Mechanical Properties and Working of Metals and Alloys

758 Pages·2018·30.97 MB·English

by  Amit Bhaduri

Springer Series in Materials Science 264
Amit Bhaduri
Mechanical Properties
and Working of
Metals and Alloys
Springer Series in Materials Science
Volume 264
Series editors
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Amit Bhaduri
Mechanical Properties
and Working of Metals
and Alloys
123
Amit Bhaduri
Department ofMetallurgical andMaterials
Engineering
Indian Institute of Technology Kharagpur
Kharagpur, West Bengal
India
ISSN 0933-033X ISSN 2196-2812 (electronic)
SpringerSeries inMaterials Science
ISBN978-981-10-7208-6 ISBN978-981-10-7209-3 (eBook)
https://doi.org/10.1007/978-981-10-7209-3
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This book is dedicated to the memory of my father
LATE ASIM RANJAN BHADURI
Preface
The book has evolved from the author’s lecture notes used for the past several years in the
teachingoftwoupper-levelundergraduate (B.Tech.)andonepostgraduate(M.Tech.)courses
intheDepartmentofMetallurgicalandMaterialsEngineering,IndianInstituteofTechnology
Kharagpur.Thebookprovidesacomprehensiveaccountofthebasicprinciplesofmechanical
testingandmetalworkingandcanbeusedasatextfortwoundergraduatecoursestaughtinthe
disciplines of metallurgical engineering, mechanical engineering and production or manu-
facturing engineering. Parts of the book can be used as study material at the undergraduate
level in the branches of civil engineering, aerospace engineering and material science. The
bookalsocontainsadvancedstudymaterialsuitableforpostgraduatestudentsofmetallurgical
engineering.
Inadditiontotheabovemultifacetedacademicapplications,auniquefeatureofthebookis
itspracticalcontentofdirectusetometallurgistsandpractisingengineersinindustry.Thebook
isdesignedtohelpthemunderstandandapplythetheoriesofmechanicaltestingandworking
todetermine,controlandimprovethemechanicalpropertiesofmetalsandalloysaswellasfor
improvingproductioninthemetalworkingindustrybyanalysingworkingproblems—boththe
mechanicsofworkingprocessesandhowthepropertiesofmetalsinteractwiththeprocesses.
Mechanical properties of metal play an important role in the processes of metalworking.
Hence,thefirstpartofthisbookcontainsadiscussiononevaluationofmechanicalproperties
by testing, relationship among different mechanical properties, factors and variables affecting
mechanical properties, engineering aspects of mechanical properties and their applications in
design,etc.Thisiscontinuedinthesecondpartofthisbookthatdealswithdetailedanalysisof
various types of metalworking or forming operations to produce useful shapes under the
application of stress arising primarily from mechanical source. The analytical methods in the
text for the treatment of mechanical working processes include slab method of analysis or
free-bodyequilibriumapproach.Theslabmethodisusedtoestimatethedeformationloadsfor
hot working processes, such as forging and extrusion under conditions of Coulomb’s sliding
friction,sticking friction andmixedsticking–sliding friction,and for cold working processes,
suchasdrawingofstrip,rodorwire,andtubeanddeepdrawingofcupunderslidingfrictional
condition.Usingtheslabmethod,thisbookprovidesanexhaustiveanalysisofBlandandFord
theory of cold rolling for sliding frictional condition and Sims’ theory of hot rolling for
stickingfrictionalcondition.Elaborateandeasy-to-understandmathematicalanalyseswithout
skipping any intermediate steps have been incorporated in this book. Not only complete
derivations of mathematical treatments have been considered, but also a comprehensive and
reasonablywidecoverageinsufficientdepthhasalsobeenattemptedinthisbook.Highenergy
rate forming, which is an unconventional metalworking process, and where chemical, mag-
neticandelectricalsourcesofenergyareused,hasalsobeenincludedasthelastchapterinthis
book. For better understanding of the theory, several solved problems have been included in
each chapter of the book. Similarly, many numerical problems along with multiple choice
questions are given as exercise in each chapter, and answers to the problems and questions
have also been provided.
vii
viii Preface
Inadditiontotheslabmethodofanalysis,thisbookalsocontainsslip-linefieldtheory,its
application to the static system, such as plane-strain indentation with flat frictionless platens
for cases of various heights of work-piece with respect to the breadth of platen, and its
application to the steady state motion, such as plane-strain frictionless extrusion and strip
drawing. Further, this book includes upper-bound theorem, and upper-bound solutions for
indentationofasemi-infiniteslab,for compression,for plane-strainfrictionlessextrusionand
strip drawing.
Thefieldofmechanicalmetallurgymayberoughlydividedintothreemodulestaughtatthe
undergraduate level of engineering discipline. These modules are deformation behaviour,
mechanical properties or mechanical testing and mechanical forming or working. Since the
subject matter of this book comprises the last two modules, which are dependent on the first
module, knowledge of deformation behaviour, consisting of elastic stress–strain relations,
plastic deformation including theory of plasticity, dislocation theory and strengthening
mechanisms, is desirable for a better understanding of the contents of this book, though
relevantaspectsofdeformationbehaviourhavebeenbrieflyincludedinthefirstchapterofthis
book.However,calculusandengineeringmechanicsareessentialprerequisitesubjectsforthis
book, and thus, the reader must have knowledge of these subjects.
Although the text has been carefully scrutinized, a few errors may still exist in the first
edition of this book. Hence, the author will be happy to receive comments along with sug-
gestions and constructive criticism.
The author acknowledges here that he was inspired by a few lectures on metal rolling
offered by Prof. (Late) R. Roy, Metallurgical Engineering Department, National Institute of
TechnologyDurgapur.Theauthorisextremelythankfultoallofhisdepartmentalcolleagues,
especially Prof. K. Biswas, Prof. R. Mitra, Prof. S. Biswas, Prof. S. Kar, Prof. T. Laha, Prof.
R. N. Ghosh, Prof. K. K. Ray, Prof. S. K. Pabi, Prof. S. K. Roy, Prof. D. Chakrabarti, Prof.
S. Mandal, Prof. T. K. Bandyopadhyay, Prof. N. Chakraborti, Prof. J. Das, Prof. J. Datta
Majumdar, Prof. G. G. Roy, Prof. M. Roy, Prof. S. Ghosh and Prof. T. K. Kundu, for their
assistance, cooperation and valuable suggestions. The author is really indebted to Prof.
A. Guha, Mechanical Engineering Department, and Prof. S. B. Singh, Metallurgical Engi-
neeringDepartment,IITKharagpur,fortheirhelpfulcommentsleadingtoimprovementinthe
manuscript. The author is also indebted to his mother, wife, brother, sister, daughter,
son-in-lawandgrandsonfortheirforbearance,encouragementandconstantsupportduringthe
preparation of the manuscript. Finally, the author is thankful to the publisher ‘Springer’,
especially its executive editor (applied science and engineering) Ms. Swati Meherishi, its
senior editorial assistant Ms. Aparajita Singh and its editorial assistant Ms. TCA Avni, for
editing the manuscript and giving it the shape of a book. The author is also thankful to
production department of Springer (Scientific Publishing Services), especially its project
manager Sri Nandhini, and its other production administrators (books), such as Ms. Krati
Shrivastava, and Vinoth. S.
Kharagpur, India Amit Bhaduri
Contents
Part I Mechanical Properties of Metals and Alloys
1 Tension . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.1.1 Description of Stress at a Point. . . . . . . . . . . . . . . . . . . . . . 4
1.2 Strain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.2.1 True Versus Engineering Strain. . . . . . . . . . . . . . . . . . . . . . 6
1.2.2 Advantages of True Strain Over Engineering Strain. . . . . . . . 6
1.2.3 Poisson’s Ratio and Volume Strain . . . . . . . . . . . . . . . . . . . 7
1.3 Conventional and True Stresses. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
1.3.1 Relationship Between True and Engineering Stresses
During Plastic Deformation. . . . . . . . . . . . . . . . . . . . . . . . . 8
1.4 Elastic Stress–Strain Relations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
1.4.1 Three-Dimensional State of Stress. . . . . . . . . . . . . . . . . . . . 9
1.5 Elements of Plastic Deformation. . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
1.5.1 Relationship Between Principal Normal and Shear
Stresses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
1.5.2 Mohr’s Stress Circle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
1.5.3 Slip. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
1.5.4 Twinning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
1.5.5 Strain Hardening. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
1.5.6 Stacking Fault. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
1.5.7 Strengthening Methods. . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
1.5.8 Spherical and Deviator Components of Stress. . . . . . . . . . . . 35
1.5.9 Yielding Criteria for Ductile Metals. . . . . . . . . . . . . . . . . . . 35
1.5.10 Octahedral Shear Stress and Shear Strain . . . . . . . . . . . . . . . 37
1.5.11 Invariants of Stress and Strain. . . . . . . . . . . . . . . . . . . . . . . 38
1.5.12 Levy–Mises Equations for Ideal Plastic Solid . . . . . . . . . . . . 38
1.5.13 Yielding Criteria Under Plane Strain . . . . . . . . . . . . . . . . . . 40
1.6 Types of Tensile Stress–Strain Curve. . . . . . . . . . . . . . . . . . . . . . . . . 41
1.6.1 Type I: Elastic Behaviour. . . . . . . . . . . . . . . . . . . . . . . . . . 41
1.6.2 Type II: Elastic–Homogeneous Plastic Behaviour . . . . . . . . . 42
1.6.3 Type III: Elastic–Heterogeneous Plastic Behaviour. . . . . . . . . 51
1.6.4 Type IV: Elastic–Heterogeneous–Homogeneous Plastic
Behaviour. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
1.6.5 Type V: Elastic–Heterogeneous–Homogeneous Plastic
Behaviour for Some Crystalline Polymers. . . . . . . . . . . . . . . 54
1.7 Linear Elastic Properties. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
1.7.1 Modulus of Elasticity. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
1.7.2 Proportional and Elastic Limit. . . . . . . . . . . . . . . . . . . . . . . 56
1.7.3 Resilience and Modulus of Resilience . . . . . . . . . . . . . . . . . 56
ix
x Contents
1.8 Nonlinear Elastic Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
1.8.1 Secant and Tangent Modulus . . . . . . . . . . . . . . . . . . . . . . . 58
1.8.2 Elastomer or Rubber Elasticity . . . . . . . . . . . . . . . . . . . . . . 58
1.8.3 Elastic Resilience or Resilience. . . . . . . . . . . . . . . . . . . . . . 59
1.9 Inelastic Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
1.9.1 Yield Strength. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
1.9.2 Ultimate and True Tensile Strength . . . . . . . . . . . . . . . . . . . 62
1.9.3 Ductility. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
1.9.4 Fracture Strength and True Fracture Strength . . . . . . . . . . . . 68
1.9.5 Toughness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
1.10 Influence of Temperature on Tensile Properties. . . . . . . . . . . . . . . . . . 70
1.10.1 Effect of Temperature on Stress–Strain Curve
of Mild Steel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
1.11 Strain Rate. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
1.11.1 Relation Between Flow Stress and Strain Rate . . . . . . . . . . . 74
1.11.2 Superplasticity. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
1.11.3 Effect of Strain Rate on Stress–Strain Curve
of Mild Steel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
1.12 Testing Machine. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
1.12.1 Influence of Testing Machine on Strain
and Strain Rate. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
1.13 Notch Tensile Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
1.14 Tensile Fracture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
1.15 Solved Problems. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
2 Compression. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
2.2 Standard Specimen . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
2.3 Elastic Range. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
2.4 Plastic Range . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98
2.4.1 Stress and Strain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
2.4.2 Strain Rate. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
2.4.3 Brittle Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
2.4.4 Ductile Materials. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102
2.5 Bauschinger Effect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
2.6 Advantages of Compression Over Tension Test . . . . . . . . . . . . . . . . . 105
2.7 Problems in Compression Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106
2.7.1 Buckling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106
2.7.2 Barreling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
2.8 Compressive Failure of Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
2.9 Solved Problems. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117
3 Hardness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120
3.2 Classification of Hardness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120
3.3 Precautions to Avoid Erratic Hardness Measurement. . . . . . . . . . . . . . 121
3.4 Mohs’ Scale of Hardness. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123
3.5 File Hardness Test. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123