High Temperature Strain of Metals and Alloys, Valim Levitin AuthorCopyright c 2006 WILEY-VCH Verlag GmbH & Co.. KGaA, Weinheim ISBN: 3-527-313389-9 V Contents Introduction 1 1 Macroscopi
Trang 1Valim Levitin
High Temperature Strain
of Metals and Alloys
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Trang 3Valim Levitin
High Temperature Strain
of Metals and Alloys
Physical Fundamentals
Trang 4The Author
Prof Valim Levitin
National Technical University
Zaporozhye, Ukraine
valim.levitin@t-online.de
Cover:
“Blish” turbine
University of Applied Sciences
Gießen-Friedberg,
Department MND, MTU
produced Nevertheless, authors, editors and publisher do not warrant the information contained
in these books, including this book, to be free of errors Readers are advised to keep in mind that statements, data, illustrations, procedural details
or other items may inadvertently be inaccurate.
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applied for
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A catalogue record for this book is available from the British Library.
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Die Deutsche Bibliothek lists this publication in the Deutsche Nationalbibliografie; detailed bibliographic data is available in the Internet at http://dnb.ddb.de
c
2006 WILEY-VCH Verlag GmbH & Co KGaA,
Weinheim
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Printed in the Federal Republic of Germany Printed on acid-free paper
ISBN-13: 978-3-527-31338-9 ISBN-10: 3-527-31338-9
Trang 5High Temperature Strain of Metals and Alloys, Valim Levitin (Author)
Copyright c 2006 WILEY-VCH Verlag GmbH & Co KGaA, Weinheim
ISBN: 3-527-313389-9
V
Contents
Introduction 1
1 Macroscopic Characteristics of Strain of Metallic Materials
at High Temperatures 5
2 In situ X-ray Investigation Technique 13
2.1 Experimental Installation 13
2.2 Measurement Procedure 15
2.3 Measurements of Structural Parameters 17
2.4 Diffraction Electron Microscopy 20
2.5 Amplitude of Atomic Vibrations 21
2.6 Materials under Investigation 23
2.7 Summary 24
3 Structural Parameters in High-Temperature Deformed Metals 25
3.1 Evolution of Structural Parameters 25
3.2 Dislocation Structure 30
3.3 Distances between Dislocations in Sub-boundaries 34
3.4 Sub-boundaries as Dislocation Sources and Obstacles 34
3.5 Dislocations inside Subgrains 35
3.6 Vacancy Loops and Helicoids 39
3.7 Total Combination of Structural Peculiarities
of High-temperature Deformation 40
3.8 Summary 41
4 Physical Mechanism of Strain at High Temperatures 43
4.1 Physical Model and Theory 43
4.2 Velocity of Dislocations 45
4.3 Dislocation Density 49
4.4 Rate of the Steady-State Creep 51
Trang 6VI Contents
4.5 Effect of Alloying: Relationship between Creep Rate
and Mean-Square Atomic Amplitudes 54
4.6 Formation of Jogs 55
4.7 Significance of the Stacking Faults Energy 57
4.8 Stability of Dislocation Sub-boundaries 58
4.9 Scope of the Theory 62
4.10 Summary 64
5 Simulation of the Parameters Evolution 67
5.1 Parameters of the Physical Model 67
5.2 Equations 68
5.2.1 Strain Rate 68
5.2.2 Change in the Dislocation Density 68
5.2.3 The Dislocation Slip Velocity 69
5.2.4 The Dislocation Climb Velocity 69
5.2.5 The Dislocation Spacing in Sub-boundaries 70
5.2.6 Variation of the Subgrain Size 71
5.2.7 System of Differential Equations 71
5.3 Results of Simulation 71
5.4 Density of Dislocations during Stationary Creep 77
5.5 Summary 80
6 High-temperature Deformation of Superalloys 83
6.1 γ Phase in Superalloys 83
6.2 Changes in the Matrix of Alloys during Strain 88
6.3 Interaction of Dislocations and Particles 89
6.4 Creep Rate Length of Dislocation Segments 95
6.5 Mechanism of Strain and the Creep Rate Equation 96
6.6 Composition of theγ Phase and Atomic Vibrations 102
6.7 Influence of the Particle Size and Concentration 104
6.8 The Prediction of Properties 106
6.9 Summary 109
7 Single Crystals of Superalloys 111
7.1 Effect of Orientation on Properties 111
7.2 Deformation at Lower Temperatures 116
7.3 Deformation at Higher Temperatures 124
7.4 On the Composition of Superalloys 129
7.5 Rafting 130
7.6 Effect of Composition and Temperature onγ/γ Misfit 136
7.7 Other Creep Equations 137
7.8 Summary 141
Trang 78 Deformation of Some Refractory Metals 143
8.1 The Creep Behavior 143
8.2 Alloys of Refractory Metals 149
8.3 Summary 155
Supplements 157
Supplement 1: On Dislocations in the Crystal Lattice 157
Supplement 2: On Screw Components in Sub-boundary
Dislocation Networks 161
Supplement 3: Composition of Superalloys 163
References 164
Acknowledgements 168
Index 169
Trang 8High Temperature Strain of Metals and Alloys, Valim Levitin (Author)
Copyright c 2006 WILEY-VCH Verlag GmbH & Co KGaA, Weinheim
ISBN: 3-527-313389-9
1
Introduction
Whoever controls the materials, controls the science and the technology
E Plummer Modern civilization is based on four foundations: materials, energy, tech-nology, and information
Metals and alloys are materials, which have been widely used by mankind for thousands of years, and this is no mere chance: metals have many re-markable properties One – their strength at high temperatures – is of great scientific and practical importance
The durability of gas turbine engines, steam pipelines, reactors, aeroplanes, and aerospace vehicles depends directly on the ability of their parts and units
to withstand changes in shape On the other hand, a significant mobility of crystal lattice defects and of atoms plays an important role in the behavior
of materials under applied stresses at high temperatures and is also of great interest for materials science research and practical applications
Mechanical tests were historically the first method of investigating the high-temperature deformation phenomenon The technique originated from practical needs to use metallic materials for various machines A deep inves-tigation of material structure was impossible in early studies because of the lack of suitable equipment and appropriate techniques Even now mechanical tests are a source of indirect information about physical processes that take place in the atomic crystal lattice of metals and alloys However, if we want
to understand the nature of these processes and to be able to use them in practice we should try to investigate them directly
The phenomena of high-temperature strain and creep have been studied for many years Numerous theories have been developed, based on the de-pendences of the strain rate upon stress and temperature The structure of tested metals was also studied The obtained results are of great value and have been described in books and reviews and important data are also scat-tered in numerous articles Previous investigations improved our knowledge
Trang 92 Introduction
of the problem and stimulated further experimental approaches It is essen-tial, however, to emphasize that the physical nature of the high-temperature strain in metals, especially industrial superalloys, is not yet understood suffi-ciently By this we mean the physical background of the deformation on the atomic microscopic scale
The problem of the high-temperature properties of metallic materials has
a number of experimental, theoretical and applied aspects Naturally, it is necessary to identify the scope of the problem considered in this book
My idea is as follows The high-temperature diffusion mobility of atoms and the effect of applied forces are the conditions under which special processes occur in the crystal lattice of metallic materials Thus, external conditions result in a distinctive structural response of the material In their turn these specific structural changes lead to a definite macroscopic behavior of the mate-rial, especially, to a definite strain rate and to a stress resistance Consequently, structure evolution is the primary stage of response; mechanical behavior is the secondary result The response in the crystal lattice is a cause, while the plastic strain of a metal or an alloy is a consequence The structural evolution
is therefore a key factor, which determines the mechanical properties of the metallic materials at high temperatures
This book treats data from experimental measurements of important struc-tural and kinetic characteristics which are related to physical fundamentals
of the high-temperature strain of metallic materials A number of specific pa-rameters of substructure, which have been directly measured, are presented Theories that have been worked out on the basis of these experiments are quantitative and contain values which have a definite physical meaning A method of calculation of the steady-state strain rate from the material, struc-tural and external parameters is developed for the first time
The book consists of eight chapters
A summary of the problem is presented in the first chapter The peculiar-ities of the strain of metallic materials at high temperatures are described The reader’s attention is drawn to the shortcomings of existing views and the author’s approach to the problem is substantiated It is advisable for the reader to remind himself of the main principles of dislocation theory by first reading Supplement 1
The second chapter is devoted to experimental techniques The unique
equipment developed by the author is intended for the in situ X-ray
investi-gation of various metals, i.e for direct structural measurements during the high-temperature tests The method of transmission diffraction microscopy
is briefly considered The studied metals and alloys are described
Data on measurements of structural parameters are presented in the next chapter Dependences on time of the size and misorientations of the sub-grains are obtained for various metals Attention is given to the dislocation
Trang 10Introduction 3
structure of sub-boundaries that are formed during strain The experimental data concerning dislocations within subgrains are presented and discussed in more detail The totalities of the structural peculiarities of the metals, which have been deformed at high-temperatures, are formulated
In the fourth chapter the physical mechanisms of the high-temperature deformation of pure metals and solid solutions are worked out on the basis of the obtained data The quantitative model of creep is considered and validated Equations are presented for the dislocation velocity and for the dislocation density The physically based forecast of the minimum strain rate is given The subject of the fifth chapter is a computer simulation of the high-temperature deformation processes A system of ordinary differential equa-tions models the phenomenon under study Evolution of structural parame-ters and the effect of external conditions on the parameparame-ters are analyzed High-temperature deformation of the creep-resistant superalloys is the sub-ject of the sixth chapter Structure changes in modern materials and the inter-action between deforming dislocations and particles of the hardening phase are analyzed A physical mechanism of deformation and a strain rate equa-tion are considered Data are presented on the connecequa-tion between mean-square amplitudes of atomic vibrations in the hardening phase and the creep strength
The seventh chapter is devoted to the single-crystal superalloys The effect
of orientation, temperature and stress on the properties of single crystals
is considered The physical mechanisms of the dislocation deformation are described Attention is given to the phenomenon of rafting and to the role of misfit between the crystal lattice parameters of the matrix and of the hardening phase
The subject of the last chapter is the peculiarities of the strain behavior of refractory metals
A detailed review of all aspects of the problem under consideration for pure metals goes beyond the scope of this book Therefore known principles and established facts are mentioned only briefly
The reader can find reviews concerning the creep of metals in different books and articles, for example [1–8]
Trang 11High Temperature Strain of Metals and Alloys, Valim Levitin (Author)
Copyright c 2006 WILEY-VCH Verlag GmbH & Co KGaA, Weinheim
ISBN: 3-527-313389-9
5
1
Macroscopic Characteristics of Strain of Metallic Materials at High Temperatures
The deformation of a metal specimen begins with the application of a load There are two kinds of high-temperature strain, namely, deformation un-der constant stressσ (i.e creep) and deformation under constant strain rate
˙ε Physical distinctions between these two processes are not essential In
this book we shall use the definitions temperature strain” and “high-temperature creep” almost as synonyms
In Fig 1.1 one can see the dependence of strain upon time,ε(t), when the
applied stress remains constant In the general case the curve contains four stages: an incubation, primary, state and tertiary stages The steady-state stage is the most important characteristic for metals, because it takes
up the greater part of the durability of the specimen Correspondingly, the minimum strain rate during the steady-state stage, ˙ε, is an important value
because it determines the lifetime of the specimen The tertiary stage is associ-ated with a proportionality of the creep strain rate and the accumulassoci-ated strain
It is observed to a certain extent in creep resistant materials The tertiary stage
is followed by a rupture
Fig 1.1 The typical curve of creep
Trang 126 1 Macroscopic Characteristics of Strain of Metallic Materials at High Temperatures
Thus, the following stages are observed:
1 The incubation deformation For this stage the strain rate ˙ε = const;
¨ε > 0.
2 The primary stage, during which ˙ε = const; ¨ε < 0 The creep rate
de-creases when the strain inde-creases
3 The steady-state strain The plastic strain rate is a constant value
˙ε = const.
4 The tertiary stage ˙ε = const; ¨ε > 0 The tertiary creep leads to a rupture.
High-temperature strain is a heat-activated process An elementary defor-mation event gets additional energy from local thermal excitation It is gener-ally agreed that above 0.5Tm(Tmis the melting temperature) the activation energy of steady-state deformation is close to the activation energy of self-diffusion The correlation between the observed activation energy of creep,
Qc, and the energy of self-diffusion in the crystal lattice of metals,Qsd, is il-lustrated in Fig 1.2 More than 20 metals show excellent correlation between both values
The measurement of the dependences ˙ε(σ, T ) was the first step in the
in-vestigation of the problem under consideration The functionsσ( ˙ε, T ) and
the rupture life (durability) τ(σ, T ) have also been studied For the
depen-dence of the minimum strain rate ˙ε upon applied stress σ several functions
have been proposed by different authors The explicit function ˙ε(σ, T ) is still
the subject of some controversy The power function, the exponent and the hyperbolic sine have been proposed
The following largely phenomenological relationships between ˙ε, σ and T
are presented in various publications
˙ε = A1exp
− kT Q
˙ε = A2exp
− Q − vσ kT
(1.2)
˙ε = A3exp
− Q kT
sinh ασ kT
(1.3)
whereA1, A2, A3, n, v, α are constant values; Q is the activation energy of the
process;k is the Boltzmann constant and T is temperature.
If we suppose that constantsA1, A2, Q, n, v do not depend upon
tempera-ture then it is easy to obtain
Q = −k
∂ ln ˙ε
∂1
T
σ
(1.4)