Mechanical Behaviour of Engineering Materials: Metals, Ceramics, Polymers, and Composites

539 Pages·2007·13.92 MB·English

by  Joachim Rösler

Mechanical BehaviourofEngineeringMaterials
· ·
J. Rösler H. Harders M. Bäker
Mechanical Behaviour
of Engineering Materials
Metals, Ceramics, Polymers, and Composites
With320 Figuresand 32 Tables
Prof.Dr.JoachimRösler Dr.-Ing.HaraldHarders
TUBraunschweig Gartenstraße28
InstitutfürWerkstoffe 45468Mülheim
LangerKamp8 Germany
38106Braunschweig,Germany [e-mail]
[e-mail]
Priv.-Doz.Dr.MartinBäker
TUBraunschweig
InstitutfürWerkstoffe
LangerKamp8
38106Braunschweig,Germany
[e-mail]
GermaneditionpublishedbytheTeubnerVerlagWiesbaden,2006,ISBN978-3-8351-0008-4
LibraryofCongressControlNumber:2007933503
ISBN978-3-540-73446-8 SpringerBerlinHeidelbergNewYork
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By the authors
Prof. Dr. rer.nat. Joachim Rösler, born in 1959, studied materials sci-
enceattheUniversityStuttgart,Germany,from1979to1985.Afterearninga
Ph.D. at the Max-Planck Institute for Metals Research, Stuttgart, Germany,
and a post-doctoral fellowship at the University of California, Santa Barbara,
usa, he worked at Asea Brown Boveri ag, Switzerland, from 1991 to 1996,
being finally responsible for the material laboratory of abb Power Genera-
tionLtd.,Switzerland.Since1996,hehasbeenprofessorformaterialsscience
and director of the Institute for Materials Science at the Technical University
Braunschweig, Germany. His main research interest lies in high-temperature
materials, the mechanical behaviour of materials, and in materials develop-
ment.
Dr.-Ing.HaraldHarders,bornin1972,studiedmechanicalengineering,
with a focus one mechanics and materials, at the Technical University Braun-
schweig, Germany. In 1999, he worked as research scientist at the German
AerospaceCenter(dlr).From1999to2004,heworkedasresearchscientistat
the Institute for Materials Science at the Technical University Braunschweig,
finishingwithaPh.D.thesis(2005)onfatigueofmetalfoams.Since2004, he has
been working in the field of life time prediction and modelling of superalloys
and coating systems at Siemens Power Generation in Mülheim an der Ruhr,
Germany.
Priv.-Doz. Dr. rer.nat. Martin Bäker, born in 1966, studied physics
at the University Hamburg, Germany, from 1987 to 1993 and finished his
Ph.D. at the II. Institute for Theoretical Physics of the University Hamburg
in 1995, where he also worked as Post-Doc for a year. Since 1996, he has
been working as research scientist at the Institute for Materials Science at
the Technical University Braunschweig, Germany, focusing on continuum me-
chanicssimulationofmaterials.In2004,hefinishedhis‘habilitation’(lecturer
qualification) in the field of materials science.
Preface
Components used in mechanical engineering usually have to bear high me-
chanicalloads.Itis, thus,ofconsiderableimportance for students ofmechan-
ical engineering and materials science to thoroughly study the mechanical
behaviourofmaterials.Therearedifferentapproachestothissubject:Theen-
gineer is mainly interested in design rules to dimension components, whereas
materials science usually focuses on the physical processes in the material
occurring during mechanical loading. Ultimately, however, both aspects are
important in practice. Without a clear understanding of the mechanisms of
deformationinthematerial,theengineermightuncriticallyapplydesignrules
andthuscause‘unexpected’failureofcomponents.Ontheotherhand,allthe-
oretical knowledge is practically useless if the gap to practical application is
not closed.
Our objective in writing this book is to help in solving this problem. For
this reason, the topics covered range from the treatment of the mechanisms
of deformation under mechanical loads to the engineering practice in dimen-
sioningcomponents.To meet the needs ofmodernengineering,whichis more
thanevercharacterisedbytheuseofallclassesofmaterials,wealsoneededto
discussthepeculiaritiesofmetals,ceramics,polymers,andcomposites.Thisis
reflected in the structure of the book.On the one hand, there are some chap-
ters dealingwiththe differenttypes ofmechanicalloadingcommontoseveral
classes of materials (Chapter 2, elastic behaviour; Chapter 3, plasticity and
failure; Chapter 4, notches; Chapter 5, fracture mechanics; Chapter 10, fa-
tigue; Chapter 11, creep). The specifics of the mechanical behaviour of the
differentmaterialclassesthatare due to their structure andthe resulting mi-
crostructural processes are treated in separate chapters (Chapter 6, metals;
Chapter 7, ceramics; Chapter 8, polymers; Chapter 9, composites).
In this book, we thus aim to comprehensively cover the mechanical be-
haviourofmaterials.Itaddressesstudentsofmechanicalengineeringandma-
terialsscienceaswellaspractisingengineersworkingonthedesignofcompo-
nents. Although the book contains an in-depth treatment of the mechanical
behaviour and is thus not to be considered as an introduction, all topics can
VIII Preface
be understoodwithout muchpreviousknowledgeofmaterialphysics andme-
chanics. To make it more accessible, the book starts with an introductory
chapter on the structure of materials and contains appendices on tensors,
crystal orientation, and thermodynamics.
Inmanycases,wethoughtitdesirabletocoversometopicsingreaterdepth
forthosereaderswithaspecialinterestinthesubjectmatter.Thesesections
canbeskippedwithoutcompromisingtheunderstandingofothersubjects.
These advanced sections are indented, as here, or, in the case of longer
sections, marked with a ∗ on thesection number.
Attheendofthemainpart,thereadercanfindsomeexerciseswithcomplete
solutions.Theyserveasnumericalexamplesforthe topicscoveredinthe text
and enable the reader to check their understanding of the subject.
This book has evolved from lectures at the Technical University of
Braunschweig on the mechanical behaviour of materials, aimed at graduate
students, and was first published in German by the Teubner Verlag, Wies-
baden. Due to its success and many encouraging remarks from readers, it
seemed worthwhile to prepare an English edition of the book. In doing so,
the nomenclature and some of the references were adapted to improve the
usability of the book for English readers.
We wish to thank Gu¨nter Lange who provided valuable help in prepar-
ing this book.Furthermore,we want to thank Ju¨rgenHuber (CeramTec ag),
Dr. Peter Neumann (Max-Planck-Institut fu¨r Eisenforschung GmbH), Volker
Saß (ThyssenKrupp Nirosta GmbH), Johannes Stoiber (Allianz-Zentrum fu¨r
Technik GmbH), the Lufthansa Technik ag, the Institut fu¨r Werkstofftech-
nik of the Universita¨t Gh Kassel, the Institut fu¨r Fu¨ge- und Schweißtechnik
of the Technische Universita¨t Braunschweig, the Institut fu¨r Baustoffe, Mas-
sivbau und Brandschutz of the Technische Universita¨t Braunschweig,and all
members of the Institut fu¨r Werkstoffe. Steffen Mu¨ller has made a signifi-
cantcontributionto the lecture notes that werethe starting pointfor writing
this book. Furthermore, we want to thank Allister James and Gary Merrill
who proofread parts of the manuscript. We are also indebted to many read-
ers who sent book evaluations to the Teubner Verlag that have been helpful
in preparing the second German edition [123]. The Teubner Verlag kindly
gave the permission to publish an English translation. We finally want to
thank the Springer publishing company for the cooperation in preparing this
edition.
Braunschweig, Joachim R¨osler
Mu¨lheim an der Ruhr, Harald Harders
May 2007 Martin Ba¨ker
Contents
1 The structure of materials ................................. 1
1.1 Atomic structure and the chemical bond.................... 1
1.2 Metals ................................................. 5
1.2.1 Metallic bond..................................... 5
1.2.2 Crystal structures ................................. 7
1.2.3 Polycrystalline metals.............................. 14
1.3 Ceramics ............................................... 15
1.3.1 Covalent bond .................................... 16
1.3.2 Ionic bond........................................ 18
1.3.3 Dipole bond ...................................... 19
1.3.4 Van der Waals bond ............................... 19
1.3.5 Hydrogen bond ................................... 20
1.3.6 The crystal structure of ceramics .................... 21
1.3.7 Amorphous ceramics............................... 22
1.4 Polymers ............................................... 23
1.4.1 The chemical structure of polymers.................. 24
1.4.2 The structure of polymers .......................... 25
2 Elasticity .................................................. 31
2.1 Deformation modes ...................................... 31
2.2 Stress and strain ........................................ 32
2.2.1 Stress............................................ 32
2.2.2 Strain............................................ 34
2.3 Atomic interactions...................................... 37
2.4 Hooke’s law............................................. 39
2.4.1 Elastic strain energy ............................... 42
∗2.4.2 Elastic deformation under multiaxial loads1........... 43
∗2.4.3 Isotropic material ................................. 46
1 Sections with a title marked by a ∗ contain advanced information which can be
skipped without impairing the understanding of subsequent topics.
X Contents
∗2.4.4 Cubic lattice...................................... 50
∗2.4.5 Orthorhombic crystals and orthotropic elasticity....... 53
∗2.4.6 Transversally isotropic elasticity..................... 54
∗2.4.7 Other crystal lattices .............................. 55
∗2.4.8 Examples ........................................ 55
∗2.5 Isotropy and anisotropy of macroscopic components.......... 57
2.6 Temperature dependence of Young’s modulus ............... 60
3 Plasticity and failure ...................................... 63
3.1 Nominal and true strain.................................. 64
3.2 Stress-strain diagrams.................................... 68
3.2.1 Types of stress-strain diagrams...................... 68
3.2.2 Analysis of a stress-strain diagram................... 73
3.2.3 Approximation of the stress-strain curve.............. 81
3.3 Plasticity theory ........................................ 83
3.3.1 Yield criteria ..................................... 84
3.3.2 Yield criteria of metals............................. 86
3.3.3 Yield criteria of polymers........................... 92
3.3.4 Flow rules........................................ 93
3.3.5 Hardening........................................ 97
∗3.3.6 Application of a yield criterion, flow rule, and
hardening rule ....................................103
∗3.4 Hardness ...............................................107
∗3.4.1 Scratch tests......................................108
∗3.4.2 Indentation tests ..................................108
∗3.4.3 Rebound tests ....................................110
3.5 Material failure .........................................110
3.5.1 Shear fracture ....................................111
3.5.2 Cleavage fracture..................................114
3.5.3 Fracture criteria...................................116
4 Notches ...................................................119
4.1 Stress concentration factor................................119
4.2 Neuber’s rule ...........................................122
∗4.3 Tensile testing of notched specimens .......................125
5 Fracture mechanics ........................................129
5.1 Introduction to fracture mechanics.........................129
5.1.1 Definitions .......................................129
5.2 Linear-elastic fracture mechanics ..........................131
5.2.1 The stress field near a crack tip .....................131
5.2.2 The energy balance of crack propagation .............134
5.2.3 Dimensioning pre-cracked components
under static loads..................................142
5.2.4 Fracture parameters of different materials ............144
5.2.5 Material behaviour during crack propagation..........146
Contents XI
∗5.2.6 Subcritical crack propagation .......................150
∗5.2.7 Measuring fracture parameters ......................152
∗5.3 Elastic-plastic fracture mechanics..........................158
∗5.3.1 Crack tip opening displacement (ctod) ..............158
∗5.3.2 J integral ........................................159
∗5.3.3 Material behaviour during crack propagation..........161
∗5.3.4 Measuring elastic-plastic fracture mechanics parameters 163
6 Mechanical behaviour of metals............................165
6.1 Theoretical strength .....................................165
6.2 Dislocations ............................................166
6.2.1 Types of dislocations ..............................166
6.2.2 The stress field of a dislocation......................168
6.2.3 Dislocation movement..............................170
6.2.4 Slip systems ......................................173
6.2.5 The critical resolved shear stress ....................178
6.2.6 Taylor factor......................................182
6.2.7 Dislocation interaction .............................184
6.2.8 Generation, multiplication and annihilation of
dislocations.......................................185
6.2.9 Forces acting on dislocations........................187
6.3 Overcoming obstacles ....................................189
6.3.1 Athermal processes ................................190
6.3.2 Thermally activated processes.......................193
6.3.3 Ductile-brittle transition ...........................196
6.3.4 Climb............................................196
6.3.5 Intersection of dislocations..........................197
6.4 Strengthening mechanisms................................198
6.4.1 Work hardening...................................198
6.4.2 Grain boundary strengthening ......................200
6.4.3 Solid solution hardening............................203
6.4.4 Particle strengthening..............................209
6.4.5 Hardening of steels ................................218
∗6.5 Mechanical twinning .....................................223
7 Mechanical behaviour of ceramics .........................227
7.1 Manufacturing ceramics ..................................228
7.2 Mechanisms of crack propagation..........................229
7.2.1 Crack deflection...................................230
7.2.2 Crack bridging ....................................230
7.2.3 Microcrack formation and crack branching............231
7.2.4 Stress-induced phase transformations ................232
7.2.5 Stable crack growth ...............................234
∗7.2.6 Subcritical crack growth in ceramics .................234
7.3 Statistical fracture mechanics .............................236
XII Contents
7.3.1 Weibull statistics..................................236
∗7.3.2 Weibull statistics for subcritical crack growth .........242
∗7.3.3 Measuring the parameters σ and m .................243
0
∗7.4 Proof test ..............................................246
7.5 Strengthening ceramics...................................248
7.5.1 Reducing defect size ...............................249
7.5.2 Crack deflection...................................249
7.5.3 Microcracks ......................................251
7.5.4 Transformation toughening .........................252
7.5.5 Adding ductile particles ............................255
8 Mechanical behaviour of polymers .........................257
8.1 Physical properties of polymers ...........................257
8.1.1 Relaxation processes...............................257
8.1.2 Glass transition temperature........................260
8.1.3 Melting temperature...............................261
8.2 Time-dependent deformation of polymers...................263
8.2.1 Phenomenological description of time-dependence .....263
8.2.2 Time-dependence and thermal activation .............266
8.3 Elastic properties of polymers.............................269
8.3.1 Elastic properties of thermoplastics ..................269
8.3.2 Elastic properties of elastomers and duromers.........273
8.4 Plastic behaviour........................................274
8.4.1 Amorphous thermoplastics .........................275
8.4.2 Semi-crystalline thermoplastics......................281
8.5 Increasing the thermal stability ...........................284
8.5.1 Increasing the glass and the melting temperature......284
8.5.2 Increasing the crystallinity..........................287
8.6 Increasing strength and stiffness...........................289
8.7 Increasing the ductility...................................290
∗8.8 Environmental effects ....................................292
9 Mechanical behaviour of fibre reinforced composites .......295
9.1 Strengthening methods...................................296
9.1.1 Classifying by particle geometry.....................296
9.1.2 Classifying by matrix systems.......................299
9.2 Elasticity of fibre composites..............................300
9.2.1 Loading in parallel to the fibres .....................301
9.2.2 Loading perpendicular to the fibres ..................301
∗9.2.3 The anisotropy in general ..........................302
9.3 Plasticity and fracture of composites.......................303
9.3.1 Tensile loading with continuous fibres ................303
9.3.2 Load transfer between matrix and fibre ..............305
9.3.3 Crack propagation in fibre composites................308
9.3.4 Statistics of composite failure .......................312