Energy minimising multi-crack growth in linear-elastic materials using the extended finite element

256 Pages·2016·6.91 MB·English

by  Danas Sutula

CARDIFF UNIVERSITY
DOCTORAL THESIS
Energy minimising multi-crack growth in
linear-elastic materials using the extended
finite element method with application to
Smart-Cut silicon wafer splitting
TM
Author: Supervisors:
Danas SUTULA Prof. StéphaneP.A. BORDAS
Dr. Pierre KERFRIDEN
Dr. KonstantinK. BOURDELLE
Alexandre BARTHELEMY
Athesissubmittedinfulfilmentoftherequirements
forthedegreeofDoctorofPhilosophy
in
AdvancedMaterialsandComputationalMechanics
SchoolofEngineering
August19,2016

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To my family and friends,
for their love and support
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CARDIFFUNIVERSITY
Abstract
AdvancedMaterialsandComputationalMechanics
SchoolofEngineering
DoctorofPhilosophy
Energyminimisingmulti-crackgrowthinlinear-elasticmaterialsusingtheextended
finiteelementmethodwithapplicationtoSmart-CutTM siliconwafersplitting
byDanas SUTULA
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We investigate multiple crack evolution under quasi-static conditions in an isotropic
linear-elastic solid based on the principle of minimum total energy, i.e. the sum of
the potential and fracture energies, which stems directly from the Griffith’s theory of
cracks. Thetechnique,whichhasbeenimplementedwithintheextendedfiniteelement
method,enablesminimisationofthetotalenergyofthemechanicalsystemwithrespect
to the crack extension directions. This is achieved by finding the orientations of the
discrete crack-tip extensions that yield vanishing rotational energy release rates about
their roots. In addition, the proposed energy minimisation technique can be used to
resolvecompetingcrackgrowthproblems. Comparisonsofthefracturepathsobtained
bythemaximumtension(hoop-stress)criterionandtheenergyminimisationapproach
viaamultitudeofnumericalcasestudiesshowthatbothcriteriaconvergetovirtuallythe
samefracturesolutionsalbeitfromoppositedirections. Inotherwords,itisfoundthat
theconvergedfracturepathliesinbetweenthoseobtainedbyeachcriteriononcoarser
numericaldiscretisations. Uponfurtherinvestigationoftheenergyminimisationapproach
withinthediscreteframework,amodifiedcrackgrowthdirectioncriterionisproposed
thatassumestheaveragedirectionofthedirectionsobtainedbythemaximumhoopstress
andtheminimumenergycriteria. Thenumericalresultsshowsignificantimprovementsin
accuracy(especiallyoncoarsediscretisations)andconvergenceratesofthefracturepaths.
TheXFEMimplementationissubsequentlyappliedtomodelanindustryrelevantproblem
ofsiliconwafercuttingbasedonthephysicalprocessofSmart-CutTM technologywhere
wafer splitting is the result of the coalescence of multiple pressure-driven micro-crack
growthwithinanarrowlayeroftheprevailingmicro-crackdistribution. Aparametric
studyiscarriedouttoassesstheinfluenceofsomeoftheSmart-CutTM processparameters
onthepost-splitfracturesurfaceroughness. Theparametersthathavebeeninvestigated,
include: meandepthofmicro-crackdistribution,distributionofmicro-cracksaboutthe
meandepth,damage(isotropic)intheregionofmicro-crackdistribution,andtheinfluence
ofthedepthoftheburied-oxidelayer(alayerofreducedstiffness)beneaththemicro-crack
distribution. Numericalresultsagreeacceptablywellwithexperimentalobservations.
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Acknowledgements
Iwishtoexpressmydeepestappreciationtomysupervisors,Prof. StéphaneBordasand
Dr. PierreKerfridenfortheirmentorship. Thankyouforyourgreatmanyteachings,for
yourcontinuedpatiencewithmeandforthemuchneededencouragementovertheyears.
However,IcannotthankenoughProf. Bordasforhisexcellentleadershipinthisproject.
Youhavehelpedmestayontargetandseethebigpictureofmyresearch,especiallyat
times when I would be consumed by details. You have also shown a lot of confidence
in me and encouraged me find my own way around problems and to experience the
learning process. For this, I am very grateful. I consider myself very fortunate to have
beenwelcomedtoyourresearchgroupandIhopeIhavemetmostofyourexpectations.
Ofcourse, thisprojectwouldnothavebeenpossiblewithoutSoitecandtheirfinancial
supportviathePresident’sResearchScholarship. Iparticularlywishtothankmyindustrial
supervisors,Dr. KonstantinBourdelleandMr. AlexandreBarthelemyfortheirtechnical
expertiseontheSmart-CutTM processandtheirmentorshipduringthecourseofmyPhD.
IwishtoexpressmysincerestappreciationofthewholeresearchgroupatCardiff,fortheir
comraderyandforthemanyfruitfulscientificdiscussionsandsharedperspectivesthat
havecontributeddirectlyorindirectlytothisthesis. InthisrespectIwanttothank: Daniel
Paladim,AhmadAkbari,OlivierGoury,ChangkyeLee,HaojieLian,XuanPeng,Claire
Heaney,IuliaMihai,andVinhPhuNguyen. Aspecialthanks,however,isreservedtoProf.
Anthony Jefferson who had taught me the finite element method in the first place and
whoinitiallyinspiredmetodoaresearchdegreeincomputationalmechanics. Duringmy
PhD,heshowedakeeninterestinmyresearchandwasopentonumerousconsultations.
Iwish toacknowledgeallstaff, particularly thewonderfulindividualsin theResearch
Office: ChrisLee,JeanetteWhyte,AderynReidfortheadministrativeassistance. Ithank
theUniversityforthetrainingcoursesandforsupportingmeonvariousconferences.
Finally,IthankmywonderfulparentsVestaandZigmas,andmydearbrotherMantasfor
theirunconditionalloveandsupport,andforhelpingmetobecomethepersonIamnow.
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