(Ashby and Veftall, 1978 and Fig.l). ... I Defomalion mechanhn map for olivine, uken lrom Ashby .'d verall .... DifJusi.hal lov ft the solid state via mjgration oi point.
/C
Ch a p i er 1- 8
Microfabric Studiesas Indicatorsof andFlow Laws DeformationMechanisms Operativein Mountain Building S . M. Sch m id Geologischesh1stitut ETH, Ziirich, S||itzerland
Abstract Afteran introductioninto rhe majordefomaiion mechanismsthefollowing applicationsto tectonicstudiesarc discussed: (i) Paleosnessestimatesbased on the exlrapolationof erperimentallydetemined flow laws and based on the size oi dynamically€crystallizedgrainsj (ii) th€ significanceoJ crystallosEphicprefenedorientationworkj and (iii) mechanismsofstlain softeningleadino to localizeddeformalionin shearzones.
I. Introduotion In discu$ionswilh fieldorientedgeologists an expe.imental geologis!somelimesnotes clilicism with reSard to the .ock deformation applicabilityof the resultsof experimental to the study ofnaturally defo.medrocks.The crilics often point ou! that the experiments wereperformedundersuctr simpleconditions(co-axialsbain path. conslan!slressor strain rate, homogeneous mononineralicrockt that thel areinadequaleto throw light on themolecomplexproeses in natural environments.However,any laboratory sludy mustbeginwilhwell deiinedboundaryconditionsso that the influenceofa greatnumberofvariableson.ock creepcanbe recogrized.Also it is necessary to learnasmuch aspossible about the physicsand lhe mechanisms ofrock deformation iD orderto avoiderroneousexlrapolationsfrom the laboratory into ihe geologicalsituation. Il is the srudy of the microfablicin bolh experimentally and naturally detorm€drocks vhich permitsdir€cl com' parisonsto be madebetweennature and experihenl.The microfabricr€cordsthe activemechmismsofdefo.mation and rrsrtudy rl"ereiorehelps,ocloserheSapbelweene\penmenl and 6eld observatior. Someof the complexities of naturallectonicsituationscan bemodelledmuchmoreeasilyby usirs analyticalornumeF ical rnelhods or by using readily defomable analogu€ materialstban by an attemplto perlbrm morecomplexexp e n me nron . nalur alr o( l c p e i.m e l (.T nrh i c .a \ei t F rm p o F tant howevertoknow asmxchasposibleaboutrherbeology of rockswhich dependson lhe activedefomation mechanismsrecordedin the miffofabric. This conribution will specificallydiscus someselected applicationsto tecronicsrudies. Th€rebysone ofthe goalsof
microfabricsludiesare illusrratedwithin lhe frameworkoi teclonicstudiesin general.Inorderto do soit wasfeit n€cesary lirst to inlrodu@ the non{peialisl reade. inio some basicconceplsot floq la$s and deformarionmechanrsm\. IL Some General Remarks on Flo$ and D€fomation Mechanisms A rock loadedunderaconstantdifferentialstreso(classical creeptest)will immedialelyshorienelastically.Later ir will undergoa permanentchangeoishapeat a strainrale e = d ?/drwhichis diclatedprimarilyby threefactorsaccording!o a flow law ofthe seneralform: a= a(6..,4) where the st.ess diffelence d (= o, oj) (informauy refered toas ttrest'), rhesrrain.andthetemperature lare the most imporlant quantitjesdelerminingthe resnlting slrainrale. Striclly,sucha 6ow law is orly valid as long as other facton suchas confiningpressure,waler contert or partial presure, grain sizeelc. are held constantor can be assunedto have no major iinuence on the lheolosical Confininepresure is usuallyassumedto be ofmrnor rmportance in the ductile field, once fiictional proceses (cataclasis) can be ruled out (Pate6on, l9?8). water can havea "mechanical effectthrough the well known pore pressureerect (Hubbelr and Rubey, 1959),asain in the briltle and calaclaslicfields.or it may havean influenceon the nalure of atomic bonding in silicates.influencinglhe resislance to deformationby crystalplasticily,a phenonen known as hydroliticweakening(Grig8s,i967).In the latler
96
S.M
casethereh evidence tha! pressure enhances thesolubililyof water in quartz and the.efore,tbat pressureslrongly influences the rock strengrhoulsidethecataclaslic fieldaswell (Tullis er a/., 1979;Patersonand Kekula{ala, 1979).The in moredetailin the influenceofg.ain sizewill bediscussed During the firsl slagesof deformalionthe strain rate stronslydependson strain(primarycreed)tafter a few per to a cent st.ain the rate of deformationusuallydecreases constantvalue.The rock is then said to deform in sleady state.Ideally.srain hasro influenceon lhe strainrate any more.We will seelater that rocksmay eventuallysoltenal high strainscausingtho slrain rate10inoeaseagain.At tbis poini i! is impo.tant to saythat the conceplofsteadystale is usedhereto merelyimply flowaiconstantstressandstrajn In ihe caseofa constantsirain rate experimenlfie stress (slrainhardening). mayrisewithincreasingsrrain i!Inaystay conslant (sleady state) thereailer,or it may eventually with increasinsstrain(strainsoftening). dec.ease For ihelmally activatedcreepone can enpiricallyderive flow laws fron a seriesof experimenlson the samerock, valid for steadystateflow only. They are usuallypresented (l ) e : i o e x p-H IR T I@ ) conslant,lJ is theapparenl whe.eaois a materialdependent activationenergyfor creepand ,Ris lhe Cas Constanl.The adequately be describedin mostcases slre$ dependencecan creeplaw) lG) = exp dlo. (exponential
(2)
(3) /(d): d" (powe.creeplaw) wherethe constaDts d0 and rdetemine the st.esssensitivity a ij of r hes r r ainr ar e.Be .d u :e .nm o c rc d \p crh ep d ra m erer lound !o be greaterthan unity, rocks usuallydeviatefrom linearviscousbehaviour. Thereis no sjngleflow law for aUconditionsofstres and temperature, simplybecaus.lhe deformationmechanisnis assell. Associated with a functionoi stressand temperature eachof lhesedeformaiionmrchanismsis a differentnow law. It is usual!osubdividelhe stress-iemperature spaceinto map Jrf ler enrf ield(b) me a n so t a d e l o m a ri o nme c h a n i \m (Ashbyand Veftall, 1978and Fig.l). Within eachofthese neldsa particularmechanism is dominant. Such deformationhechanismmaps are nornally cal' culated from fire1 principies by assuming specific Dicrodynafticalnodeh. Experimentsoften merelyprovide numberefor the variols naterial dependenl constanlsin the lheoreticalflow laws. T hep na, y din o i ' h e \ed e to rmrri o me n chJnnm mapsi s to oudine the expectedconditionsoi appearance of given deforrnationmechanishsoLltsidethe range of e-d-Tconditions accesible to the experimentalisl.The main problemin the applicalionofthe laboratorydatais theenoF moDSgap belweengeologicalst.ain rales of the o.der of | (i n v o l v i n g ti m e s p a nosf b e l w een30 l 0' os ' lo l0' \ yearsfor and3 million l0%shorlenins_strain) andthelaboral o r y s bain. at esus u a l l yb e tw e e n l 0 -' a n d l 0 _ t' . A ! can beseenin Fig. i onehasa highchanceoffiosinga boundary betweendeformalion m€chanismfield, by extrapolaling downto lowersfain ratesardconsequently to Iow€rslresses at any SiventemperalureThereforea flow law observedat high stresses underlaboratorysbain ralescan only be exlrapolaledovera Iimitedrangeofstrainratesandsresses.In orderLoexplorethe llo" behaviourallos .rrese. rhee\perinentalist is fo.ced to elevatethe tenperatLfebeyondthe range of temperaturesexpecteduder natural conditlons
Fig.I Defomalionmechanhn mapforolivine, ukenlromAshby .' d veral lrl q-8.f i e.l 4).Thenrp . \orrrr. Fd' o a em'1'/ p of 100!n ahdaorzeroconlinins prcssure. Thcsolidlincsdclincatc delornadon mechanism bou.darics, superinposed arelheconstant strarnrarcconrous.Thevarioussynbolsindicate lhe posilionol experimental daraon thisnap.
(Palerson.1976).Thus,elevatedtemperatures areessentially usedasa 'lrade olf ior unathinablyslowgeologicalstrain rates.Once a flow law has beeneslablishedat bigh len, peratu.esand lo{ stlesses the geologisthas !o extrapolale downto lowertemperalure!. alonga pathwhichis les likely to crossdeformationmechanismboundaries. Thereare somep.oblemswith the conceptofsteadystate creepand the asociatedconceptofflow lawsand deformaO
S ,," i n may aherrhemi crosrruc' ure and rhF rn r ur n carsesstrajn hardeningor strain softening(seesection VI).In thesecasesthe situationcanno longerbe descdbed in termsof asingledefomationmechanisn map which assumesconstant microstrucLu.cano sleaoysralecreep.
(ii) As will be discussedin the nexr section,thereis a subtledifferencebelweenthe defornarion mechanismaccounlingforalormost ofthe tolal strainin the rock and tt'e conceplof a ratecontrollingltep which conlributesonly a smallpartofrhe tolal srain Guch as dislocationclimb in powerlaw creep). (iii) Slricdy a defornalion mechanismmap only applies to a particularmineralin a rock and it is ralher difficult to lalk about the defornationmecbanisnofa polymineralicrock. Many nylonites offer good examplesfor oystal plasticflow accompanied with reoystallizationwithin quarrz domains white the ftldspaB deformby cataclastic processes. W i th Ihesegenerdl remark\In mi nd$e shattnos revr ew the majormodesofdeformationnore specifically. Thh will auow us to discusssome eeologicalapplicarionssuch as paleostress estmates!cryslallo8raphic prefeffedorientation work and finallysirain softeningmechanisms. IIL Defomation Regimes DilTerenlapproaches towardslhe problen of defomarion mechanisms arc posible. The physicistwants to be very
97
Microfabric Studies,Defovation Me.hanifus ahd FIo'| La||s exaclaboultheproeses onan atomiclevelandi! is possible 1o theorelicallypostulalespecifichicrodynamicalmodels. Thereisa greatnumberofsnchnodelsandfor acornprehensivereviewthe readeris referred1oPoirier(1976). Here we will follow a more empiricalapproacb.The expenmenrali(roflen deri\e\ emprricalflo{ lawsfrom d series ofexperihentsand it is rarelyclearwhat the exactmechanisns of deformationare. In suchcasesi1 is usefulto talk aboul defo.maiionregimes,definedby empiricalflow laws a n da ss oc r ar ed diagnoi ri m c i c ro l r'u .ru ,a li m p ri n l ' .
fusedwith thenechanishoferain sizereductionbydynamic recryslallizalion, typical for mylonites(White er a/.. 1980). Sincethe pioneeringwork ofCarter el a/. (1964)it h clear that moltar quartzir mylonitesis the producl ofdynamic recrystallization during powerlaw creepand that mtlonites rocks(Higgins,l9? I ). shoLrld noi bereferred1oascataclaslic Ar moreelevaledlemperatures and pressures crystalplastic deformation*ill successfully compelewith fracturing becauseelevatedlemperaturespromole the easeof glide within cryslals and becausehigher pre$ures prohibit cataclasiicprocesse!associated with volume inffeasesand
A. CataclasticFlow Ihe term cdracla"ric refers (o a rode ol delormarioD wherefractureand subsequentlo$ofcohesionmayoccuron The brittle'ductiletransiliondoesnot necessarily all scalescoincide wilh the transilion from cataclasliclo noncalaclasticproesses.If inlra- and intergranularfracture occu6 along a dispersednetworkofmic.ocracks,tbe bulk defonnationofthe rock may stiu be duclilein the sensethat corsiderableamounlsofpemanent straincan be takenup withoul the rypical stressdrop associatedwith localized for the brittie field (Pale6on, 1969). faulting,characteristjc Calaclasticflowismade possibleby rolling and slidingof granulaled g.ainsand crystalfragmenlsofa calaclaslically rock. Since &iciional resistan@betw@n the fiagments dependson the maSnitudeof nomal slressacrosscohesionlesssurfaces,this mechanismis stongly dependenton confiningpressureand.in the preseneolfluids, on the ellrclive pressure,i.e. the differencebetweenlithostalic and liuid pressnre(Hxbbert rnd Rubey.1959). Because !o a irst approximationdeformarionby cataclastic flow is not ihermallyactivated.temperatureand straln rate havelittle infiuenceon the strergthofrhe rock. Figure2 illustrateslhe microstructure typicalfor calaclas' prodrced fracturezone: ric flow within an experimentauy grainsizereduclionby cataclastic procesesproducesa wide spectrumof argular fragmenrswith a wide rangeof grain sizes.Thh lype of grain sizereducljonshouldnot be con.
B. Low TemperalurePlasticity wirhin thisreeimestraininrhelock islargelyachieved by the conservaiive motion ofdislocaliors throughthe cryslallat tice (i.e. the dislocationspropagatestrictly within crys tallographicplanet. or, on a largerscaleofobservation,b! glideonslip systemsdefined byslipplaneanddireclion.The resistance to glideis not controlledby frictior and thus inglide dependentoiconfi ningpressure. Thereisa resistanceto causedby eitherthe necessity ofbreakingatomicbondsasa dislocationmovesor by obslaclessuchas impurities,other dislocationsor g.ain boundaries(lattice resistanceversus obslaclecontrolledplasticity,Ashby and Verrall, 1978). The resistance to dislocationglideis the rate conlrolling factorduringdeformationand usuallyan exponentral stress dependence of strain rate (equation2) is observed.The morion ofdislocationsis lhermallyactivated,the appar€rt acdvaiionenergyfor creepis usuallysmallerthan for the latlice self-dillusion.Thus, srress,temperatureand strarn ratebeconeirter.elaledin the fom of a pseudoviscous flow l aw(Fi s.1). The fac! tha! grain boundadesare obstaclesto the free propagalionof slip (andtwinningin the caseofcalcite)into the neighbouringgrain is reflectedby the obs€ration thal the yield stressof fine-grained materialsis generallyhigher thanthat of coarse-grained materials.This grainsizedepen'
/
.\, fsoyr-i .l
Fig.2 Grain sie reductionby tacturing within a shcarfraclue zoncin expc.incntallydcfomed quartzile.Nole the angularshapeand lhe widespeclrumofgrain sizesofthe cryslalfrasments.
9rJ
:rqoFT Fie 3 Bro.d twin (t), causinginhomogeneous defomationin lh€ fom of a defomationbandin a neishbouring grainwhichrieaorms by glide. Nore b€nr lwin la@llae indicarinsrh€ srrainassocialed wirh rh€ deformarionband. calrara harbh, exp*irenrally detomed ar id(),C, l0 \'. 3k bc onf iningpr e$ur eandallt 5o b a r d i f f e r e n l i a l s t r c $ b y 1 3 %s h o r r e n i n s . C o m p r e s s i oi n ! et . ca
denceis known as lhe HalfPerch law in materiahscience (Nicolasand Pojrier,1976).The hardeningellecrofa small grain size is causedby the fact tbat the shearstrain. as producedby the conservalive motion ofdklocations or by twinningwilhin onegrain,cannolsimpl] be accommodated by the neighbouringgrains which have differen! crye talloSraphicorierlations.Figure3 illustralesthisfor thecase of twinningin calcite.Olsson(1974)shosedthe Halt-Petch relatiorship1()hold within a temperalure rangeof 20 300rC As a consequence of inlracrystalline slipa ffystallographic prelered orientationwilldevelop(seesection9. Sleadystaleis rarely acbievedwithin this regimeand in casesof work hardeningmany experimentalists iormulate flow laws refering to an arbitrary levelof srain (usually l 0 %) . C. Power Law Creep In nany naterials one observesa transilion lrom an exporentialstressdependerce into powerlaw creep(equation 3) wilh increasin8 lemperalureand decreasing stress.Al the sametime the apparentaclivalionenergies cometo lie near the activationenergiesfor diftusion.Microslructurally,one observesthe formationofcelis and subgrainson the TEMscaleand of oplically visible subgrainsuder the oplical microscope(Fig.4). In a transienlregion from low !emperatxre plasticity inro power law creep core'mantle microslrucluresnay be observed(Fig.5), suggesting that subgrainformation first sla.ts near the g|ain boundaries wberestraincompatibililyreasonsforcethe dislocalionsto rearangeinto subgrainwalls. As in thedomainoflow tehperatureplasticity.dislocation andhence slideis still themajorstrainproducinsmechanism preierredorientationwill develop.Howa cryslallographic ofdislocationsinto subgrainwalh is ever,the arranSement In er ar ec ont r olI n gs re p .Ih u s .th es rra rnra rea r a n ) B ,ven srre$lelel is conlroll€dbt the velocityat whichdislocalions
rearange.Theyenherhavetoclimb orcrossslipin orderto leavelbe glideplanes(Poirier.1976).Thereis a erealrumber of microdynamicalmodels ior power law creep(Poirier. 19?6)and host of them predicl an aclivationenergynear tha! of lattice self dirusior. which in the speciic caseof dislocationclimb creep (Weertmann,1968)conrots tbe clinb velocity.Th€ powertrin lhe powerlawfor creep(equalion 3) is predicledro be in the rangefrom 3 to 5. Dynamicrecrystallization oflen acconpaniespower law crep and, togetherwith subgfain fomalion ano oner manifeslations ofa recoreryproces, helpsto keepthe dislocationdensitysumcientlylos to avoidstrainhardening.tn sectionlY specificmechanisms of recryslallizalionwill be discussed in moredetail. The notion thatdislocationdensiryandihe sizesofTEM, subgrains, opiicalsubgrainsand reoystalliad grainsshould be in equilibriumat a givendifferentialsrressis only valid and applicableto paleostresdeteminatiors,providedthat rhe rock defomed in the regimeof power law crep (see discussion in chapterD). The rheologyofmateriahin thepowerlaw creepregionis la.gelyindependent ofthe slarling grainsize. A largenumberof exp€rinentallydetemined flow laws havebeehoblainedon rocks deformedwilhin the field of powerlaw crep (Carter,l97q Tu is, 1979).
D. Glain SizeSensitiveCrcep At evenhighertedperaluresand lower sresses.and/or for fine-erained naterialsthereexistsa numberofmechanishs which are grain sizesensitivein the sensethat fine-grained materialsare les flow resistanland where: edd
h
(4)
w hereJi 5rhee,arn\i /eandbane\porenr i nl herange2 l The defomation of thepolycrystalline aggregate lakesplace by eilher dirusional hass lransfer (dirusional now and
Mt.t.lahh.
S,udpr. D.Iathrti
r, ue.ha4^q. dnd tla,r Lo\,1
99
F 1g. 4 Op ricrllyrn ible subc r ains in Car r at unar blc .c x pc r im c n t a ldl )c' l o m . d a l 1 0 0 0 'C1. 0 \ r . l k b . o n 6 n i n E p r c s s u r c a . d a l l l 2 b a t dillerenlial(ress b] l2-"; shorlenins.Comprc$ionverlical.
-l
5Opm Fig.5 Core manlle nructurc i. Catr,ra naible erpeiinenull, delorned al ?00'C. l0 \ ',3tb coniiningpre$ure and ar 685 bar difcrenrirlsresbyl2l';shorlenins.conpre$ionrcnical Nolc lhal cquiaxedsubgrdins !'e confinedto ihe srain boundaryregions.whereas dcformdlionb.ndsaE charrcterkic lor the srainintcrior
100 presure solution)or by slidingalong grain boundariesof essentially rigid dystaLlitesGuperplasticjly). DifJusi.hallov ft the solid statevia mjgrationoi point defectsalonga stressgradientis known asNabado-Hedng or Coble c.eep, dependinson whether dirusion occurs throughthe latticein the graininterior or rear grainboundaries-For strain cornpatibilityreasons,sliding at grain boundarieshas to occur but the grain boundary shear stre$esaresololv that dillusionremainsihe raieconlrolling stepduringdeformalion(Beer€,i 978).The strainratecanbe calculatedfrom firs! principlesby considelingthe stress dependence of theequjlibriun densityofpoint defects(fo. a sinple derivatlonseePoirie!, 1976)-lt hasthe form: (5) ?: C D"noQlkT.l'1 whereC is a geometricalcons1anl,Dq.,.h the effectivedil fusioncoemcient.O is the alomic volumeand dis tbe grain size. The effeclive diflusion coefficient is made up of lwo components:the latticediffusjoncomponertdominalingin Nabarro-Herlingcreepand the grain boundarydiffusion componentdominatingin the Coblecreepfield.ln the latler casethe ereciive dillDsioncoefncientis inverselypropoF tional to the Brainsizeand thusthe exponentb in equation There b as yel no experimentalevidencefor solid stale difusional flow in rock materials.Difusional flow is likely only. and high temperatures to occurat ver! low stresses n |J $ rrrn s porL i n an P ar ( , , ? \ r / r no r, rn \o h e \d i l l u s i o n 8 aqueous environnent via solDtion and redepositionof modeofdeformatronin material(Fis.6). Ir is a widespread low sraderocks (Durney, 1972)but hard 1{)observeDnder ii is expectedto domiDaledl laboraloryconditionsbecause and stresses and at very slow srain rates los temperalures only (Rut!er, 1976).Rulter (19?6)delived a constilutive equationlor presure solulionon ihe domainoiindividual g.ains(Fig.6) whoseformalismisanalogousiotheequarion for Coble creep:insleadof a gradienlin the €quilibrium alongfte Crainboundarylhereis concentration of vacancies a direrence in solubiliry in the fluid films at the srain boun-
daries.The rale ofdeformation also dependson the grain bounddrJ d.l l u\i ' rU rn rhepresence of d fl ui dfi l m. The situation bsomes more complex howeverif the soluliontransfero@u6 over much largerdislancesas, for example,from a stylolileto acalcitevein(Durneyand Rarnsa!, 1973).Sucha situalioncar no longerbe desoibedin terns ofa microdynamicalmodel. creep,likelyto operale Anothe.kind ofgrain siE sensitive atlowstresesandsmallsrainsizes,is grainboundarysliding L^diry to srperyl6ti. fo||- ln thiscasegrainboundarysliding actsas the prime strainproducingmecharismand it is not just a consequence ofstrain compatibilityproblems asis lhecaseduringdifusionalcreep. Aho rhegrainsarenowfree to rotate and to swilch neighbours after high amounts of strain (Edingtoner al, 1976).Midodynamical modelsfor superplaslic flow usuallyassumethar the srrainrate is not conbolledby theviscousresistance to glidingatgrainboundaliesbur by the slowesteventduring slidirg, nanely the minor chang€s ir shapethe grairs haveto unde.goin order to dide past each other. Ball and Hurchinson (1969) proposedlhaldhlo@lions pile up at unfavourablyoriented gruinboundaries andthat th€sedislocalions escape by climbine into the grain bounda.ies.An alternativemodel by Ashby and verrall (1973)proposeslocal dirusioral mass transieralonggrain boundaries. In conlrastto diffusionalcreepand presnre solution,a nonlinear strainrale vs. stressrelationshipis observed.bul the valueofthe exponent, in equation3 is alwayssmaller than 3. The grain sizeexponent, in equation4 h usuaUy found to lie b€tween2 and 3. Thereis someambiguitlaboutihelermsuperplasticily. In a wider \en.e. rh€ nolron of \uperpla{rc flow r. d phenohenologicalone aDd just implies extremeductility dlring an exlensionexperiment.a commonmodeoftesting metals.Ductility is a neasureof resishnceto neckingin a tensilelestand not direcdyrelatedto a specificmechanism. In geology,the term superplastic in this wide sensecan be usedfor any rock which is highly sraiDed, such as any
FiC.6 Pressure solurionon tne eal€ olindividual grainsin a cnnoid.l lineslone.Solulionlook pla@alonghorizontallyorienredsrrlolires, continuityover tne dart gey inpurc orisinalsinglccrystalsoacalcite. rhe whitercdcpositionareasgrow in cryslallographic
Micrc[abrit Stt.l'es, Dafunatior Mechdh6ns und Fla|| La\|s
l 0l
Higb ductilily and resistanceto necking are howeve. indirectlythroughlhe relaledto thedeformationmechanism valueofthe paramete in equation3.If, = I necksdo not propagate(Cittus. 1978)and lhereforemateriakdefo.ding by diflusionalcreepcan be refered to as beingsuperplastic too in this wide sense. In a morerestrictedsensehoweversuperplasticity implies (i) srain boundaryslidinsis the major sbain prodlcins (ii) that the microslruclureremainssrable,i.e. thal the grainsremainequiaxedevenailer largeanounts of (iii) that the stresssensilililyofsl.ain ratein lermsofthe p 3r J m e, er I n equ a rro nI r\ b e rs e e n a n d I. AII thesecrileriado not applyin thecaseofdillusionalcreep. .o h e rer helem \ uper p L \ri c n ,s rl l b e u .e di n _ h i .n a ,,o$ Superplastic flow in rockmaterialshasonlyrecentlyb€en reported(Bouillerand Guesuen.1975:Schhid er 4l, 1977). Il isdifficult howeverto find directevidencelor grarnboundary sliding in nalurally deformed rocks and a stable micfostruclurecan aho be explainedby dynamicrecrystal' lizationduring power law creep.It is only lhe absence ofa prefenedorienlalionwhich can inslrongcrystallographic dicale thal grain boundary sliding may be the dommant strainproducingmechanism.
lV. Pal€ostr€ssEstimates
Fie.7 Slnopricdiasrrns forconsrantsbainrarcsof lO ros (.) and 10 \ '{b) illustratinsrhe relati!enensth otdiflerent rock r!tcs,s d luncrionof lenpcrature.Theconstanr{rain rateconrou$ {re basedonexpcrimcnrally delermined florvlass for polycrysulline resresalesoahalite(Heard. r972).anhydrile(Mnller and ariescl, 1930),rinegrrinedlinrestone(Schmid./ dl, l9?7).cod4e srrrned nrarblc(Scbnid ?/ aa. 1980)-*et rnd dry quartz (Patrhh ar a/1976).dolonire (l.leard,1976)anddunire(Pon. 1977).
A. EsrimatesBasedon the Exoapolationof Flow Laws Ideally.the magnitudeof differeDlialstres can beestimated by €xlrapolationof laboratorydeterminedflow Iawsinro and dependsnol only on the apparentactivationenergyfor geological conditionson the basisoia deformalionmechancreepbut alsoon the valueofthe stres exponent,. ;m map, providedthat thefeare indeperdentestinatesof It is readilyseenlbat accuatesl.essestimates aredifficult renperal ure stfain rate and lemperatufe.Theseexkapolalionsheavily becaure el ti mare\are ucudl i )not l oo preche. re l ) o n r heac . J r . , c yo' rh e d e l o rn a ri o nm e \h .,r\m ra r\ Aho thereare dependencies on watercontenrin the caseof ,he \i l i cares used,and thus also on the reliability of the theoretically and rhe hme.roredaraemphdi /e rhc rmpoG calcnlaledflos lawsfor regimesollside the rangeofexpeitanceofgrainsize(noletherevesalin relativesbength ofrhe mentalcondilionsaccessible to the experimentalist. two calciterocksfrom the bigh strelsareainlo the low sbess Most of the elperimenlallldelermiredflop lals applyro area).On lop oflhes€dimcultiescome sohe oithe problems plaslicityandpowerlaw the mechanisms of low lemperature discusedin the previouschapters. creep(tbr reviewsseeCarter. 1976;Tullis, 1979).Sresses Figure 7 howeler illustratesthe vasl diferencesin 8ow operalingdu.ing brittle fraclu.eand cataclastic flow can be stress1obeexpect€dbetweendirerenl materiahundercon, estimaledthroxghthesell knownMohrCoulonb criteion. ditionsof conslantstrainrate.ln reality,lhesedifferences are Fl o w l a ps f or gr ains iz e s e n s i ti v e c re e p a re a v a i l a b l eonl ylrelaxed or by inhomogeneous deformationand salr.anhydriie superplasticauy deformedcalciteand olivine(Schnidei a/.. andlimestoneinpaniculararegooddecollement horizons!r 1977;Twiss, 1977on lhe basisofdala by Posl, 1973,197?). moderaletempelatures!where dolomire and the silicates Figure7 is a graphjcalsynopsisofsomeof the laboratory remaine$entiallybrittle.Miillerand Hsn (1980)showedby derivedflow laws on various mononineralicrocks in the Dumericalmodellingthat the decollement ofthe SwissJura coordilates of a delormationmechanhmmap (compare mounlainsincludingthe Swissmolassebasinh compatible Fis.7). Possiblelransilions into cataclasticflos al high wilh the experimentally delerminedflow lawsfor anhydrite (Miiller er dr, I 981). a nalor consliluentwithin rheTriassic 'l re se s( dependingon c onni nfig p re ..u re ).,ni ndro Bran s ze sensilivecreep lawsat lor skesses arenot considered in this figurebecauseoi the lack oi experimentaldata (exceptfor At somewhatmore elevakd temperaturescalcile may nne-grainedlimestone,deformiig superplaslicallyat low becomean imporlantdecollenrnthorizonprovidedthar it slresses).The curvesare drawn ior geologicallyrealistic delormsby superplaslicflow. Basedon the flow law for strain ratesby simpleextrapolations oiempirical fiow lals superplaslically deiormedlimestone.the llow stess ar the and lhey exhibit a more or les draslicdrop in strengthat baseoftheClarusolerthrustandwilhin a thin calc,mylonite vastlydifferenttehpe.atures.The relativeslrengrhof lhese layer (Schmid,1975)can be estinated to be lower rhan naterials corespondsnicelyto rhe relativecompetence of l00baf ar the eslimatedlemperalures and strainrates.New theserocksin the field. nicrofabric work on this mylonire horizon produced The slopeat constantskain rate.asderivedLom a power e\i dencerhar B ran boJndarys| drnB ," rhe operal i vc deformationmechanisn(Schnid .r o/., l98l). law relationship(equalion3) is givenby: The relativestrengthofdecollementhorizonsand thrust blocksalsohasahajorinfluenceon thequestionsofgravity 2 .3R n T z spreadingversusacriverectonicpushat the rear ofa thrust
t02 block. This is illusrratedin Fig.s basedon ihe tollowing fomula derivedby Chapple(1978): 2 K(\ e J Pgz which eipressestbe suriacesloped oi a thrust wedgeas a functionof tbeyieldslressr(within thethrustblock,theratio I ofthe shearslressin the basallayerovertbe yieldsbessr. the basalslope9oflhe thrus!block.way lrom the foreland and lhe overburdenpressurepg,. The surfaceslope d in yieldthroudout Chapple\ nodel ha corseqDenceofplastic the thrustwedgeand hasto b€ positivewith a slopelowards the forelandin order 1()producea componentol gravily
spreadingin the d.iving forc€.Figure8 illustratesthat for basal shear stressesof les than lO0ba.s, exp€ctedfor decollement horizonssuchasevaporites and limestoncs,Lne resulting surfaceslope ris negativeand thus gravity spreading must be ruled out in suchcases. Becausenegalivesurfaceslopesaway from fte foreland are geologlcallyunrealislic,Cbapple\ assumptionof peF vasiveyieldwithin lhruslwedges hasto berelaxedifthe basal wiihin the shearstressis verymuchlowerrha, theyieldslress thrusl wedge.It can be shown in the caseof the Helvetic nappesof easlernSwitzerlandthat internal deformalion within the Helveiicihrust block predatesthe final phaseof thrustirs (Schmid.1975;Milnes and Pfirner. 197?).The gravityspreadingconcepland Chapple'smodelhoweverceruinly apply for caseswherethereis a more homogeneous stres distributionin basaldecollementhorizonand thrust
9sz=15OObar B. PaleoslrcssDeterminationsBasedon Microstructural
The classicmelhodsfor the derivationofstress diretions basedon lwinning in calcite ud dolomite (Tumer and weiss, 1963)havebeenfurther delelopedby Spans(1972) and they havebeenappliedfor mappingof principalslress diretions in cross-s€ctions thlough the Rocky Mounlains (Spangand Brown, l98l)- Thesemethodsrely on the facl that twinningincalciteand dolomitecanonly be opelatedin a uniqueshearsense relative!o thecrtslalloeraphy,conlrary to slip systemswhichgenerallyhaveno prescribedsenseof shear.This method horevef only works for moderately strained locks where twinning did not go to neaF Other,similar.methodswhich can only be appliedin the britlle neldrely on fracturepatterns.slickensided faulrsand fault planesolutions.
99z=25OObar
Fis.8 Crapbicalrcpresenldtion of equation6dhcussed Inthetcxt (Chlpple, l9?8,equalion16).Th; sraphilluslruleslhe dependence oflhc surfaceslopcd o. thc ahsolutelalue ol the basaishedr slress in d4 olle men rorr) lonir ehor / on Tlo. c F or c or r oLh r r . f r \ o n lo ra0 .l0 a nd 15 s lope0olr hebas lldeollem enl hor i z o nd w a y from the aoreland: lhe solidandbrokenlincsassunca yicldshe$ K ol l000bar and 500b!r resperilely.Tne top lisu.e (a) rcf€r ro a tbicknessol the overthruslblock oa 6kn, lhc bouom ngure(b) a$lnes l0km overburden. Nolie lbal positivesurfaceslopcs,a.d conscqucnlly a componcntofgravny spreadineae only oblained for rclalivelystronsdecollement borizons(far in exccssof l00bas considered lo be the maximun shearsftngth of a nylonite sucbas thc Lochscilcnmylohilear the Glarus.verthrusl).
Thereis a numberofmethodsto delerminethe paleosbes irom microstructuraldala ard thesemethodshavereceived a lot oiatrention during the last few yeaB.The disrocation densityoffree dislocations. the sizeoisubgrairsand the size grainshavebeenusedto infer ofdynamicallyrecryslallized paleosress.The equationsrelatiDgthesemicrostruclural pafamelersto diflerentialst.essarepartly basedon theorei, ical considerations and partly on the empiricallaboratorr calibrationswhich are availablefor a numberof nnncra,s (for reviewsseeNicolasand Po;ier, 1976;Mercierer a/., l9?7j Twiss,1977tWhite, 1979). There are a numberof diificultiesassociated with these I . All oi thesemethodsasume a steadyslatemiffoslructxre which developedunder dynamical conditions during powerlaw creep-They are not valid ior all th€ olher defomation regimesand in siluationsof stain hardeningor strainsofteoingthejrusebecomes, !1lhe very least,problematic. 2. The microslructDralimprint of the main phase of steadl state defonation in which the geoloeisris interesredma) be overprintedby fie laler geological hrnor) D bl ocauondenqry i n parl i cui ar.( \ er y susceptibleto late overprinls associatedwith small amouf,rsof slrain. The hosr stable paleosrres!iDdicatorisprobablythe recryslallizdgrainsizeand the discussionwill focus on some of the problems associared with rhisparricularmelhod.
M i crofabr ic Stu.lies, Deforna t ion MechanishlsMti FIo|| La$ grainsizedis relatedto dillerentialsress The recryslallized 6lr = K l d l b )P
(8 )
and to lhesbearmodulus wheref (anelasticmodulusrelsled Poissonsratio) and b (the Burgersvector)are used!o nor quantitiesand malizestressand grainsizeinlodimersionless ( and p are constants(seeTsiss. 197?). Figure 9 sunmarizes the data available for vanous minerah.The scatte!in Fig.9a becomessomewhalreduced by normalizingstressand grain sizeaccordirgto the equalion given above(Fig.gb)i lhe dope / howeler still varies betweenvaluesof 0 67 and 1 43 (ior ihe samemiftral, Twiss( l9?7)predict€d olivine).Usingfteoreticalarsuments, slopesof l 0 and 0 7 for subgrainsand refflstallizedgrains that thesecalibrations shouldbe Thelargescatlersuggests applied to geologicalsituatiors with caution and that paleostressdetelminalionsare only ordeFof-magnitude eslinates.The scaltermay haveseveralreasons: of I . Thereareproblemswith lhe technicaldetermination grain size (for a discussionof the methods, see Erheridgeand wilkie, l98l). 2. Other iactorssuchas temperatlre,waterconleni,impuritiesand secondphaseminerahmay also havean influenceor the 6nal grain sia. Slatic lhermaltreat-
I03
ment after the experinentmay Ieadto 8ftin growlh (annealingrecryslallialon).Waler demonsrablyhas an efect on thegraiosize(Fig.9),whilstimpuritiesand secondphasemineralsmay pin the grain boundanes. L Ther€ are several mechanismsof recrystallization which may lead to diflerenl grain sizes.Apart from annealin8rrcrystallizarion, nol relatedto sires, there are lhe following categoriesof mecharisns durjng dynamic(= syntectonic) recryslalliznlion: the roratlb, nechanisminvolvesthe relativerolation ofsubgrains as a consequence of addingmore dhlocationson the samesisn into a subsrainbound:ry (Hobbs, 1969; Nicolas and Poilier, 1976). This mechanism 's sometimes referredto as dsir! reqystallizalronand (Sellars, it is a mereextensionof recoverypro@sses 1977).'lhenigrution m..hznism keepsthe dislocatron densittloa by themovementor migrationof highangle boundariesfrom gains with a low dislocationdensily grainswilb a hieherdensiiy(Ponier into neighbouring and Guiuop6,1979).Finally Mercie. er dl (1977)jn\oked model sol ,r./cafto, ordsrow fl rol new grai ns fron pleformed nuclei"suchas subsrains,deformation bandsand grain boundarybllges. Cuillop€and Poirier(1979)havedemonslrated thai, in thecaseofhalite. the grainsizefor grainsr@rystallizedby migrationis largerthanthegrair sizeproduced (Fig.9). In this casethe lwo by lherolatior mechanism mechanismsoperatesimultareouslyabove a cfilical temperature, an observationmadefor the caseol calciteas\rell (Schmide, a/.. 1980).For quartzandolivine are noi howeverthe mecbanisms of recrystallizarion krown or speciliedin the literature.While Hobbs (1969)and Pojrier and Nicolas(1975)inrer roration meharhms for quarrzaDd olivinerespectively, MeF ciereral (1977)and Rosserat (1980)pr€ter lhenuclea' tion and growth model.Kirby and Green(1980),in a sludy ofdunib xenoliths,observer€cryshllizalionby a nigration nechanism. This disclsion on leryslallization nechanismsindicates tha! a betterundeNtardingofthe nechanismsof reffystallizationisneeded lormore acarale stressdeterminalionsIn the caseof quartz. thereare somedata availablenow for naturally deformedrocks (seereview by Elheridge aid Wilkie, l98l). The magnirudes of diffelentialslressall valy belweena lew hund.edsofbars up to the order of I lbar. Theseestimatesare probablyrelarivelyreliablebecalseno great extrapolations from labolatoly streses down to the eslimatedgeologi€alstresses are involved.In olivine, the situationis differentin lhat lhe slres estinatesfor the upper mantle(below L00bars,Ave Lallemanter al. 1980)involve 3n exkapolationof aboui an orderof magnitudein dillereniial stress(mosl experimentswere perfolmed al streses aboveI kb in solidmediumequipnent). ln spiteofall theledifficullies,the paleostessdeteminalionshavegiver us diret informationon rhe order of magnitudeoi differenlialstresses activeduring powerlaw creep shouldnor ir raturally defomed rocks-Eve, lowersrresses be excluded,however,for the caseof grain size sensilive
V. Crystallographic Prefened Orientation (Texture)
Fie.9 Experimenrally deleminedcuivesof dillerentialstressvs. rhe size of dynanically r€rystalliad grains aor larious rock nalenah (a) and nomalizedaccordi.slo equation7 dcsribed in lhe lexr (b).
Thh topicoffersa particularlygoodexampleof the progress madeover the past few yearsthrough a combinedero( from bolh the experimeDhlapproach and from attenpts to simulate the developmenlof cryslallographicprefeffed orientation(whichwill be refered to astexturehere,following the malerials scienceteroinology) by usiDg conputor
I04
S.M. S.hnid
basednumericalmodels.Thereis a vasl amountoflexture datain theeeological literature.but in manycases interpretations of the pole igures have rema'nedhighly sp€culalive and sometimes nebulous. The work of Lister and co-aulhos (Lister .r a1.,1978i Listerand Pate6on,1979;Lister and Hobbs. 1980)in particularmadeit veryclearthat texluredevelopment is governed by tbreemain lactors: l
Theparti.ulats.t a:fgli.le ,,s tens uctiv duriis.lefomapatlernsfroh which rirn. This producescharacteristic we can learn about the stress.straiDrate and tem, peralure conditionsduring deformation(Lister and Paterson.1979).Experimentalwork on singlecrystals providesimporlantinput parameters for rhesenumer, ic al m odehi n p ro r.d i n gi l l o n a ri o n o n rh e rel au\e maenitudesof lhe critical resolvedshear shesses glide*rlems asd fun.ron neded ro operd,epaflicular of the environmentalparaneteB.
2. Fdre rr.4r)r.With the samesetof acliv€glidesyslems tbe lype oi finitestrain(flattening,constriction.plane p a rre rn\tl i ss r r ar ner c . ,pr o d u c edsi m e re n rp ofil eBU re ter and Hobbs, 1980).ln the caseof texluredevelopment through glide,inducedlattice rotation!. as modeiledby Lister and co-authors,it is dimcult to *r im ar e r l" en a g n i ru d eo f n ra i n F o r d n a h ernal i \e mechanism,such as the pasive rotation of sheet silicatesira ductilernakix,attemptshaleb€enmade1o relatethestrengthoflhe texturetothestrainmagnilude (March, 1932). 3. The strcir path at the kircnatic ltanevo*. 'lhe influenceofthese on rhe nnal iextlre patiern has been studiedby Lister ard Hobbs (1980)and Etchecopar (1977).StarlinSwitb a randon texlureand excluding complexmultiphaseslrain histories,an asymmety ol the pole figuresin respectto the macroscopicfabric axes(foliarion,lineation)isindicativefor a non-coaxial slrainpalh wilh a largecomponenl ofsimpleshearand the senseolthe asymmetryreflectsthe senseofshear. I t k slill nol clearhow muchandin exactlywhichway intracrystalline slip occurringin low temperalureplas ticity and powerlaw creepdetermines the laiticero!ations of individualgrains.Many rocks with a srong texlure are dynamicallyr€crystallizedand dynamic recrystallizatiorwasnotconsidered by themodelwork (19?8). olEtchecopar(1977)and Lisrer "1a1. Figu.e 10,takenfrom Caseyerd/. l9?8,is a goodexample for how lhe deiormationmechanisms and lbe set oi aclive glidesystemsinnuencethe texlurein the caseolcalcite.The type I lexrures(Fig. 1l ) areindicaliveoftlinning. known to The type 2 be fte €asiestglidesystemat low temperatures. oftwinning and Lhter (1978) texturesoccurin the absence simulatedthis texture remarklbly well by aclivaling slip nainly on the rhonbs r and i. The type 3 texturesa.e comparativelyweak and the transitionirom lype 2 inlo type 3 exactlycoincides wilh thechangein deformationnechanistn flow (Schmid?r dl, form power law $eep into superplastic l9'17tCaseyet al.,1978).'fhefact thdt a weaktexturedoes delelopindicalesthat sohe inlraffystallineslip takesplace during grain boundarysliding. Usually the laboralory experimenlsproduceuniaxialll ofthls, the pole and.as a consequence deformedspecimens l m e rr! d ro u n drh ec o m presi on h g ur es er hr birr ola u o n a)m axis (this is the reasonfor usirg inversepole figuresfor detaihi seeBunge.1969).The experimenlalwork of Keln (1971)is the only exampleofa morecomplextypeofcoaxial demo.straledhow the type of slrain and he €xperimentally straininfluences the texture. Experiftentsin simpleshearare very dimcult to p€rforn
Fig l0 lnvcBepolefisuEsfor expcrinenlally delom€dcdlcire rocks.conlourcdinnultiplesofa unilormdistribuLion.takenfton Cascy ?ri/ (1978). and beiewe .ely on modelwork and on lhe interpretalionof texturesin naturallydeformedrocks.Nature providesindependenlevidencefor shearingdefomation and for lhe \en,eot(heari n mdnJ,hear zone.(R amsa).1980: S rnp: on. 1980).Figure Il illuslratesthe textureof a quarlz mylonite within sucha shearzone.Xiay texturegoniometryallows the deierminationofa let ofpole figuresand we do nofuely onlyon the polefigurefor thec-axisin quartz.as is the case (Schmid?r zl. l98rb). ln in oplical U-slagemeasurements addilion,thecalculationof theorientationdistribu!ionfunction (Bun8e,1969),Bu.ge and Wenk. l9?7! Casey,l98l) allows ideal crystal orientrlions in terms of all ffys tallographicaxesto be delerminedtroh a setofpole llgures fordirerent crystallographic dilections.Figure l2 plorsthe
Fig. ll X{ay delermibed pdleiigureslor thcquartzc-axisand rhe r-direction(1120)in quarrznelakcn from r sbearzone(Schmid?/ a/.. 1981b).Thc counloursare given in nultiples ol a uniform dislribution.Th. odentationoffolialion (F) and linearion(L) fe labelledtoEelhcrwilh the shearzonc boundary(S). Thc atrows indicdrelhe senseofshearinfe(ed ftom rheshc,r zoneCconerD.
Microfubric Stu.lies.Delonlation Me.hanism ahd FIor Laws most likely orientation of a qDartz grain in caseof lhe presented specimen in Fig. I L The a-direction(normal ro rhe secondorderprism in quartz),an importanlglidedirection. is alignedwith the inferredsheardirectionwithin rhe shear zone.ln addition,the positionofthec-axissuggests thatlhe posiliverhombspreier to be alignedwilh the shearzone boundaryand this is connrmediD Fig. 12.Tbis is a stable orjenlationfor easyglide on the rhomb planesand in the following chapterthe rheologicalconsequences of such a slableend-orieniaiionwill be discused. Figure l3 illustrateslhat this samespecimen dynamically probablyby a rolation mechan;m.Dynamic recrystallized. recrystallizarion did no! destroythe texture.which can still be readilyinterpreledin termsofintracrystallireslip.There is thusno needto invokesepalate modelsof texturedevelopmentfordynanlcalll recrystallized grains.suchastheKanb model(seediscussioniD Nicolasand Poirier.1976). An immediateapplicationofsuch asymmetri€s liesin the determiDation olshearsense,nol knownin rnanygeological settings.and in kinemalic inlerpretationof lineationsin termsoia' and b-lineationsfollowingSand€rsleminology. In our case,the lineationis at a small angleto the shear directionand thereforerepresents a stretchinglineationsub' parallelto the relativedisplacenentof the shearzoneboundaries(alineation).There a.e no{ nunerousexamplesof ihe determinationof shearsenseusingthis principle(Eisbacher, I970j Boucher, 1978i Burg and Laurenl. 1978; Bouchezand Prcher, l98l). Syslenalicregionalstudieson the significanceof lineationsfor inferringlhe directionof relativedisplacement ofnappeso. during internaldeformation ofgnehsicbodieswill cenainlybe of ma.jorgeotectonic importancein the future. VL Strain Soft€ning Mechanisms Localizeddeformalionin shearzonesis an importanlmode ofdeformationin basedenhocks(Rahsay. 1980)and ductil€ floe in myloiile Iaye6 accountsforlarge nappetranslations.The formation of shearzonesand mylonitehorizons is a consequence Ther€is a variety of localshearinslabiljties.
Fig. Il
105
Fis.l2 Fdlouredcrystal odentation forthesp*inenDresenredin Fig.IL Thec dxn posirionlabcllcd cj andc, cotrcspond 1otbe positions ofthcc-arisnaxind in Fis.ll, thepositions ofthc polcs to (l lZ0)arclabelled a Gccond orderprisns),lheposilions of lhc pohs10( l0I I I and(01T1) arelabelled r ard z (posnive andnegarile rhombs rcspectively)
of posible hechanisnswhich can leadto strain softening Ge reviewsby Poirier, 1980and White a1..1980)and "1 heaiing(Brun henceto shearinslabilities.Alihough shear and Cobbold, 1980tFleilout and Froidevaux,1980)probably is the mostpopularsofteringnechanism,we wiU only discus two otherposible mechanisms, because they relale closelyto the topicsdiscussed so far: (l) Geomehicalsofteningcaus€dby the rotalion oleasy glide systemsinro orienlationsof high resolvedshear slresesduring lexlureformalionand (2) softeningasa consequence ofa chansein deformation mechanism from powerlawcreepinto grainsizsensitive
Microsfuclureorlhe dynanicallyrerystauizedquarrile specinenr€ferredto in Fis. 11.
1 06 creep.The latler processcan be inducedby dynamic
B . S ofteni ngby a S trai nInducedC hangei n Defomation Mechanism
Boih these hechanisds rely on 1ro aspecls of the midofabric which a.e typical fo. mllonitesra skong crystallographicpreferredorientationanddynamicrecystallizalion towardssnall grainsizes.
Dynamicf ecrystallization duringpoler law creepeffectively changeslhe grain sizcof the startingftaterial as ilhstated in Fig.5 ior experimenlallydelormed calche. The same pfoces ol grainsizereductionin thecaseoilhe calc-myloni!e alongtbe Clarus overlhruslin the HelveiicnappesofSwi! zerlandis illustratedin Figs 14, 15, 16 Fo. Fig. 16it is paF A. Geomelical Softenins ticllarly obviousthat lhe mechanismofdynamic recrystalljzationbys!bgrainrolationinducesthecbange in grainsizc. In thepreviouschapt€r.thedeveloplnent of lexluresjn sbearThe newffystallized g.ainsizehasbeendetermined to be ing situationswasdiscused.nd il wasdemonstrated that a around 6-7Fm and accordingto the stressvs. gratrrrzc type of kxrure may developwhich increasesthe avefage relationshipof Fig.9 this indicatespaleostresses ofaround resolvedshearstresson oneo.. inmany othe.clses,on a iew 700bar during subgrainfomation and recryslallization in powerlaw creep.As theinilialg.ainsizeis reduced,gfainsize of the slip systems.In the caseofquariz. a good alignmenl of the !-directionswith the shea.directionis observedin senslt'veffeep may or may not take overdependinS on rhe mrny cases(Bouchez.1978:Schhid ?r a/., l98l). sizeof the new g.ains and the positionof lhe mechanhm ln sucha situation,thc flow strcs for intracryslalline dip boundaiybetweenpo{er law creepand grain sizesensitive sillevenlually drop 1oa minimum.Both Etch€copar(197?) creep.Thh willnow bediscussed in somedetailo. the basis and Lisler and Hobbs(1980)simulaledthe delelopmenlof ol Fig. l?. whichshowsadefo.mationregimemapwithgrain suchend-orientations iD their models. sizeas a variableat conslanltemperatures. This graphwas Experimentaldata by Burows e, a/. (1979)suggests that constructedtor calcile aggregatcs by combiningthe conthe reorientalionof the latticenay be assistedby dynabic sljtuliveequationsfor exponentialand power law creepas rccrystallization and many myloniteswilh a strorg texture observedin Carara marble(Schmid?r ul, I980)wi!h those are dlnahically recrystallized. The nechanism ol grain lbr superplasiicflow observedin Solnhofen limestoDe (Schmid.r d/.. l9?7).Because boundarymigralion in particularore6 a good empnical superplastic flow is grain sjze explana!ionfor the enhancement ofthe ra!eofreorientation dependent.the resultirSdeiormationregimeboundary is grain sizedependentas well and separales of the crystal lattice towardsan end,o.ienlationior easy a high stres glide.Thosegrainswhich are unsuilablyorientedfot easy largegrainsizeareaof predominanllypowerlawcreepfrom glide will accumulatehigh levelsof inrernalelasticstrain a low stres snall grain sizeareaofsuperplasticflow. energythrotrgha highdislocationdensityand latlicedistor, Superimposed or lhis defornalion reeime map is lhe tions in the form of undulouseextinction. kink bands. curveofslressvs.1hesizeofnew grainsrsryslallizing by a d e f or m alionban d s e l c .C ra i n s o ri c n tc d fo re a sygl i deonl h€ rotalionmechanism ofdynanic recrystallizalion GeeFig.9). otherhandhavea lowerdislocation densityandbecause they Sbictly speakingthiscurveshouldfallwithin the powerIaw deiorm in conpalibility wilh the bulk aggregale they store Iield because this rsrystallizario! by subgrainrotationcan lesselaslicslrainenergy.This promotestheconsumptionof only bebroughtaboutbypowerlawcreepand thenotion of unsuilablyorienledg.ainsand hencestrenglhens thetexlurc. an "equilibriumgrainsize"h meaningless in the domainof
Fis.14 Recrystallizalion concenhatedulonc srain boundariesatlhe besinningsraseof progressilenylo.itiarion. L@hseitenmylonire,
t07
Microfabric StuAies.Defamatioa Mechanisns and Flow Lavs
Fig. t5
Lochseiten nylonite. in rhemarrix.Old crains(porphyroclasts) areheavilylwinncd. aggrcgale Rsryslallizalion10a n€wfine,grained
superplastic ilo* (EtheridgeandWilkie. 1979).The slressvs. grair sjzecuweboweveris superinposed on thedeformation the mechanhmmapsolelylor the purposeof demonstrating straini followingevolutionwith increasing A calciteaggregate deformsby a slrain rate and undera stressindicatedby the posilionof poinl A in Fig. 17.The p o sl r onof r hs por nrA rn d rc a rerhsrl rl ' em a re ri a l h a (a C rarn
sizewhichis largerthan the sizeofthe subgrainsand rccry$ slrain.The lallizedgrainsexpectedto form wilh increasine materialdeforming by disiocalioncreepal point A will eventuallyrecrlstallizeto a grain sizealong a curvewhjch The pathsto comesto lie within the field oi superplasticity. poinl B and C indicaledin Fig.l7 indicatetwo exlreme posibiliti€sofwhat can hypotheticallyoccurifthe produc' would lion of a new g.ain sizeby rotation recrystallizalion
\
.t'
A
lOum
we.t .tmost ro conplerion.The nev grainsaE free of opri.al shain fearures,the glain boundaricsare w€ll Fis.16 R€crvsrallization equilibraledGompareFi8.l8). L@heiten ntlonile, Glarus.
108 behaviourcan only occDrifthe positionolthe equilibrium grain size curve is inside the supe.plasticfield. It is emphasizedagain that once the changein mechanNmhas occuftedi the culve of recrystallized8.ain size vs. stress becomes meaningless.
Frg 17 Delormationregimenup ibr culcireal ! Lenneralureof 400 C oresenred in diferenti.l sfes vs.grainsizccoordih.tcs.Thc ifrnr rntc contoursarc ldbcucdwnh lhc ncgalivccxponcnlotlhc {ranr hte in s I. The maDis brsd on experimentally deremlned fid{ hss.f calcitc.In rhcsut*plastic rcgimcthccquationforerain siTesensilivecreep ofSolnhofenlim€stonewasused(equation2 in 1977)The llow ldws lbi rheexponentirldnd power Schnid.T "1. e trL€n fronr dat! on Carrarum ble (Ruller, l9?4i lxN rc-lincs Schmide/dl, 1980,slrcssrel.xdriondrid). SuFrinposcd on ihh dcfornation resine nap is tbe curve hbelledrecrystallized cranrsiz takenLom rhecalciredata presen red in Frg 9 Fo.! dncus\nJnol rhisgrdth rnd rhdcxplrmton.l thc poiDs l,bcllcd A. B lnd C, sccrcxr.
be inslanlaneous Thecase Billusfdtes tba! underbound.ry conditions of coDstaDtstress an acceleralion of stain ra1e over severdlol ders of agnitude will occur .s . consequence olthechange in Srain size.The cdseCahernalivelyillustrates a nress drop under th€ extreme opposite boundary conditions of constant slrain rate. This change in rheological
However,il is obviousthat instahlaneous recrlslalllzalonis d \eF unrea\onabla$umpl f ronl or w ha, mdy oc.u' il nature.As observedin the experiments on Carraramarble and aho in many mylonitic rocks the evolution of an equiaxedline-grainedaggregale of rrcryslallizedgrainswill lead ro a bimodal srain size distribution. Some fabric donains will be fully recrlstallizedwhile the original grain sizewill be preserved in otherdomains.This may leadto a situalionwhereboth pow€r law creepand superplaslicity occur simullaneouslyin differebl fab.ic domains.Such a siiuationcan no longerbe desclibedby a singlepoinr h the diagramoi Fig. I7. Initially the fully recrystallized domains willbe isolatedand willmake !p a smallvollne f.actionof the rock. Thus, flow will renain stable and can still be definedby the positionofpoint A in Fig. 17.As the volume fractionof f!l1y recrystalliedmaterialgrows,the bulk slrain raleofthe rock willinoeaseand/o! the bulk stresswilldrop due io the contributionof rhe superplastically deiorming domainslotheoveralldeformationintherock.Therheology of the bulk rock can tben be tbousht to be gilen by ihe positionof a point somewhere alonethepath belweenA and In conclusion.dynamic recrlstallizationwiu indDcea changein mifioslruclurewhich in turn inducesa changein deformatioDmechanismleadingto work softening. Thn conclusionapparenlly conlradicls the facr that duringexperimental defornationofCarara marbleDowork soltenrngwasobservedasaconsequence ofdynahic recrrstrllization,evenaftermoretban 30%shortening(Scbmider r' /. l 9E r H otrever.* hen" ri mr.ardc,ormari ol ep r m er nip is conslructedfor the 900 1050'Ctemperatureregion(1he temperatures at whichreoystalli2ationoccured jn theseex, periments)one ends up with a ditferenrpositlon oi rhe
Fial8 Microsfudure, typicallor superplastic Sowin solnbolcnlimstone,exp€rimcntall! defo.medal 90o.c, ? x l0 as r,lkbcon6ni.e pressure and ar 280bardilTeftndalstrcs by 16%sho enins.Note lbe wellequilibrated and rheabseneofsrain fl!fienin; srain boundaries in spileoi the larecanount ofslrdin.
M;'uJrb,i
StuJi '. D4oInaion
due boundaryinstressvs.grainsizecoordinares mechanism to tbe direren! activalionenergiesfor oeep in dislocation creeDand (uoerpl3\uc llo$ re"pecu\ely.The nechrnnm u o u n d ar yno" it m o. r c o n c ro e .$ i th th e p o s rro no i the €quilibriumgrainsizecurveorcomeslolieinsidethedisloca lion creepfield.In otherwords.lhenewgrainsizeproduced by reffyslallizationdoesnot fall insidetheareaof dominanr llo{ at the high tenperaturesand $erefore ly superplastic no work softeningis expected.The mechanisnof work softeningp.oposedhereis thus expectedto be importanla! relativelylow temperatures. In thecaseolthecalc-mylonitementlonedearli€ritls very likely tbat the stres estimateof700ban is only validfor the inilial deformationwithin the power la$ creepneld The ofthis mylonite, similarilybetseenthe final microstructure after reffyslallizalioris alnost complete(Fig 16).and lhe mi$ostructure of superplasticallydeformed Solnholen linestone(Fig.l8) is striking.The textureoftotally recrys ofthismyloniteisveryweak(Schnid
