Elastoplastic Behavior of Highly Ductile Materials

181 Pages·2019·4.605 MB·English

by  Maosheng Zheng, Zhifu Yin, Haipeng Teng, Jiaojiao Liu, Yi Wang

Maosheng Zheng · Zhifu Yin ·
Haipeng Teng · Jiaojiao Liu · Yi Wang
Elastoplastic
Behavior
of Highly Ductile
Materials
Elastoplastic Behavior of Highly Ductile Materials
Maosheng Zheng Zhifu Yin Haipeng Teng
(cid:129) (cid:129) (cid:129)
Jiaojiao Liu Yi Wang
(cid:129)
Elastoplastic Behavior
of Highly Ductile Materials
123
MaoshengZheng ZhifuYin
Northwest University Institute of YanchangPetroleum
Xi’an,Shaanxi, China Group Co.Ltd.
Xi’an,Shaanxi, China
Haipeng Teng
Northwest University Jiaojiao Liu
Xi’an,Shaanxi, China Northwest University
Xi’an,Shaanxi, China
YiWang
Northwest University
Xi’an,Shaanxi, China
ISBN978-981-15-0905-6 ISBN978-981-15-0906-3 (eBook)
https://doi.org/10.1007/978-981-15-0906-3
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Preface
Nowadays,theindustrializationsignificantlypromotestheprogressandapplication
ofelastoplasticity.Variousnewdemandsandphenomenaemerged,whichrelatedto
the development of materials with high ductility and strength in recent years.
Therefore, it requires an appropriate description to present the wide classes of
elastoplastic behaviors of such materials.
In 2008, a book entitled “Notch Strength and Notch Sensitivity of Materials”
(authored by Zheng X., Wang H., Zheng M., and Wang F. H., Science Press,
Beijing, China) was published, which is devoted to quantitatively characterize the
notchstrengthandnotchsensitivityofbothductileandbrittlematerials,andaimed
to formulate the fracture criteria for notched structures. The present authors have
madeuptheirmindtopublishthecurrentbookasanaccompanyingcontributionto
ductile materials, especially due to their wide applications.
In writing this book, the fundamental knowledge in the general elastoplastic
theories was carefully selected from various formulations to date in the first three
chapters, which are relevant to the study of the elastoplastic behaviors of highly
ductile materials.
The first author has investigated elastoplastic behaviors of materials with high
ductility since the early 1990s and has lectured materials and elastoplastic
mechanics more than 20 years, various books and research papers both in Chinese
andinEnglishconcerningthissubjectarepiledathand,andthisbookaddressesthe
latest phenomena and formulations of elastoplastic behaviors of highly ductile
materials in the last seven chapters comprehensively. Various approaches devel-
opedbytheauthorsareincludedamongthecontentsofthisbookinacertainroom
as well.
The main purpose of this book is to expedite the application of elastoplasticity
theorytoanalyzeengineeringproblemsofelastoplasticbehaviorsofhighlyductile
materials in practice. It is our great pleasure if the readers including researchers,
engineers, and students in the relevant fields could get valuable knowledge from
this book.
v
vi Preface
As a foundation, the fundamental knowledge of general elastoplastic theories is
introduced in Chaps. 1–3. Chapter 1 addresses the fundamental assumptions in
elastoplasticmechanics;consequently,somemodels,assumptions,andrelationsare
described in detail. Explanations for models and assumptions are to the extent that
issufficienttounderstandthesubjectofelastoplasticbehaviorsofductilematerials;
Chap.2displaysthedescriptionofphysicalrelationshipinelastoplasticmechanics,
which includes the generalized Hooke’s law, plastic yielding criteria in plastic
mechanics, and relationship of incremental strain depending upon stress status in
plastic mechanics. The damage evolution in ductile materials is presented quanti-
tatively as well; Chap. 3 presents the solutions to some typical problems of
elastoplasticity, such as the planar problems in elastic mechanics, elastoplastic
analysis and plastic limit analysis of thick-walled cylinders, and elastoplastic
bending and plastic limit analysis of beams; stress analysis of tube under uneven
external load is provided, too.
Chapter 4 especially represents the transfer and relief of stress concentration at
the notch root of structures of ductile materials, and analytical expressions are
presented; Chap. 5 shows the analysis of elastoplastic deformation in the manu-
facturing process of bimetal composite pipes, which can be exceptionally consid-
ered as a typical application of the classical overmatching problem in engineering;
Chap. 6 devotes to the plastic buckling of tube bending, as well as the strain
hardening effect; Chap. 7 gives defect effect on pipe bending behavior, and both
diffusiveandlocalizedcorrosivedefectsareinvolvedseparately;Chap.8addresses
thermal stress problems, and grain-reinforced Al matrix composite is particularly
taken as a typical example due to its potential application; Chap. 9 describes the
general description offatigue problems first, then the uniform fatigue life equation
for both low-cycle fatigue and high-cycle fatigue conditions and its improvement
arepeculiarlypresented,andthemeanstresseffectisincluded.Chapter10provides
energy absorption of highly ductile materials and characteristics of
energy-absorbingcomponentsfirst,andthenbothhorizontallycompressedringand
axial compressions of round tube are given specially.
This book presents the research on some basic phenomena and laws of highly
ductile materials during elastoplastic deformation, and their typical engineering
applications, which are from the available literature and our group. The authors
wish that the publication of this book would contribute to the relevant research in
both theoretical research and engineering applications.
At this moment, the authors would like to express sincere thanks to relevant
colleagues for their remarkable works in early days, especially Prof. Zheng X. L.
(Zheng Xiulin) from Northwestern Polytechnic University in China for his crucial
supervision and outstanding contributions in this field. The authors acknowledge
their arduous and creative works.
It should be noted that the early research works on the ductile behaviors of
metals were done by Zheng M. in Northwestern Polytechnic University, Xi’an
Jiaotong University in China, Lappeenranta University of Technology in Finland,
and Freiberg University of Mining and Technology in Germany. The authors also
wishtoexpressthankstotherelevantcolleaguesandinstitutions.Inaddition,Prof.
Preface vii
SihG.C.ofLehighUniversityisacknowledgedforhismeaningfulenlightenments
and valuable discussions. The authors would like to express special gratitude to
Prof.NiemiE.fromLappeenrantaUniversityofTechnologyinFinlandforhiskind
hosting,AlexandervonHumboldtFoundationofGermanyforitssupport,andProf.
Kunz L. from Institute of Materials Physics of Czech Republic Science Academy
for his effective collaboration.
Theauthorswishthisworkwouldmakethecontributionstorelevantfieldsasa
paving stone.
Xi’an, China Maosheng Zheng
Zhifu Yin
Haipeng Teng
Jiaojiao Liu
Yi Wang
Contents
1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1 Fundamental Assumptions of Elastoplastic Mechanics. . . . . . . . 1
1.1.1 Task of Elastoplastic Mechanics . . . . . . . . . . . . . . . . . 2
1.1.2 Basic Assumptions of Elastoplastic Mechanics. . . . . . . 3
1.1.3 Solving the Problem of Elastoplastic Mechanics. . . . . . 4
1.2 Deformation Characteristics of the Material . . . . . . . . . . . . . . . 8
1.2.1 Stress–Strain Curve . . . . . . . . . . . . . . . . . . . . . . . . . . 8
1.2.2 Basic Models of Materials . . . . . . . . . . . . . . . . . . . . . 13
1.3 Constitutive Model of the Deformed Body. . . . . . . . . . . . . . . . 15
1.3.1 Simplified Model of Uniaxial Stress–Strain
Relationship. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
1.3.2 Limitations of Conventional Elastoplasticity
Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
1.4 Equilibrium Equations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
1.5 Principal Stresses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
1.6 Spherical, Deviatoric, Von Mises, and Octahedral Stresses . . . . 21
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
2 Physical Relationship in Elastoplastic Mechanics . . . . . . . . . . . . . . 23
2.1 Generalized Hooke’s Law . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
2.1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
2.1.2 Elastic Deformation and Elastic Constants . . . . . . . . . . 24
2.1.3 Description of Generalized Hooke’s Law. . . . . . . . . . . 25
2.2 Yielding Conditions in Plastic Mechanics. . . . . . . . . . . . . . . . . 26
2.2.1 General Concept of Yielding Conditions . . . . . . . . . . . 26
2.2.2 Two Commonly Used Plastic Yielding Conditions. . . . 27
2.2.3 Experimental Verification of Plastic Yielding
Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
2.2.4 Comparison of Two Plastic Yielding Conditions . . . . . 30
ix
x Contents
2.3 Relationship Between Stress and Strain in Plastic
Mechanics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
2.3.1 Incremental Theory in Plastic Mechanics. . . . . . . . . . . 31
2.3.2 Deformation Theory in Plastic Mechanics . . . . . . . . . . 32
2.4 Ductile Damage and Fracture . . . . . . . . . . . . . . . . . . . . . . . . . 33
2.4.1 General Description of Ductile Damage and Fracture
Corresponding to Plastic Deformation . . . . . . . . . . . . . 33
2.4.2 Ductile Damage Model Corresponding to the
Dissipation of Ductility of Metal. . . . . . . . . . . . . . . . . 34
2.4.3 Prediction of Ductile Crack Initiation Near Notch
Tip Under Mode I Loading by the Ductile Damage
Theory. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
3 Solutions to the Typical Problem of Elastoplasticity . . . . . . . . . . . . 39
3.1 Planar Problems in Elastic Mechanics . . . . . . . . . . . . . . . . . . . 39
3.1.1 Plane Stress . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
3.1.2 Plane Strain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
3.2 Stress Function. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
3.3 Example of Plane Problem in Cartesian Coordinates. . . . . . . . . 44
3.4 The Plane Problems in Polar Coordinates. . . . . . . . . . . . . . . . . 45
3.5 Elastoplastic Analysis and Plastic Limit Analysis
of Thick-Walled Cylinders . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
3.6 Elastoplastic Bending of Beams. . . . . . . . . . . . . . . . . . . . . . . . 55
3.6.1 Plastic Limit Moment and Plastic Hinge
of Beam Section. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
3.6.2 Limit Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
3.6.3 Relationship Between Bending Moment
and Curvature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
3.7 Stress Analysis of Tube Under Uneven External Load . . . . . . . 59
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
4 Transfer and Mitigation of Stress Concentration at the Root
of a Notch for Highly Ductile Materials . . . . . . . . . . . . . . . . . . . . . 65
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
4.2 Stress Concentration at the Edge of the Hole . . . . . . . . . . . . . . 66
4.3 Transfer and Mitigation of Stress Concentration in the Root
of a Notch for Highly Ductile Materials. . . . . . . . . . . . . . . . . . 67
4.4 The Role and Significance of Stress Concentration Transfer
and Relief at the Root of a Notch . . . . . . . . . . . . . . . . . . . . . . 73
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
Contents xi
5 Elastoplastic Problems in the Manufacturing Process
of Bimetallic Composite Tubes . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
5.2 Overmatching Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
5.2.1 Stress Analysis of Hydro-Forming Process. . . . . . . . . . 77
5.2.2 Stress Analysis of Mechanical Drawing Process. . . . . . 81
5.3 Application in the Manufacturing Process of Bimetal
Composite Tubes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
5.3.1 Interface Bonding Strength and Residual Stress . . . . . . 82
5.3.2 Cone Size Effect on the Interfacial Bonding
Strength of Bimetallic Composite Tube Integrated
by Drawing Method . . . . . . . . . . . . . . . . . . . . . . . . . . 83
5.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
6 Plastic Bending and Failure of Highly Ductile Tubes . . . . . . . . . . . 87
6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
6.2 Classical (Elastic) Solution for Tube Bending. . . . . . . . . . . . . . 89
6.3 Elastic Buckling During Bending of the Tube Considering
Cross-Sectional Change. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
6.4 Plastic Buckling During Bending of the Tube. . . . . . . . . . . . . . 92
6.4.1 Flattening Cross-Sectional Model for Plastic
Bending Tube . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
6.4.2 Elliptical Shape Cross Section-Based Expression
for Plastic Bending Tube at Buckling . . . . . . . . . . . . . 94
6.5 Effect of Strain Hardening on Plastic Flexural Buckling
of Tubes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
6.5.1 Effect of Strain Hardening on Critical Buckling
Strain of Plastic Bending Tube . . . . . . . . . . . . . . . . . . 99
6.5.2 Expression for Critical Buckling Strain Including
Strain Hardening Effect for Plastic Bending Tube
at Buckling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
6.6 Failure of Plastic Flexural Buckling. . . . . . . . . . . . . . . . . . . . . 104
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
7 Effect of Defects on Pipe Bending Behavior . . . . . . . . . . . . . . . . . . 107
7.1 Defect Types and Simplification . . . . . . . . . . . . . . . . . . . . . . . 107
7.1.1 General Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . 107
7.1.2 Assessment of Corrosion Damage in Radial
Direction of Pipeline . . . . . . . . . . . . . . . . . . . . . . . . . 108
7.2 Treatment of Diffusive Defects . . . . . . . . . . . . . . . . . . . . . . . . 109
7.3 Effect of Diffusive Defects on Pipe Bending Behavior . . . . . . . 111