Microstructure Sensitive Design for Performance Optimization

409 Pages·2012·16.518 MB·424\409

Microstructure-Sensitive
Design for Performance
Optimization
Brent L. Adams
Surya R. Kalidindi
David T. Fullwood
AMSTERDAM(cid:129)BOSTON(cid:129)HEIDELBERG(cid:129)LONDON
NEWYORK(cid:129)OXFORD(cid:129)PARIS(cid:129)SANDIEGO
SANFRANCISCO(cid:129)SINGAPORE(cid:129)SYDNEY(cid:129)TOKYO
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Preface
The prominent “grand challenge” in materials engineering for the twenty-first century is to effect
a reversal of the paradigm by which new materials are developed, especially for highly constrained
design (HCD) applications. Traditional methodologies for new materials development are driven
mainly by innovations in processing; it follows that only a limited number of readily accessible
microstructures are considered,1 with attention focused on a small number of properties or perfor-
manceobjectives.ForHCDapplications,thedesignerfacesincreasinglycomplexrequirementswith
multiple property objectives/constraints and material anisotropy affecting system performance. It is
evidentthatthetime-andresource-consumptiveempiricismthathasdominatedmaterialsdevelopment
duringthe past centurymustgiveway toa greater dependence on modelingand simulation.2
Weneedtoinvertthecurrentparadigminnewmaterialsdevelopmentfromthepresent(deductive)
cause-and-effectapproachtoamuchmorepowerfulandresponsive(inductive)goal–meansapproach
(Olson,1997).Thisshiftcouldsubstantiallyreducesystemdevelopmenttimeandcostformaterials-
sensitiveHCDproblems.Therehasexistedafundamentalincompatibilityduringthepasttwodecades
between materials science and engineering and the engineered product design cycle. Current meth-
odology for introducing new materials into engineered components requires up to 10 years of
developmenttime.Thiscompareswithdesignoptimizationmethodologiesthatarepresentlycapable
of introducing sophisticated design evolvements (excluding materials considerations) in a matter of
daysorweeks.Oneconsequenceofthisincompatibilityisafundamentalweaknessinthenexusthat
linksmaterialsscienceandengineeringtothedesignenterprise,wherethegoalistotailoramaterial’s
microstructuretomeetthestringentpropertiesandperformancerequirementsofcomplexcomponents
and systems.Addressing this gap isthe primarymotivation for this book.
To the best of the authors’ knowledge, this book presents the first mathematically rigorous
frameworkforaddressing the inverse problems of materials designand process design,while using
acomprehensivesetofhierarchicalmeasuresofthemicrostructurestatisticsandcompositetheories
that are based on the same description of the microstructure. The framework presented in the book
utilizes highly efficient spectral representations to arrive at invertible linkages between material
structure, itsproperties,andtheprocessingpathsusedtoalter thematerialstructure. Severalrecent
high-profile reports (“Integrated Computational Materials Engineering (ICME),” The National
Academies Press, 2008; “Materials Genome Initiative for Global Competitiveness,” National
Science and Technology Council, 2011; “A National Strategic Plan for Advanced Manufacturing,”
NationalScienceandTechnologyCouncil,2012)haveallcalledforthecreationofanewmaterials
innovation infrastructure to facilitate the design, manufacture, and deployment of new high-
performance materials at a dramatically accelerated pace in emerging advanced technologies. We
believe that the framework presented in this book can serve as the core enabler for these strategic
initiatives.
1Itisknownthatthespaceofpotentialmicrostructuresisvastlylargerthanthesetthatistypicallycharacterized.
2ThispositionhasbeenstronglyarticulatedinthereportoffindingsofaNationalScienceFoundation(NSF)-sponsored
workshopentitled“NewDirectionsinMaterialsDesignScienceandEngineering,”editedbyMcDowellandStory(1998).
vii
viii Preface
This book is primarily intended as a reference for specialists engaged in the emerging field of
materialsdesign.Itcanalsobeusedasatextbookforasequenceoftwocoursesofferedforahigh-level
undergraduateclassoragraduateclass.Chapters1through3serveasbackgroundmaterialandcanbe
skipped(orassignedasself-reading)ifstudentshavefamiliaritywiththismaterial.Chapters4through
11introducethebasicconceptsofthefirst-ordertheoriesandillustratetheirusageinfirst-orderinverse
solutionstomaterialsandprocessdesignproblems.Thesechapterscouldbethefocusofafirstcourse
in MSDPO (microstructure-sensitive design for performance optimization). In a second follow-up
course,thefocuscanbeonthemoredifficultconceptsassociatedwithsecond-ordertheoriespresented
inChapters12through15.Chapter16providesusefulbackgroundmaterialonmicroscopytechniques
(with astrong focus onelectron backscatterdiffraction) thatcan beusedineither course togivethe
student a solid introduction to at least one characterization technique that complements the compu-
tationalapproachesfound intherestofthetext.Ourpastexperienceindicatesthatthese courses are
highlyamenabletotheincorporationofteamprojectsbysmallgroupsofstudentsasanintegralpartof
the course.
Acknowledgments
Theauthorswouldliketoacknowledgethemanypeoplewhohavecontributedtotheproductionofthis
book. Much of the groundwork for the book was undertaken during a sabbatical leave that Brent
AdamstookatDrexelUniversitytocollaboratewithSuryaKalidindiin2004–2005.Theauthorsare
thankful for the support of Brigham Young University and Drexel University that facilitated this
fruitful period ofidea development.
Innumerablecolleaguescontributedtotheprogressofthiswork,withparticularthankstoHamid
Garmestani and Graeme Milton. Stuart Wright of Edax-TSL kindly provided various Orientation
(cid:1)
ImagingMicroscopy(OIM )imagesusedinthebook,andtheoverviewofOIMthatformedthebasis
for Chapter16.
Furthermore, numerous students contributed directly or indirectly to this development, including
StephenNiezgoda,SadeghAhmadi,MaxBinci,HariDuvvuru,BradFromm,CarlGao,BenHenrie,
Eric Homer, Josh Houskamp, Marko Knezevic, Colin Landon, Scott Lemmon, Ryan Larsen, Mark
Lyon, Gwe´nae¨lle Proust, Craig Przybyla, Joshua Shaffer, Xianping Wu, and Tony Fast. Bradford
Singleyproduced manyofthe figures.
Partial funding was also provided by the Army Research Office, under program manager David
Stepp,andvariousNSFgrants.EarlierworkwasalsomadepossibleunderagrantfromtheAirForce
Office of Scientific Research with program manager Craig Hartley. Surya Kalidindi was partially
fundedforhiseffortundergrantsfromtheOfficeofNavalResearch(ONR)withprogrammanagers
Julie Christodolou and William Mullins. Generous supplemental funding, provided through the
Warren N. and Wilson H. Dusenberry Professorship held by Brent Adams, was instrumental in
providing support for undergraduate students engaged in developing the case studies, and for travel
that hasgreatly facilitatedthis work.
ix
Nomenclature
a,b,. (lowercaseitalic)scalar
v,n,. (lowercase,bold)vector
vi,. (lowercaseitalics)vectorcomponent
e ,. basisvector
1
T,C,. (uppercasebold)tensor
T12,Cijkl,. (uppercaseitalics)tensorcomponents
u,v dotproductofvectors
juj modulusofavector
u(cid:2)v cross-productofvectors
˛ permutationsymbol
ijk
e5e dyadic(outer)productofvectors
i k
d deltasymbol
ij
I ¼ dijei5ej ¼ ei5ei identitytensor
ST transposeofamatrix/tensor
trðSÞ traceofamatrix/tensor
Qij unitarymatrix(transformation)
g coordinatetransformationusingarotation
ij
f4 ;F;4 g Euleranglesdescribingarotation
1 2
det T determinantofamatrix/tensor
R rotationmatrix
V deloperator
grad gradoperator
div v ¼ V$v divergence
curl v ¼ V(cid:2)v curl
V2f ¼ V$Vf Laplaceanoperator
s stresstensorcomponent
ji
sji;j commadenotesdifferentiation
ε straintensorcomponent
ij
c “forall”
ε_ dotdenotesdifferentiationbytime(i.e.,arate)
ij
Cijkl stiffnesstensorcomponent
Sijkl compliancetensorcomponent
Cij stiffnesstensorcomponentinreducednotation(i.e.,matrixform)
b Burgersvector
ð111Þ slipplanes
xi
xii Nomenclature
h110i slipdirections
na slipplanenormal
ma slipdirection
sa resolvedshearstress
RSS
s criticalresolvedshearstress
CRSS
g_a effectiveshearrate
Lapp appliedvelocitygradienttensor
Lp plasticvelocitygradienttensor
W* rigid-bodyspin
Wp anti-symmetriccomponentofLp
Dp symmetriccomponentofLp
sgnðaÞ signofa
* “because”
a averagevalueofa
C*,Ceff effective(macroscopic)valueofC(theasteriskisalsousedfor‘complexconjugate’
invariousequationsinvolvingFourieranalysis)
Cr referencevalueforC
C0 polarizedvalueofC(i.e.,Cr(cid:3)CorC(cid:3)C)
h localstate
Mð!x;hÞ microstructurefunction
dV=V volumefraction
dh theinvariantmeasure
H thelocalstatespace
fao;ao;aog latticebasisvectors
1 2 3
Lo locallattice
ðao; ao; ao; ao; bo; go Þ latticeparameters(magnitudesandangles)
1 2 3
~I signifiestheinversiontensor
FZ fundamentalzone
SOð3Þ specialorthogonalgroup(rotationgroup)
SOð3Þ=G leftcosetofGwithSO(3)
FZðOÞ fundamentalzoneforcubiclattices
FZðD6Þ fundamentalzoneforhexagonallattices
ðkÞð(cid:129)Þ kthelementofanensemble
h(cid:129)i ¼ 1PK ðkÞð(cid:129)Þ ensembleaverage
K k¼1
f2ðh;h0j!rÞ two-pointlocalstatecorrelationfunction
U sampleregion,representativevolumeelement(RVE),etc.
Ujr subsetofUsuchthataddingthevectorrtoanypointremainsinU
JðUÞ spaceofvectors,r,thatcanfitinU
vH localstatespaceofinterfaces(betweengrains)
vh localstateataninterface
Nomenclature xiii
SV surfaceareaperunitvolume
SVðRA;n^;RBÞ grainboundarycharacterdistribution(GBCD)
DR ¼ RTARB latticemisorientation
SVðDRÞ misorientationdistributionfunction(MDF)
½0;DkÞ realintervalgreaterthanorequaltozero,lessthanDk
us1s2s34uns subcellofU
cðxÞ ¼ 1ifx˛us spatialindicatorfunctionforsubcells
s 0otherwise
g orunsubcelloflocalstatespaceH,containinglocalstatehn
n n
cnðhÞ ¼ 1ifh˛gn localstateindicatorfunctionforsubcelln
0otherwise
Dn microstructurecoefficientsinprimitiveFourierapproximation
s
Ftnn0 ¼ Hss0t DnsDns00 two-pointcorrelationfunctionFouriercoefficients
S2 thesetofallphysicallydistinctunitvectors
TðRÞ complexrepresentationofthespecialorthogonalgroupSO(3)
L2ðS2Þ setofsquareintegrablefunctionsonunitsphere
kmðn^Þ surfacesphericalharmonicfunctions(SSHFs)
l
TmnðRÞ generalisedsphericalharmonicfunctions(GSHFs)
l
T__mnðRÞ GSHFwithcrystalsymmetry
l
T_mnðRÞ GSHFwithstatisticalsymmetry
l
S statisticalsymmetrygroup
T€_mnðRÞ GSHFwithcrystalandstatisticalsymmetry
l
WpqðxkÞ Haarwaveletfunction
Wpq11pq22pq33ðxÞ 3DHaarwaveletfunction
ds orientationdistributionincellsinprimitivebasis
d^ðiÞ singleorientationincells,oreigentexture
s
M microstructurehull
s
dk0 distancebetweenmicrostructurefunctionskandk0
k
Pr($) probabilityof
PrðT[dbÞ probabilitythatT“hits”db
LðdbXTÞ linesegmentofintersection
Apð(cid:129)Þ areaofprojection
P,L ,A ,V point,line,area,andvolumefraction
P L A V
LA linelengthperunitofarea
fe^ig labcoordinatebasis
fe^Sg sectioningcoordinateframe
i
PtðcosnÞ normalizedassociatedLegendrefunctions
r
s2 varianceoffunction,f
f n
qðxÞ ¼ 10iofthxe˛rUwise localizationfunction
HðUÞ caliperlengthofU
vMð!x;vhÞ interfacefunction
CHAPTER
1
Introduction
CHAPTER OUTLINE
1.1 ClassicMicrostructure–PropertiesRelationships.................................................................................2
1.2 Microstructure-SensitiveDesignforPerformanceOptimization.............................................................3
1.3 IllustrationoftheMainConstructsofMSDPO......................................................................................7
1.3.1 Identificationofprincipalpropertiesandcandidatematerials............................................7
1.3.2 First-orderhomogenizationrelations..............................................................................10
1.3.3 Microstructurehull......................................................................................................12
1.3.4 Propertiesclosure........................................................................................................13
1.3.5 Back-mappingtodiscoveroptimizedmicrostructures......................................................15
1.3.6 Second-orderhomogenizationrelations.........................................................................17
1.3.7 SummaryoftheMSDPOprocess..................................................................................18
1.4 ImplementationofMSDPOinDesignPractice...................................................................................18
1.5 TheCentralChallengeofMSDPO.....................................................................................................20
1.6 OrganizationoftheBook.................................................................................................................21
Summary..............................................................................................................................................21
Design is that mysterious process, at the same time human and divine, that conceives the shaping of
material into objects and systems of clever functionality, useful in leveraging and enhancing human
activity. Microstructure-sensitive design for performance optimization (MSDPO) describes a new
component ofdesignactivityinwhich the specific requirementsinpropertiesand functionality ofthe
materialsarerealizedonlyinspecificpreferredmicrostructures.MSDPOrequiresbridgesthatcrossover
twodistinctlengthscalesdthemacroscopicscalediscernedbythenaturaleyeinwhichspecifiedmaterial
propertiesarerequiredtomeettheneedsofthedesigner,andamicroscopicscaleofthemicrostructurethat
usuallyrequirestheassistanceofmicroscopytoexamine.Itishereinthedetailsofthemicrostructurethat
thematerialcanbedesignedtomeetthemacroscalepropertiesdesignrequirements.
It is difficult to imagine what our world would be like without microstructure-designed pro-
ductsdjet aircrafts that transport people across continents in a matter of hours; computers and tele-
communications systems that rapidly perform calculations, store data, and communicate vast
quantities of information around the world and into the solar system; modern pharmaceuticals
specificallydesignedtoarrestdiseaseandimprovehealthinplants,animals,andhumans.Intheseand
many other examples, matter is organized in particular ways that provide the designer with the
propertiesandfunctionalityessentialfortheconceiveddesign.Forexample,inthehotsectionofjet
enginesnickel-basedsuperalloyshavebeendeveloped,containingprecipitation-strengtheningphases
thatarestableathightemperatures.Thesepermitthedesignertorealizeenginesthatoperateathigh
levelsof thermodynamic efficiency.
1
MicrostructureSensitiveDesignforPerformanceOptimization.http://dx.doi.org/10.1016/B978-0-12-396989-7.00001-0
Copyright(cid:1)2013ElsevierInc.Allrightsreserved.
2 CHAPTER 1 Introduction
Shifting from aluminum to highly textured copper-based alloys in the metallic interconnects of
computer chips facilitates smaller circuits with higher current densities and higher operating temper-
atures, suppressing the electromigration and void failures that limited the application of aluminum
alloys.Secondaryrecrystallizationhasbeenexploitediniron-siliconalloystoobtainhighlevelsofthe
{110}<001> Goss orientation that is ideal for the magnetic properties required in electric power
transformers. Thin aluminumbeveragecans became a technological realitywhen materials engineers
learnedtoexactlybalancetherollingandrecrystallizationtexturecomponentsofthemicrostructureof
the sheet product that is input into deep drawing and ironing operations. Thus, in each of these
examples, and many others, particular characteristics of microstructure are sought that lead to
combinationsofpropertiesthatfacilitatethedesiredfunctionalityofthedesign.
Asourabilitytotailormaterialstomeetthefunctionalityenvisionedbydesignersincreases,sodoesthe
range of possibilities and performance of designs. We say that the design space is “enhanced” or
“openedup.”Foranyaugmentationofthedesignspacethatincreasesorimprovesfunctionalityiswelcome
newstothedesigner.Thepurposeofthisbookistointroducetheengineertorigorousmethodologyfor
specificallytailoringthemicrostructureofmaterialstomeetthepropertiesandfunctionalityrequiredby
the designer. Where this is achieved, the design process transcends the traditional materials selection
componentofdesignbyintroducingmaterialmicrostructureasadesignvariable.
1.1 CLASSIC MICROSTRUCTURE–PROPERTIES RELATIONSHIPS
Futuristsenvisionthedaywhenindividualatomsmightbemovedintoposition,constructing,atomby
atom, materials of specified chemistry, molecular arrangement, and internal structure, to achieve
desirablecombinationsofpropertiesandfunctionality,muchlikeanarchitectwoulddesignabuilding
onebeamatatime.Weareveryfarfromrealizingthisfuturisticvisioninatleasttwoways.First,the
concept of moving individual atoms into prescribed locations faces many practical limitationsdone
cannot simply push atoms aroundbymechanical devices.
Thesecondlimitationisintermsofpredictingmacroscopicbehaviorofmaterialsonthebasisofatomic-
scale theory. Quantum theory is currently the best available physical theory of a solid state, but if one
imaginesthesystemof3NwaveequationsthatmustbesolvedforasamplecontainingNelectrons,eachwith
threedegreesoffreedom(addingtheprotonsandneutronsrequiresadditionalequations),onerapidlycomes
totheconclusionthatmoderncomputationalresourcesfallfarshortofwhatwouldberequiredtosimulateat
theatomiclevelthepropertiesofevenaverysmallmacroscopicsystemconsistingof,forexample,onemole
of atoms. If, however, classic nineteenth-century physics can be used to model material properties, then
significantprogressismadetowardthegoalofdesigningmicrostructuressuitableforspecificdesigns.
Themethodologyoffocusinthisbookembracesclassic(pre–quantummechanics)microstructure–
propertiestheory.Thebasicbuildingblocksofmaterialsaretakentobesmallgrainsorcrystallites,or
small regions of homogeneous material phase. It is presumed that the local physical laws governing
thepropertiesofthesebuildingblocksareknown,bypreviousexperimentaldetermination.Perhapsthey
areestablishedbysimulationwithreliabletheoriesatfiner-lengthscales.Inthiscontext,localproperties
relationships can be thought of as the averaged or homogenized behavior of quantum mechanical
relationsthatgoverntheatomic-scalebehavior.Theoscillationsofthatbehavioroverdistanceandtime
scales appropriate for atomic simulations are no longer present in the classic relations. For many
properties of interest, atomic-scale physics can be ignored, and models incorporating mesoscale