Modeling and Simulation for Material Selection and Mechanical Design Part 1 ppsx

Modeling
and
Simulation
for
Material Selection
and Mechanical
Design
edited
by
George
E.
Totten
Lin
Xie
Kiyoshi
Funatani
G.E.
Totten
&
Associates,
LLC
Seattle, Washington,
i7.S.A
Solidworks Corporation
Concord, Massachusetts,
U.S.A
IMST
Institute
Nagoya, Japan
MARCEL
MARCEL DEKKER,

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ENGINEERING
A
Series of Textbooks and Reference Books
Founding Editor
L.
L.
Faulkner
Columbus
Division, Battelle Memorial Institute
and Department
of
Mechanical Engineering
The Ohio State University
Columbus,
Ohio
1.
Spring Designer's Handbook,
Harold Carlson
2.

Computer-Aided Graphics and Design,
Daniel L. Ryan
3.
Lubrication Fundamentals,
J.
George
Wills
4.
Solar Engineering for Domestic Buildings,
William .A. Himmelman
5.
Applied Engineering Mechanics: Statics and Dynamics,
G. Boothroyd and
C. Poli
6.
Centrifugal Pump Clinic,
lgor J. Karassik
7.
Computer-Aided Kinetics for Machine Design,
Daniel
L.
Ryan
8.
Plastics Products Design Handbook, Patf A: Materials and Components; Patf
6: Processes and Design for Processes,
edited by Edward Miller
9.
Turbomachinery: Basic Theory and Applications,
Earl Logan, Jr.
10.

Vibrations of Shells and Plates,
Werner Soedel
1
I.
Flat and Corrugated Diaphragm Design Handbook,
Mario Di Giovanni
12.
Practical Stress Analysis
in
Engineering Design,
Alexander Blake
13.
An lntroduction to the Design and Behavior of Bolted Joints,
John H.
Bickford
14.
Optimal Engineering Design: Principles and Applications,
James
N.
Siddall
15.
Spring Manufacturing Handbook,
Harold Carlson
16.
Industrial Noise Control: Fundamentals and Applications,
edited by Lewis H.
Bell
17.
Gears and Their Vibration: A Basic Approach to Understanding Gear Noise,
J. Derek Smith

18.
Chains for Power Transmission and Material Handling: Design and Appli-
cations Handbook,
American Chain Association
19.
Corrosion and Corrosion Protection Handbook,
edited by Philip A.
Schweitzer
20.
Gear Drive Systems: Design and Application,
Peter Lynwander
2
1
.
Controlling In-Plant Airborne Contaminants: Systems Design and Cal-
culations,
John D. Constance
22.
CAD/CAM Systems Planning and Implementation,
Charles S. Knox
23.
Probabilistic Engineering Design: Principles and Applications,
James
N.
Siddall
24.
Traction Drives: Selection and Application,
Frederick W. Heilich
111
and

Eugene
E.
Shube
25.
Finite Element Methods:
An
Introduction,
Ronald L. Huston and Chris
E.
Passerello
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26.
,
Brayton Lincoln,
and
27.
Lubrication in Practice: Second Edition,
edited by W.
S.
Robertson
28.
Principles of Automated Drafting,
Daniel L. Ryan
29.
Practical Seal Design,
edited by Leonard J. Martini
30.
Engineering Documentation
for
CAD/CA M Applications,

Charles
S.
Knox
31
.
Design Dimensioning with Computer Graphics Applications,
Jerome C.
Lange
32.
Mechanism Analysis: Simplified Graphical and Analytical Techniques,
Lyndon
0.
Barton
33.
CAD/CAM Systems: Justification, Implementation, Productivity Measurement,
Edward
J.
Preston, George W. Crawford, and Mark
E.
Coticchia
34.
Steam Plant Calculations Manual,
V.
Ganapathy
35.
Design Assurance for Engineers and Managers,
John A. Burgess
36.
Heat Transfer Fluids and Systems for Process and Energy Applications,
Jasbir Singh

37.
Potential Flows: Computer Graphic Solutions,
Robert H. Kirchhoff
38.
Computer-Aided Graphics and Design: Second Edition,
Daniel L. Ryan
39.
Electronically Controlled Proportional Valves: Selection and Application,
Michael J. Tonyan, edited by Tobi Goldoftas
40.
Pressure Gauge Handbook,
AMETEK,
U.S.
Gauge Division, edited by Philip
W. Harland
41.
Fabric Filtration for Combustion Sources: Fundamentals and Basic Tech-
nology,
R.
P. Donovan
42.
Design of Mechanical Joints,
Alexander Blake
43.
CAD/CAM Dictionary,
Edward
J.
Preston, George W. Crawford, and Mark
E.
Coticchia

44.
Machinery Adhesives for Locking, Retaining, and Sealing,
Girard
S.
Haviland
45.
Couplings and Joints: Design, Selection, and Application,
Jon
R.
Mancuso
46.
Shaft Alignment Handbook,
John Piotrowski
47.
BASIC Programs
for
Steam Plant Engineers: Boilers, Combustion, Fluid
Flow, and Heat Transfer,
V.
Ganapathy
48.
Solving Mechanical Design Problems with Computer Graphics,
Jerome C.
Lange
49.
Plastics Gearing: Selection and Application,
Clifford
E.
Adams
50.

Clutches and Brakes: Design and Selection,
William C. Orthwein
51.
Transducers in Mechanical and Electronic Design,
Harry L. Trietley
52.
Metallurgical Applications of Shock- Wave and High-Strain-Rate Phenom-
ena,
edited by Lawrence
E.
Murr, Karl P. Staudhammer, and Marc A.
Meyers
53.
Magnesium Products Design,
Robert
S.
Busk
54.
How to Integrate CAD/CAM Systems: Management and Technology,
William
D.
Engelke
55.
Cam Design and Manufacture: Second Edition;
with cam design software
for the IBM PC and compatibles, disk included, Preben W. Jensen
56.
Solid-state AC Motor Controls: Selection and Application,
Sylvester Campbell
57.

Fundamentals
of
Robotics,
David D. Ardayfio
58.
Belt Selection and Application for Engineers,
edited by Wallace D. Erickson
59.
Developing Three-Dimensional CAD Software with the ISM PC,
C.
Stan Wei
60.
Organizing Data for ClM Applications,
Charles
S.
Knox, with contributions
by Thomas C. Boos,
Ross
S.
Culverhouse, and Paul
F.
Muchnicki
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61.
Computer-Aided Simulation in Railway Dynamics,
by Rao
V.
Dukkipati and
62.
fiber-Reinforced Composites: Materials, Manufacturing, and Design,

P. K.
Mallick
63.
Photoelectric Sensors and Controls: Selection and Application,
Scott M.
Juds
64.
finite Element Analysis with Personal Computers,
Edward
R.
Champion,
Jr., and J. Michael Ensminger
65.
Ultrasonics: Fundamentals, Technology, Applications: Second Edition,
Revised and Expanded,
Dale Ensminger
66.
Applied finite Element Modeling: Practical Problem Solving for Engineers,
Jeffrey M. Steele
67.
Measurement and Instrumentation in Engineering: Principles and Basic
Laboratory Experiments,
Francis
S.
Tse and Ivan E. Morse
68.
Centrifugal Pump Clinic: Second Edition, Revised and Expanded,
lgor J.
Karassik
69.

Practical Stress Analysis in Engineering Design: Second Edition, Revised
and Expanded,
Alexander Blake
70.
An Introduction to the Design and Behavior of Bolted Joints: Second
Edition, Revised
and
Expanded,
John H. Bickford
71.
High Vacuum Technology: A Practical Guide,
Marsbed H. Hablanian
72.
Pressure Sensors: Selection and Application,
Duane Tandeske
73.
Zinc Handbook: Properties, Processing, and Use in Design,
Frank Porter
74.
Thermal fatigue
of
Metals,
Andrzej Weronski and Tadeusz Hejwowski
75.
Classical and Modern Mechanisms for Engineers and Inventors,
Preben W.
Jensen
76.
Handbook of Electronic Package Design,
edited by Michael Pecht

77.
Shock- Wave and High-Strain-Rate Phenomena in Materials,
edited by Marc
A. Meyers, Lawrence E. Murr, and Karl
P.
Staudhammer
78.
Industrial Refrigeration: Principles, Design and Applications,
P.
C.
Koelet
79.
Applied Combustion,
Eugene
L.
Keating
80.
Engine Oils and Automotive Lubrication,
edited by Wilfried J. Bartz
8
1
.
Mechanism Analysis: Simplified and Graphical Techniques, Second Edition,
Revised and Expanded,
Lyndon
0.
Barton
82.
fundamental Fluid Mechanics for the Practicing Engineer,
James

W.
Murdock
83. Fiber-Reinforced Composites: Materials, Manufacturing, and Design, Second
Edition, Revised and Expanded,
P. K. Mallick
84.
Numerical Methods for Engineering Applications,
Edward
R.
Champion, Jr.
85.
Turbomachinery: Basic Theory and Applications, Second Edition, Revised
and Expanded,
Earl Logan, Jr.
86.
Vibrations of Shells and Plates: Second Edition, Revised and Expanded,
Werner Soedel
87.
Steam Plant Calculations Manual: Second Edition, Revised and Expanded,
V.
Ganapathy
88.
Industrial Noise Control: Fundamentals and Applications, Second Edition,
Revised and Expanded,
Lewis
H.
Bell and Douglas H. Bell
89.
finite Elements: Their Design and Performance,
Richard H. MacNeal

90.
Mechanical Properties of Polymers and Composites: Second Edition, Re-
vised and Expanded,
Lawrence
E.
Nielsen and Robert F. Landel
91.
Mechanical Wear Prediction and Prevention,
Raymond
G.
Bayer
Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.
92.
Mechanical Power Transmission Components,
edited by David
W.
South
and Jon
R.
Mancuso
94.
Engineering Documentation Control Practices and Procedures,
Ray
E.
Monahan
95.
Refractory Linings Thermomechanical Design and Applications,
Charles A.
Sc hac h t
96.

Geometric Dimensioning and Tolerancing: Applications and Techniques for
Use in Design, Manufacturing, and Inspection,
James D. Meadows
97.
An lntroduction to the Design and Behavior of Bolted Joints: Third Edition,
Revised and Expanded,
John H. Bickford
98.
Shaft Alignment Handbook: Second Edition, Revised and Expanded,
John
Piotrowski
99.
Computer-Aided Design of Polymer-Matrix Composite Structures,
edited by
Suong Van Hoa
100.
Friction Science and Technology,
Peter J. Blau
1
0
1
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lntroduction to Plastics and Composites: Mechanical Properties and Engi-
neering Applications,
Edward Miller
102.
Practical Fracture Mechanics in Design,
Alexander Blake
103.
Pump Characteristics and Applications,

Michael
W.
Volk
104.
Optical Principles and Technology for Engineers,
James
E.
Stewart
105.
Optimizing the Shape of Mechanical Elements and Structures,
A.
A. Seireg
and Jorge Rodriguez
106.
Kinematics and Dynamics of Machinery,
Vladimir Stejskal and Michael
ValaSek
107.
Shaft Seals for Dynamic Applications,
Les Horve
108.
Reliability-Based Mechanical Design,
edited by Thomas A. Cruse
109.
Mechanical Fastening, Joining, and Assembly,
James
A.
Speck
1 10.
Turbomachinery Fluid Dynamics and Heat Transfer,

edited by Chunill Hah
1 1 1.
High-Vacuum Technology: A Practical Guide, Second Edition, Revised and
Expanded,
Marsbed
H.
Hablanian
1 12.
Geometric Dimensioning and Tolerancing: Workbook and Answerbook,
James
D.
Meadows
1
13.
Handbook of Materials Selection for Engineering Applications,
edited by
G.
T.
Murray
114.
Handbook of Thermoplastic Piping System Design,
Thomas Sixsmith and
Reinhard Hanselka
1 15.
Practical Guide to Finite Elements: A Solid Mechanics Approach,
Steven M.
Lepi
1
16.
Applied Computational Fluid Dynamics,

edited by Vijay K. Garg
117.
Fluid Sealing Technology,
Heinz K. Muller and Bernard
S.
Nau
1 18.
Friction and Lubrication in Mechanical Design,
A.
A. Seireg
119.
lnfluence Functions and Matrices,
Yuri
A.
Melnikov
120.
Mechanical Analysis of Electronic Packaging Systems,
Stephen A.
McKeown
1 2 1
.
Couplings and Joints: Design, Selection, and Application, Second Edition,
Revised and Expanded,
Jon
R.
Mancuso
122.
Thermodynamics: Processes and Applications,
Earl Logan, Jr.
123.

Gear Noise and Vibration,
J. Derek Smith
124.
Practical Fluid Mechanics for Engineering Applications,
John J. Bloomer
125.
Handbook of Hydraulic Fluid Technology,
edited by George
E.
Totten
126.
Heat Exchanger Design Handbook,
T. Kuppan
Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.
127.
for Product Sound Quality,
Richard H. Lyon
in
Franklin
E.
Fisher and Joy R.
Fisher
129.
Nickel Alloys,
edited by Ulrich Heubner
1
30.
Rotating Machinery Vibration: Problem Analysis and Troubleshooting,
Maurice L. Adams, Jr.
131.

Formulas for Dynamic Analysis,
Ronald L. Huston and C.
Q.
Liu
132.
Handbook of Machinery Dynamics,
Lynn
L.
Faulkner and Earl Logan, Jr.
133.
Rapid Prototyping Technology: Selection and Application,
Kenneth G.
Cooper
134.
Reciprocating Machinery Dynamics: Design and Analysis,
Abdulla
S.
Rangwala
1 35.
Maintenance Excellence: Optimizing Equipment Life-Cycle Decisions,
edi-
ted by John
D.
Campbell and Andrew K.
S.
Jardine
136.
Practical Guide to Industrial Boiler Systems,
Ralph L. Vandagriff
137.

Lubrication Fundamentals: Second Edition, Revised and Expanded,
D.
M.
Pirro and
A.
A. Wessol
138.
Mechanical Life Cycle Handbook: Good Environmental Design and Manu-
facturing,
edited by Mahendra
S.
Hundal
139.
Micromachining
of
Engineering Materials,
edited by Joseph McGeoug h
140.
Control Strategies
for
Dynamic Systems: Design and Implementation,
John
H. Lumkes, Jr.
141.
Practical Guide to Pressure Vessel Manufacturing,
Sunil Pullarcot
142.
Nondestructive Evaluation: Theory, Techniques, and Applications,
edited by
Peter J. Shull

1 43.
Diesel Engine Engineering: Thermodynamics, Dynamics, Design, and
Control,
Andrei Makartchouk
144.
Handbook of Machine Tool Analysis,
loan D. Marinescu, Constantin Ispas,
and Dan
Boboc
145.
Implementing Concurrent Engineering in Small Companies,
Susan Carlson
Skalak
146.
Practical Guide to the Packaging of Electronics: Thermal and Mechanical
Design and Analysis,
Ali Jamnia
147.
Bearing Design in Machinery: Engineering Tribology and Lubrication,
Avraham Harnoy
148.
Mechanical Reliability Improvement: Probability and Statistics for Experi-
mental Testing,
R.
E.
Little
149.
Industrial Boilers and Heat Recovery Steam Generators: Design, Ap-
plications, and Calculations,
V.

Ganapathy
150.
The CAD Guidebook: A Basic Manual for Understanding and Improving
Computer-Aided Design,
Stephen J. Schoonmaker
151.
Industrial Noise Control and Acoustics,
Randall
F.
Barron
1
52.
Mechanical Properties of Engineered Materials,
Wole Soboyejo
153.
Reliability Verification, Testing, and Analysis in Engineering Design,
Gary
S.
Wasserman
154.
Fundamental Mechanics of Fluids: Third Edition,
I.
G. Currie
155.
Intermediate Heat Transfer,
Kau-Fui Vincent Wong
156.
HVAC Water Chillers and Cooling Towers: Fundamentals, Application, and
Operation,
Herbert W. Stanford

Ill
157.
Gear Noise and Vibration: Second Edition, Revised and Expanded,
J.
Derek Smith
Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.
158.
Handbook of Turbomachinery: Second Edition, Revised and Expanded,
Earl Logan, Jr., and Ramendra Roy
1
59.
Piping and Pipeline Engineering: Design, Construction, Maintenance, lnteg-
rity, and Repair, George A. Antaki
160.
Turbomachinery: Design and Theory, Rama
S.
R. Gorla and Aijaz Ahmed
Khan
161.
Target Costing: Market-Driven Product Design, M. Bradford Clifton, Henry
M.
B. Bird, Robert
E.
Albano, and Wesley
P.
Townsend
162.
Fluidized Bed Combustion, Simeon
N.
Oka

1
63.
Theory of Dimensioning: An lntroduction to Parameterizing Geometric
Models, Vijay Srinivasan
164.
Handbook
of
Mechanical Alloy Design, George
E.
Totten, Lin Xie, and
Kiyoshi Funatani
165.
Structural Analysis of Polymeric Composite Materials, Mark E. Tuttle
166.
Modeling and Simulation for Material Selection and Mechanical Design,
George
E.
Totten, Lin Xie, and Kiyoshi Funatani
Additional Volumes in Preparation
Handbook of Pneumatic Conveying Engineering, David Mills, Mark G.
Jones, and Vijay K. Agarwal
Mechanical Wear Fundamentals and Testing: Second Edition, Revised and
Expanded, Raymond G. Bayer
Engineering Design for Wear: Second Edition, Revised and Expanded,
Raymond
G.
Bayer
Clutches and Brakes: Design and Selection, Second Edition, William C.
Orthwein
Progressing Cavity Pumps, Downhole Pumps, and Mudmotors, Lev Neli k

Mechanical Engineering Sofmare
Spring Design with an IBM PC, Al Dietrich
Mechanical Design Failure Analysis: With Failure Analysis System Software
for the IBM PC, David G. Ullman
Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.
In Memoriam
During the preparation of this book, one of our most valued authors and
mentors passed away on April 29, 2003. Professor George C. Weatherly
(1941–2003) graduated from Cambridge University in 1966. He began his
career as a research scientist in the Department of Metallurgy at Harwel l.
In 1968 he moved to Canada where he worked for the University of
Toronto for 22 years as a professor in the Department of Metallurgy and
Material Science. In 1990 he became a professor of Materials Science and
Engineering at McMaster University. He was Director of Brockhouse
Institute for Material Research from 1996–2001 and a Chair of the
Department of Materials Science and Engineering. Dr. Weatherly has
published over 200 pap ers in different areas of Materials Science. He was
Fellow for the Canadian Institute for Mining and Metallurgy and Fellow
of ASM International. George was a devoted scientist in the field of electron
microscopy and an educator with a distinguished career at McMaster
University and the University of Toronto. He will be cherished by his
friends, colleagues, and students for the richness of his life, his quiet humor,
his humanity and care for others, and above all for his unfailing honesty.
His contributions were many and are written clearly in the lives of those
with whom he taught and worked. This book is dedicated to his memory.
Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.
Preface
In every industry survey, development and use modeling, an d simulation
technology are cited among the top five critical needs for manufacturing
industries to remain viable and competitive in the future. This is particularly

true for materials and component design. To address this need, various
research programs are currently underway in government, academic, and
industry laboratories around the world. This book addresses a number of
selected, important areas of computer model development.
Effective material and component design procedures are vitally impor-
tant with increasing pressures to improve quality at lower production costs
for all traditional industrial markets. Advanced design procedures typically
involve computer modeling and simulation if the necessary algorithms are
sufficiently advanced or by using advanc ed empirical procedures. The objec-
tive is to be able to make design decisions based on numerical simulations as
an alternative to time-consuming and expensive laboratory or production
experimental process development. In fact, advanced engineering processes
are becoming increasingly dependent on advanced computer modeling and
design procedures.
This book addresses various aspects of the utilization of modeling and
simulation technology. Some of the top ics discussed include hot-rolling of
steel, quenching and tempering during heat treatment, modeling of residual
stresses and distortion during forging, casting, heat treatment, mechanical
property prediction, modeling of tribologic al processes as it relates to the
design of surface engineered materials, and fastener design. These chapters
summarize and demonstrate key numerical relationships used in computer
Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.
model development and their application at various stages in the material
production process.
In particular, the material covered in this text includes:
 Modeling and simulation of microstructural evolution and
mechanical properties of steels during the hot-rolling process,
calculation of metallurgical phenomena occurring in steel during
hot-rolling, and prediction of mechanical properties from micro-
structure.

 Heat treatment processes such as quenching and tempering is an
active area for process model development. Models used to
simulate the kinetics of multicomponent grain boundary seg-
regations that occur in quenched and tempered engineering
steels are discussed. These models permit the evaluation of the
effect of alloying elements and various tempering pa rameters on
hydrogen embrittlement, stress-corrosion cracking, an d other
phenomenon.
 Of all the various problems associated with component design and
production, none are more important that residual stress and
distortion. Chapter 3 discusses the metallo-ther mo-mechanical
theory, numerical modeling and simulation technology, coupling
of temperature, inelastic behavior and phase transformation and
solidification involved with elastic-plastic, viscoplastic and creep
deformation as they relate to quenching, forging, and casting
processes.
 Modeling and simulation of mechanical properties, in particular,
material behavior during plastic deformation, low-cycle fatigue,
creep, and impact strength. This discussion includes the impor-
tance of the determination and implementation of adequate mate-
rial data, consideration of inelastic material behavior, and the
formulation of physically founded material models.
 Chapter 5 discusses the role played by physico-chemical interac-
tions in modifying and controlling friction and wear of critically
loaded tribo-couple surfaces during high-speed cutting operations.
 A comprehensive overview of one of the most important processes
in manufacturing is presented in Chapter 6. Threaded fastener
selection and design is addressed with many equations and figures
included to aid in the design process.
Chapters 1 through 4 describe advanced computer modeling and

simulation processes to predict microstructures, material process behavior,
and mechanical properties. Chapters 5 and 6 describe more empirical
process design procedures for tribological and fastener design.
Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.
This book will be an invaluable resource for the designer, mechanical
and materials engineer, and metallurgist. Thor ough overviews of these
technologies seldom encountered in other handbooks for materials design
are provided. The book is an excellent textbook for advanced undergraduate
or graduate engineering courses on the role of modeling and simulation in
materials and component design.
We are indebted to the vital assistance of various international experts.
Special thanks to our spouses for their infinite patience with the various
time-consuming tasks involved in putting this text together. We extend
special thanks to the staff at Marcel Dekker, Inc. including Richard
Johnson, Rita Lazazzaro, and Russell Dekker for their invaluable
assistance. Without their assistance, this text would not have been possible.
George E. Totten
Lin Xie
Kiyoshi Funatani
Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.
Contents
Preface
Contributors
1 A Mathematical Model for Predicting Microstructural
Evolution and Mechanical Properties of Hot-Rolled Steels
Masayoshi Suehiro
2 Design Simulation of Kinetics of Multicomponent
Grain Boundary Segregations in the Engineering Steels
Under Quenching and Tempering
Anatoli Kovalev and Dmitry L. Wainstein

3 Designing for Control of Residual Stress
and Distortion
Dong-Ying Ju
4 Modeling and Simulation of Mechanical Behavior
Essam El-Magd
5 Tribology and the Design of Surface-Engineered
Materials for Cutting Tool Applications
German Fox-Rabinovich, George C. Weatherly,
and Anatoli Kovalev
Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.
6 Designing Fastening Systems
Christoph Friedrich
Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.
1
A Mathematical Model for
Predicting Microstructural
Evolution and Mechanical
Properties of Hot-Rolled Steels
Masayoshi Suehiro
Nippon Steel Corporation, Futtsu-City, Chiba, Japan
I. INTRODUCTION
A model for calculating the mechanical properties of hot-rolled steel
sheets from their processing condition makes it possible not only to
design chemical compositions and processing conditions of steels through
off-line simulation but also to guarantee the mechanical properties of
hot-rolled steels through on-line simulation. From this point of view,
some attempts have been made to develop a mathematical model for
calculating the evolution of austenitic microstructure of steels during
hot-rolling process and their transformations during cooling subsequent
to hot-rolling [1–3]. The mathematical models basically consist of four

models for calculating metallurgical phenomena occurring in hot-strip
mill and a model for predicting mechanical properties from the micro-
structure of steel calculated by the metallurgical models. In this
chapter, the basic idea and several applications of the mathematical
model will be presented.
Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.
II. THE OVERALL MODEL
Since mechanical properties of hot-rolled steels are determined by their
microstructure, a model for calculating the mechanical properties of
hot-rolled steels is composed of two kinds of models: one for calculating
microstructure of steels from their processing conditions, and the other
for calculating their mechanical properties from their microstructure. There
are several kinds of hot-rolled steel products: sheet and coil, plate, beam,
wire, rod, bar, etc. Although the processing conditions are dependent upon
each process, each product is produced through the processes such as heat-
ing, hot-working, and cooling.
Figure 1 shows the schematic illustration of a hot-strip mill. Hot-rolled
steel sheets are produced through slab reheating, rough hot-rolling, finish
hot-rolling, cooling, and coiling. Table 1 shows the typical thickness and
temperature changes in this process and the metallurgical phenomena occur-
ring through this process. In the slab-reheating process, transformation
from ferrite and pearlite to austenite and grain growth take place. The
Figure 1 Schematic illustration of a hot-strip mill.
Table 1 The Changes in Thickness and Temperature of Steels
and Metallurgical Phenomena in a Hot-Strip Mill
Process
Thickness
(mm)
Temperature
(8C) Metallurgical phenomena

Slab
reheating
250 1200 Transformation, grain growth,
dissolution, and precipitation of
precipitates
Rough
rolling
!40 1200–1000 Recovery, recrystallization,
grain growth, precipitation
Finish
rolling
!3 1000–850 Recovery, recrystallization,
grain growth, precipitation
Cooling 3 — Transformation, precipitation
Coiling 3 600–700 Precipitation
Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.
recovery and recrystallization, and grain growth of austenitic microstructure
occur during and after rough and finish hot-rolling and the transformation
from austenite to ferrite, pearlite, bainite, and martensite takes place during
cooling and coiling. In the case where steels include alloying elements that
form carbides or nitrides, precipitation of such carbides and nitrides takes
place and affects recovery, recrystallization, and grain growth in each pro-
cess. Accordingly, in order to calculate the microstructural evolution of
hot-rolled steels, the model used to calculate recovery, recrystallization,
grain growth during and after hot deformation, transformation kinetics dur-
ing cooling and precipitation kinetics in each process is shown in Fig. 2.
III. BASIC KINETIC EQUATION
In recrystallization and transformation, a new phase forms and grows.
These new phases continue to grow until they meet each other and stop
growing. This situation is called hard impingement and can be expressed

by using the Avrami type equation (4a,4b,4c)
X ¼ 1 expðkt
n
Þð1Þ
or the Johnson–Mehl equation (5). In these equations, the concept of
extended volume fraction is adopted. By using this concept, the hard impin-
gement can be taken into consideration indirectly. The extended volume
Figure 2 The structure of the model for calculating microstructural evolution and
mechanical properties of hot-rolled steels.
Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.
fraction is the sum of the volume fraction of all new phases without direct
consideration of the hard impingement between new particles and is related
to the actual volume fraction by
X ¼ 1 expðX
e
Þð2Þ
where X is the actual volume fraction and X
e
is the extended volume
fraction.
The general form of the equation was developed by Cahn [6]. A brief
explanation is presented here. The nucleation sites of new phases would be
grain boundaries, grain edges, and = or grain corners. In the case of grain
boundary nucleation, the volume fraction of a new phase after some time
can be expressed as follows. Cahn considered the situation illustrated in
Fig. 3 and calculated the volume of the semicircle.
In his calculation, firstly, the area at the distance of y from the nuclea-
tion site B is calculated. The summation of this area for all nuclei gives the
total extended area. From this value, the actual area can be calculated. The
extended volume can be obtained by integrating the area for all distances.

Finally, the actual volume fraction can be derived.
Figure 3 Schematic illustration of the situation of new phase at time t which
nucleates at time t at grain boundary B.
Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.
The area of the section at a plane A for a semicircle nucleated at a
plane B is considered. The radius r at time t can be expressed as
r ¼½G
2
ðt  tÞ
2
 y
2

1=2
for y < Gðt tÞ
r ¼ 0 for y  Gðt tÞð3Þ
where G is the growth rate of new phase and t is the time when the new phase
nucleates at plane B. In this calculation, the grow th rate is assumed to be con-
stant. From this radius, the extended area fraction dY
e
for the new phases
nucleated at time between t and t þ dt can be obtained as
dY
e
¼ pI
s
dt½G
2
ðt  tÞ
2

 y
2
 for y < Gðt tÞ
dY
e
¼ 0 for y > Gðt  tÞð4Þ
where I
s
is the nucleation rate at unit area. By integrating for the time t from
0tot, the extended area fraction at the plane A at time t can be obtained as
Y
e
¼
Z
t
0
dY
e
¼ pI
s
Z
ty=G
0
½G
2
ðt  tÞ
2
 y
2
dt ð5Þ

By exchanging y=Gt for x, this equation leads to
Y
e
¼ pI
s
G
2
t
3
1  x
3
3
 x
2
ð1  xÞ

for x < 1
Y
e
¼ 0 for x > 1 ð6Þ
The actual area fraction of new phases at plane A, Y can be calculated using
Y
e
from
Y ¼ 1 expðY
e
Þð7Þ
The integration of Y for y from 0 to infinity gives the volume of new phases
nucleated at unit area of plane B,V
0

,as
V
0
¼ 2
Z
1
0
Y dy ¼ 2Gt
Z
1
0
1  exp pI
s
G
2
t
3
1 x
3
3
 x
2
ð1  xÞ

dx
ð8Þ
Multiplying V
0
by the area of nucleation site, the extended volume fraction
is obtained as

X
e
¼ SV
0
¼ b
1=3
s
f
s
ða
s
Þð9Þ
Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.
where
a
s
¼ðI
s
G
2
Þ
1=3
t; b
s
¼
I
s
8S
3
G

¼
N
s
8S
4
G
f
s
ða
s
Þ¼a
s
Z
1
0
1  exp pa
3
s
1  x
3
3
 x
2
ð1  xÞ

dx ð10Þ
and N
s
the nucleation rate for unit volume. The actual volume fraction X is
expressed as

X ¼ 1 expðb
1=3
s
f
s
ða
s
ÞÞ ð11Þ
From this equation, two extreme cases can be considered. One is the case
where a
s
is very small and the other is extremely large. For these two cases,
the equation becomes
X ¼ 1 expðp=3N
s
G
3
t
4
Þ a
s
51 ð12Þ
X ¼ 1 ð2SGtÞ a
s
41 ð13Þ
Equation (12) is the same as the one obtained for the case of random nuclea-
tion sites by Johnson–Mehl. This equation implies that the increase in the
volume of new phases is caused by nucleation and growth. On the other
hand, Eq. (13) does not include nucleation rate and it implies that the
nucleation sites are covered by new phases and the increase in the volume

is dependent only on the growth of new phases. This situation is referred
to as site saturation [6].
Cahn did this type of formulation for the cases of grain edge and grain
corner nucleations. Table 2 shows all the extreme cases. For all cases, the
increase of the volume of new phases for the case of small a
s
conforms to
the case of nucleation and growth and site saturation for the case of large
a
s
The value of a
s
increases when the nucleation rate is small when compared
to the growth rate. The early stage of reaction corresponds to small a
s
and
Table 2 The Kinetic Equations Depending on the Modes and the
Nucleation Sites of Reaction in Accordance with Cahn’s Treatment
Nucleation site Nucleation and growth Site saturation
Grain boundary X ¼ 1 expðp=3
_
NNG
3
t
4
Þ X ¼ 1  expð2SGtÞ
Grain edge X ¼ 1  expðpLG
2
t
2

Þ
Grain corner X ¼ 1 expðð4p=3ÞCG
3
t
3
Þ
Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.
the latter stage corresponds to large a
s
. From Table 2, we can recognize
that the exponent of time depends on the mode of reaction and the type
of nucleation site for the case of site saturation. A comparison of this
information with the experimental results gives useful information on the
mode of reaction and the nucleation site. The equations in Table 2 can
be used for calculating actual reactions such as transformation and
recrystallization by introducing fitting parameters obtained from
experiments [7].
IV. UTILIZATION OF THERMODYNAMICS FOR THE
CALCULATION OF TRANSFORMATION AND
PRECIPITATION KINETICS
As transformation and precipitation kinetics are closely related to phase
equilibrium, thermodynamics can be utilized for their calculation. In this
section, the method for utilizing thermodynamics for the calculation will
be explained.
For the consideration of kinetics, the Gibbs free-energy–composition
diagram is much more useful and should be the basis. Figure 4 sho ws the
Gibbs free-energy–composition diagram for austenite and ferrite in steels.
Chemical composition at the phase interface between ferrite and austenite
is obtained from the common tangent for free-energy curves of ferrite and
austenite. The common tangent can be calculated under the condition that

chemical potentials of all chemical elements in ferrite are equa l to those in
austenite. This condition is expressed as
m
a
i
¼ m
g
i
ð14Þ
where m is the chemical potential, the suffix i represents all elements in the
system and a and g indicate ferrite and austenite, respectively. In Fig. 4,
the driving force for transformation from austenite to ferrite, DG
m
, is indi-
cated as well. It can be calculated by
DG
m
¼
X
x
a
i
m
g
i
 m
a
i

ð15Þ

where x is the fractions of elements. These values are necessary for the cal-
culation of mo ving rate of the interface during transformation and precipi-
tation. The Zener–Hillert equation [8,9], which represents the growth rate of
ferrite into austenite, is expressed as
G ¼
1
2r
D
C
ga
 C
g
C
g
 C
a
ð16Þ
Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.
V. BASIC MODELS
A. The Concept of the Model
As mentioned above, the overall model for predicting mechanical properties
of hot-rolled steels consists of several basic models: the initial state model
for austenite grain size before hot-rolling, the hot-deformation model for
austenitic microstructural evolution during and after hot-rolling, the trans-
formation model for transformation during cooling subsequent to hot-roll-
ing, and the relation between mechanical properties and microstructure of
steels. In the case where steels include alloying elements which form precipi-
tates, the model for precipitation is necessary. Precipitates affect all the
models mentioned here. In this section, these basic models will be explained
[14,15].

B. Initial State Model
In this model, austenite grain sizes after slab reheating, namely before hot
deformation, are calculated from the slab-reheating condition. In steels con-
sisting of ferrite and pearlite at room temperature, austenite is formed
between pearlite and ferrite and it grows into ferrite according to decompo-
sition of pearlite. After all the microstructures become austenite, the grain
growth of austenite takes place. We should form ulate these metallurgical
phenomena to predict austenite grain size after slab reheating. In hot-strip
mill, however, the effect of initial austenite grain size on the final austenite
grain size after multi-pass hot deformation is small. This can be due to the
high total reduction in thickness by several hot-rolling steps in which the
recrystallization and grain growth are repeated and the size of austenite
grain becomes fine. This means that the high accuracy is not required for
the prediction of the initial austenite grain size in a hot-strip mill. From this
point of view, the next equation (14) can be applied
d
g
¼ exp 1:61 ln K þ
ffiffiffiffiffiffiffiffiffiffiffiffiffiffi
K
2
þ 1
p

þ 5
no
K ¼ðT  1413Þ=100 ð18Þ
where d
g
is the austenite grain size after reheating of slab and T is the tem-

perature in K.
On the other hand, the initial austenite grain size affects the final
austenite grain size in the case of plate rolling because the total thickness
reduction is relatively small compared to hot-strip rolling. In this case, the
high accuracy of the prediction may be required and the model that is
applicable for this case has been reported [16]. Thr ee steps are considered
in this model: (1) the growth of austenite between cementite and ferrite
according to the dissolution of cementite, (2) the growth of austenite into
Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.
ferrite at a þg two-phase region, and (3) the growth of austenite in the g
single-phase region. The pinning effect by fine precipitates on grain growth
and that of Ostwald ripening of precipitates on the grain growth of auste-
nite are taken into consideration. This model is briefly explained in the fol-
lowing paragra phs.
The growth of austenite due to the dissolution of cementites can be
expressed as
dðd
g
Þ
dt
¼
D
g
c
d
g
C
yg
 C
ga

C
ga
 C
a
ð19Þ
where t is the time, D
g
c
the diffusion constant of C in austenite, and C
g
,C
ga
are the C content in austenite at g=y phase interface and g=a phase interface,
respectively. In the a þ g two-phase region, the austeni te grain size depends
on the volume fraction of austenite, X
g
, which changes according to tem-
perature. This situation is expressed as
d
g
¼
3X
g
4pn
0

1=3
ð20Þ
where n
0

is the number of austenite grains at a unit volume when cementites
are dissolved. Grain growth occurs in the austenite single-phase region. For
grain growth, it is necessary to consider three cases; without precipitates,
with precipitates, and with precipitates growing due to the Ostwald ripening.
There are equations which are formulated to theoretically correspond to
these three cases. They are summarized by Nishizawa [17]. The equation
for the normal grain growth is expressed as
d
2
g
 d
2
g0
¼ k
2
t ð21Þ
where k
2
is the factor related to the diffusion coefficient inside the interface,
the interfacial energy, and the mobility of the interface. With the pinning
effect by precipitates, the growth rate becomes
dðd
g
Þ
dt
¼ M
2sV
R
 DG
pin


; DG
pin
¼
3sVf
2r
ð22Þ
where f is the volume fraction of precipitates and r is the average size of
precipitates. When precipitates grow according to the Ostwald ripening,
the average size of precipitates used in the Eq. (22) is obtained from
r
3
 r
3
0
¼ k
3
t ð23Þ
where k
3
is the factor related to temperature, interfacial energy and the dif-
fusion coefficient of an alloying element controlling the Ostwald ripening of
Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.
precipitates. By this calculation method, it is possible to predict the growth
of austenite grain during heating when precipitates such as AlN, NbC, TiC,
and TiN exist in austenite [16].
C. Hot-Deformation Model
The hot-deformation model is required to predict the austenitic microstr uc-
ture before transformation through recovery, recrystallization, and grain
growth in austeni tic phase region during and after multi-pass hot deforma-

tion. Sellars and Whiteman [18,19] made the first attempt on this issue and
then several researchers [20–27] developed models to calculate recovery,
recrystallization, and grain growth. These models are basically similar to
each other. In some models, dynamic recovery and dynamic recrystallization
are taken into consideration. The dynamic recovery and recrystallization are
likely to occur when the reduction is high for single-pass rolling or strain is
accumulated due to multi-pass rolling. They should be taken into considera-
tion in finishing rolling stands of a hot-strip mill because, the inter-pass time
might be less than 1 sec and the accumul ation of strain might take place.
Here, the hot-deformation model will be explained based on the model
developed by Senuma et al. [20].
In this model, dynamic recovery and recrystallization, static recovery
and recrystallization, and grain growth after recrystallization are calculated
as shown in Fig. 5. The critical strain, e
c
, at which dynamic recrystallization
occurs is generally dependent upon strain rate, temperature, and the size of
austenite grains. The effect of strain rate on e
c
is remarkable at low strain
rate region [28]. One of the controversial issues had been whether the
dynamic recrystallization took place or not when the strain rate is high such
as that in a hot-strip mill. Senuma et al. [20] showed that it takes place and
the effect of strain rate on e
c
is small at a high strain rate.
The fraction dynamically recrystallized, X
dyn
, and can be expressed
based on the Avrami type equation as

X
dyn
¼ 1  exp 0:693
e  e
c
e
0:5

2
!
ð24Þ
where e
0.5
is the strain at which the fraction dynamically recrystallized
reaches 50%. On the other hand, the fraction statically recrystallized can
be expressed as
X
dyn
¼ 1  exp 0:693
t  t
0
t
0:5

2
!
ð25Þ
Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.
calculated from the average dislocation density which is obtained by calcu-
lating the changes in the dislocation density in the region dynamically recov-

ered, r
n
, and in the region recrystallized dynamically, r
s
, according to time
independently.
This method makes it possible to calculate the changes in grain size
and dislocation density. Table 3 sho ws the summary of equations used in
the model developed by Senuma et al. The numbers of phenomena in
Table 3 correspond to those in Fig. 5. Figure 6 shows an example of calcu-
lation of the changes in grain size and dislocation density [14]. Figure 7
shows the calculation result of the effect of the initial austenite grain size
on the final micr ostructure in the finishing stands of a hot-strip mill, which
shows that the initial austenite grain size does not affect very much the final
grain size. This model can be applied to the prediction of the resistance to
hot deformation as well and it can contribu te to the improvement of the
accuracy in thickness. In this method, the average values concerning the
grain size and the accumulated dislocation density are used taking the frac-
tion recrystallized into consideration. This averaging can be applied to the
hot-strip mill because the total thickness reduction is large enough to recrys-
tallize their microstructure. In the case of plate rolling, the use of the average
values is unsuitable because the reduction at each pass is small and the total
thickness reduction is not enough to recrystallize the microstructure of
steels. The model applicable to this case has been developed by dividing
the microstructure into several groups [26].
This type of modeling was carried out for Nb-bearing steels [19,21,25],
Ti- and V-bearing steels [21], Ti- and Nb-bearing steels [22], Ti-, Nb-, and V-
bearing steels [27] as well as C–Mn steels. In these steels, the recovery and
recrystallization are retarded by alloying elements. This retardation might
be caused by the pinning effect due to fine precipitates or by the solute-drag

effect. This effect can be considered by modifying the values of fitting para-
meters from experimental data.
D. Transformation Model
1. Basic Idea of the Modeling
In the cooling process subsequent to hot-rolling, steels transform from
austenite phase to ferrite, pearlite, bainite, and=or martensite phases. Trans-
formation model predicts the micr ostructural change during cooling and the
final microstructure of steels after cooling. The modeling of transformation
kinetics can be performed by obtaining the parameters k and n in Avrami
equation [29–31], formulating new equations corresponding to transforma-
tion kinetics obtained experimentally [32], and adopting the nucleation and
growth theory [33–36].
Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.