The Influence of D amage on the Creep Behaviour of I ce Subject to Multiaxial Compressive Stress States
by
©
Shewn PatrickKenny,B.Eng,Athesis submitted to the Schoolof GraduateStudies in partial fulfillment oftherequirements for the degreeof
Masterof Engineering
Faculty of EngineeringandAppliedScience Memorial UniversityofNewfoundland
May 25,1992
St.John's Newfoundland Canada
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Abstract
Medium-scale indenta tion tellU, suchasPondInlet (984)and Hobson's Choice Ice Island (1989,1990), have sbown that duringrll.J:I.idcrushing events thefailure zonecanbecbaract.erized by distinctsub-rezions.The behaviourort1H~da.rnagl'll iceand crushedrnaterill.1loutedathardspotsor'critical eoncs'ormoucrateto
~~gc~u~i:nn:i=fo~s:~dl:;a,.1~tkt;~:~~~~ventsis seen asHi(:keftod)"lIamic
;;~h~q~~~~~~~:::e~r;~I~~J:~~I~~, i:;:~~~t}~:s~~~ti:rf1ic~L~~bj~~li~~I)I~;~I~~;~
st atic confinement was conducted. The main objectiveofthe test programWlUI
to betterunderstand the creep behaviourof damagt"dicegeneratedatthe ccute ct zone during ice-stru ctureinteractions. Aseriesofccmpressivestress pulses,which
~~1e~c~~~i~~:;~:u~~,2~~ ~t'I~e;:da~gl~t~ +n~:CJa~~~~~~~~:Il~e~o'~~~II;
uniformforallt~ t.whichwas developedby loading theice sampleat aconstl\/lt displacement rat e of10-4I-Ito2% axialst rain.
Alt hough the elasticresponseru marginallyinfluencedby the pre-damagingJl<'ll., the magnitude andrate ofut.Cp strain wusignificantlyenha nced indcIK"ndclIlly ofthe hydrostatic pressure.Also,the creepdeformAtion wu non-linearwithI\p.
plied deviatoric.tressud exhibiteda.tendency (orviKou' prc cesaeatodominate at higherloadlevels.Oneo(thekeyfinding,wu the magnitudeoflate ralslrain, hence volumetri cdeformat ion,and .hear strain developedindependently of theconfining pressuresinvestigated.Theeoneiderable enhancementand non-lineari tyof creep str&inevidentin the experimental progr&mhas si!nifiantim plicationswhen eon- sidering full-scale event•.Furthermo re,thefindingspointtoposslble simplification.
toice-load modelsand constitu tiverelationship'thatmaybe utilizedineontl nuum a.nalysis oflee-st ructu re interact ion.
Ackn owle dgements
~~ec~~~~~rof:hi~l}~~~er~~csm~h~ua;:r~i:~ tUri.di~~eJ~~~~~~n~s;~i 'af~hau~~o~~
Dr.Garry Timeo,NationalResearchCouncilCanada (IME), (or thoughtful input
Co~~~irc~ t~~d~ (1~[»)?~u~ie~~e:~ognni~1o~:heT:ec~;:a~:ii~na:d~~i~~r~
Finally, thankstoMr.JlngXiao,MemorialUniversity,for helpfulcomments and interestingdiscussions on iccengineering.
Financialassistancefor this workwas providedby Atlantic Accord Career Develop- ment AwardsBoard and NSERC.
iii
Contents
Abst ra ct
Acknowled gem ent s Tableor Cont e nts Listof Figures ListofTab les Nomencl at ure
1 Ice-S t ructureInteraction: Ratio nale for-Ice Mecha nicsRes ear ch 2 DeformationalBeh avio ur
o r
Ice2.1 ContinuumViscoelasticResponse , . 2.2 TheProgressive Dama ge Processinfcc.
iii
12 2.2.1 Microcra.ckEvolutionUnder CompressiveStrcssSlales I~
2.2.2 Macromechanics of theleeCrushingProcess• .... 17
3 Expe rim ent alPr ogra m 37
3.1 PreparationofT~tSpecimens. •.•.. ... 38
3.2 TestEquipment 41
3.3 TestProgram . . ... 46
4 Analyais and Discussion of ExperimentalResult! 54 4.1 Creep Enhan cementunderTriaxial Stress State ...
4.1.1 Adel Deformati on ..
55 55
4.1.2 LateralDeformation and DilatationinIce 66
4.1.3 Triaxial Behaviour i7
4.2 Relat ion toObservedFieldEvents. .. . .. . . ... 94 4.2.1 Mode llingMechanicalBehaviour:Preliminary
Analysis... ... ... .... .... 99
5 Conclusionsand Reccmmendatlcne 106
References 109
Appendix A 115
List of Figures
1.1 Pressure-Area Curve for Ice.
2.1 Long-Term CreepforPolycryetalllncGranularIcc. 2.2 Generaliz edViscocla.~licModel
2.3 Four Eleme nt RheologicalModel for PclycryarellincIcc. 11 2.4 Photograph of a Multiyear Ice FloeImpact ingHansIsland . 1:1 2.5 SchematicIllustration of Wing CrackDevelopmentin a Solid.... 17 2.6 Logaritbmi cPlotofthe Variation inUnia xialCrushing Streng thof
Ice with IncreasingStrainRate ...•,••.• . . ..• . ..•. 18 2.7 Schemat iclJIustrat ion ofthe Stress- StrainBehaviour forIce 19 2.8 TypicalStress-StrainCurve forPolycrystal line,Granular Icc. , . •. 21 2.9 Creep EnhancementDueto MicrocrackingorDamage... .. 22 2.10 FailureModes
or
Ice underCompressive Stress Statesat IIigh StrainRates(> 10-3 ,-1) ,.. 24
2.11 Datasetfrom Constant StrainRate Tests under HydroetatlcConfine-
ment . . ... . .. 25
2.12Teardrop ModelDevelopedbyNadreauct al.{1988} 27 2.13 Multiaxia.lDeformationMechanisms inIce••• ••• •• • ••• . 28
2.15 Schernet.cIllust rationof a TypicalFailure Surface. 32
2.16Idealizationof Ice-StructureInteraction Events ... 35 3.1 Schematic of Equipment Used in the ManuraduringofIce Samples 38
3.2 MoldforMaturingIce Samples 39
3.3 Horizontal Thin Section 42
3.4 Schematic Illustration of the Triaxial Cell.. 43 3.5 Photographofan Undamaged Ice Sampleand a Fully Instrumented
Specimen ..._ ... .•. ..._ .• . ... ... . 45 3.6 TypicalAxialStress-StrainCurve .._ ..__ . 47
3.7 Photographof aPre-DamagedIce Sample 48
3.8 Thin Section through a Pre-Damaged Ice Sample 49 3.9 VerticalThin Section througha Pre-DamagedIce Sample _.. 50 3.10 UnaxialStressPulse History•. .•.._.. . 51 3.11TriaxialStressPulseHistory•..._•.._. _ _ 51 4.1Typical DeformationalResponse._..•.• . • • • •. ... .. •_ 56 4.2 Axial StrainResponseunderUniaxialLoadingConditions .. . 57 4.3 AxialStrainResponse at 4 MPa Confinement•• .._ . . ... ... 58 4.4 Axi:l.l StrainResponse at10 MPa Confinement._ . 59 4.S AxialStrain Response at20 MPa Confinement.••.... .. 60 4.6 Stress-StrainResponseforInt act Ice Samples .. _ . .. ....•.. 62 4.7 Stress-Strain Responsefor Pre-damaged Ice Specimens ...• •. 63 4.8 Non-Linearityof AxialStrain •.•_. .... • • •. . . .•.. 65 4.9 LateralStrainResponse under UniaxialLoadingConditions ._. _. 68 4.10 LateralStrai nResponseat-tMPa Confinement ... . . .•_.. 69 4.llLat eral StrainResponseat10 MPa Confinement... ...••.. 70 4.12 Lat eral Strain Responseat 20 MPa Confinement.... . . 71
vii
4.13Non·Linearity orLatera!Strain .. . . • • • . .. .. . . ... . 73 4.14 StrainJatio01Mu lt i·Yt'u Sea Ice. .•. . ..• ... • •. . . ....75 4.15 Stra inRatioror Pre- Damagedlet'd20MP~COlllint'lllt>nt...76 4.16Volume tr ic andEquivalen t StrainunderUnia xilll l.o.'l.d ingCon ditio n, ;9 4.17Volumetric andEquivalent Strainat·1MP..Canlillcmcnt... ... SO 4.18Volumetr ic and EquivalentStrainat
to
Mpa.Conlinel")ClIl .. 81 4.19Volumet ricand Eq uivalent Strain at20Mpa Conlinemell t . .•. . . 82 4.20Dilata t ional Strain·R.I,tc as....Funct ionof Volu metric St rese.. .... 81 4.21Dilat a tional St rain- Rateas aFu nctionof DeviatoncStrcs~. .... . 85 4.22Equiva.lentStrain·RateasaFuncti onof Devietceie Stres, 87 4.23LogarithmicPlot orShe.uStrain·Ratea.saFu nctionorShear Strt."", 88 4.24Logarithmic Plot orEquiva lentShain-Ralt'andDeviatorStrl'!l.'1. .. 89 4.25Non.linearity01EquivalentShain·Rate withDevletcrleStres,.... . 90 4.26Rat ioorbulk &lid vonMise8 stress-draindata•• • ••.... . ... 93 4.27FailurePrOCt':UroraSpherical IndentorPm .eh atins anIce~'cature 96 4.28Ho rizont&!ThinSection,orSamplesTakenfromTClitFacenor· OJ . 97viii
List of Tables
3.1 ReferenceStres sSignaland MeasuredAppliedDeviatoricStress. . . 53 U Mean ElasticModuli••. ... . . . .. . ... 64
Nomenclature
A •constant,reference strain-rateper unit stress(mm·mm-l·s-I .MPa-ll.
b •power index=:::lIn .
e, • constantfor referencegrain size (nun ).
d •material grainsize(mm).
dl •reference grainsize.
D(l-r)• creep complianceIunctlon.
e •equivalentstr ain[mrn-mmrl],
e -
equivalentstrain-rate(mm·mm-t·s-1 ).E -elestlemod ulus (MPa ).
E~ -elsetic modulusofthe Kelvinunit (MPa).
E", •elaaticmodulus of the Maxwellunit(MPa).
Ep -isthe initial modulusof intact material(MPa).
/(5. ) • damage effectparameter•.
•constant.
• powerlaw constant,typicallytaken as3.
N... •numbe rof grainsper unit area.
tV •
isthe rateof crack nuclee rion.N. .is therateconstant.
p •hydrostaticpressure(MPa).
q • stress exponent.
• GOodant'"1.
S •von Mises stress(MPa).
S. -Schapery',dlLIllage parameter.
t -time (,).
T'" ~meltingpoint(0Kelvin).
-inverse relaxation rat e(,-I). -strain(mm-mm'").
e(t) -time-dependentdeformation[mm-rnmt"].
(c -vi,coUlstrai n[mm-mm rl], (J -delayed elastic strain [mm-mm'"}.
(, ~elast icstrain[mm-mmr"],
(ij -deviatoric,tra in(mm·mm-I).
ev -volumetric,train(mm 3·mm- 3).
(1,2,3 -princi palstrain ,(mm 'rom- I).
i _,train- rate (mm·mm- l ·s-1).
i. -reference viscousstrain-rate(mm·mm-1 ., -I).
(.~ -referen ce ,tr ain -rate (mm·mm- I·s-I).
('v -volumet ricstrain ·rate(mm3·mm-3's- I).
• isthe damage parameter.
•applied stress(MPa).
Uc •crit icalstressfor cracknucleation(MPa).
Uij •deviatori cstress(MPa).
u. .normal izingor unitstress(MPa).
u~ •volumetricstress(MPa).
• app liedshearstress(MPa).
Tj~ •viscosityof theKelvin unit(MPa·s-I).
Tj", •viscosityoftheMaxwellunit (MPa·s-I) .
xi
Chapter 1
Ice-Structure Int eraction:
Rationale for Ice Mechanics Research
The majority ofCanada'soffshor:'l naturalresources,such as mineral depositsand hydrocarbon reserves,are situated onthe continentalmargins.Explorationand recovery of thesereecurcea,in Arcticandsub-Arctic waters,presentsafon nideblc challengeto the engineering andscientificdisciplines. One of the most important factorstoconsider in design isthe magnitu deofice pressureexertedon offshore st ructures andvessels.Est imating reliabledesign icc loads is csscnlialto ensure structural integrity andeconomy of design.
The developmentof inter a ction modelsbased on how icc deforms and ultimately Cails app ears to be a relatively str aightforwardengineeringdesignproblem. flow- ever,putinvestigationshave shownthat average global ice pressuresrange from 10MPa in smell-scalelabo ratory tests to0.5 MPaforimpactsof multi·yearsea ice with artificial islands,Thispronounced variation betwee n measuredindexme-
chanical propertiesand full-scale icebehaviour isknownasthescale effect.The phenomenonhas beengenerallyassociat edwithnon-simulta neous, britt le failure and st alistical distribut ionof Raw size;seefor exampleIyer(1989) orSanderson (1988).Consequently,prediction oficeforcesistypicallyempiricalin nature and based.onextrapolationof data byconsidering theconta ctarea oraspect ratio (Fig- ure1.1).Moreover,icc-stru ctur einteraction events arccomplexanddependupon manyfactors, suchas inherentmaterial andmechanical properti esof ice, degree of confinement,str ucturalcomplianceand contact geometry. Also,recent laboratory andfield investig...tiona have indicated thatfriction orpressuremeltingand sintering areact ivemechanisms.Althoughthe crushingmode of failureisgenerallyobserved during interactionevents, the process can be compoundedby mixed-modedeforma- tion(l.c. crushing coupled withsplitt ing, out of planeflexure,spalling, or buckling).
Typicallyduring crushingevents,regions ordamagedand crushedice are generated atthecontactzone and discrete particlesare ejected.at the freesurface.
Experie ncewith small-scaleindentation tests [Kry, 1978), lighthouses(Multa nen, 1977) and CookInlet platforms (Blenkarn, 1970) revealedthatduringapredomi- nantly crushing mode of failure,there was a cyclical variation inthe loadaccompa- nied by structural vibrations.Althoughrecognizing the significance of ice-induced vibrations ,put designphilosophyconsideredthat cnlynarrow,flexible structures would be susceptible.In the winterof 1986,however,theBeaufortSea structure Molikpaqexperiencedsevere vibrations dueto the repeated crushingfailure ofa multi-yearice80c whichproduced an eight metre high pile of pulverized iceadja- cent to the structure(Jefferiesand Wright,1988).A prominent feature of the
~ d
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9
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0
interaction wu a,luu e-lod; phenomenonwhich enhanced the peak ice1o&ds and increased the amplitudeofvibration.
In an effort tounden tandthe scale effectand dynamicsof theice crushinr;crushing process,&numberof medium-laic indentation test.,such uPondInlet (J ohnson and Benoit,1987) andHobson'sChoiceIce bland (Frederkinget al., 1990) have been jointlyundertakenby government,industry anduniversity researchest eblishmenta.
Typicalaverageglobalpressuresexerted were onthe orderof3-5MPa,whereaslocal peakpressures attained magnitudes of 60 MPaormore whichhada cha racteristically variedspatialand temporaldist ributionaccompaniedwithsteeppressu re gradients.
Clearly,the designof offshore.tructurestoresist ice forcesisademandingtuk which mustconsider averager;lobatpressures (foundation, .tability), magnitudesanddis- tributions ofpeakJoca1 pressures(framing members,plates) and dynamicvibra tion.
(workingcondit;ooll,structuralintegrity).Thecomplexity of ice-structure interac- tions has hinderedthe developmentof anyrigorousmethod for thecalculation of design iceforces. Although there aremany empiricallybased methods oriented towarddeterminist ic orprobabilisticdesignloads,the difficultylieswithin thede- velopmentof aI.implified'ice load model based on indexmechanicalpropertiesand fielddata which eccuretelypredicts full-scalebehaviourCora numberofscenarios.
Consequently,in thedevelopmentofconst itutive laws and failurecriteriaforice, numericaltechniquel,
.um
asthe finiteelementmethod (FEM)appeartobe most promising. However,&Dyanalytical ornumericalmodel is dependentonthequality of input parameten and basic unders tan dingoCice mechanics.Onlybyinvestigati ngtheunderlyin~f&iluremechanismsinvolvedcanonedevelopa. morerealisticapprou h inicc mechaniatoanalyse interactio n eventsandestablish afounda t ion upon which accurateand reliabl e iceload,canbedeter mined.
The focus ofthisthCJisistoinvesti gate the inOuenceofmicrocrackson theerccp deformationof~ranular,freshwater icesubject10triaxialcompressive stressstale., The expe rimentalprogram "iIM to'simulate'thebeh aviour of thehighlyda mageu crushed material, 6ubjectto volumet ricand devlucrlc stressstates,whichis created atthecontact surfaceduringice-structureinleractions.Using thisapproa ch, the ultimate goal is thedevelopmentofaTcalisti c iceload modelto aidinthe designof offshore structures.Thescopebf theworkpresentedhereinmay be summarizedu follows:
1. Literaturereview of thedama geprocessin ice witb spec ificreferenceto lebe- ra.toryand field dataconcerni ngcompres!livefailure.
2.Description ofthe testprograminclud inglaboralory appa.l'atul and experi- mental procedure,
3.Analysis anddiscussion of thetest da ta.
4, Crit icalessesementofthemajorfindingsAndrecommen dations i'orfuturerc- seare h.
Chapter 2
Deformational Behaviour of Ice
Recentinveltigl.tion. havesbowntbarthe dynamiCl associated with ice-structure interact ionevent sanbe, inpart,related. tothephysicalattrib utesoftheecn- tact zone. Theproceuwhereby&Dintactice featureprogressively dam&&ClII and crushedm.ateria!islubsequentIyextruded ...ithcontinued deformationisrresently the subjectof considerableinterest.
The sca leell'ectnecessit a ta the combinati onoffull-scaleobservat ions, fieldmea- surementsand controlled laborato ryexpe riments wherebykeyparameters for the development. ofanice-loa dmodel canbecharacterized.
2.1 Continuum Viscoelas ti c R esponse
Unlike most engineeringmaterial s,ice naturallyexists athighhomologoustempera- tures, typically2::0.85T ...,whereT", isthem cltingpointin degrees Kelvin.Similar to metals, concrete and rockathightemper at ures,iccwillcreep when subjectedto any slress otherthMl a purely hydrostatic stressstale.This isevident inthenow ofglaciers, where thestrains experienced atthe hue, subjectto enormousconfin- ing pressures, has essentially the same deformational responsewben iccis loaded under uniaxialconditions.Alt houghcreepisgenerallyassociatedwith acontinuum process, at higherloadingratesitissignificantly influencedbythepresenceofcreeks.
Long-term creep is developedthroughthreestages of varying strain-rales; aninitial tran sientcreep rate, secondary steady-statephaseand, finally,anincreasingcreep rate(Figure2.1).Thereis somedebateas to whethe rthesecondary or minimum cree p rateis alundament al material propertyormerely marks the transit ionfrom the primarytotertiarystages - see lorexample Sinha (1990&). Thetertiar ystage isolt en associated with microcrackingand large str ains, whichresultsinaccelera ted deformationratesand possible failure (Gold,1972).Thishaaalsobeen evident in the time-dependent deformation01brittlerock (Costin,1985).However,Sanderson (1988) points out that dynamicrecrys t allizationCAllalsoinitiatetcrtiuy creep.
Thus it is diflkulttodifferentiatebetween theint rinsicdeformat ional responseand thatdueto damage.
Straia
Thne Figure2.1:Long-Term CreepCorPolycrysta.Uine Granul arIceMarking theThr ee Stagcs, Pri maryI,SecondaryIIand Tert iaryIII.
The time-depen den t deCorm&tioDalbeha viouroCice underload,modeled as a linear viscoewticsolidunder.. uniaxialstress It.tC,canbeexpressed&3,
t(f)
=[
D(e-1')~dT',
(2.1)where 0$T$lendD(t-T)isthe ereepcomp1i&Jlce(rat io oCela )when aconstant stressisappliedat timel
=
O. Mechanicalmodels aimulati ngtheviscoelastic behaviour of materialstypicallyemploythe combina.tion ofIpring (Hookean)and da.shpot (Newtonian)elemenh ; see Figure2.2.~~J-4JQ-~
I
Max well·1
Kelv inI
Figure2.2:Generalized ViscoelasticModel. TheFirstTwo Elements,a.Single SpringandDeshp ot,ComprisetheMaxwell80dy and the Sequence of Parallel Element!Correspon dto KelvinUnits.
The cree pcompliance fortherheologicalmodelshownin Figure2.2isgivenhy (Fhigge ,1967),
1 " 1 [
(-E. )]' -
TD(t-r):::: - + E - l-ezp - (I-r )
+- .
Em i.I E. 'II< '1...
whereEisthe elas ticmodulus, ,.,isthe viscosityand
i
is the inverseretarda tiontime.(2.2)
Jordaanetal.(1990a)andSenapery(1991)pointout that for theseries of Kel vin units a spectrumofretard ationtimes withd.distribut ionfunctionilrequired.How- ever, inpra ctice, th edeterminationof such a formulationproVf'.lI tobedifficult and oneresortsto approximatemethods- see JordaanandMcKenna(1988).
Duringcontinuousicecrushing andclearingevents the force-t imehistoryisdyn a mic in nature (l-tiOHz) and thetime of loadingcanbeconsideredrapid.The creep
10
response canbethus generalizedbyconsideringtheprimary andsecondary terms and the lota ldeformat ionexpressed83,
(2.3)
wheree,is the elastic strain, (~is thedelayedelasticstrain and c.is theviscous flow,
Delayed elast ici ty(transientor primarycreep) isarecoverable strain processwhereby grainboundaryslidingoccurs, through diffu sional flow,dueto theshearstresses generatedbet ween grains. Viscous dow (power-laworsecondarycreep),however, is non-recovera ble deformat ion as aresultof intrag ranulardislocationmovements.
The readeris referred toHobbs (1974)andSin ha(1978) for furtherdiscussionon thephysicsofcreepin ice.
Ondiscussing the creep processill ice,the approach.taken in thisthesisisto de- scribe thenonlinearviscoelastic behaviour by a{our-clement Burgersmodel(Figure 2.3). The abse nceof aKelvin series,to describethethenon-lineardeformational character isticsotice,precludes simpleclcsed-fcrmsolutio nsusing linearviscoelastic theory based onthebasicBurgersmodel.Consequently, Jordaan and McKenna (1988)and Szyukowskiand Glockner(1985)prop ose tbattheviscositiesbe consid- eredst ress-dependent,
II
Figure2.3:Four Element RheologicalModelfor PolycrysullineIcc.The Burg..
- ,!
Model is.. Combina ti on ofa Kelvin Unit, wh ich Ccr rcepcndeto DelayedEIMtic Strain, end a Muwell Body, which Represents ElasticDd ormdionandVi~coll~
Flow.
Therearcmanypheno menological and constitutivemo deleproposed fortilecree p behaviouroficc;see(Ofexample,Ashbyand Du val(1985) and Duval ct1.1.(199 1).
Althoug hthereisxeneu.l ilgrecmenton theform of ..secondar ycreepcxpl'Cl'sion (i.e.power law),tbetime-dependent deformationislesswellcharacterized.Thisis a consequenceofthe early workon creepof icc which concent rateddTa ft!onthe long termflowoC gladen.The basicrelationship morecommonly adopt ed,asill thisthesis,forcreep complianceisthat dueto Sinh..(1978).
where(Tistb eapplied.stres.at timef
=
O.Eisthe bulk elastic modulus,CIi.l aconst ant for a Kiveneeierencegrai n size(dl ) ,distheice grainsize,0Tisthe inverserelaxa ti on rate ,icisthe referencevisco usstrain-tale atfT.and&, -',and11areconstants.
The semi-emp iricalequation isvalidCotisotropicpolyctys~allineicein whichthe micr{., .~ructureh...Dot deteriora ted dueto thepretence
or
void.OJ {JactUJtI,A.willbediscussed in moredetaillater, thecreep responseislignifie.l ntly influenced by mlcrccr ecki,J.
12
2.2 The Progressive Damage Process in Ice
Dama ge connotesa.cban gein structu ralintegrity whichresultsin the weakeningofa mate rialbyred ucingtheeffective modulusor sti ffness.There are many microstruc - turalcharacleris tia which canbe att ributed to damage;these include,nucleation and growthofcavitieswhich causegrain boundary emb ritt lement,the creationof fracturesurfaces,andeven the presenceofvoids,solidinclusionsorpre-existin g defects ,suchas brine pockets and draina geehannels.Forthe purposesofthisinves- tigation,the da mage process usodated with microcracksif ofprimary importance anda descript ionbased. onlaboratoryandfieldexperiencewillbe presented.
2.2.1 MicrocrackEvolution Under CompressiveStress States
Ice is a unique materia l,inthatitcanbehaveas a viscoelastic solid andyetexhibit extremebritt1enCl~under highloading ordefor mat ion eetee. Theprop ensityfor
£ract urin& canbe appreciated bythe low valuesof fracture toughness(150-200 kPa ·ml/2) andstrainenergy release ra te(0.5-2.0J·m2·s-I) ,which is of thesame ordera.sglass . Thesplittingofice floes severalkilometresindimension markedly illustratesthebrittl ebeh aviour o Cice (Figure2.4).Althoughthisdescribesascenar io differentfromtha t ofa progressivedama gingpro cessundercompressivestress states, itneverthelessdemonstrates theextenttowhich fractu ri n g may takeplace.
decently,there has beensignificantresear ch effor tconductedon thecharacterization of events leadi ng up toinitialcreel:Corm at ion and thesubsequentdamageprocess in ice. Theseinvestiga tions include Cole(1985,1991),HaJlam(1987) andSinha
13
14
(1984,1990b).The compressivefracture process can be essentiallydivided into two distinctevents:crack nucleation and crack coalescence.Unlike deformationunder tensile stresses wherea single crack dominatessuddenCailure,an arrayof stable microcracksisformed under compressionand the nucleationis considered to be, at leastinitially,independent of neighbouringevents. Generallyspeaking , for high deformat ionrates(i::::10-49-1),theinitial cracks form at approximately 0.05%
strainwhich correspondstostress initiationlevels on the order of 2 MPa.(Cole, 1991).The cracks grow rapidly relative to theloading rate andshow notendency to propagat e after formation(Hawkes and Mellor,1972). Thustheir evolutioncan beconsidered Insrentanecue growthto full size whichis on the orderofa grain facet. Kalifaet11.(1990)studied crack nucleation throughvideo recordingand determinedthat the nucleationof a crackoccurswithin0.07-0 .14seconds.Also, a numberoCinvestigationson polycrystalline freshwaterice have shown that the cracksdeveloped are predominantlyalignedparallel with the principalcompressive srross axisand randomlyorientedin a plane perpendicularto thestressaxis; see for exampleKaliCaet al.(1989) or Cole (1991). Interestingl y,Jordaan andTime- (HI88) showed that,duringsmall-scale indentation tests,cracksorientedparallel tothe loadingdirectionwere generatedalong linesof maximum shear. Continued deformationcauses the crack densityto increasewherebyinteraction orcoalescence occurs and possiblycl.'1minatingin abruptfailure.Althoughthe characterization
o r
the microcracking processiniceiswell understood,there is still debate on the physical mechanism(s)responsiblefor thegenerationof cracks.15
Gold (1972) was the firat toconduct acomprehensive experimentalstudyon the {aJiuIeprocess in ice wherean analysis onthe dependenceof microcracking activit y wit hstress, strainand timewaspresented.Itwas observed that thecracking activity cons isted oftwoindep endentdistrib utio ns:one populati onof crackswas a function of the strainlevel and the otherindependent ofslrain. The {ormer wasconsidered to be associatedwith a dislocationpileup mechanism,based on theSmith-Barnby model,due toa resolved shearstresson theslipplane, and thelatter was related to theinhomogeneouscrysta lline struct ure.
Sinha(1984) proposed thata criticalgrainboundaryslidingdisplacementwasre- spo nsible fortheonset ofcracking activit y. An alysis on hundredsof grains showed that dislocation glide didnot playaroleinthe formation of microcracks. Fur- thermore,itwas statedthatthe contribu tionof delayedelasticand viscous creep componentsindicatedthatthe fractureprocesswasnot truly brittle.However,this could alsobeattributedtothe relatively lowstrain ratcsemployed intheexpert- menta(:=:::10-6to 10-40s-l)sincetherewas a sharp decrease instra in to first cracks overa narrowrange of increasing stress. Thisisalso supportedby observat ions made byGold(1972) and Kama eta1.(1989), wher eat higherloading anddeformation rates,the crackswere predominan tly generat ed atgrainboundaries.Obviously, sinceice isa viscoelasticsolid,the influence of thecreep components on fracture events issignificantly dependenton time or rateprocesses.
Theincreasingfractionof intergranu larcracks athi.~berdeformation rates w&sease- ciatcd with theanistropyof elastic material propertiesfor neighbou ring icecrystals withinthe solid matrix , that is, random orientation of thec-axis(Cole, 1988; Sunder
16
and Wu, 1990).When a remote stressis applied, nonuniform strainenergiesdevelop dueto the incompatibilty associated withneighbour inggrainswhich leads to stress concentrationsand the{ormation ofcracks . Unfortunately, locat ion doesnot neces- sad lydictatethe mechanismforcrack nucleationsincedislocationglidewillproduce both inte r-and intragran ularfract ures.Also, similar grain sizedependencies make itdifficult to determinethe source of the microcrackingevents(Cole, 1988 ).
Withinc reasi ngdeformation,cracksmay begin tointera ct orcoalesceat higher strains, butCole (1991)did not observegrowthofpre-existingcrades past the peakstrength.However,experiencewithotherbrittlematerials,such as ceramics, concrete,PMMA,androcks,therehas been observed growthof wing cracks- see(or exampleAshbyand Hallam(1986),Cannonet al.(1990), Horii and Nemat-Nasser (i.985).Wingcracks areout of planeextensions ofpre-existingcracks inclinedto themajorcompressivestress axis(Figure2.5).A tensile etreee zone develops at the tipof thefracturesurface due to resolvedshea rstress and tbe crack isreoriented in thedirectionofthema jor stressaxis.Furtherincreaseinstrain energycauses the crackgrowth which couldpossibly propa gatethroughtbesampleends causing failure.
From&scientific viewpoint,the understandingof physical mecheursmsrespon sible
forcracks nucleationisimportant;however,forengineeringpurposesonlythe end effect on materialbehaviour is critical. A parallelcanbe draw mtoplesticitytheory whcre only tbe effectsof dislocation movementsAre accountedfor in theanalysis.
In anyevent ,itwould bepracticallyimpossible to follow the myriad of microcracks which aregenerated during theprogr essive damaging process in ice.Thekey devel-
17
opmentis thestructuraldeteriorationduetoa.networkof crackswhichreducesthe effect ivemodulusofthe materialresulting in aloss of deformationa lresistance.
p
Ten s ile Zon es Format CrackTipDu e to Shea rStlIC;;:\
p
Figure 2.5:SchematicD1ustration of Wing CrackDevelopmentina Solid .
2.2 .2 MacromechanicsoftheIceCrushing Proc ess
Present knowledgeof themechanicalbehaviouroficehasbeenfounded on field measurements ,contro lled laborator y tests, as well as,pMtdesignexperience.With the developmentor Arctic oil fields,earlyicemechanics research(1960-70's)con- centrat edon peakforces andfound not onlyconsiderablescatterinthe databut also thatice strengt hwasdependent uponanumberof parame te rs.Indeed,Brown (1926)was one ofthe first to recognizethis: ... theterm compressionorcrush-
18
lng strengthofice ismeaningless in-itself.Thebehaviour ofice in compression is differentat thesamerates01loading at differenttemperaturesand at different rates ofloadingat the same temperature. The timelactoris theall important quantity."Brown'sinsight on thedeformational response of iceisshown clearly in Figure2.6.Dependingmainly on confinementand deformationrate, ice canbehave as a nominally ductile creepingsolidor an extremelybrittlematerial.
Crus hin g Stre ngth (MPa)
101
10·
10'
....L."T""---...---r---"T""---...
-=:~10. 2 Strai nRate
Figure 2.6: Logaritbmic Plot of th eVariationin Uniaxial Crushing StrengthofIce with Increasing StrainRate.
19
ForincreMingstrain-rat es there exists acorrespon dingtrend {orhigherpeak strengths.
witha.maximum occurring aroundi:::10-3, - 1.This regionhasbeen termed the ductile-bri tt letrans it ionzone and isof particular engineeringimportan ce since the crushing strengt h isa maximum. The transition isrelatedtoachange in theob- served deformatio nal behaviourwhichcan be mainlyatt ributed to microcracklng activity. This phenomenon is schematically illustrated in thegeneralizedstress- strain curvesCoriceasshowninFigure2.7.
AxialStress (MPa)
10
!ill r:.8
>10.3
Fractureor'Brit tle' Failur e @ j';l/
.1....
I~·',
o
.3
>10
<10·6
uj4
<10·6
0 .'
1.0Figur e2.7:Schemat icIllustr ation oftheStress-S trainBehaviourand Failure ModC8 forIce under UniaxialCompression.with Increasing Stra.inRates.
20
ForthelowerdeformatioDratts(~10-8,-1)thebeha viour isnominally ductile andcontinuumcreepresponseisobserved.As thestrain-rateapproa.chesthebrit- lieregime,~10-3
,-1
foruni&Xialcondit ions, thepropensitytoIorm microcracks increases. AlthoughpeAkstressisattainedat.relativelylow strain level{ee O.OO2), thereis"considerabledegreeofdamagedue tothepreseenceofmicrocra.cks;this has been abo observedbyCole (1991).Gold(1972)reportedtha twhena rapid and extensive network ofcracks developed,this caused<tostru cturalinstability whereby thespecimenlosesresist ancetodeformat ionand creep is acceleratedfrom thepri- marystage directly totertiarybehaviour. it should benoted thatthe transilion strain-ratc anddegreeof microcrackingactivityaredependent uponthe same pa·remetera.Forexample,Janel (1982) andCole (1985)haveshownthatthetransition strain·rateiDcreueswith confinement andfinergrainedice respectively.
Prior topeakstressthecracksdo not significantly in8uence the bulkmechanical properties.Thisanbeappreciatedbythe slope ofthe strell-Straincurvewhere microcra.ckin~leadsto nonlinearity a.nd'strain softeninK'descendingbranch.This isaboevident in ot herbritt le materialslikeconcrete androck;seeforexample Dougill(198S).Animportant. featureolthest ress-straincurvessbownin Fisure 2.7isthe horizontal plateau reachedafterpeakstress.Thisgivesan indication of the active deformational mecha.nism;thatis,one of continued energy dissipation throughviscouscreep('1
=
ali).Also,ifthe sample isreloaded at thesamestrain- rate , tbentheplateauisfollowedand thestress-.t rain curve hasbecomestabilized.However,witha subsequentincrease in str ain-ratethe sampleisfurtherdamaged andrestahilizes(Figure 2.8).
21
Figure2.8:TypicalStress -S trainCurveforPolycrysta llinc,Granular Icc Loade dat Various Strain Rates,Jordl1ond al.(1990b).
The directeffect of microcraekingor damage is the degrad atio nof themechanical propertiesof thematerial,such as the loss inshear resistance (G) orbulkstiffncsll (E).Microc raekingtend sto reducetheoverall struct ural resistan ce to defor ma tion andenhancesthe basiccreep response(Figure2.9).Meyssonnicrand Duval (1989) andJcr daa n etel.(19901.)have shownthat damage or prcst tainCAUSClIa significant degradatio ninthe mechanicalpropertiesof icc.
Athighstrain-rates(>10-3 ,-I),whicharemoreapplicabletodynami c icc- struct ure interec t iccevents,phen omena known&5slabbingoraxialsplitt ingcan be observed inadditiontomicrocracking. These eventsareassociatedwiththe out or plane extensionofa pre·existi n ll;crackinclined to themajor str essaxis (Figure 2.5).The growth of wing cracksresultinthereorienta tionorthecracksurface par-
22
-e
lIndamaged (-)andp'~damaged( ••.)
Figure 2.9:CreepEnhancement Due to Microcra.cldngor Damage.Jordaan d al.
(/9910).
allelto the principalstressdirection ;l.e., maximum tensile force is perpend icular to crack plane. Atlower strai n-r ates(... 10-·5. 1)wingcracks are typicallystable; however theimposition
o r
a small,lateral tensile stress causesthe crackstopropa- gate rapidlyunt ilfailure .EvidenceoCwing crackshas been reportedin otherbrittle materials ,suchas concret e, rock,sulphur,glassand PMMA,Wang (1981) observed thisphenomenon intests on multi-year sea ice.The process of axial splitting or shear (aulting, shown in Figure 2.10,is predomi- nantlyafunct ionoCconfinement; see forexample, Horiiand Nemat Nasser (1985).
Axialsplittin goccurs athighst rain-rates, under nominally uniaxial conditions,with no platen-s pecimen end restraints,wherea single fracture, typically associatedwith wing cracks,prop agates through thematerial resultinginfailur e of the sample.
23
Conversely,sla bbingdominates with increasingconfinement or end effects where continueddeformation causesthecracks tocoalesce whichT'elulhintheIormatlou of ashear {auh.Thisprocess is attributedto "("milyofstable wing cra ckswhich has coalesced along thefault surface,whereby a matrixof coarseand fine powdered material iscreated - see Schulson(1990). Thereader is alsoreferred to articlesby Cannon e!at.(1990),Murrellet al.(1991) andSchulson ctal. (1989)for furt herdis- cussionand experimental evidenceon theaxialsplitting andslab bing phenomenon.
The shearzoneis also evidentduringuniaxial compreealcntesting of multi·year sell.
ice atlower strain-ratesthan whenthe phenomenonis observed inpolycrystallinc ice(Kenny etat.,1991).This couldpeseibfybe attributedto theearlydevelopment of wingcracks atpre-existingdefects,evidentinrock mechanics, or that the interna l porosity features[i.e. brine pockets,drainage channels) createa planeofweakness for thefault todevelop. Ashbyand Hallam(1986) developed a wingcrack model to describethefailure ofbrittlematerials andthe concept of axialsplitting andshear faulting.
The ice crush ingprocessbee been thus fardiscussed onlyin termsof the uniaxial behaviour;thishardly describes the complexstress slatesencounteredduringtypical ice-structureinteractions.Any realisticconstitutivemod el musttake into account the mechanicalbehaviourof ice undermultiaxialstresses. For example,a biaxial stress state woulddescribealevelice fieldadvancingagainsta wide offshorcstruc- ture. On theother bend,atriaxialstress state is experiencedduringiceberg impacts orramming ofmulti-yearridges. Figure 2.11isareproductionofthe data froma testseriesconductedby Jones(1982).Lab oratory grown,equiaxed,pelycrystallinc ,
24
, , "
" I . I 1 / ' - _
/, I
'"
I ,I I \ I,
5 Axial Splitting
5 Shear Faulti ng
Figure2.10: Failu reModes of Ice under Compressive Stress Statesa.t HighStrain Rates(>10-3 , - 1)where S Represents the Applied DeviatoricStress and p is the Confining Pressure.
25
freshwa tericewas deformedat a constant strain-tateunderhydrostat ic cc nfincmcat.
Thereareessentiall y two main regionsof interest: (I) thearea bounded by lower confiningpressures« 20 MPa)and higherstrain.re tce(»IO-~5-1)and (2)~lw family of horizontalcurves for all other data.points.
~~ ~r~o'm~~~~~~:~~
Pres!Urep:If. 30
'" If'
6-
2520
15
10
102030 40 5 0 6 0 70 80 90
ConfininQPressUfl'0"3,MPa Figure 2.11:Dat uct {romConstant Strain RateTestsunder HydroelaticConfin<,...
men!Conducted by Jones(1982).
26
Intheles ionofincreui nspeak differential.,l res, . (or&lJiven .train-riLle,the defer- mational behav iourisassociatedwith aprogressivedamagine:process.Withhieher confiningpressuresthepeak str ess stabilizesto a maximum,microcrackingact ivity is inhibitedand pure creepobserved.Thus thecreepresp onseof iceisinvariAntwith hydrostatic pressure and dependentonly upon thedifferenti alordeviato ricstress, this isalsoexh ibitedby metal sand concrete.Themajorityof studies investigat ing the behaviourofice under multiaxialstressstates are concerned primarilywiththe 'strength'ofthe materialunder constant strain -rat etests;see for example,Hau sler ctal.(1988),or MurrelletaI.(1991).Understandingthedamageprocess and ddormationalbehaviouroficeundermoderat etc hiShconfining pressures i. seenas thekey, sincethis istheprincipal mechanism involvedduring full-scaleicecrushing events.
A characteristicoCiceduetothehighworkingtemperature, is the rela tivelylow magnitudeoCconfining pressu rerequiredtoinduce a phasechange.Jones (1982) .tatesthatwith respecttothe pressure meltin g temperature,thehydrost aticcon- finement bAlIDOinfluence onthecreep.train-rate butmerelycbangetthe ell'ect ive temperat ure. For Curtherdi. cussionon pressuremeltingthe readerisreferredto work.by Kheisinand Cherepanov(1970) and Barneset a1.(1971).V.in gJones' data,Nadreauetal.(198B)proposedthat the tendency for thedecrease in peak differential.t re.. athigher confiningpressures,i.in effect, duetopressure melt- ing (Figure2.12). A teardropmodelwu developedto describean anisotro pic, three-dimensic nal Cailure surface forice.Recently,Gagnonand Sinha (1991)have reported thatpressure meltingWASevidentduring medium-scale indent ationtesll
27
where interfacetemperaturemeasurementsand thinsections revealedthe presence
of a melt.
..30 .. . , - , -,-- ,- ,__,-_-.__,---_,
e
Cii
!
20.j
Q
10
Figure 2.12: Teardrop ModelDevelopedbyNadreau ct0.1.(1988).
However, the teardrop model isempirical and docs not attempt to explainthe uu- derlyingphysical mechanisms responsiblefor the observed mechanical behaviour . Conceivabl).he principal mechanismsinvolvedduring the deformation of ice under multiaxial stressstat es areschemat ically illustratedin Figure 2.13. Referring to Figure 2.11,(or the lowerbydrcet ati e pressures and higher st rain rates there isa zone where a progressivedamaging process associatedwith the development
or
rni- crocracka.For a given strain-rate,upon theimposition of higherconfining pressure th edamage is eventually supressedwithpure creep becoming thedominant modeor
deformation. Furtherincreases in the confinement, fora constan tstrain-rateand23
temp erature,would resultin creep deformationan d pressuremelting with the end resu ltbeing aphasechange.Notethat , duringtransitiona lperiodsthere arestress stateswherethemechanisms competelordominance.Abo,pressur e meltingcould beactiveon a localizedlevel, lor global stress states lessthanthat requiredfora phasechange,due to intense stress concentrations at cracktipsand triplepointsor Irictionel mechanisms ,sucha.'Ishear alonggrainboundaries orcrac ksurfaces.
Deviat or icSt ress
Dam agin g Creep
Creep and Press ure Melting
Confining Pressure
figure2.13:MultiaxialDefcrmatlonMechanisms in Icefor a.Constant StrainRate
Althoughlaboratory tests cannot directly model the interactionevents at full-scale, one candevelop a basicunderst anding of the failure processin ice,undernomi- nally similarconditions,whichcouldbe thefoundationforinput into numericalor
analyti c&1 models.However,damagingormicrocracking,in-Itsel l, docs not fullyex·
plain ice-structurelate rectic nevents. Li'kbamanov andKhcisin(1971)wereamong theca.rlie5tinvestigators to recognizethisfact.Duringdrop-banimpacttestsit was observed thatthespecific crushingenergy[l.eresistancetoimpact)wasnota lunda- mentalindexpropertybutdepended upo nclasticdeformation, creationoffracture sudaces,friction alprocesses,clearingmechanisms andpressure melting.Clearly, thefailure processesduringevensmall-scale interactionevents are highly complex and dependent upon a numberof physicalmechanisms. Consequently,primarily due to thescaleeffect,laboratoryinvest igationsmustbe verifiedbyobservations andexperiencegainedatfull-scale.
Previous fieldtests,Han sIsland(1981),PondInlet(1984),andHobson'sChoice Island(1989,1990),have demonstratedtheimportanceof largeandmedium·scale experimentalprograms.This huledtothe development ofnew iceIo&dmodels and significantlyadvancedthe levelof underst andingofice-et ructureinteractionevents.
Hans Island dramatically showed thatglobaliceloadsexerted during impact
or
largemulti-yearfloes(1-3km diameter)wasonlyonthe orderor ooSMPa.Themedium- scaleindentationle8h ,whosemainobjectivewastost udy dynamic ice-induced vibrations,revealedthat localpeakpressures,whichreached 60 MPaor grea ter,had avaried.spatialand temporaldistr ibutionwithsteep pressuregradieull.Generally, interactionmodels make assumpt ionsregarding thephysicalcharacteristicsofthe failurezone; thus thedevelopmentand enh ancementofsuch modelsrequire detailed description.To bett erunderstan d theinteraction processduringfield events,an account ofthetestteriCllconducted al Hobson'sChoiceIceIsland in 1990will be
30
presented .Also, the discussionwill bring to focusthe logic underlying the present tes t program.
For all tests,crushing was observedduring indentati onand discreteice parti cles wereejected fromthe free edges of the indentor (Figure2.14).However.for several testespalling or 6aking events,associated with large macro cracks,were observed.
Although a number of parameters were investigated in the test program, there were characteristic featuresconunon to all of the failure surfaces. Illustratedschemati- cally in Figure 2.15are thety pical featuresassociatedwith the failure zoneafter indentation.
Thereare essentiallythree distinct regionsassociatedwith theinteractionzone;
first, spallarCaJlon the periphery of the contactsurface, second,regions of crushed icc and discretegranula.r particles,generally but not exclusivelyassociated with low pressures, where the material iseventuallyextruded from the free edgeswith continued indenta.tion, and third, hard spots or critical zones consistingof damaged iccwhich are considered to be centersof extrusion. Macroscopically, thisregion appears to be'intact ' but thin sectionanalysisrevealedsignificant local damage (Meaney et al.,1991).
The crushed layer typicallycontained large,25 nun diameterorgreater ,relatively undamaged particles surrounded by finely pulverizedicc, suggest in g a grinding ac- tion as the larger particlesslideandrotate during extrusion.The developmentof a crushed layer during indentation seems to be analogous to the shear zone gen- eratedin the uniaxialand triaxial laboratory tests . The steep prenure gradients
3\
32
FRONTAL PLANE OF TEST FACE
Figure2.15:Schematic Illustration ofa TypicalFailureSurfa.ce Exhibited During the1990 Medium-ScaleIndent ation Testson Hob son'sChoiceIce Island.The Test Face canbeSubdivided into Three MajorZones;(i) Spall Areas,(ii)Regions
o r
Cru shed Mater ialand(iii)Damaged Zones.
r I
!
It
!
exhibi ted,which can berela ted tozones ofintense she ar,app eartobethe drh'ing forcebehindthe grindingand pulveriz ationoftheice,which israpidly transpo rlcJ to the peripheryof theice-stru cture interlace.Altho ughthefeatures ofthefailure su rf acesuggestthat peak pressuresshouldcorrelatewiththe hardsp o tsor criti cal zon es,superi mposing the final recordedpressureson theinte r face did notproduce concl usive evidenceforsuch apheno menon.Itisalsoimportanttonote tha tthe crus hed ice layerappeared to have sintered orbevc experiencedpress uremelti ng.
This wasevident from densit yprofiles ofthe failurezone Andinterfacetemper ature measu reme nts . Thus regions of thecrushed layer co uld be considere d comp et ent ma te rial andexperie ncesig nificant lo ads duringinden tation.
Obviously, there hasbeena significa ntmet a morphis min the metcr talstruct.ure;
that is&transformatio n(ro man intact solid continuumto a denselymicrocre ckcd body andarrayof discreteparticles.Not only thephysi calpropertiesof the icehave changedbut abothe mechanicalbeha viour, since there isagrad ualredu ctionin the st iffness and shearresistance in theice matrix- see forexample Stone etal.(198 9).
Itis important to realize th atanycon stit utive models must recogeieethis fact.For examp le, the degradation of iceproperties ca n he analyzedusingcontinu umdamage mechanics andthe crushedmaterial,whichlacks apprecia ble shear resistance, could hemodeledas a.viscousfluidor Mohr-Coulombmateri al.
Con ceivably,the local strain-rateswould in crease substantiall y towa rdthe icc- stru ct ure interface; i.e.fromthe parent ice, to regions of influence,.to finallythe highly damagedzones and crushed icelayer.Also, therewouldbeva rying deg ree of deviatori cstresses and con finingpressuresthroughou tthe failureregion.These
34
ideas are illustratedin Figure 2.16. Crushed layer thicknessmeasurement s,density profiles andth in section analysis of thefailure zone (seeKenny etal.,1991) indi- cated that the bulkofthedeformation,relatedtoenergydissipated orexpended, occurs within thenea r field.Jordaanand Timco(1988) haveestimatedthatthe energy consumedby thecrushed layerdevelopedduringsmall-scaleindentat iontest to be 99%of thetotal energy.
EarlyworkbyKheieinand Cherepanov (1970) showed thatthe contact facewas characterizedby subregions ofcrushedand damaged icewhich they charact erized asa"distinctdestructionsurface",Si~ilarIeilurezonefeatures were alsoreporte d inemall-sceleice crushing testsby Franssen(1991),Riska (1991)and Lindholmetal.
(1990 ) ,uwell83,ship-ice interactionsbyRiskaetel.(1990),Hence,icecrushing eventscan begeneralized into a numberof observedmechanisms:(1) spalling events in regionsoflow confinement,(2)adam aging processwithincriticalzones orhard spob,(3)floworejectionof crushed.material due to pressuregradients,and(4) pressureor fridionmeltin~and sintering.Thebehaviourof tbe crushed ice located at hardspots or criticalzonesisseen as the key to dynamicfluct u ations inload and peakpressuresexerted during interactionevents.
o
St r uctul'1!l
35
_ _ _IccFeat ur c,V
~
P" ..~ o;",ibu"un
~ u"Cu"'ndF"u
tn-er ea. mKHydr o.t ati e Stre.. Statc
(n)
_ _- - -....;:::::~ Spall AI'i:'R'
~- Region. ofC ru..hcdIcc
...~Cr itica lZone. ofDa m ag ed1':1)
(b)
Figure2.16: IdealizationoC Ice-Structu reInteractionEvents;(a) ShowsthePres- sure Gradienton the ContactFaceandtheVar iationinDeviatori c and Volumetr ic Stresses,(b) Illustr at estheSpatial Distribut ionof PressureZoneswit h Elevation Across the Conta ctFace, such as LowerPressuresAssociated with the Crushed Layerand Hard SpotsorCriticalZonesoC HigherPressurewhereDyna mic Effects areDecuring.
36
Clear ly, the calculat ioncf ice forces{or offshore structures is an endeavourwhich requires knowledge{rommany fieldsof science.Althoughempirically-basedmodels haveproved theirmerit,albeit with simplificationsforpracticalengineering design , development oflawlbasedon physics of thedeformation processes isrequired.This willenablethe iceengineer to developstrategiesfor variousstructural c.onfigurat ions lo be deployed under wideranging scenarios.
Chapter 3
Experimental Program
Mostlaboratoryinvestigation1onthe multia xial behav iouroficc haveinvcst lgated the 'crushi ngItreosth'underconsta ntstrain-rate laadinEcondit ions. Tothe au- thor'sknowled ge therehubeen nosystematicstudy on thedeforma tional behaviour ofdamagedice as&function of confinementand appliedstress.
Evidencefro m medium-scale indentationtestsshowedthatthe cont.acl zonewas characterizedbylubregions ofcrushed orpulverizedmaterial and damaged icc.
Thebehaviourofdam at;ocIice and crushedma te rialioutedathudspob in zones of moderatetohigh confiningpressure! is seenasthekey to thedyn amics of the icc crushin gproceee.
Consequently,astudy onthecreepresponseofintactand pre-dam agediccund er hydrostaticconfinementWi15conducted.Withthesethoughts in mind.the following diecueaicnIocueeeeonthe experimental prog ram.
37
38
3.1 Preparation of Test Specimens
AlltC3tswerecon du ctedusinglaboratory preparedpclycryst .alline,equlaxed, fresh- waterice.Figure3.1 schematicallyillustratesthe equipmentsetupused duringthe molding processtomanufact ureicesamp les.The system was housedin anantero om whichwasmaintainedatanominaltempera tur eof0°C.
line to deionized,distilledwat e r
1.Vacuum pump 2.Thickwall tubing 3. Cold trap
4.Dry trap 5. Vacuum gauge 6.Threewayvalve
7.One way valve 8.Glassmanifold 9.Deaerator Figure 3.1:SchematicDCEquipment UsedintheManufacturing of Ice Samples.
To ensure qualityandrepea tabilityofthe icesampl es the followingprocedu rewas adop ted.Pureweter,obtainedbyfilteringanddistillingmunicipaltapwater,was usedthroughoutthe manufacturin gprocess.Themeasuredresistivity ofthepure wate rwas onthe order of 10 MO'c:m-1,The nextstage was to developsam pleswhich
I /
I \
i
l
39
wereuniform and homogeneous in grainsize, thereby ensuringisotropicmechanical behaviour. Dictatin ggrain size can be easilyachievedby the introduction of a nucleatingagentjsuch. as,seed ice.Bubble freecolumnargrainedice, grownfrolu unidirectional freezingofpure water,was crushed usinga,Cl4wonModel#PC·75, commercial mechanicalicecrusherand then sieved. Iceparticleswhichpassed the
*-4 US (4.75mm) screenand retained on the #6 US (3.35mm) sieve wereueod as seeds.Theseedice wu then placed in a tapered,rect angular,flbreglas8mold (Figure 3.2) which wasused to set theseedice-pure water mixture.The bcuom of the mold wasbolt edto an aluminum plate and the matingsealed by a rubber gasket . Todevelop the vacuum, aflexiblemem~)fanefabricatedfroma weatherballoon was used to coverthe mold.Snow wasthenplacedontopoftheseed icc toadlISa protectivebuffer so that the membrane wouldnotbe punctured.A sealwasensured using elasticban ds andhighvacuumsilicon~rease.
190mm
-I_ _-,-F",lb,reg l... mold
18 0 mm q~EE4fEEq~i-~A~luminumplate
Figure3.2: MoldforMaturingIce Samples.
'0
Subsequently,themoldand tubins system,shown in Fi«ure3.1, was placedunder ...vacuum forapproximately2 houreandbroushtto ... gauge pressureoC0.5mm IIg.The deaeratorwu then filled withdist illed deionizedwater,cooledto 00C.
and thechamber wu evacuated for 10-15minutes. Finally, the mold was filled with the deaerated water throughtheevacuated tubing. Aft er flooding,the mold wascoveredbyaninsulatingjacketleaving the bottom alumi nu mpleteexposedto encourageunidirect ional{reezinl!.Typically,the icewo uld maturein 3 days at·10·
C and wouldtbenberemoved fromthemold by allowingthefibreglU5 shell to w&rm slightl y.Onceremov ed from themold, the icesample was sealed in plasti cbagsand tem porar ilystoredat-30"C untilthe daybeforea test. The ice block wo uld then be allowedto equilibriateto·urC overnightpriorto machinin&ofindividualtC!t speci mens.
Thismoldin&techniquewouldproduce equiaxed,uan u1arpolyo)'lltallineicehavins arandom c·msorientation.Cole(1986)present s exp er imentalevidenceontherole inwhichtrainsizedictatesthe mechaniC&1 behaviourofice.wherevariancein the Staindiameterchan ge dthebulk failuremodeofthespecimenfrom ductiletobrit tle forthesamedeform a tio n rat e.Themeanvaindlemetee fortheicesampleswas 4.3 mmwhichWa.!calcu la tedusinStheexpression ,
(3.1)
whereNAistheDumber orgain.perunitareLThinteCtion s,essential inthe
developmentoffabric diagranu,grains size analysisanddama~echaracterization, wereobtainedbyusinS aLeitzbioloPe&!microtome and thedouble microtomins teehniqueoutlinedinSinha (1978) wasemployed.Atypical horizontalthinsection is showninFigure3.3.
Generally,therewouldbelar~erthan average grainsgenerat edat thebase of till,:
moldanda.concent rationof fine airbubblesncartheSIlOWlayer at top.Con~e·
quently, to ensure qua lityicespecimens,the top and bott om75 mm wereremoved and discarded.The icewas thencut,using abandsaw,into fourequalsections.
Individualsampleswenmachinedintorightrectangula rprisms,usingajointeranu amillingunit,havingdimensionsof60±O.l mmsquareand 120±O.lmminlength.
Themachininsprocess produced samples with .. wryllmoot hsurfaceand pMalld ends- acritiulpuameter ,p&rticularlyat higher.train-rates,whichinnuences the mechanical behaviourofthespecimendueto eccentricloading.
3.2 Test Equipment
AM4teriaJ~Te.stingSylt erru(Mr S) CorporationMo del#311.31 test frame was used
roc
allexperimentsand washousedin astand a rdcold room, whichcould maintain a workingtemperatu rewithintherangeof 00Cto·"O'C.Axialload, in-situice displacement,hydrostaticpressure,temperatureand time werereeoeded on a personal computer,using the Viewdacdat a acquisit ionsoftware packageata samplingrate of200 Hz.Also,a hardecpybackupWallrecorded usingaYokogawa 3066penrecordertomeasure,in realtime,MTSloa d , triaxialcell pressureand temperatu reand& YohgotDlILR4!JOpen recorderwas usedtorecord the uialFigure 3.3: Horizontal Thin Section of a.n Intact Ice Sample.
42
and lateraldisplacementof theice sample.Figure 3.4schematically illustratesthe triaxialcellconfigurationusedduring the testprogram.Details ofthe mounting collars fortheLVDT', and brass endcapsare presentedinAppendixA.
Exte rn alLoad Cell
- - - -I£:l\M I
AxialandLat eralLVDT's
---+--1.1--=11
BraBsEndcap
Intern alLoadCell--=!==E!!:
MTS Ram- -- - + _
Pressur eGAuge
Figure3.4:SchematicIllustrationof theTriaxialCellSystem Employed During the TestProgram.
Thetriaxialcell, fabricated fromstainless steel,wasequipped with four portals:
two withaccess for viewingorvideo monitoring thetests and twoothers usedto
44
provide a light sourcetrilluminate the cell interior.The viewing windowsrestr icte d the maximum confiningpressureto 20 MPa (3000 psi). Const an t pressurewas maintainedduringthetest bythe useof a compensatingpistonwhich was att ached totheactuatorpis ton via a fulcrum- see KaliCael al.(1989). Atra nsluce ntsilicone oil. with a viscosityor eightcenris tokes(200C),was usedasthe pressuri zingfluid.
TwoMTS-661.£3B-0 12SOkNca pac it y loadcells,one internalandtheotherexte rnal ofthe cell,were usedto measurethestressappliedtothe ice sample.The former directlymeasured the axialstressapplied to t'.especimenand was used as the reference signal during load controlphases.TwoSchatvitzMHR· l OO serieslinear variabledifferential transformers (LVDT),with a stroke of±2.54 nun,were mount ed on thesa mple, via an aluminum suppo rt collarwithknifeedges,to measureaxial stra ins directlyfrom thesample.Lateral st rain was measured byaSchaevil:MHR· 250 LVDT with a strokeof±6.35 mm.The latera lgaugeWMattachedto the sam p le byan aluminummounting block,with 30 millimetree contactalong the corners of the specimen,which was supportedby elasticbands.The axial gaugelengt h was 70millimetres andthe lateralgaugelengthwas 55 mlllimetres.A photographof an undamagedice sampleanda fully instrumentedspecimen is shown in Figure3.5.
46
3.3 Test Progr am
Alltests were conducted atthe Insti t ut e Cor MarineDynamics, National Resea rch CouncilCanadain St .John's, NF. As statedearlier, the purposeof the investiga- tions wu tostudythe influenceof damage onthe creepdeformation of pclycrye- talline,granularfreshwat er ice underhydrostatic confinement.
The experimental programconsistedof applyinga seriesof compressiveloads to undamaged and prc-damagedice sam plesat va riousconfining pressures ;whereby the subsequent deformational responseof tlte specimens couldbeanalysedwithres pect to theinfluence of microcr acks on the strain developedunder a multiaxialstress st at e. Pre-damaged sampleswereobtained by loading thespecimen uniaxiallyata constantdisplacementrate of10-45-1to an axial strain of0.02. Theseparameters werechosensothatthecreep response,under uniaxial condition s, could becompare d toaimiliartestsconductedatMemorial University.
A typical stress-straincurve for thedamaged iceisshown in Figures3.6.Tohinder the pressurizedfluid from penetratinginto the cracks of the pre-damaged specimens, all sampleswerejaclr-::tedby alatexmembranesimilar tothoseused insoil androck mechanics, Figure 3.7 illustratesthe dilatation typicallydevelopedwhenthe ice sampIe waa loadeduniaxiall yat8.constan t displacementrate of 10-4to a tot al stra hl of 2%. Profilesof pre-demeged samples weremeasured,using8.micrometer, which supported the LVDT measurementsendrevealed that the barreling was quite uniform. Athin sectionthrough a pre-damagedice sampleis shownin Figure 3.8.Note the finegrained struct uredeveloped betweenthe grainboundaries which
could be the result of a grindingaction betweengrains.Figure 3.9 isa photograph of a typicalverticalthinsection through a pre-damagedicesample. A number of possiblewing crackswereobserved Corseveral thin sectionsthrough different samples,alt houghitisnotknown whether theywere developedduringthe pre- damagingphaseor load pulse series.Alternati vely,the wingcracks features could havedeveloped. throughthe coalescenceof grain boundarycracks.
00 0.O()j 0.01 0.01$ 0.02 0.02.5 Suain
Figure 3.6:Typical Axial Stress-StrainCurvefor Pre-DamagedSamples.
The confining pressures studied were0, 4,10 and 20 MPa andthe applied deviat otic load sranged from 0.5-1.5MPa for uniaxialconditions and 0.3-2.6MPa for triaxial stressstates.Figures 3.10 and 3.11illustrate the load pulses for the uniaxial and tri- axial cases respectively.The constant stress levelswer eapplied,under load conircl, for 20 seconddurationwhichW&!Ifollowedby a relaxationperiod of approxima tely 150 second s.Peak stress was ath:inedin approximately 0.02 seconds.
48
49
Figure 3.8: Thin Section through a Pre-Damaged Ice Sample. Note the Fine Grained Particles Dispersed Througbout the Sample between Individual Grain Boundaries.
50
Figure 3.9: Vertical Thin Section through a Pre-Damaged Ice Sample. Note the Presence of a Possible Wing-Crack Near the Center of the Photograph.
"
'500 2000 1000 Time(s) 500 2 8 6 4 2 1 8 6
4
~ ~ ~
2 0
l
1.~
1.~
.~£! O.
.
~Cl o.
o.
o.
Figure3.10:CommandSignalCorUnAXialStress PulseHistory.
a.s
Time(J)
Figure 3.11:Command Signalfor TriaxialStressPulseHistory.
'2
Analysisofthepube record,measuredbythe twoloadscells indicatedthat the aclua! stcessappliedtotheicewu1eslIthan thereferencesignal,as measuredby theexternallo&dcell,whenthespecimen wu subjecttohydrost atic confinement.
Thediscrepancybet weenapplied and measu red .tressWallattributedtofriction on theloadingpisto nbythesealing gasketswhichredu ces thestress experienced by theicesample.Table3.1summarizes thestresses for theteat series,foundedto thenearest0.05MPa, (or thereferencesignal(l.e.external loadcell)and actual measured,lrellwhich was recordedbytheinternalloadcell. Consequentl y,itis important torealize that themeasureddeformat ionalresponsecannotbedirectly compa.redfordifferent confining pressures.
Forfuture experimentsitisrecommendedthat theinternalload cell be used as thereferencemeasurement with respect tothecommandsignal.Thestress maA- nitudeme.uUrN bythe intemalloadcell(me.u ured deviatoricstress)willbe used throu~hO\1ttheanalysis
o r
the experimentalresults.Table 3.1:ReferenceStress Signal andMeasuredApplied DcvlatorlcSlIl'8S
Confi~~gp:)essure Reference(MP.)DeviatoricStress MeasuredDcviatoricStress (MPa)
0 0.50 0.50
0.75 0.75
1.00 1.00
1.25 1.25
1.50 1.50
4 0,50 0.30
1.00 0,75
2,00 1.60
3,00 2,60
10 0.50 0.30
1.00 0.75
2,00 1.60
3.00 2.60
20 0.50 0.30
1.00 0.50
2,00 1.40
3,00 2.40
Chapter 4
Analysis and Discussion of Experimental Results
Inearlier chapters ,it was shown that the progressivedamaging processplays an importantrole duri ng ice-str uctur e interactions. Recently bastherebeensignificant effort to relatethe observedstress-strain behaviour of ice;from laboratorytests and field programs, tothe development of aconstitu tive ice- toadmode1- seeCor exampleWinkler and Dorris(1990),and Jordaan et al. (1990b). Thefollowing sectionwiUfocus onthe presentationofthe experimental results andsubsequent analysis.
54
4.1 Creep Enhancement under Triaxial Stress State
4.1.1 Axial Deformation
The observed deformational behaviourof pre-dam aged ice underuniexiel conditions isshown in Figure4.1.The applied constant stress pulsewas previouslyillustrat ed in Figures3.9 and 3.10. Although theicehas experiencedconsiderab lepermanent or non-recoverable defor mat ion,betweenthefirstand tenthload pulse,there is netany apparent influenceon the def_'l'mationalresponseforthesam e applied stress.Thus, one can a.ssume that repea tedloadingsdidnot appreciab lycontr ibuteto anyfurther .damage within the specimen.ThesecharacteristiC!at .. typical and were observed throughout thelestprogramforallconfiningpressures anddeviatceicstrClSCS.
The signifianceofdaJfl&l;c[i.e.microcracks]on thedd'ormdion&1beha viourof icc is illustrated in Fi&Ure4.2, where the straindeveloped in the pre-d amag ed specimens iscolllliderabtyenhancedandseveral timesthe magnircde expe rienced bytheintAct ice. Thisisin geed acreementwith Jordaanet1.1.(1990a) ,where similarrelultsAtC presented,lor uniaxialconditions using a differenttes ting eyatern. The effect of creep enhancement was markedlydemonstratedduring the triaxia ltests wherehigher stress levels could be appliedwithout sub jectingtheice sampletofur th er damage, Figures4,3~4.5,since rep eatedloadings exhibitednomina llysimilardetormaUonal behaviour.Thesefisurespresentth~averageaxialdeforma tional respo nse, foreach applied stress pulse, andcomparethe measured strainstrom the intacticesample to thepre-dam agedspec imenfor a~venconfinifi&preuure.
56
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