equations

(r=0) (T_ 27)(f=2Qs) (T_ 2g)

for t < 20 s for t > 20 s

Constants

C-Mn steel VT steel 900A Eutectoid steel

A, =6.6 A, =7.1 A, = 7.0

B,=6200 Bj = 7180 B, = 5900

A2 = 8.1 A2 = 9.5 A2 = 8.4 B2 = 9000 B2 = 10 920 B2 = 8520
E

TOCO

CD

CD

CD

3U

40 - measured

predicted

+_____ 30 - """"

s^ +

20 -

>

10 - 1

1 i i i i i

1 i i 10 20 30 40 50 60 70 80 90

Time, s

Figure 12. Characterization of the recrystallized austenite grain-growth kinetics in the

VT steel based on a modified Roberts equation [7] (Drex = 22 (im; Td = 950°C).

4.2 Phase Transformations on Cooling after Hot Working

4.2.1 Ferrite-Pearlite Steels

The kinetics of decomposition of the austenite can be described quantitatively by classical nucleation and growth theory [3]. This approach, however, is time-consuming, and it may not give accurate predictions in many situations. Therefore, we developed an empirical model for the experimental steels that is capable of predicting the basic microstructural parameters of the

ferrite-pearlite microstructure: ferrite grain size and volume fraction, pearlite interlamellar spacing, and pearlite colony size. These parameters correlate with austenite grain size before the

ferrite transformation and with the cooling rate over the transformation temperature range. The

model was developed during the course of the experiments conducted with the dilatometer.

In the experiments, one reheating schedule (l 180°C for 10 min) was adopted to dissolve

vanadium carbonitride precipitates. Variation in austenite grain size was achieved by changing

the compression of the specimens at 950°C.

Selected measurements of the ferrite-pearlite microstructural parameters in VT steels are given in table 12. These data, together with the results of other studies [15-17], were used to develop predictive equations for the microstructural parameters of the VT steels. All the equations developed in the study are summarized in table 13. Although regression analysis gave

constants for the VT steels that were slightly different from the C-Mn-steel constants, we decided to use one set of equations for these steels because the results generated by the different

20
Table 12. Selected experimental results describing the dependence of the ferrite- pearlite microstructural parameters in the VT steel on the austenite grain size and

cooling rate over the transformation temperature range. Dy

, (xm Cr

, °C/s Da

, urn SQ

, urn fa /u

55.2 0.1 19.1 0.220 0.72 0.00

55.2 0.3 17.8 0.168 0.69 0.00

55.2 0.5 13.2 0.155 0.63 0.00

55.2 1.0 10.8 0.139 0.65 0.05

55.2 2.5 10.9 0.130 0.57 0.18

45.4 0.5 15.0 0.157 0.70 0.00

41.9 2.5 10.7 0.122 0.68 0.12

40.0 0.1 12.6 0.230 0.75 0.00

38.8 1.0 9.2 0.132 0.70 0.03

37.7 1.0 11.3 0.140 0.72 0.00

30.1 0.1 12.1 0.200 0.75 0.00

34.4 0.5 13.2 0.152 0.74 0.00

26.8 2.5 8.7 0.119 0.62 0.15

Table 13. Predictive equations for the calculation of the ferrite-pearlite microstructural parameters.

For the VT steelAx = A

1 + (0.036 + 0.0233C

r

°' 5 )Z)

Y For the other steels—

Da

= [3.85 - 5.9(%C)- 1 .56(%Mn) + 8.5(%V) - 20(%N)]Z)

Y

°' 58 Cr

" ' 26

For all steels—

S = 0.1307 + 1. 027 (%C)-1.933 (%C)2 - 0.11 08 (%Mn) + 0.0305 C' ^2 C = cooling rate in °C/s

/eq = 1 " %C

0.789-0.1671 (%Mn) + 0.1 607 (%Mn)2 -0.0448 (%Mn)3

fw = /eq - 0.829exp( - 0.210C,.) - 1 .0097exp( - 0.08D

y

)

fa =/eq- 5 - 48 [

1 " exP( ~ 0.01 06C,.)] - 0.723 [1 - exp( - 0.0009 Dy

)]

(T-29)

(T-30)

(T-31)

(T-32)

(T-33)

(T-34)
sets of equations agreed within experimental error. We assumed that the equations listed in table 13 are valid for the austenite grain size before the transformation of less than 100 p.m. The reference state for the calculation of the ferrite volume fraction is the equilibrium content of this phase in a steel. We used a commercial computer program (Thermocalc) to calculate this parameter; it can also be obtained with eq (T-32). We also estimated the Widmanstatten or non- equiaxed ferrite volume fraction in the experiments. Increasing the austenite grain size and cooling rate is known to increase the propensity for the formation of nonequiaxed ferrite. On the

basis of the measurements, we suggest that the nonequiaxed ferrite volume fraction depends

exponentially on the austenite grain size and cooling rate (table 13). By setting the nonequiaxed

ferrite volume fraction to zero, we could place a border between the nonequiaxed and equiaxed

ferrite regions on the austenite-grain-size and cooling-rate coordinates. An illustration of the

criterion developed for nonequiaxed ferrite formation is given in figure 13.

22
(a)

CDM

CO

COen

CD

cr

CDCO

T

'

1

' 1

'

1 1 1

'

1 1

' r 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0

o, Cooling rate C / s

(b)

V

. **

Figure 13. (a) Conditions for the occurrence of nonequiaxed ferrite in the VT steel: (b) microstructure (400x) developed after cooling at a rate of l°C/s (D = 70 \xm).

Widmanstatten structure was observed in this specimen.
4.2.2 900A Eutectoid Steel

A mathematical model for pearlite transformation in eutectoid steels was developed during

the research conducted by Kuziak [9], which is based upon the fundamental studies of Campbell

et al. [18] and Umemoto et al. [19]. To describe the pearlite transformation quantitatively, we

must be able to calculate the incubation time x and changes in the pearlite volume fraction X(t) as a function of time. The following equations quantitatively describe these parameters under

isothermal conditions [18, 19]:

KT exp

t = RT

(T -T)w

(3)

and

X(t)

p

= 1-exp -KT)

D

m

y

(4)

where / is the transformation time, D is austenite grain size before the transformation, and Tq

is the equilibrium transformation temperature, which was computer calculated. The values of the constants and parameters in eqs (3) and (4) are given in table 14, and the measured and calculated incubation periods and transformation kinetics are compared in figures 14 and 15.

Equations (3) and (4) were developed during the course of the isothermal tests conducted

with the dilatometer. By means of quantitative analysis of the specimens after the experiments,

we were able to relate the pearlite interlamellar spacing and the pearlite nodule and colony sizes to the chemical composition, pearlite transformation temperature, and austenite grain size of a

particular steel (see table 15). Using eqs (3) and (4) and the additivity rule [20], we calculated

the progress of the pearlite transformation during continuous cooling. We used the following

formulation of the additivity rule, combining it with eq (3), to calculate the the transformation

starting temperature during continuous cooling:

dt . (5)

Table 14. Constants in the equations for the incubation period and the pearlite transformation

kinetics in the eutectoid steel (Kuziak [9]).

K = 2.6- 1.44(%C)- 2.95 (%C)2 + 0.69(%Mn) + 1.5(%Mn)2 + 13.9(%Cr) + 65.5(%Cr)2

» = 1 .96, m=\.94, w = 4.65, Q = 1 14 500 J/mol

(T-35)

\n\h(T)] = - (2.546 x \0~ 4 )T 2 -0.219 T- 72.23

T in degrees Celsius

(T-36)

24
700

3o 650

a)

Z3

COCDQ.

E

<D

1

600

550

calculated

measured

a 1080 steel

900A steel

• 900A Cr steel

10 100

Time, s 1000

Figure 14. Model-predicted time-temperature-transformation curves (solid lines) versus experimental data (symbols) for different eutectoid steels [9].

-I

1

1

1

1 f—i

1

i

i

\

i i

i r 10 20 30 40 50 60 70 80

Time, s

Figure 15. Model-predicted effects of the transformation temperature on the kinetics of

pearlite transformation in 900A eutectoid steel (DQ = 60 pm) [9].
A procedure developed by Campbell et al. [18] was the basis for calculating the increase in the

pearlite volume fraction as a function of transformation time during continuous cooling. As an example, the calculated and measured transformation start and finish temperatures for specimens

of 900A eutectoid steel cooled in the dilatometer [9] are shown in figure 16. Equation (5) was

used to calculate T in table 15.

Table 15. Predictive equations for the quantitative description of the pearlite microstructure. _V

= A-BT

PD A = 129.28 - 54.373(%Mn) - 4.378(%Cr) - 17.5(%Si)

B = 0.1783 - 0.0723(%Mn) - 0.012 l(%Cr) - 0.0274(%Si)

(T-37)

D.

0.857 -0.001 189 7^ (T-38)

*d = 6500[l-exp(-0.016£>v)] 0.6

(T -T

p

) 1.2

(T-39)

700

650 - o

o

2 600 -

CD

CD h- 550 -

500

calculated

measured

0.5°C/s

0.3°C/s

0.7°C/s

2°C/s

5°C/s.

1

1 1 1—I—i I I

| 10 100

Time, s

t

1—i—i—i—i i i 100()

Figure 16. Model-calculated and measured values of the pearl ite-transformation

start and finish temperatures in the 900A eutectoid steel [9].

26
5. Microstructure-Mechanlcal-Property Relationships

5.1 Ferrite-Pearlite Steels

One of the most successful approaches to the prediction of mechanical properties in products made of plain carbon steels was developed by Gladman et al. [1]. It relates the yield

strength, ultimate tensile strength, and impact transition temperature to the microstructural

parameters of the ferrite-pearlite microstructure. In trying to rationalize the results obtained

in this study, we found that the equations of Gladman and coworkers were unsatisfactory for predicting the yield and ultimate tensile strengths for our experimental steels.

Following this observation, we developed new equations from measurements of mechanical

properties of diverse products rolled from steels with a carbon content from 0.05 to 0.6 mass

percent. We took an approach similar to that of Gladman and coworkers. In the correlation

analysis, data from 60 specimens were included. For illustration, a description of and selected

data from 13 specimens are listed in tables 16 and 17. The best-fit equations developed for the

average yield and ultimate tensile strengths of all the specimens are given in table 18. Major

differences between these equations and Gladman's consist in the linear law of mixtures for the

yield-strength calculation and the inclusion of the nonlinear dependence of the ultimate tensile

strength on the pearlite interlamellar spacing, which followed our observation that the pearlite

interlamellar spacing plays a significant role in shaping the ultimate tensile strength when the

ferrite loses its continuity in the microstructure. Figure 17 illustrates the predictive capability of

the equations developed in this study.

A model for the precipitation-induced increases in yield strength and ultimate tensile

strength was developed by using the approach of Hodgson and Gibbs [21]. These researchers

assumed that the contribution of the vanadium carbonitride precipitates to the overall strengthening effect depends linearly on the nitrogen and vanadium contents and logarithmically on the

cooling rate.

The dependence of the strengthening effect on cooling rate is known to reach a maximum

within a cooling-rate range of 5 to 10°C/s, depending on steel composition and processing route. However, since the cooling rate of air-cooled products is typically less than 5°C/s, a logarithmic

representation of the cooling-rate effect on the strength properties is justified for all the rolling

processes considered in this study.

Although it is not found in the equation developed by Hodgson and Gibbs, the contribution

of carbon to precipitation-strengthening is included in the analysis of the effect of vanadium

carbonitride on the strength properties; the effect of carbon content on the transformation temperature justifies its inclusion. Most vanadium precipitation occurs during ferrite transformation

(interphase precipitation) and in the ferrite after transformation. Increasing the carbon content should lead to a decrease in the mean particle size of vanadium carbonitride by depressing the

precipitation start temperature. Consequently, precipitation-strengthening components should be

increased as the carbon content increases. Our correlation analysis for the model development is based on the results of this investigation and the data of Sawada et al. [16] and Burnet [17]. The

increases in yield strength and ultimate tensile strength originating from the vanadium carbonitride precipitates were estimated by subtracting structure-related values of these parameters

(calculated from the equations listed in table 18) from the measured values of yield strength and

ultimate tensile strength. The predictive relationships for the calculation of precipitation-related

increases in yield and ultimate tensile strengths are given in table 19, and the predictions of

these equations for different products, in table 20.

27
Table 16. Selected chemical compositions and forms of the steel products used

for the development of the microstructure-mechanical-properties relationships.

No. C

Content

Mn Si P/S N

Steel product form

1 0.04 0.23 0.05 0.010

0.015

0.008 8-mm-diam. rod

2 0.05 0.31 0.05 0.010

0.016

0.007 10-mm-diam. rod

3 0.18 0.57 0.26 0.028

0.026

0.009 12-mm-diam. rod

4 0.65 0.52 0.21 0.014

0.012

0.006 10-mm-diam. rod

5 0.19 1.20 0.33 0.019

0.021

0.007 12-mm-diam. rod

6 0.22 1.23 0.34 0.059

0.038

0.009 14-mm-diam. rod

7 0.33 1.20 0.52 0.015

0.028

0.008 8-mm-diam. rod

8 0.20 1.15 0.35 0.044

0.029

0.005 8-mm-diam. rod

9 0.19 1.31 0.36 0.024

0.030

0.007 I-beam

10 0.18 1.32 0.35 0.023

0.028

0.008 I-beam

11 0.20 1.32 0.39 0.033

0.022

0.009 I-beam

12 0.48 0.86 0.22 0.026

0.024

0.009 I-beam

13 0.42 1.01 0.61 0.029

0.042

0.007 20-mm-thick plate

28
Table 17. Measured microstructural parameters and strength properties of the products specified

in table 16 (strength properties predicted from the relationships in table 18 are also included).

No.

Measured

Microstructural Parameters

Strength Properties

meas.

MPa

pred. meas.

MPa

/« Da

, urn S0> pm pred.

1 0.90 23.6 0.220 278 232 390 408

2

0.91 18.8 0.201 272 240 417 405

3 0.78 18.4 0.168 331 328 530 509

4 0.15 8.20 0.245 450 437 630 793

5 0.71 13.9 0.155 380 395 582 542

6 0.65 10.6 0.182 421 447 635 600

7 0.51 9.73 0.158 482 461 690 654

8 0.57 9.10 0.158 430 452 636 613

9 0.61 17.2 0.182 402 398 550 575

10 0.67 15.1 0.185 400 402 567 565

11 0.64 19.2 0.221 390 393 582 576

12 0.20 9.43 0.230 460 453 770 780

13 0.34 10.5 0.213 448 452 750 740

CD Q.

c

cp

-t-< CO

TJ

CD >-

CD

CD

3UU i

measured

i

predicted

400

300 -

inn ' I

1 '

"

200 300 400 500

Measured Yield Strength, MPa

CO Q.

D)C

CD

I—' CO

CD

3 500

T3£o

T3

CD

800

700

^ 600

400

300

A measured

predicted

300 400 500 600 700 800

Measured Ultimate Tensile Strength, MPa

Figure 17. Model-predicted versus measured values of yield and ultimate tensile strengths

for various products.

29
Table 18. New relationships for the contributions of structure and chemical composition to the

yield and ultimate strengths in plain-carbon steels. Equation (T-42) is from Gladman et al. [1]

0.5 0.5,

<* v = fo\lin + 59.5 (%Mn) +9.1 Da

] +[145.5 +3.5S

Q

] +478(%N)U - 5 + 1200(%P) (T-40)

0.5, 0.5, oM = /a

[20 + 2440(%Np + 18.5Z)a] + [750(1 -/a)] + [(1 -/„ )QSq )] + 92.5(%Si) (T-41)

ITT = /a

[-46 - W.5Da

] + (1 -/a

)[-335 + 5.6S

" ' 5 - \3.3D^5 + (3.48x 106 )/J

+ 49(%Si) + 762(%N) - 5 + 0.22(Ao

v

)p

tc = carbide thickness in mm

(T-42)

Table 19. Relationships for calculating precipitation-strengthening additions.

(Act ) = 19.9(%C) + 552.8(%C)2 +590(%V) + 8650(%N) + 19.91n(Cr)

(Act

m

) = 160 + 4.8(%C) + 176(%C)2 + 414(%V) + 5370.4(%N) + 231n(Cr)

(T-43)

(T-44)

Table 20. Precipitation-strengthening components of the yield- and ultimate-tensile-strength

calculations for different products employing equations (T-40) through (T-44).

Product

number

Chemical composition, mass percent

C Mn Si P S V Al N

1. I-beam 0.19 1.43 0.32 0.022 0.016 0.10 0.005 0.016

2. 20-mm flat 0.17 1.12 0.27 0.014 0.019 0.06 0.008 0.012

3. 20-mm flat 0.20 1.36 0.32 0.014 0.017 0.12 0.004 0.012

4. V-shape 0.25 0.72 0.17 0.016 0.016 0.05 0.005 0.009

Microstructural parameters Yield strength

Product

number °C/s

/a

Da- Sq, V MPa

p.m u.m measured predicted

1 2.5 0.68 9.80 0.170 600 585

2 1.2 0.72 18.5 0.231 450 458

3 1.2 0.69 12.7 0.210 525 536

4 0.5 0.62 13.2 0.181 435 420

30
A relatively good characterization of the effect of various parameters on the impact transition temperature can be obtained from the equation of Gladman et al. [1], which is given in table 18. The negative effect of the vanadium-carbonitride precipitates on the impact transition

temperature can be estimated by assuming a linear dependence of impact transition temperature on the precipitation-related increases in yield strength, with the constant equal to 0.22.

5.2 900A Eutectoid Steel

The mean true interlamellar spacing Sq is the most important parameter affecting the

strength properties of the pearlite microstructure. Traditionally, a Hall-Petch type of relationship

is used to characterize the effect of this parameter on the yield and ultimate tensile strengths.

However, in this study, we took an approach suggested by Dollar et al. [22], in which the yield

and ultimate tensile strengths correlate with Sq instead of Sq . In the predictive equations,

we used the mean free path for slip Min the pearlitic ferrite to characterize strength instead of

the mean true interlamellar spacing. To obtain the predictive equations for the yield and ultimate

tensile strengths in fully eutectoid steels, a correlation analysis was based on results published in reference 9, which were measurements of rails and bars (average of three specimens). In that study, different strengths were achieved by varying the chemical composition and cooling rate of the experimental materials during heat treatment. The best correlation was achieved with two

sets of constants for small and large values of the mean free path for slip in the ferrite. This

result can be associated with the different deformation mechanisms in fine and coarse pearlites

[22]. The equations relating yield and ultimate tensile strengths to the mean free path for slip in the ferrite are given in table 21.

Table 21. Equations for the yield and ultimate tensile strengths in eutectoid steels (Kuziak [9]).

For Sq > O.J 5 fim—

av = 308 +0.07M"1 (T-45)

ou = 706 + 0.072 M~] + 122(%Si) (T-46)

For Sq < 0.15 fxm—

ct v - 259 +0.087M" 1 (T-47) aM = 773 +0.058M" 1 + 122(%Si) (T-48)

where M= 2{SQ -/);/ = $.\5Sq{%C) in micrometers

31
6. Laboratory Experimental Validation of the Microstructural Evolution Models

6.1 Laboratory Experiments and the Linkage to the Finite-Element Codes

Mathematical models for static, dynamic, and metadynamic recrystallization and for grain

growth after recrystallization were used in computer-simulated thermomechanical processing

of the experimental steels. The computational procedure is described in figure 18. At the beginning of the calculation, strain is checked. If the strain has reached the critical value for dynamic

recrystallization, the volume fraction of recrystallized material is calculated. (This fraction is assumed to recrystallize metadynamically after deformation. The rest of the deformed material

is assumed to recrystallize statically.) If the critical strain is not reached, static recrystallization

prevails throughout the material after deformation. The pause between consecutive deformations

may not be long enough for complete recrystallization; in this case, the retained strain is calculated from the predicted volume fraction of recrystallized material by using equation [12],

e; = [i -X^e,,, (6)

where e^j is the total strain imposed on a specimen during the previous deformation and X(t) is total volume recrystallized by different mechanisms. To calculate microstructural evolution, the

retained strain is added to the current strain imposed on a specimen. At high temperatures and

after long intervals between deformations, the recrystallization processes will be complete; in this case, grain growth follows recrystallization. Therefore, recrystallization kinetics are essential

in the control of grain size during processing.

Dynamic

recrystallization

model

X(t)dyn n

YES

1-Xfr;dyn

Metadynamic

recrystallization

model

Input data: -austenite grain size -deformation parameters

Conditions for dynamic

recrystallization initiation

NO

Static recrystallization model

[1-X(M-Xfi)d

Wt

Recrystallized grain growth

yn

Next deformation

1-Xfls

Calculation:

-dislocation structure recovery

-effective grain size of the austenite

Output data

Figure 18. Procedure for calculating microstructural evolution

during thermomechanical processing of the experimental steels.

32
The computational procedure described in this section was verified in laboratory experiments conducted in the dilatometer that simulated thermomechanical processing. We used a commercial program to calculate strain, strain rate, and temperature distributions in the deformed specimens during the simulations [4]. Then, from these parameters, we used a specially

developed computer program coded in FORTRAN77 and based upon the procedure shown in figure 18 to calculate the austenite microstructural evolution.

Experiments were conducted to evaluate the model predictions. In this section, mechanicalproperty values represent the average of three to four specimens. Microstructural parameters are the average of about 200 measurements of one specimen. The data included from reference 9

represent the average of three specimens. The results of this study and another by Kuziak [9] on the eutectoid steel confirmed the good predictive capability of the computational procedure

described in this section.

For illustration, we discuss an experiment in which the C-Mn and VT steels were deformed

twice; some details of the experiment are given in table 22. The model-predicted and measured

changes in the austenite grain size (average of three specimens) in the central region of the deformed specimens are compared in figures 19 and 20.

For further experiments (section 7), this procedure was incorporated into the FEM codes

for rolling flats, plates, rods, and rails. Metal flow in these codes was calculated by using the

general plain-strain approach [22, 23]. A solution was obtained for a rigid-plastic body [23] that obeys the Levy-Mises flow rule. Effective stress was calculated from flow curves developed for the experimental steels in compression experiments, which were conducted in a hydraulic-pressbased hot-deformation apparatus and in the dilatometer. The nonuniformity of plastic deformation was corrected by using an inverse method [24]. We obtained a mathematical description

of flow behavior in the experimental steels from the Voce equation [6] by using the constants given in table 23. Only one form of the Voce equation (specified in table 23) was used in the

FEM calculation. The effect of dynamic recrystallization was included automatically during

the calculation, because this effect is directly related to the volume fraction of recrystallized

material.

The real velocity field in the FEM calculation was determined by optimizing this equation

[25]:

W CjEjdV + X VvdV zf

\v\dS , (7)

Table 22. Characterization of the two-deformation experiment conducted in the dilatometer on C-Mn and VT steel specimens.

_, . . c . „ . . ., . Cooling rate between

Reheating First detormation Second deformation , °

deformations

Td = 1000°C Td =950°C

1 150°C for 10 min 8 = 0.29 s = 0.32 l°C/s

e = 2.2 s_1 e = 2.7 s"

1
CDM

CO

£Z

CtS CO

CD

cz

CD

CO

100

90 -

< 80 -

70

60

50

40 -

30 -

20-

10 -

predicted

measured

-I 1 1 1- T

«" -i 1 i 1000 950 900 850

Temperature, C

Figure 19. Austenite grain size in the C-Mn steel specimen center during the

two-deformation experiment compared with predicted values (DQ = 85 u.m).

100

80 -

E

CDM

•« 60 -

COen

CD ~ 40-

CD

CO

=3 <

20 -

predicted

measured

1000 950 900 850

Temperature, C

Figure 20. Austenite grain size in the VT steel specimen center during the

two-deformation experiment compared with predicted values (DQ = 72 u.m).

34
where A. is a penalty coefficient, |v| is the relative velocity at the tool-material interface,

S is the boundary surface, Xr is the vector of boundary traction, and V is the control volume.

The temperature field in a deformed material was calculated by employing the FEM

solution of the general heat-transfer equation

V

r(KVr> + Q = Cp p— , (8)

where k is the material's thermal conductivity, Q is heat generated during deformation, Cp

is specific heat, and p is density.

The microstructural evolution models developed in this study were validated during the course of the laboratory experiments. Described below are the main results obtained from the

press-compression and flat-rolling experiments.

Table 23. Voce equations [6] for the stress-strain curves of the experimental steels.

For C-Mn steel—

a(s) = a [l-exp(-9.l8)] - 32 (T-49)

a = 1.35Z " 3

For VT steel—

a(e) = a [l-exp(-7s)] - 4 (T-50)

a = 1.5Z 04

For 900A eutectoid steel—

a(e) = a [l-exp(-3.4s)] - 27 (T-51) a. = 1.84Z - 14

6.2 Press Compression of Carbon-Manganese Steel

6.2.1 Experimental Procedures

Cylindrical specimens, 60 mm in diameter and 90 mm long, were machined from hotrolled billets of steel whose chemical composition is given in table 24. The aspect (height-todiameter) ratio was kept at 1.5 to promote homogeneous deformation. All specimens were

heated to 1 175°C, held at this temperature for 20 min, air-cooled to the testing temperature,

and then subjected to two-deformation experiments conducted by compression in a 100-kN

hydraulic press. During compression, a nearly constant strain rate of 0.2 s~ was maintained.

The initial austenite grain size resulting from the reheating procedure was 160 jo,m. Temperature changes during experiments were monitored with thermocouples mounted in the drilled hole; the tips of the thermocouples coincided with the centers of the specimens.

35
Figure 21 shows (schematically) the processing schedule employed in the experiment. The

first deformation was applied at 1050°C. Following the deformation, the specimens were placed

in still air and allowed to cool to the temperature of the second deformation (820, 720, or 650°C). Deformations at 720 and 650°C were performed in the two-phase region of the Fe-C

equilibrium system. In the second deformation, homogeneous strains were also varied.

After the experiment, the specimens were sectioned, and the yield strength, ultimate tensile strength, reduction in area, elongation, and hardness were measured in the central regions of the

specimens.

Table 24. Chemical composition (mass percent) of the cylindrical

specimens compressed in the hydraulic press.

c Mn Si P S N

0.21 1.37 0.28 0.033 0.021 0.0065

o.E

CD

Time

Figure 21. Schematic of the two-deformation experiment conducted on the hydraulic

press: TR = 1175°C for 20 min; Td] = 1050°C; Td2 = 820, 720, or 650°C. Reduction

range: 1st stage = 0.35; 2nd stage = 0.2, 0.5, 0.8.

36
6.2.2 Thermomechanical Behavior during Compression

The thermomechanical part of the modeling is based on a coupled FEM solution of the

rigid-plastic-flow formulation and general heat-transfer equation describing the temperature field

in the deformation zone. We used a commercial program [4] to calculate the temperature, strain,

and strain-rate distribution, together with the microstructural evolution, during the two-stage

deformation. Measured cooling curves, such as that in figure 22, and the profile of the speci- mens after deformation were used to estimate the boundary conditions and friction coefficient

during the deformation.

An example of the calculated temperature and strain distributions after the second deformation is shown in figure 23. As expected, in the compression experiment, severe variations in the deformation conditions resulted from rapid heat transfer to the dies. Such thermomechanical

behavior significantly affects microstructural evolution in both the austenite and the ferrite regions. This feature of the process, specifically the calculated austenite grain-size distribution

after the first deformation at 1050°C, is shown in figure 24.

1300

J st deformation (35% reduction)

300

Figure 22. Cooling curve recorded by a thermocouple located at the center of the cylindrical

C-Mn specimen subjected to the two-step deformation schedule in the hydraulic press.

37
(a)

5 10 15 20 25 30 35 40 45

(b)

5 10 15 20 25 30 35 40 45

x, mm

Figure 23. Calculated distribution of (a) temperature and (b) effective strain on a cross section of the cylindrical specimen after the second deformation.

x, mm

Figure 24. Calculated distribution of the austenite grain size (in micrometers)

after the first deformation of the cylindrical specimen at 1050°C.

38
6.2.3 Effect of Processing Conditions on the Mechanical Properties

From the results of the present investigation, we constructed a quantitative description of

the strengthening mechanisms operating in the steels. After deformation in the austenite region

and the subsequent phase transformation, the dislocation density in the ferrite structure is rela- tively low. However, deformation in the two-phase region results in a significant increase in the

dislocation densities in the ferrite grains. The contribution of dislocations to the strengthening

is very complex; usually it is caused by interactions between the forest and mobile dislocations

and the substructure. An example of the correlation between the accumulated strain in the ferrite region and hardness is presented in figure 25. The contribution of dislocations to the strengthening at a specific temperature is described by equation [26]

i Gj = aGbp0.5 (9)

where a is a constant, G is shear modulus, b is Burgers vector, and p is forest-dislocation

density. Since dislocation measurements are tedious and often inaccurate, an approach developed

by Majta et al. [27] was adopted in this study. Based upon results published elsewhere [28], the

correlation between dislocation density and the deformation temperature was found to be

f A

pd

= p Bexp(efl -l) _ (10)

(a)

x, mm

(b)

10 15 20 25 30 35 40 45

x, mm

Figure 25. Comparison of (a) the computed effective strain in the ferrite phase and

(b) the measured hardness distribution.

39
where A, B, and s are constants, p is initial dislocation density, FDT is the finish deformation

temperature, and &a

is the strain retained in the microstructure after deformation. From published data [28], we inferred that the best fit to the observed experimental data could be obtained when A = 1030, B = 1.8, and s = 8.8 and when we assumed p = 10 /m . Although the

applicability range of eq (10) is limited, it does correlate well with experimental data published

in the literature.

The yield-strength predictions for the deformation condition used in the experiment were

obtained by calculating the structure-related yield strength and the dislocation-related component

of yield strength. Next, we calculated total yield strength using the root-sum-of-squares method

[29]:

1

I 2 2\2 ( 1] ) CT tot =

(as + ad

The results of the tensile test are shown in table 25 and are compared with the predicted results

in table 26. A good correspondence between the experimental and predicted data was obtained

for most of the deformation schedules.

Table 25. Measured mechanical properties and microstructural parameters at the center of the press-compressed specimens whose chemical composition is given in table 24.

No.

Td2>

°C

Strain

at 7^, u.m /«

Sq,

p.m MPa MPa HV5

1 0.5 16.9 0.69 0.17 375 580 197

2 820 1.1 10.5 0.69 0.18 390 587 190

3 1.6 8.70 0.67 0.15 405 601 177

4 0.5 12.1 0.63 0.16 390 584 199

5 720 1.1 8.40 0.69 0.15 401 586 185

6 1.6 7.60 0.64 0.15 479 604 218

7 0.5 7.00 0.69 0.16 425 599 195

8 650 1.1 6.80 0.64 0.16 410 590 205

9 1.6 5.80 0.68 0.14 502 620 208

40
Table 26. Comparison of measured (table 25) and calculated yield strengths

in the compressed specimens.

Temperature of the second deformation, °C

Effective 820 720 650

strain in 2nd stage

Gv

, MPa

measured calculated measured calculated measured calculated

0.5

1.1

1.6

375

390

405

354

391

401

390

401

479

392

427

456

425

410

502

473

495

528

6.2.4 Effect of Processing Conditions on Microstructure

The microstructural parameters measured by means of metallography are presented in table 25. The most interesting results of our experiment relate to the deformation in the twophase region. The ferrite-transformation starting temperature, as calculated and observed in the

experiment, was in the range 710 to 735°C. Since the strain and cooling rates in the specimens were kept constant, the amount of strain retained in the ferrite increased as the deformation temperature decreased. Figure 26 shows a calculated distribution of retained strain in ferrite after deformation at 650°C. Inhomogeneity in plastic deformation and temperature resulted in the

nonuniform distribution of the retained strain. Increasing the amount of deformation before and

after the transformation start temperature causes grain refinement, but to different levels and by

different mechanisms. The evolution of the ferrite-pearlite microstructure in deformed

specimens is shown as a function of effective strain in figure 27.

5 10 15 20 25 30 35 40 45

x, mm

Figure 26. Calculated distribution of the retained strain concentrated

in the ferrite after the second deformation at 650°C.

41
The microstructures of the specimens are significantly diverse; thus, inhomogeneity in the

plastic deformation, which is caused by increasing total reduction, plays an important role in the

microstructural evolution during diffusional transformations. Figure 27c clearly shows significant

ferrite grain refinement in the slip bands. From transmission-electron microscopy, we learned

that dislocation density increased significantly in 20 to 30 percent of the ferrite grains of speci- mens deformed near the transformation temperature. Nevertheless, most grains of these speci- mens are dislocation-free (fig. 28). As expected, high dislocation densities were observed in the

ferrite grains in specimens deformed at lower temperatures. In specimens deformed at 650°C,

dislocation densities increased in about half the grains. This observation suggests that the evolution of dislocations during plastic deformation in the two-phase region should be included in the

mechanical-properties model.

In the two-phase region, ferrite is softer than austenite. Thus, when the primary nucleated

ferrite grains link to form a continuous layer at the austenite boundaries or deformation bands,

deformation should concentrate in the ferrite. Strain has a strong effect on ferrite grain refine- ment at temperatures just below Ary As shown elsewhere [26] and confirmed in the present

work, at 650°C the ferrite occupies most of the available austenite grain-boundary area. Thus,

the deformation of this microstructure should lead to longer, pancake-shape ferrite layers (with

similar dimensions and volume fractions) at the austenite grain boundaries plus finer, strain- induced ferrite grains at the ferrite-austenite interfaces. In the example shown in figure 29, large

ferrite grains are present in the specimens compressed at 820°C. These grains were produced by

transformation from statically recrystallized austenite.

42
(a) (b)

Figure 27. Ferrite-pearlite microstructures in the compressed cylinders with

different amounts of deformation at 820°C. (a) 8 = 0.4; (b) e = 1.1; (c) s = 1.6. Light microscopy (lOOx).
(a)

Figure 28. Transmission-electron micrographs of specimens deformed at different temperatures

and strains: (a) Td = 820°C, e = 0.4; (b) Td = 720°C, s = 1.1; (c) Td = 650°C, e = 1.6.

44
(a)

Figure 29. Microstuctures (lOOx) obtained at different deformation temperatures:

(a) 820°C; (b) 720°C; (c) 650°C. After the second deformation, e = 1.1.

45
6.3 Forging of Vanadium-Treated Microalloyed Medium-Carbon Steel

Over the last decade, microalloyed medium-carbon steels have become a cost-saving substitute for the quenched-and-tempered grades traditionally used to produce forged automotive

components. However, their use is restricted to components that do not undergo excessive

impact loading during service. The limitations of microalloyed forging steels are related to the

specific morphological features of the ferrite-pearlite microstructure that can be modified only

to a certain degree. Furthermore, the dispersion of fine precipitates that harden the ferrite matrix

substantially lowers the ductility of forgings. Optimal properties depend on the complicated

interaction between thermomechanical processing parameters and the chemical composition of

the steel.

The severe service conditions for automotive components require steels with a combination

of high strength and good ductility, which can be attained only by a high degree of microstructural refinement, well-balanced volume fractions, and a favorable distribution of the ferrite and

pearlite phases. The pursuit of more economical processing and less microalloy consumption

demands good control over the forging operations. The first step toward these goals is mathematical modeling of microstructural evolution during thermomechanical processing.

In this section, we give an example of our mathematical modeling to determine the

processing routes that will achieve an optimal balance between the strength and toughness

of forged steels.

6.3.1 Experimental Procedures

The chemical composition of the steel investigated in this study is given in table 27. The

material was a 100-kg laboratory heat cast into 25-kg ingots. With an industrial hydraulic press, as-cast ingots were forged into square bars and machined into blocks 55 mm x 55 mm in cross

section and 120 mm in length. During the experiment, the reheating temperature and time, forging starting temperature, and cooling rate after deformation were controlled. One deformation was applied to reduce the length of the blocks from 55 to 20 mm. During the forging experiments, temperature changes were monitored with thermocouples inserted into drilled holes. The

tips of the thermocouples coincided with the symmetrical center of the billets. The processing

schedules are described in table 28. One variant of the forging schedules included accelerated

cooling with pressurized air. Specimens for mechanical-property measurements and quantitative

metallography were extracted from the forged blanks after cooling to ambient temperature. The

mean- linear- intercept method was used to measure ferrite grain size and pearlite interlamellar

spacing.

Table 27. Chemical composition (mass percent) of the VT medium-carbon steel selected for the forging experiment conducted with a hydraulic press.

C Mn Si P S V Al

tot N

0.29 1.42 0.38 0.023 0.015 0.14 0.035 0.014

46
Table 28. Deformation schedules applied to the block specimens of the VT mediumcarbon steel (table 27) during simulation of forging on the hydraulic press.

Deformation

schedule

20-min

reheating temperature,

°C

Forging starting

temperature,

°C

Cooling

A

B

C

1100

1200

1200

1050 still air 1100 still air

1 150 forced cooling at 1.5 °C/s

6.3.2 Mathematical Modeling

An interesting feature of the forging process was the possibility of initiating dynamic

recrystallization in the central part of the deformed material. The substantial drop in temperature

precludes dynamic recrystallization in the areas near the surface. However, since the critical strain for dynamic recrystallization (-0.21) is very small for deformation start temperatures, this process may initiate at the beginning of deformation.

The three deformation schedules used in the simulated-forging experiments (table 28) pro- duced quite different changes in the specimen microstructures, which our mathematical model was able to predict fairly well. For illustration, the cooling curve obtained for schedule A is shown in figure 30, and the calculated distributions of strain and temperature at the end of

schedule B processing are shown in figure 3 1

.

1200 -

1100 -

o° 1000 -

B 900 -

cc

CDQ.

E

CD

100 200 300

Time, s 400 500

Figure 30. A cooling curve obtained during the forging experiment (schedule A).

The thermocouple was mounted at the symmetrical center of the specimen.

47
strain

Figure 31. Finite-element calculation of the effective strain and temperature

distribution in the specimen at the end of deformation (schedule B). Since the

forging process is symmetrical, only one quarter of the specimen is shown.

The nonuniformity of deformation parameters in the processed material caused some

inhomogeneity in the distribution of recrystallized grain size, which was maintained upon

cooling to the transformation temperature (fig. 32). The initial austenite grain sizes used in the

calculations shown in figure 32 were measured in specimens quenched after the reheating stage;

the values were 40, 180, and 180 u.m for processing schedules A, B, and C, respectively. The

measured austenite grain sizes in the forged blanks prior to the transformation and the predicted

values are compared in table 29. Predicted and measured microstructural parameters in the

center of the forged blanks cooled to ambient temperature are compared in table 30. To cal- culate the values, we used the relationships given in table 13. The corresponding ferrite-pearlite

microstructures are shown in figure 33.

The capability of our equations to predict strength properties is demonstrated in table 31. We used the commercial computer program to estimate the amount of vanadium and nitrogen

soluble in the austenite at the reheating temperature, and their precipitation-strengthening contribution to yield strength and ultimate tensile strength were calculated from the equations in table 19.

48
(a)

grain size after growth

grain size after growth

10

(b) I 5

I

i

i i

10 20 30 40 50 60

x, mm

(c)

grain size after growth

10

j E

E 5

Figure 32. Calculated austenite grain-size distribution in the forged blanks after cooling

to the transformation temperature.

Table 29. Comparison of the measured and predicted austenite grain sizes

in the center of the forged blanks prior to transformation.

Deformation Austenite grain size, u.m schedule

measured predicted

A 25 22

B 33 30

C 43 40

49
Table 30. Comparison of the measured and predicted parameters of the ferrite-pearlite

microstructure in the center of the forged blanks after cooling to ambient temperature.

Deformation

schedule

Microstructural parameters

/a Da

, urn Sn, urn

measured predicted measured predicted measured predicted

A 0.57 0.59 9.20 7.3 0.162 0.165

B 0.50 0.56 10.5 8.5 0.159 0.165

C 0.42 0.43 8.70 6.0 0.147 0.132

(a)

(b) (c)

Figure 33. Ferrite-pearlite microstructure (200x) in the central part of the forged blanks

after cooling to ambient temperature, (a) Schedule A; (b) Schedule B; (c) Schedule C.

50
Table 31. Comparison of the measured (average of three specimens)

and predicted strength properties of the forged blanks.

Deformation c

y

, MPa au

, MPa

schedule measured predicted measured predicted

A

B

C

630 626

665 651

705 729

870 864

900 873

963 988

6.4 Flat Rolling of 900A Eutectoid Steel

To verify thermomechanical and microstructural evolution models for the flat rolling of

steels, we conducted flat-rolling experiments on 900A eutectoid steel. Small block specimens

(50 mm x 38 mm x 400 mm) were rolled into 20-mm flats and cooled in still air. The rolling

schedule consisted of two passes, which are detailed in table 32. The schedule was repeated

several times, and the specimens were quenched at different stages of the rolling process to determine austenite grain-size evolution. The initial austenite grain size after reheating was

estimated in a block specimen quenched just after its removal from the furnace. During rolling,

temperature was monitored with two thermocouples mounted in holes drilled one above the

other, just below the contact surface and in the center of the blocks, respectively. An example

of the measured and predicted temperature changes is shown in figure 34.

Generally, the thermomechanical model characterized the temperature changes well. The

most important feature of the process was a very rapid drop of temperature in the subsurface

area. We also observed a small increase of temperature in the central region of the specimen.

However, the temperatures usually equalized during the intervals between passes.

For the rolling schedule applied in the experiment, static recrystallization was the major

microstructure-restoration process. In the process under investigation, the large deformations

resulted in very fast static recrystallization. As a consequence, grain growth controlled the grain

size before the second pass and after the last. Calculated and measured changes of the austenite

grain size in the specimen during rolling are shown in figure 35. The measured and calculated

strength properties of the flat are compared in table 33. Generally, the computer calculations

compared fairly well with the results obtained in the experiment.

Table 32. Description of the flat-rolling experiment of the 900A eutectoid steel.

R

, . Time pause First Time pause after Second

after reheating deformation first deformation deformation

1174°C

for 20 min

22 s 38 ^ 28 mm 25 s 28 -> 20 mm

51
1250

900

• — center — surface

—i 1

1

1

1

1

1

1

1 .1

1

1 1— 10 20 30 40 50 60 70 80

Time, s

Figure 34. Calculated (lines) versus measured (symbols) temperature changes during

laboratory-mill two-pass rolling of the eutectoid steel on the into 20-mm-thick plate.

250

200 - E

M

"55 150 H

cz

CO £ 100

£ZCD

CO <

50 -

a measured — calculated

second pass

first pass

1150 —i

1 1

1100 1050 1000

Temperature, °C 950 900

Figure 35. Changes of austenite grain size with temperature and time during 20-mmthick flat rolling of the eutectoid steel. Calculations and measurements were made at the center of the specimen.

52
Table 33. Comparison of the measured and predicted microstructural parameters

and mechanical properties of the 20-mm flat of 900A steel cooled to ambient

temperature after rolling according to the schedule in table 32.

Microstructural parameters

measured

jim Nd, fim

predicted measured predicted

S , \xm

measured predicted

30.2 35.1 8.7 7.5 0.12 0.11

Mechanical properties

measured

a MPa

predicted measured

ou

, MPa

predicted

650 666 1086 1077

7. Industrial Experiments

Successful validation of the microstructure and thermomechanical models in the laboratory

experiments led to implementation of these models in industrial practice.

The following industrial experiments were conducted in this study:

• plate rolling of VT microalloyed medium-carbon steel

• rod rolling of C-Mn, VT microalloyed medium-carbon, and eutectoid steels

• rail rolling of eutectoid steel The experiments were motivated by industry's need to rationalize manufacturing technologies

and chemical compositions of particular steels. In this section, mechanical-property measure- ments represent the average of three to four specimens, and the microstructural parameters are the average of about two hundred measurements of one specimen. Described below are the most

important results obtained from the experiments.

7.1 Plate Rolling

Plate rolling is the most frequently modeled process. Plastic flow, heat transfer, and microstructural evolution calculations are represented in the model by FEM codes.

In this research program, we tested our model by plate rolling VT microalloyed mediumcarbon steel; its chemical composition is given in table 34. The rolling schedule (table 35)

consisted of 14 passes of 5- to 27-percent reduction with approximately 20-s intervals between

passes to reduce a 140-mm-thick slab to a 14-mm-thick plate. The surface temperature measured

in the experiment (table 35) was used to adjust the temperature distribution in the model.

53
On the basis of experimental results and computer simulations, we postulated that, in multipass rolling, the last five to six passes were crucial in the development of the final microstructure. Calculation of the microstructural evolution showed that, during the last few passes of

plate rolling, static recrystallization restored the austenite microstructure. This process proceeded

very rapidly, and substantial grain growth was noted between the last two consecutive passes. The fast recrystallization kinetics and grain-growth rate were promoted by the small size of

the austenite grains that were present after the preliminary passes and by the high deformation

temperatures during the last few passes.

Calculated changes in the austenite grain size in the midthickness of the workpiece during

the last seven passes of the rolling are shown in figure 36. Also included in this figure is the

austenite grain size measured in the specimen cut from the plate after the finish pass and water

quench. The grain sizes indicated in figure 36 refer to the state after grain growth just before the next pass.

Table 34. Chemical composition (mass percent) of the VT medium-carbon steel rolled into 14-mm-thick plate.

c Mn Si P S V A'tot N

0.24 0.70 0.21 0.017 0.017 0.033 0.001 0.007

Table 35. Deformation schedule used to roll the VT steel (table 34)

from a 140-mm x 160-mm slab to a 14-mm-thick plate.

Deformation schedule

Pass no.

relative reduction temperature, °C

1185

1163

1147

1 0.05

2 0.12

3 0.15

4 0.14

5 0.17

6 0.16

7 0.19

8 0.18

9 0.23

10 0.27

11 0.23

12 0.22

13 0.17

14 0.07

1131

965

54
100

80 -

CD

Nl

03

CD

CO

20

after cooling to 850°C

predicted

O measured

-1 1— 10 11 Pass No.

12 —i

13

Figure 36. Austenite grain-size development in the VT medium-carbon steel during the last seven passes in the rolling of 14-mm-thick plate. Results of the calculation refer to the state after grain growth, either during time intervals after consecutive passes or after cooling to 850°C after the last pass.

The results of the final microstructural parameters and mechanical-property predictions,

together with the measured values, are given in table 36. An example of the ferrite-pearlite

microstructure in the midthickness of the plate is shown in figure 37. On the basis of the

experimental results, we postulate that the rolling model gives a good representation of the

microstructural events taking place during the plate-rolling experiments.

Table 36. Measured and predicted microstructural parameters and mechanical properties

of 14-mm-thick plate of VT medium-carbon steel rolled according to the schedule listed

in table 35.

Microstructural parameters

Da

, u.m 5"q, u.m fa

Mechanical properties o , MPa au

, MPa 27-J ITT, °C

measured

predicted

0.62

0.60

12.5

10.7

0.234

0.22

410

430

572

580

24

TO

55
*sr

Figure 37. Ferrite-pearlite microstructure of the 14-mm-thick VT medium-carbon steel cooled to ambient temperature after rolling (200x).

7.2 Rod Rolling

The rod-rolling process has stimulated many experiments and theoretical considerations

related to the mechanisms of microstructural restoration in deformed austenite. Some researchers believe that dynamic recrystallization initiation takes place during the last few passes at low

temperatures [30-32] and that it is related to the strain accumulation due to the short intervals

between consecutive passes. Despite a long history of experimental efforts to understand the

dynamic and postdynamic recrystallization mechanisms, our knowledge of the role of these

processes in microstructural development is still far from satisfactory.

7.2.1 Experimental Procedures

The chemical compositions of the steels investigated in the industrial experiments are given

in table 37; they are different from the compositions of steels used in the laboratory experi- ments. Vanadium was added to the plain-carbon steels to increase the yield strength of the rods

from 520 to 550 MPa. Continuously cast VT-steel and conventionally cast eutectoid- and C-Mnsteel ingots were rolled into preliminary slabs, which were then rolled into 8-mm-diameter rods. The rod-rolling process consisted of several stages, including reheating, roughing passes, inter- mediate and finish rolling, and cooling in the cooling bed. The finish rolling in the rod-rolling

process consisted of six consecutive passes with a very short interval (<0.2 s) between passes. At different stages during the rolling, the specimens were cut and quenched for austenite grainsize measurement at the entry to the last stand and approximately 1 5 s after the last pass. The

temperature of the rods was measured with an infrared pyrometer. Specimens for mechanicalproperty testing and quantitative metallography were taken from the rods after cooling in the

cooling bed. Austenite and ferrite grain sizes and pearlite interlamellar spacing were measured

by the mean-linear-intercept method.

56
We determined that the finish rolling and cooling in the cooling bed are the most important

stages in the development of the final microstructure in the rods. Therefore, our experimental

and theoretical efforts on rod rolling focused on these stages.

Table 37. Chemical composition (mass percent) of plain-carbon, VT,

and eutectoid steels rolled into 8-mm-diameter rods.

Steel C Mn Si P S Al

tot N

plain carbon 0.22 1.23 0.34 0.060 0.038 0.044 0.007

VT 0.18 1.34 0.33 0.024 0.021 0.006 0.009

eutectoid 0.71 1.15 0.28 0.018 0.019 0.005 0.006

7.2.2 Validation of the Model

For rod rolling of VT steel, the results of the finite-element calculations of strain, strain

rate, and temperature distribution in the cross section of the workpiece at the end of the first and

last passes are shown in figures 38 and 39. The results of the calculations for the rolling of the

eutectoid and C-Mn steels are essentially the same.

The model predicted strong inhomogeneity of the plastic flow during the rolling. The

temperatures of the rods entering the first pass were very stable, in the range 900 to 925°C.

However, the most striking feature of the process was the increase in temperature at the exit from the last stand—approximately 100°C more than that in the initial state (fig. 40). This in- crease, attributed to the plastic work during deformation, was confirmed by infrared-pyrometer

measurements.

The measured initial austenite grain size at the entrance to the finishing stand was approximately 20 jim for all the experimental steels. Predicted austenite grain-size evolution in the

eutectoid steel during the rod-rolling process is shown in figure 40. Our microstructural evolution model predicts that dynamic recrystallization initiates in the second pass in all these steels as a result of strain accumulation due to the short interval between passes. The distribution of

the volume fraction of the recrystallized material and the retained strain in the cross section of

the workpiece after first pass are illustrated in figure 38. As a consequence of dynamic recrystallization initiation, metadynamic recrystallization occurred during the interval between passes. However, the short intervals precluded a full recovery of the dislocation structure.

On cooling following rolling, significant grain growth occurred in the eutectoid steel rods. Measured austenite grain size was within the range 35 to 45 urn 15 s after the last pass. Thus,

the grain-growth process diminished the beneficial effect of dynamic recrystallization on austenite grain refinement. In the C-Mn and VT steels rods, grain growth was less intense: austenite grain sizes were 20 to 25 u,m 15 s after the last pass.

57
(a) (b)

(c) (d)

4 - 1 5

- 14 F

3 ; ^ - 12 E 3k±*f~>*i :^A ~s /^- - 10

>; 2 ^mg o \

1 8

1 fi§\ \\

I 5

u

i

^-—x. i i \ 1 11 1 4 '3 112 3 4 5 6 7 8 9

x, mm

(e) (f)

Figure 38. Calculated deformation parameters and the state of the austenite microstructure at the end of the first pass during finish rolling of 8-mm-diameter rod of the VT

steel: (a) effective strain; (b) effective strain rate; (c) temperature (in degrees Celsius);

(d) recrystallized volume fraction; (e) retained strain; (f) austenite grain size (in micrometers). Owing to the two-axial symmetry, only one quarter of the cross section is shown.

58
.0 0.5 1.0 1.5 2.0 2.5 3.0

x, mm

.0 0.5 1.0 1.5 2.0 2.5 3.0

x, mm

(a) (b)

5.0 0.5 1.0 1.5 2.0 2.5 3.0

x, mm

i.O 0.5 1.0 1.5 2.0 2.5 3.0

x, mm

(d)

.0 0.5 1.0 1.5 2.0 2.5 3.0

x, mm

Figure 39. Calculated deformation parameters and the state of the austenite microstructure at the end of the last pass during

finish rolling of 8-mm-diameter rod of the

VT steel: (a) effective strain; (b) effective

strain rate; (c) temperature (in degrees

Celsius); (d) recrystallized volume fraction;

(e) austenite grain size (in micrometers).

Owing to the two-axial symmetry, only one

quarter of the cross section is shown.

59
50 -i

40 - E

3.

CD o

M O

CO 30 -

CD

£= *—

Z3

CTS -^-* i— co O)

CD

CD

cz 20 - Q.

E

CD CD

in - \—

rs <

10 -

J

1100 -i

1050

1000 -

950

900 -

850

1 5 s after last pass

Figure 40. Calculated temperatures and austenite grain sizes during finish rolling of

8-mm-diameter rod of the eutectoid steel.

The most important feature of the cooling process pertains to the heat-transfer conditions.

The rods were cut and collected at the exit of the rolling stand in bundles of 10 to 15 rods,

and the bundles were transferred into the cooling bed. The cooling history of a particular rod

depends on its location in the bundle. Approximate cooling curves were obtained during the

laboratory experiment in which the rods' arrangement and the heat-transfer conditions were

very close to those in the rolling mill. For illustration, cooling curves for eutectoid steel rods

arranged in a 12-rod bundle are illustrated in figure 41.

Estimates of the rods' cooling rates (1 to 2.5°C/s) over the diffusional transformation temperature range were used to calculate the microstructural parameters and strength properties. The

measured and calculated results of microstructural parameters and strength properties are listed

in table 38. The eutectoid steel rods experienced the most significant variations in microstructural parameters and mechanical properties caused by the diverse cooling conditions in the

bundle. The C-Mn and VT steels rods were less sensitive to variations in cooling rate.

60
100 200 300

Time, s 400 500

Figure 41. Cooling curves of the 8-mm-diameter rods of the eutectoid steel at different

locations in the 12-rod bundle. Data are from a laboratory experiment.

Table 38. Measured (M) versus predicted (P) microstructural parameters and mechanical

properties of 8-mm-diameter rods of the C-Mn, VT, and eutectoid steels.

Microstructural parameters Mechanica 1 properties

/o "d> |am 0* u.m oc

> urn s , p.m <v MPa gu

, MPa

M P M P M P M P M P M P M P

C-Mn 0.66 0.62 11.6 12.1 0.18 0.20 407 392 635 618

VT 0.65 0.63 9.6 10.1 0.17 0.18 550 540 690 670

Eutectoid

bundle exterior 15 18 6 9 0.15 0.16 580 560 1020 1010

bundle center 23 28 8 13 0.17 0.18 540 530 1000 998

61
7.3 Rail Rolling

In Poland, rails are manufactured mainly from a 900A eutectoid-grade steel, UIC-60, whose

chemical composition is similar to that in table 1. The rolling of UIC-60 rail was used to demonstrate the capability of our model to predict microstructural evolution during this process.

Seventeen passes, generally Bartscherer-type passes, were used in the process. Owing to the

complexity of the material flow and heat transfer, the generalized plain-strain model used in the

FEM calculations was too complicated to use for the entire process. However, several consecutive passes were modeled successfully with this approach, which was sufficient to calculate the

development of the final grain size in the rail.

For example, the distribution of deformation parameters after the last pass in the rail-rolling

process is shown in figure 42. In this case, a severe nonuniformity of deformation and temperature existed in the workpiece. Simulation of the austenite grain-size evolution in the rail's head during the last five passes is shown in figure 43; it was calculated by assuming two finish- rolling temperatures. The influence of deformation conditions on austenite grain-size evolution is illustrated in figure 44. This calculation refers to the microstructural evolution in the foot of the

rail during the five last passes. In this case, the temperature is lower and the strain and strain rates are higher than those in the rail's head.

The microstructural evolution model predicts that static recrystallization restores the austenite microstructure after deformation. No dynamic recrystallization occurred because the low

deformation temperatures and small strains did not exceed the critical value for its initiation. The pauses between consecutive passes were sufficient, however, for complete static recrystallization to occur early after each pass, even though recrystallization in the rail's foot is more

sluggish than in the rail's head. Thus, austenite grain growth is the main process shaping the

final austenite microstructure. Computer calculation shows that the austenite grain size after cooling to the pearlite transformation temperature should be approximately 80 to 100 u.m in the head and 30 to 40 \im in the foot of the rail. This result was confirmed by measurement of

the austenite grain size of the quenched rail approximately 60 s after the last pass. The results of the measurement are included in figure 45, which shows the austenite microstructure in the

quenched rail.

Some of the complicated cooling history of the rail after rolling was shown in the laboratory experiment (fig. 46). Depending on the region of the rail, the pearlite transformation shifted

in time, an effect associated with the diverse heat-transfer conditions prevailing in the rail's cross section. The characterization of the cooling history of different elements of the rail by

FEM modeling is shown in figure 47. For the calculation shown in this figure, the pearlite

transformation model was incorporated into the FEM code, which characterized the contribution

of the transformation heat to the evolution of the temperature field in the rail during cooling.

The calculation shows that the effect of transformation heat should yield equalization of temperatures in the head, web, and foot centers approximately 600 s after the start of cooling

(fig. 48). This effect was observed in the laboratory experiment (fig. 46).

62
(a)

0.7

0.6

0.5

0.4

0.3

0.2

0.1

(b)

1000

950

900

850

800

750

700

650

600

550

Figure 42. Distribution of (a) strain and (b) temperature (in degrees Celsius)

in the UIC-60 rail's cross section after the last pass.

63
COM

CO

cz

CDen

c:

CD

CO

120

100 -

80

60

40

20

120

-100

80

60

-40

-20

1050 1000 950

-i 1—i

1 1 i 1 i 900 850 800 750

Temperature, C

Figure 43. Simulated austenite grain-size changes in the head of the UIC-60 rail during

the last five passes of the rolling process for two finish-rolling temperatures: 970°C

(dashed line) and 930°C (solid line). DQ = 50 urn.

120

100 -

E

<d 80 M

OO

cz2 60

CD 2 40-

<

20 -

I i i

120

-100

80

-60

-40

20

950 900 850 iOO 750

Temperature, C

Figure 44. Simulated austenite grain-size changes in the foot of the UIC-60 rail during

the last five passes of the rolling process.

64
(a)

(b)

**£j

Figure 45. Austenite microstructures (200x) at different locations in the UIC-60 rail quenched 60 s after the last pass. Austenite grain size: (a) 96 urn; (b) 33 urn.

65
1000

oo

CD

to 750

CD

~i ii

1

1 1

1

1 r 200 300 400 500 600 700 800 900 10

Time, s 00

Figure 46. Cooling curves of the foot, web, and head of the UIC-60 rail measured

during a laboratory experiment. Thermocouples were installed at the symmetrical

centers of the web and foot.

1000

3

OB

E

CD

500

calculated

annmm measured 4 mm below the running surface

T—'—I—'—I—«—1——I—'—I—'—I—'—I——I—'—I—i—I—

r

200 400 600 800 1000 1200

Time, s

Figure 47. Temperature changes in the head of the UIC-60 rail during a cooling

experiment in the laboratory (T = 940°C for 20 min).

66
E

-80 f 1

-60

-40 690

670

-20 650

630

610

590

20 570

40

550

530

60 ^^tfl ;J^^^

-60 -40 -20 20 40 60

x, mm

Figure 48. Calculated temperature distribution (in degrees Celsius) in the UIC-60 rail 600 s after the start of the cooling under laboratory conditions.

The rail-rolling experiments also confirmed the model predictions of the mechanical properties of the rails. For the chemical compositions of the rails shown in table 39, the microstructural parameters and mechanical properties of the rails are given in table 40. Taking into account the results obtained from the model, we infer that the variations in the microstructural

parameters observed in the rails were caused mainly by the variations in cooling rates after the

rolling. The microstructural parameters and mechanical properties of the pearlite were calculated on the basis of the calculated average cooling history in the rail. The results of the calculation

(given in table 41) compare fairly well with the measurements.

Table 39. Examples of the chemical composition (mass percent)

of the UIC-60 rails rolled from 900A steel continuously cast ingots.

No. C Mn Si P s A1

tot

1 0.74 1.10 0.28 0.016 0.018 0.001

2 0.71 1.10 0.25 0.017 0.020 0.002

3 0.72 1.00 0.21 0.021 0.018 0.004

67
Table 40. Measured microstructural parameters and strength properties of the UIC-60 rails rolled from 900A steel continuously cast ingots having the chemical compositions specified

in table 39.

Microstructural parameters Strength properties

No.

Nd, pm Dc

, pm SQ, pm ay

, MPa au, MPa

1 28 14 0.168 540 967

2 36 19 0.220 480 915

3 35 11 0.199 500 935

Table 41. Calculated average values of the microstructural parameters and the strength properties in the UIC-60 rails (table 39) based upon the cooling curve measured in the laboratory

experiment, which gave a cooling rate of 0.3°C/s at the location corresponding to the place in the rail's head extracted for the mechanical-properties measurement.

Microstructural parameters Strength properties

Nd, fxm Dc

, pm S , pm oy

, MPa au, MPa

37 13 0.194 510 945

8. Summary

8.1 Mathematical Modeling

Conventional models were developed to calculate the microstructural evolution during

thermomechanical processing of experimental C-Mn, VT, and 900A eutectoid steels. These

models quantitatively relate strain, strain rate, and temperature to the parameters describing

the state of the austenite microstructure. The parameters include the volume fractions of the

dynamically, metadynamically, and statically recrystallized material; recrystallized austenite

grain size; and austenite grain size after grain growth. To characterize microstructural evolution

occurring in the C-Mn and VT steels, we used the general form of the relationships developed

by Sellars [2] and Roberts et al. [7], which well-represented the experimental results. However,

to improve the quantitative characterization of deformation parameters and austenite grain size

during static recrystallization in the eutectoid steel, we used the model of Choquet et al. [10]

for static recrystallization. The models of microstructural evolution during thermomechanical

processing were validated by laboratory experiments and incorporated into the FEM codes for the industrial plate, rod, and shape (rail) rolling processes.

Phase transformations in the C-Mn and VT steels were treated in a purely empirical way:

ferrite grain size and volume fraction, as well as the mean interlamellar spacing in pearlitic

cementite, were quantitatively linked to the austenite grain size, cooling rate over the transfor- mation temperature range, and chemical composition of the steels. This approach was substantiated by the experimental results.

68
Finally, microstructure-mechanical properties relationships were developed for the experimental steels. For the ferrite-pearlite steels, we took an approach similar to that of Gladman et

al. [1], except that we used the linear law of mixtures to characterize the contribution of the

ferrite and pearlite phases to the yield strength. The effect of the mean true interlamellar spacing on the ultimate tensile strength was described by a term that expresses its significant contribution when the ferrite phase loses continuity in the microstructure. For the eutectoid steel, the

yield and ultimate tensile strengths were correlated with the mean free path for slip in the

ferrite. The best correlation was achieved when this parameter was raised to the -1 power

instead of the -0.5 power used in the Hall-Petch relationship.

8.2 Industrial Experiments

8.2.1 Plate Rolling

1

.

The assumption of constant deformation parameters and temperature through the thickness

direction during plate rolling leads to significant errors in the prediction of microstructural

evolution because, during the last few passes, the temperatures of the surface and interior regions of the workpiece differ significantly.

2. A temperature gradient between the surface of the workpiece and its center develops during

plate rolling owing to contact with the rolls.

3. The most important austenite-microstructure-restoration process during plate rolling is static recrystallization. Since at high rolling temperatures this process proceeds very rapidly, grain

growth contributes substantially to the overall microstructural development.

4. The most effective methods of refining austenite grains during the rolling process are substantial lowering of the finish-rolling temperature or introducing microalloys to hinder austenite grain growth. Increasing deformations in subsequent passes at elevated temperatures

does not influence the grain size after processing, since the more refined recrystallized grains

have a greater propensity for growth.

5. The final austenite microstructure is shaped in the last four to six passes of multipass rolling;

therefore, the starting grain size after reheating and before rolling has little effect on the final grain size.

8.2.2 Rod Rolling

1. An effect of strain accumulation leading to dynamic recrystallization initiation during the last few finish passes of the rod-rolling process was predicted by mathematical models.

2. Grain growth caused a significant increase in grain size despite substantial grain refinement

that occurred during the last few finish passes. The effect was more pronounced in the

eutectoid steel than in the C-Mn and VT steels.

3. A thermomechanical FEM calculation predicted a substantial increase in the rod's temperature during the last few finish passes. The effect was confirmed by measurements, and it can

be associated with the plastic work.

4. An FEM calculation predicted that more extensive plastic flow would occur in the near- surface area than in the central region of the rod during the last few passes.

69
8.2.3 Rail Rolling

1. An FEM calculation revealed a marked difference in the deformation conditions prevailing in the cross section of the rail during the last few passes.

2. Static recrystallization restores the austenite microstructure during the last few passes of the

rail-rolling process.

3. Grain growth of the recrystallized grains, which is very extensive in the eutectoid steel, determines the final size of the austenite grain in the rail. As a result, large grain sizes

(~90 u.m) are achieved in the rail's head prior to pearlite transformation.

4. Pronounced variations in thickness in the cross section of the rail produce very complicated

temperature patterns on cooling. The patterns may change substantially during the pearlite

transformation, which is connected to the effect of transformation heat.

5. The nonuniformity of deformation and temperature in the workpiece during rolling and

subsequent cooling results in marked differences in microstructural refinement in the cross

section of a rail.

9. Acknowledgments

The authors thank Teddy Bold (Institute of Ferrous Metallurgy, Gliwice, Poland) and

Harry I. McHenry (National Institute of Standards and Technology, Boulder, Colorado) for their

support and encouragement of this project and Janusz Majta (Academy of Mining and Metallurgy, Cracow, Poland) for his help in interpreting the results of the press-compression experiments for low-carbon steel. The research was supported by the United States-Poland Maria

Sklodowska-Curie Joint Fund II.

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72

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other special publications appropriate to this grouping such as wall charts, pocket cards, and

bibliographies.

Applied Mathematics Series—Mathematical tables, manuals, and studies of special interest to physicists,

engineers, chemists, biologists, mathematicians, computer programmers, and others engaged in scientific and technical work.

National Standard Reference Data Series—Provides quantitative data on the physical and chemical

properties of materials, compiled from the world's literature and critically evaluated. Developed under a worldwide program coordinated by NIST under the authority of the National Standard Data Act (Public

Law 90-396). NOTE: The Journal of Physical and Chemical Reference Data (JPCRD) is published bi- monthly for NIST by the American Chemical Society (ACS) and the American Institute of Physics (AIP).

Subscriptions, reprints, and supplements are available from ACS, 1155 Sixteenth St., NW, Washington,

DC 20056.

Building Science Series—Disseminates technical information developed at the Institute on building

materials, components, systems, and whole structures. The series presents research results, test methods, and performance criteria related to the structural and environmental functions and the durability

and safety characteristics of building elements and systems.

Technical Notes—Studies or reports which are complete in themselves but restrictive in their treatment of a subject. Analogous to monographs but not so comprehensive in scope or definitive in treatment of

the subject area. Often serve as a vehicle for final reports of work performed at NIST under the sponsorship of other government agencies.

Voluntary Product Standards—Developed under procedures published by the Department of Commerce

in Part 10, Title 15, of the Code of Federal Regulations. The standards establish nationally recognized

requirements for products, and provide all concerned interests with a basis for common understanding of

the characteristics of the products. NIST administers this program in support of the efforts of privatesector standardizing organizations.

Consumer Information Series—Practical information, based on NIST research and experience, covering

areas of interest to the consumer. Easily understandable language and illustrations provide useful background knowledge for shopping in today's technological marketplace.

Order the above NIST publications from: Superintendent of Documents, Government Printing Office,

Washington, DC 20402.

Order the following NIST publications—FIPS and NISTIRs—from the National Technical Information

Service, Springfield, VA 22161.

Federal Information Processing Standards Publications (FIPS PUB)—Publications in this series collectively constitute the Federal Information Processing Standards Register. The Register serves as the

official source of information in the Federal Government regarding standards issued by NIST pursuant to the Federal Property and Administrative Services Act of 1949 as amended, Public Law 89-306 (79 Stat. 1127), and as implemented by Executive Order 11717 (38 FR 12315, dated May 11, 1973) and Part 6 of

Title 15 CFR (Code of Federal Regulations).

NIST Interagency Reports (NISTIR)—A special series of interim or final reports on work performed by

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