Introduction to Computational Plasticity

259 Pages·2005·4.19 MB·English

by  Fionn Dunne

IntroductiontoComputationalPlasticity
This page intentionally left blank
Introduction to
Computational Plasticity
FIONN DUNNE AND NIK PETRINIC
DepartmentofEngineeringScience
OxfordUniversity,UK
1
3
GreatClarendonStreet,Oxfordox26dp
OxfordUniversityPressisadepartmentoftheUniversityofOxford.
ItfurtherstheUniversity’sobjectiveofexcellenceinresearch,scholarship,
andeducationbypublishingworldwidein
Oxford NewYork
Auckland CapeTown DaresSalaam HongKong Karachi
KualaLumpur Madrid Melbourne MexicoCity Nairobi
NewDelhi Shanghai Taipei Toronto
Withofficesin
Argentina Austria Brazil Chile CzechRepublic France Greece
Guatemala Hungary Italy Japan Poland Portugal Singapore
SouthKorea Switzerland Thailand Turkey Ukraine Vietnam
OxfordisaregisteredtrademarkofOxfordUniversityPress
intheUKandincertainothercountries
PublishedintheUnitedStates
byOxfordUniversityPressInc.,NewYork
©OxfordUniversityPress,2005
Themoralrightsoftheauthorshavebeenasserted
DatabaserightOxfordUniversityPress(maker)
Firstpublished2005
Reprinted2006(withcorrections)
Allrightsreserved.Nopartofthispublicationmaybereproduced,
storedinaretrievalsystem,ortransmitted,inanyformorbyanymeans,
withoutthepriorpermissioninwritingofOxfordUniversityPress,
orasexpresslypermittedbylaw,orundertermsagreedwiththeappropriate
reprographicsrightsorganization.Enquiriesconcerningreproduction
outsidethescopeoftheaboveshouldbesenttotheRightsDepartment,
OxfordUniversityPress,attheaddressabove
Youmustnotcirculatethisbookinanyotherbindingorcover
andyoumustimposethesameconditiononanyacquirer
BritishLibraryCataloguinginPublicationData
(Dataavailable)
LibraryofCongressCataloginginPublicationData
(Dataavailable)
TypesetbyNewgenImagingSystems(P)Ltd.,Chennai,India
PrintedinGreatBritain
onacid-freepaperby
BiddlesLtd,King’sLynn
ISBN 0-19-856826-6(Hbk) 978-0-19-856826-1
3 5 7 9 10 8 6 4 2
ToHannahandRoberta,withlove
This page intentionally left blank
Preface
The intention of this book is to bridge the gap between undergraduate texts in
engineeringplasticityandthemanyexcellentbooksincomputationalplasticityaimed
at more senior graduate students, researchers, and practising engineers working in
solid mechanics. The book is in two parts. The first introduces microplasticity and
covers continuum plasticity, the kinematics of large deformations and continuum
mechanics, the finite element method, implicit and explicit integration of plasticity
constitutiveequations, andtheimplementationoftheconstitutiveequations, andthe
associatedmaterialJacobian,intofiniteelementsoftware.Inparticular,theimplemen-
tationintothecommercialcodeABAQUSisaddressed(andtohelp,weprovidearange
ofABAQUSmaterialmodelUMATs),together,importantly,withthetestsnecessary
to verify the implementation. Our intention, wherever possible, is to develop a good
physical feel for the plasticity models and equations described by considering, at
everystage,thesimplificationoftheequationstouniaxialconditions.Inaddition,we
hopetoprovideareasonablyphysicalunderstandingofsomeofthelargedeformation
quantities(suchasthecontinuumspin)andconcepts(suchasobjectivity)whichare
oftenunfamiliartomanyundergraduateengineeringstudentswhodemandmorethan
justamathematicaldescription.
Thesecondpartofthebookintroducesarangeofplasticitymodelsincludingthose
for superplasticity, porous plasticity, creep, cyclic plasticity, and thermo-mechanical
fatigue (TMF). We also describe a number of practical applications of the plasticity
modelsintroducedtodemonstratethereasonablematurityofcontinuumplasticityin
engineeringpractice.
Wehope, aboveall, thatthisbookwillhelpallthose—undergraduates, graduates,
researchers, and practising engineers—who need to move on from knowledge of
undergraduate plasticity to modern practice in computational plasticity. Our aims
have been to encourage development of understanding, and ease of passage to the
moreadvancedtextsoncomputationalplasticity.
September2004 F.P.E.D.andN.P.
This page intentionally left blank
Contents
Acknowledgements xii
Notation xiii
Part I. Microplasticity and continuum plasticity
1. Microplasticity 3
1.1 Introduction 3
1.2 Crystalslip 5
1.3 Criticalresolvedshearstress 7
1.4 Dislocations 8
Furtherreading 10
2. Continuumplasticity 11
2.1 Introduction 11
2.2 Somepreliminaries 11
2.3 Yieldcriterion 17
2.4 Isotropichardening 23
2.5 Kinematichardening 27
2.6 Combinedisotropicandkinematichardening 36
2.7 Viscoplasticityandcreep 38
Furtherreading 45
3. Kinematicsoflargedeformationsandcontinuummechanics 47
3.1 Introduction 47
3.2 Thedeformationgradient 48
3.3 Measuresofstrain 49
3.4 Interpretationofstrainmeasures 52
3.5 Polardecomposition 57