Material Forming Process Simulation, Drawing, Hydroforming and Additive Manufacturing

265 Pages·2016·14.25 MB·English

by  Bouchaib Radi

Material Forming Processes
Mathematical and Mechanical Engineering Set
coordinated by
Abdelkhalak El Hami
Volume 1
Material Forming Processes

Simulation, Drawing, Hydroforming
and Additive Manufacturing

Bouchaib Radi
Abdelkhalak El Hami
First published 2016 in Great Britain and the United States by ISTE Ltd and John Wiley & Sons, Inc.
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The rights of Bouchaib Radi and Abdelkhalak El Hami to be identified as the authors of this work have
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Library of Congress Control Number: 2016945874

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A CIP record for this book is available from the British Library
ISBN 978-1-84821-947-2
Contents
Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xi
Chapter1.FormingProcesses . . . . . . . . . . . . . . . . . . . . 1
1.1.Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2.Differentprocesses . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2.1.Smelting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.2.2.Machining . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.2.3.Powdermetallurgy. . . . . . . . . . . . . . . . . . . . . . . . 5
1.3.Hotandcoldforming . . . . . . . . . . . . . . . . . . . . . . . . 6
1.3.1.Influenceofthestaticparameters . . . . . . . . . . . . . . . 9
1.3.2.Hydroforming . . . . . . . . . . . . . . . . . . . . . . . . . . 12
1.3.3.Thelimitationsoftheprocess . . . . . . . . . . . . . . . . . 13
1.3.4.Deepdrawing . . . . . . . . . . . . . . . . . . . . . . . . . . 14
1.4.Experimentalcharacterization . . . . . . . . . . . . . . . . . . . 14
1.5.Formingcriteria . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
1.5.1.Influenceofthestructureofsheetmetal. . . . . . . . . . . . 18
1.5.2.Physicalstrainmechanisms. . . . . . . . . . . . . . . . . . . 20
1.5.3.Differentcriteria . . . . . . . . . . . . . . . . . . . . . . . . . 21
Chapter2.ContactandLargeDeformationMechanics . . . . 23
2.1.Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
2.2.Largetransformationkinematics . . . . . . . . . . . . . . . . . . 23
2.2.1.Kinematicsoftheprobleminspatialcoordinates . . . . . . 24
2.3.Transformationgradient. . . . . . . . . . . . . . . . . . . . . . . 25
2.4.Strainmeasurements . . . . . . . . . . . . . . . . . . . . . . . . 26
2.4.1.PolardecompositionofF . . . . . . . . . . . . . . . . . . . . 26
vi MaterialFormingProcesses
2.4.2.Strainratetensor. . . . . . . . . . . . . . . . . . . . . . . . . 27
2.4.3.CanonicaldecompositionofF . . . . . . . . . . . . . . . . . 28
2.4.4.Kinematicsoftheprobleminconvectivecoordinates . . . . 28
2.4.5.Transformationtensor . . . . . . . . . . . . . . . . . . . . . . 29
2.4.6.Strainratemeasures . . . . . . . . . . . . . . . . . . . . . . . 32
2.4.7.Straintensor . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
2.5.Constitutiverelations . . . . . . . . . . . . . . . . . . . . . . . . 36
2.5.1.Largeelastoplastictransformations . . . . . . . . . . . . . . 38
2.5.2.Kinematicdecompositionofthetransformation . . . . . . . 41
2.6.Incrementalbehavioralproblem . . . . . . . . . . . . . . . . . . 42
2.6.1.Stressincrementation . . . . . . . . . . . . . . . . . . . . . . 42
2.6.2.Strainincrementation . . . . . . . . . . . . . . . . . . . . . . 44
2.6.3.Solutionofthebehaviorproblem . . . . . . . . . . . . . . . 46
2.7.DefinitionoftheP.V.W.inmajortransformations . . . . . . . . 49
2.7.1.Equilibriumequations. . . . . . . . . . . . . . . . . . . . . . 49
2.7.2.DefinitionoftheP.V.W. . . . . . . . . . . . . . . . . . . . . . 50
2.7.3.Incrementalformulation . . . . . . . . . . . . . . . . . . . . 51
2.8.Contactkinematics . . . . . . . . . . . . . . . . . . . . . . . . . 52
2.8.1.Definitionoftheproblemandnotations . . . . . . . . . . . . 52
2.8.2.Contactformulation . . . . . . . . . . . . . . . . . . . . . . . 53
2.8.3.Formulationofthefrictionproblem . . . . . . . . . . . . . . 53
2.8.4.Frictionlaws . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
2.8.5.Coulomb’slaw . . . . . . . . . . . . . . . . . . . . . . . . . . 54
2.8.6.Tresca’slaw . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
Chapter3.Stamping . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
3.1.Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
3.2.Forminglimitcurve . . . . . . . . . . . . . . . . . . . . . . . . . 59
3.3.Stampingmodeling: incrementalproblem . . . . . . . . . . . . 60
3.3.1.Modelingofsheetmetal . . . . . . . . . . . . . . . . . . . . 61
3.3.2.Spatialdiscretization: finiteelementsmethod . . . . . . . . 62
3.3.3.Choiceofsheetmetalandfiniteelementapproximation . . 63
3.4.Modelingtools . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
3.4.1.Toolsurfacemeshingintosimplegeometryelements . . . . 64
3.4.2.Analyticalrepresentationoftools . . . . . . . . . . . . . . . 65
3.4.3.Bezierpatches . . . . . . . . . . . . . . . . . . . . . . . . . . 65
3.5.Stampingnumericalprocessing . . . . . . . . . . . . . . . . . . 72
3.5.1.Problemstatement . . . . . . . . . . . . . . . . . . . . . . . . 73
3.5.2.TheaugmentedLagrangianmethod . . . . . . . . . . . . . . 75
3.6.Numericalsimulations . . . . . . . . . . . . . . . . . . . . . . . 79
3.6.1.Sollactest . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
Contents vii
Chapter4.Hydroforming . . . . . . . . . . . . . . . . . . . . . . . . 83
4.1.Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
4.2.Hydroforming . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
4.2.1.Tubehydroforming . . . . . . . . . . . . . . . . . . . . . . . 85
4.2.2.Sheetmetalhydroforming . . . . . . . . . . . . . . . . . . . 86
4.3.Plasticinstabilitiesinhydroforming . . . . . . . . . . . . . . . . 87
4.3.1.Tubebuckling . . . . . . . . . . . . . . . . . . . . . . . . . . 88
4.3.2.Wrinkling. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
4.3.3.Necking. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
4.3.4.Springback . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
4.4.Forminglimitcurve . . . . . . . . . . . . . . . . . . . . . . . . . 92
4.5.Materialcharacterizationforhydroforming . . . . . . . . . . . . 94
4.5.1.Tensiletesting . . . . . . . . . . . . . . . . . . . . . . . . . . 95
4.5.2.Bulgetesting . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
4.6.Analyticalmodelingofainflationtest . . . . . . . . . . . . . . . 97
4.6.1.Hill48criterioninplanarstresses . . . . . . . . . . . . . . . 97
4.7.Numericalsimulation . . . . . . . . . . . . . . . . . . . . . . . . 100
4.8.Mechanicalcharacteristicoftubebehavior . . . . . . . . . . . . 101
Chapter5.AdditiveManufacturing . . . . . . . . . . . . . . . . . . 105
5.1.Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
5.2.RPandstratoconception . . . . . . . . . . . . . . . . . . . . . . 107
5.3.Additivemanufacturingdefinitions . . . . . . . . . . . . . . . . 109
5.4.Principle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
5.4.1.Principleofpowderbedlasersintering/melting . . . . . . . 114
5.4.2.Principleoflasersintering/meltingbyprojecting
powder . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116
5.5.AdditivemanufacturingintheIT-baseddevelopment
process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117
5.5.1.Concept“fromtheobjecttotheobject” . . . . . . . . . . . . 117
5.5.2.KeyelementoftheITdevelopmentprocess . . . . . . . . . 118
Chapter6.OptimizationandReliabilityinForming . . . . . . . 121
6.1.Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
6.2.Differentapproachestooptimizationprocesses . . . . . . . . . 122
6.2.1.Limitationsofthedeterministicapproaches . . . . . . . . . 124
6.3.Characterizationofformingprocessesbyobjective
functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
6.4.Deterministicandprobabilisticoptimizationofa
T-shapedtube . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126
6.4.1.Problemdescription . . . . . . . . . . . . . . . . . . . . . . . 126
viii MaterialFormingProcesses
6.4.2.Choiceoftheobjectivefunctionanddefinition
ofthestresses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127
6.4.3.Choiceoftheuncertainparameters . . . . . . . . . . . . . . 128
6.4.4.Choiceoftheobjectivefunctionandthestresses . . . . . . . 130
6.4.5.Deterministicformulationoftheoptimizationproblem . . . 132
6.4.6.Probabilisticformulationoftheoptimizationproblem. . . . 133
6.4.7.Optimasensitivitytouncertainties . . . . . . . . . . . . . . . 140
6.5.Deterministicandoptimization-basedreliabilityofatube
withtwoexpansionregions . . . . . . . . . . . . . . . . . . . . . . . 142
6.5.1.Problemdescription . . . . . . . . . . . . . . . . . . . . . . . 142
6.5.2.Deterministicandreliabilistformulationofthe
optimizationproblem. . . . . . . . . . . . . . . . . . . . . . . . . . 147
6.6.Optimization-basedreliabilityofcircularsheetmetal
hydroforming . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150
6.6.1.Problemdescription . . . . . . . . . . . . . . . . . . . . . . . 150
6.6.2.Constructionoftheobjectivefunctionandofthe
stresses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151
6.6.3.Effectsdiagram . . . . . . . . . . . . . . . . . . . . . . . . . 151
6.6.4.Deterministicsolutionoftheoptimizationproblem . . . . . 155
6.6.5.Reliabilistsolutionoftheoptimizationproblem . . . . . . . 157
6.6.6.Effectofuncertaintiesontheoptimalvariables . . . . . . . 159
6.7.Deterministicandrobustoptimizationofasquareplate . . . . . 160
6.7.1.Robustresolutionoftheoptimizationproblem . . . . . . . . 166
6.8.Optimizationofthinsheetmetal . . . . . . . . . . . . . . . . . . 168
Chapter7.ApplicationofMetamodelstoHydroforming . . . . 171
7.1.Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171
7.2.Sourcesofuncertaintyinforming . . . . . . . . . . . . . . . . . 172
7.3.Failurecriteria . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173
7.3.1.Failurecriteriafornecking . . . . . . . . . . . . . . . . . . . 174
7.3.2.Failurecriteriaforwrinkling . . . . . . . . . . . . . . . . . . 174
7.4.Evaluationstrategyoftheprobabilityoffailure . . . . . . . . . 175
7.4.1.Finiteelementmodelandchoiceofuncertainty
parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 176
7.4.2.Identificationoffailuremodesanddefinitionof
boundarystates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 180
7.4.3.Identificationofelementsandcriticalareas. . . . . . . . . . 181
7.5.Criticalstrainsprobabilisticcharacterization . . . . . . . . . . . 185
7.5.1.Choiceofnumericalexperimentaldesign . . . . . . . . . . . 186
7.5.2.Constructionofmetamodels . . . . . . . . . . . . . . . . . . 186
7.5.3.Validationandstatisticalanalysisofmetamodels . . . . . . 187
Contents ix
7.5.4.Fittingofdistributions. . . . . . . . . . . . . . . . . . . . . . 187
7.6.Neckingandwrinklingprobabilisticstudy . . . . . . . . . . . . 193
7.7.Effectsofthecorrelationsontheprobabilityoffailure . . . . . 196
7.7.1.Spatialestimationoftheprobabilityoffailures. . . . . . . . 197
Chapter8.ParametersIdentificationinMetalForming . . . . 199
8.1.Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 199
8.2.Identificationmethods. . . . . . . . . . . . . . . . . . . . . . . . 199
8.2.1.Validationtest . . . . . . . . . . . . . . . . . . . . . . . . . . 200
8.3.Weldedtubehydroforming . . . . . . . . . . . . . . . . . . . . . 203
8.3.1.Thinsheetmetalhydroforming . . . . . . . . . . . . . . . . 205
Appendices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213
Appendix1.OptimizationinMechanics . . . . . . . . . . . . . . 215
Appendix2.ReliabilityinMechanics . . . . . . . . . . . . . . . . 223
Appendix3.Metamodels . . . . . . . . . . . . . . . . . . . . . . . . 233
Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 243
Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 253
Preface
In the current economical climate, the automotive, aviation, aerospace,
defense, etc., industries have established the following priority: improve the
quality and the reliability of products while reducing production costs. To
achieve this goal, the industry strives to modernize its work tools in order to
minimizethedurationofdesigncyclesandimprovemanufacturingprocesses.
The field of metal forming (stamping, thin sheet metal deep-drawing,
tubesand plates hydroforming, forgingof solidmaterials, cutting, composite
draping,foundry,etc.)isthesubjectofmuchresearchandofdifferentcourses
destinedtoengineersandacademics(aspartofmastersanddoctoralschools).
Thisinterestisduetotheincreasingdemandsfromdifferentindustrialsectors
forgraduateswithexperienceinthesedisciplines.
In different industries (automotive, aeronautics, etc.), metal forming
constitutes, in the course of the entire manufacturing processes, a decisive
phase in the overall quality and cost of the final product. A vehicle is first
judgedonitsdesign.
Currently, numerical simulations of forming processes are being used
almost systematically in the development of industrial products. The studies,
basedonthemodelingofphysicalphenomenainvolvedinthemanufacturing
ortheutilizationofindustrialproductsorinfrastructures,answerthegrowing
needto:
–decreasethedurationoftheproductdevelopmentcycle;
–optimizeproductdevelopmentprocedures;
–improvetheproductivityindesignandmanufacturingphases;
xii MaterialFormingProcesses
–improveproductqualityandprocessreliability;
–optimizetestingandreducingitscosts;
–simulatenon-reproduciblecomplexphenomenabymeansoftrials.
Theuseofdigitaleducationaltoolsmaintainsastrongrelationshipwiththe
trainingandresearchstrategy(http://mediamef.insa-rouen.fr/).
This book presents the various methods for forming used in the industry:
stamping,hydroformingandadditivemanufacturingandproposesamodeling
of the latter by providing the theoretical and numerical advances for each
process involving large deformation mechanics on the basis of large
transformations.Itpresentsthevarioustechniquesrelativetotheoptimization
andcalculationofthereliabilityofdifferentprocesses.
Acknowledgments
We wish to thank everyone who has directly or indirectly contributed to
this book, in particular the engineering students and the PhD students of the
INSARouenthatweworkedwithinrecentyears.
BouchaïbRADI
AbdelkhalakELHAMI
June2016