What Is Rheology ? from the Root Work “Rheo-” Current: Flow Greek

Home , Deformation (physics), Strain rate

What is rrhheeoollooggyy ?

From the root work “rheo-” Current: flow

Greek: rhein, to flow (river)

Like rheostat – flow of current

Rheology

What physical properties control deformation ? - Rock type - Temperature - Pressure - Deviatoric (differential) Stress - Others ?

What are the different types of strain ? - Brittle Low T,P, Shallow - Elastic > - Plastic - Viscous > High T,P, Deep

Rheology

 Strain rate measured by GPS in Southern California

 What do the GPS measurements indicate ?

 At what depth do these movements occur ?

 How can we test this ?

Rheology

Guest Lecture from Dr. Miranda!

- Brittle Deformation - Plastic Deformation - Brittle/Plastic Transition

ChChapaptteerr 116:6: MMaaccrroscoposcopicic AspeAspeccttss ofof RoRocckk DeDefforormmatationion

PARPARTT II:: RRHHEOEOLLOOGYGY ANDAND MMAACRCROOSCOSCOPPIICC DDEFEFOORMRMAATITIOONN

EarEartthh mmatateerriaialsls rreespspondond ttoo ststrreessseses,s, causcausiningg ssttrrainain.. SSttrreessss andand ststrraainin araree rreelatlateedd tthhrroughough rrhheeoloologygy.. WeWe ddeescrscribeibe tthhee ststrrainain pprroceocesssseess anandd ccatateegorgorizizee tthehemm iinnttoo difdifffeerreenntt bbeehhavaviorior;; tthheessee rreelalattionionsshhipipss araree alsoalso dedescscrribeibedd mmaatthheemmataticallyically..

ChChapaptteerr 116:6: MMaaccrroscoposcopicic AspeAspeccttss ofof RoRocckk DeDefforormmatationion

ThThee nnamamee rrhheeoologylogy dederriviveess ffrromom tthhee GGrreeeekk worwordd “r“rhheeo”,o”, whwhichich mmeeananss ““ffllowow”.”.

RRhheeoologilogiccalal ssttudiudieess hhanandldlee tthehe ffllowow ccomomponponeentnt ofof dedeffoorrmmatation,ion, witwithh eemmpphasishasis onon tthhee iinntteerrppllayay bbeettweweeenn ststrreessss,, ststrraainin,, aanndd tthehe rratatee ofof fflow.low. IInn ggeeososccieiennccees,s, rrhheeologologyy rreeprpreesesennttss aa brbrananchch ooff tthhee sciesciencncee ofof rrockock mmeecchhaannicicss..

RReemmeemmbeberr…… eevveerrytythhiningg fflows,lows, eevevenn ssolidolids,s, undeunderr tthehe rrightight conconditditiiononss ofof ttimimee anandd ststrreess!ss!

ChChapaptteerr 116:6: MMaaccrroscoposcopicic AspeAspeccttss ofof RoRocckk DeDefforormmatationion

RRhheeoologilogiccalal bbeehhavavioriorss rraanngege ffrromom ppeerrffeectctlyly eelaslastticic solsolidsids atat oneone ExtExtrreemmee ttoo viviscscoousus NeNewtwtonianonian ffluidsluids atat tthhee otothheerr..

HowHoweeveverr,, tthhee rrhheeolologyogy ofof nnaattururalal mmatateerriaialsls ssucuchh asas rroocckkss,, ffallsalls betbetwweeeenn tthheesese eextxtrreemmees.s.

QQueuessttionion:: tthhee rreespspoonnsese ofof mmatateerriaialsls ttoo ststrreessss dedepepenndsds onon wwhhaatt pprropopeerrttieies?s?

ChChapaptteerr 116:6: MMaaccrroscoposcopicic AspeAspeccttss ofof RoRocckk DeDefforormmatationion

WeWe wwiillll nnooww eenngagegage inin aa mmororee quaquannttititatativeive ststuudydy ooff hhowow mmaatteerrialialss bebehhavavee inin rreesponsponsese ttoo ssttrreesss.s.

AA mmatateerrialial ccanan eexhibitxhibit::

• BBrrititttllee bebehhavaviorior • ElasElastticic bebehhaaviorvior • PlasPlastticic bebehhaaviorvior • ViscousViscous bebehaviohaviorr • PowePowerr-law-law bebehhaviavioror

ThTheerree araree otothheerr ttypypeess ooff bebehhaviavioror,, butbut wwee willwill ffococusus onon tthheessee mmaiainn ttyyppeess inin tthhisis ccouourrssee..

ChChapaptteerr 116:6: MMaaccrroscoposcopicic AspeAspeccttss ofof RoRocckk DeDefforormmatationion

11.. BBRRIITTLTTLEE MMAATERTERIIALALSS

BBrrititttllee bebehhavaviorior ccaann bebe gegenenerralizalizeedd byby MMohohrr CouloCoulommbb ffaiailurluree::

σσ µµ σσ s == ** n ++ CC

σ µµ σ where s iis the shear stress, isis the coefficicieient of friictioion, n iis the llininear straiin, and C isis cohesiion.

ThThee ComComppososititee FFailurailuree EnEnveveloplopee:: 33 parparttss

I: Tensile failure II: Coulomb failure III: von Mises criterion (deep crust)

σσ s CC φφ 22θθ τ σσ σσ 3 1 σσ n

II IIII

IIIIII

ChChapaptteerr 116:6: MMaaccrroscoposcopicic AspeAspeccttss ofof RoRocckk DeDefforormmatationion

22.. EELALASSTITICC MMATERATERIIALALSS

ElasElastticic mmatateerrialsials dedeffoorrmm byby anan amamounountt pprropopororttioionnalal ttoo tthhee apappliepliedd ststrreess,ss, butbut wwhheenn tthehe ssttrreessss isis rreeleleaseased,d, tthehe mmaatteerrialial rreettuurrnsns ttoo ititss ororiginaliginal undeundeffoorrmmeedd ssttatatee.. ThThee dedefforormmatatiionon isis sasaidid ttoo bebe rreeccooveverrablablee.. ThThiiss rreelatlatioionnshshiipp dedeffinineess eellastasticic bebehhavaviorior::

σσ == YY εε

where σ iis the applliied stress, ε isis the lliinear strainin, and Y iis Young’s’s modullus (materiiall specififiic).

ChChapaptteerr 116:6: MMaaccrroscoposcopicic AspeAspeccttss ofof RoRocckk DeDefforormmatationion

22.. EELALASSTITICC MMATERATERIIALALSS

ThThisis rreelalattionionsshhipip dedeffiinneess eelalaststicic bebehhaviavioror::

σσ == YY εε

where σ iis the applliied stress, ε isis the lliinear strainin, and Y iis Young’s’s modullus (materiiall specififiic).

ChChapaptteerr 116:6: MMaaccrroscoposcopicic AspeAspeccttss ofof RoRocckk DeDefforormmatationion

22.. EELALASSTITICC MMATERATERIIALALSS

σ == YY εε

Ellasticic behaviior isis modelled very wellll by a sprining that iis compressed and then relleased. The sprining recovers the deformatiion. Thisis equatioion isis essentiaialllly the same as Hooke’s’s Law.

ChChapaptteerr 116:6: MMaaccrroscoposcopicic AspeAspeccttss ofof RoRocckk DeDefforormmatationion

33.. PPLALASSTITICC MMATERATERIIALALSS

PlasPlastticic mmatateerrialsials dedeffoorrmm byby anan amamounountt pprropopororttioionnalal ttoo tthhee apappliepliedd ststrreessss (e(elaslasttic)ic) atat ffirirstst,, butbut whwheenn aa ccrrititicalical yyieieldld ststrreessss isis rreeachacheedd,, tthheeyy fflowlow rreeadadilyily anandd undeunderrgogo ppeerrmmaanneenntt dedeffoorrmmatation:ion:

ChChapaptteerr 116:6: MMaaccrroscoposcopicic AspeAspeccttss ofof RoRocckk DeDefforormmatationion

33.. PPLALASSTITICC MMATERATERIIALALSS

PePerrffeeccttlyly pplalaststicic mmatateerrialialss eexxhhibiibitt nnoo dedeffoorrmmatationion atat aallll bebelowlow tthehe tthhee yiyieeldld ststrreesss:s:

σσ s == KK σσ Where s iis the shear stress and K isis the yiielld stress.

ChChapaptteerr 116:6: MMaaccrroscoposcopicic AspeAspeccttss ofof RoRocckk DeDefforormmatationion

33.. PPLALASSTITICC MMATERATERIIALALSS

AA mmeecchhaannicicaall ananalalogog ffoorr pplaslastticic dedeffoorrmmatationion isis tthhee ideideaalizelizedd ffrrictictionionaall rreessististananccee ttoo tthhee slidislidinngg ooff aa blblocockk onon aa sursurffaaccee..

Just the plastic deformation: yield stress

σ σ

ε ε•

ChChapaptteerr 116:6: MMaaccrroscoposcopicic AspeAspeccttss ofof RoRocckk DeDefforormmatationion

4.4. VIVISSCCOOUUSS MMATEATERRIIALALSS

ViscousViscous mmatateerrialsials dedefforormm byby fflolowwiningg inin rreespsponseonse ttoo aa ststrreesss,s, butbut whwheenn tthhee ststrreessss iiss rreemmoveoved,d, tthhee mmaatteerrialial doedoess nnoott rreettuurrnn ttoo tthhee ununddeefforormmeedd conconffigigururatation.ion. IItt cancan bbee ssaidaid tthhatat ststrreessss isis pprropopoorrttionionalal ttoo sstraintrain raterate durduriningg visvisccououss dedefforormmatationion.. VisVisccououss bebehhavaviorior isis dedessccrribeibedd byby::

σ = 2 η ε

Where σ iis stress, η isis viiscosiity, and ε isis shear straiin rate.

ViscousViscous bebehaviohaviorr isis comcommmoonn inin NNeewwttononianian ffluiluidsds..

ChChapaptteerr 116:6: MMaaccrroscoposcopicic AspeAspeccttss ofof RoRocckk DeDefforormmatationion

4.4. VIVISSCCOOUUSS MMATEATERRIIALALSS

IItt cancan bebe ssaidaid tthhatat ssttrreessss isis pprropopoorrttionionalal ttoo sstraintrain raterate durduriningg viviscscoousus ddeefforormmaattionion.. VViiscscoousus bbeehhavaviorior iiss dedescscrribibeedd bby:y:

σ = 2 η ε•

Where σ iis stress, η isis viiscosiity, and ε• isis shear straiin rate.

ε•

ChChapaptteerr 116:6: MMaaccrroscoposcopicic AspeAspeccttss ofof RoRocckk DeDefforormmatationion

4.4. VIVISSCCOOUUSS MMATEATERRIIALALSS

AA googoodd mmeecchhanicanicalal ananalalogog ffoorr visvisccououss dedefforormmatatiionon isis aa ddashashpotpot.. WhWheenn aa ffororccee isis aapppplieliedd acracrossoss tthhee sysyststeemm,, tthehe mmoottionion ofof tthehe ppisisttonon isis govegoverrnenedd byby tthehe rratatee atat wwhhiicchh tthhee ffluidluid fflowslows tthhrroughough tthhee ppororeess inin tthhee ppisisttonon..

slslopopee == 22ηη σ σ

ε• ε

ChChapaptteerr 116:6: MMaaccrroscoposcopicic AspeAspeccttss ofof RoRocckk DeDefforormmatationion

55.. PPOOWERWER-L-LAWAW MMATERATERIIALALSS

NonNon-Ne-Newtwtononiianan ffluluidsids dodo nnoott hhavavee aa cconstonstantant slslopopee onon tthehe ststrreessss-st-strrainain rratatee grgrapaphh.. IInnststeeadad ofof viviscscoousus bbeehhavaviorior,, tthheeyy eexxhhibitibit ppoweowerr-la-laww rrhheeoloology.gy.

• NeNewtwtononiianan σ = 2 η ε slslopopee == 22ηη

nnon-Non-Neewtwtoonnianian ••εε σσ n == AA(( diff))

ε•

ChChapaptteerr 116:6: MMaaccrroscoposcopicic AspeAspeccttss ofof RoRocckk DeDefforormmatationion

55.. PPOOWERWER-L-LAWAW MMATERATERIIALALSS

• •ε NeNewtwtononiianan σ = 2 η ε = σ η slslopopee == 22ηη 2

nnon-Non-Neewtwtoonnianian ••εε σσ n == AA(( diff))

ε•

ChChapaptteerr 116:6: MMaaccrroscoposcopicic AspeAspeccttss ofof RoRocckk DeDefforormmatationion

55.. PPOOWERWER-L-LAWAW MMATERATERIIALALSS

RRocockkss oofftteenn dedefforormm asas ppoweowerr-law-law mmaatteerrialialss inin ductductileile shsheearar zozonneess.. ComCommmoonn ststrreessss eexponxponeennttss aarree nn == 33,, 55,, anandd 7.7.

σ viviscscoousus diff NeNewtwtononiianan slslopopee == 22ηη ε˙ σ ppoweowerr-la-laww Power-law curves nnon-Non-Neewtwtonianonian

ε• ••εε σσ n == AA(( diff))

ChChapaptteerr 116:6: MMaaccrroscoposcopicic AspeAspeccttss ofof RoRocckk DeDefforormmatationion

NowNow tthhatat wwee’ve’ve ccovoveerreedd 55 comcommmonon ttypeypess ofof rrhheeologologieies,s, wwee ccaann ususee tthehemm ttoo ununddeerrststaanndd eexperixperimmentaentall duductictilele flflowow..

WhWhoo carcareess??

ThThee eexxppeerrimimeennttss araree iimmppororttantant ttoo gegeoologislogisttss bbeeccaauseuse tthheeyy pprroduoduccee tteexxtturureess tthhatat araree ssimimililarar ttoo tthhoseose obsobseerrvevedd inin nnatatuurraallylly dedefforormmeedd rrocockks.s. TheThe lalabb eexxppeerriimmeennttss araree dondonee atat aa spspeecciiffieiedd tteemmppeerratatururee,, pprreessssururee,, ststrrainain rratatee,, wwaatteerr ccoonntteentnt,, eettcc.... TheThe eexxppeerriimmeennttss araree tthheenn useusedd ttoo ““calibcalibrraattee”” tthhee ccoonnditditiiononss tthhatat pprroduoducceedd tthhee tteexxtturureess obsobseerrvevedd inin nnatatuurraally-dlly-deefforormmeedd rrockocks.s.

ChChapaptteerr 116:6: MMaaccrroscoposcopicic AspeAspeccttss ofof RoRocckk DeDefforormmatationion

ThThee eexxppeerrimimeennttss ininvvolveolve tthhee slslowow ccontontininuouuouss dedefforormmatationion,, oror crcreeeepp,, ofof tthhee ssppeeccimimeenn.. ThTheeyy araree ddononee atat mmuucchh ffaaststeerr ststrraainin rratateess tthhanan natnatururalal gegeolologicogic ststrraiainn rratatees.s. LLaabb rratateess ~~1100-7.

AArree tthhee rreessultultss ststililll apapplicableplicable??

ExpExpeerrimimeentntss aarree eeiitthheerr ddononee atat 11)) conconssttanantt ststrreesss,s, oror 22)) conconststanantt ststrraainin rratatee..

IIff wewe wwantant ttoo ccomomppararee ttwowo sseettss ofof eexpexperrimimeennttalal datdata,a, tthheenn wewe ccoommppararee tthheemm inin tteerrmmss ofof aa hhomomolologousogous tteemmppeerratatururee,, whwhichich isis tthhee rratatioio ofof tthhee tteemmppeerratatururee ofof aa subssubsttanancece ttoo ititss mmeeltltiningg ppoioinntt..

ChChapaptteerr 116:6: MMaaccrroscoposcopicic AspeAspeccttss ofof RoRocckk DeDefforormmatationion

WeWe ccanan eexxamamininee tthhee rreesusultltss ofof anan eexxppeerrimimeenntt bbyy grgraapphhiningg ststrraainin vveerrsususs ttimimee,, oror difdifffeerreennttiialal ssttrreessss vveerrsussus ttimimee..

WeWe difdifffeerreennttiiatatee bebettweweeenn ccooldld worworkkinging eexxppeerrimimeennttss whwheerree ThThee hhomomologoologousus tteemmppeerratatururee iiss << 00..55,, andand hhotot wwoorrkkiningg eexxppeerriimmeennttss whwheerree tthhee hhomomolologousogous tteemmppeerratatururee isis >> 0.50.5..

ChChapaptteerr 116:6: MMaaccrroscoposcopicic AspeAspeccttss ofof RoRocckk DeDefforormmatationion

##11:: ThisThis iiss aa hhotot--worworkkeedd,, conconssttanantt ststrreessss eexpexperrimimeenntt rreessultult..

11)) IItt hhasas aa veverryy sshhorortt dudurratationion ofof ssomomee ininititiialal eelastlasticic bebehhavaviorior whwheenn tthhee ststrreessss isis apappplilieed.d. IItt ququicickklyly eexcxceeeedsds yiyieeldld ststrreesss.s.

ChChapaptteerr 116:6: MMaaccrroscoposcopicic AspeAspeccttss ofof RoRocckk DeDefforormmatationion

##11:: ThisThis iiss aa hhotot--worworkkeedd,, conconssttanantt ststrreessss eexpexperrimimeenntt rreessultult..

22)) TheThe crcreeeepp rraattee isis iinnititiaiallylly hhighigh,, butbut sstteeaadilydily dedecclinlineess aass tthhee eexxppeerriimmeenntt pprrococeeeedsds--t--thhisis isis pprrimimararyy ccrreeeepp..

ThThee pphheennomomeenonnon ofof ddeecrcreeasiasinngg ccrreeeepp rratatee witwithh ccoonnststantant ssttrreessss isis ccalalleledd ““worworkk hharardedeninningg””

ChChapaptteerr 116:6: MMaaccrroscoposcopicic AspeAspeccttss ofof RoRocckk DeDefforormmatationion

##11:: ThisThis iiss aa hhotot--worworkkeedd,, conconssttanantt ststrreessss eexpexperrimimeenntt rreessultult..

33)) TheThe crcreeeepp rraattee eevevennttualuallyly ssttabiabilizelizess aatt sosommee conconssttanantt lelevveel,l, anandd tthhiiss isis callecalledd ststeeadyady ststatatee,, oorr seseconcondardaryy ccrreeeepp..

ChChapaptteerr 116:6: MMaaccrroscoposcopicic AspeAspeccttss ofof RoRocckk DeDefforormmatationion

##11:: ThisThis iiss aa hhotot--worworkkeedd,, conconssttanantt ststrreessss eexpexperrimimeenntt rreessultult..

33)) SSoommeettiimmeess tthhee ststeeadyady-st-statatee rreeggimimee givegivess wayway ttoo tteerrttiariaryy ccrreeeepp,, wwhheerree tthehe ssttrrainain rraattee aacccceelelerratateess aanndd tthhee ssamampplele ffrractacturureess..

ChChapaptteerr 116:6: MMaaccrroscoposcopicic AspeAspeccttss ofof RoRocckk DeDefforormmatationion

##22:: ThThisis isis aa hhotot--worworkkeedd,, ccononssttanantt ststrraiainn rratatee eexpexperrimimeenntt rreessultult..

SSimimiilarlarlyly,, tthhee samsampplele displaysdisplays pprrimimaarryy,, sstteeadady-sty-statatee,, anandd tteerrttiaiarryy ccrreeeepp rreegimgimees.s. HHoweowevveerr,, eelastlasticic ssttrrainain isis nnotot bubuiltilt uupp ququicickklyly bebeccauausese tthhee sstraitrainn raterate iiss conconssttanantt,, soso tthhee ststrreessss bbuildsuilds slslowowlyly..

ChChapaptteerr 116:6: MMaaccrroscoposcopicic AspeAspeccttss ofof RoRocckk DeDefforormmatationion

WeWe ccararee aboutabout tthheesese eexxppeerrimimeennttss bebecausecause ductductileile ffloloww dedeeepp IInn tthhee EarEartthh isis larlargegellyy chchararactacteerrizeizedd bbyy ststeeadadyy ststatatee ccrreeeepp.. LLaarrggee amamooununttss ofof ddeeffoorrmmaattionion ccanan acaccumcumulaulattee iinn tthheesese rrocockks,s, pprroduoducciningg ccomompplelexx ffololds,ds, eettc.c. ThThee ffloloww llawawss useusedd ttoo dedescscrribibee tthhiiss bebehhavaviorior araree useuseffulul fforor mmodeodelinlingg rreealal shsheearar zozonneess anandd tthhee ststrraainin rratateess uunndederr whwhichich ttheheyy dedeffoorrmm..

ChChapaptteerr 116:6: MMaaccrroscoposcopicic AspeAspeccttss ofof RoRocckk DeDefforormmatationion

WeWe wwiillll jjusustt ffooccusus onon mmodeoderratatee-st-strreessss ffloloww llawawss fforor tthhiiss courcoursese bebeccauausese 11)) tthhisis rreegimgimee isis tthehe mmosostt inveinvessttigaigatteed,d, anandd 22)) isis tthhooughughtt ttoo bebe mmosostt appapplicablelicable fforor dedefforormmatationion inin tthhee EarEartthh..

ffloloww llawawss ttakakee tthhee ffoorrmm::

˙˙εε σσ n == AA (( diff)) ((ffO2 )) eexxpp [-E+[-E+PV/RPV/RT]T]

GGeeolologicogic mmatateerriialsals hhaveave nn == 33 andand ccanan bebe upup ttoo nn == 55

ChChapaptteerr 116:6: MMaaccrroscoposcopicic AspeAspeccttss ofof RoRocckk DeDefforormmatationion

ffloloww llawawss ttakakee tthhee ffoorrmm::

˙˙εε σσ n == AA (( diff)) ((ffO2 )) eexpxp [-E+[-E+PV/RPV/RT]T]

FFlowlow lalawwss araree dedetteerrmminineedd fforor:: e SSingleingle mminineerralal pphhasaseess e MMululttipiplele mmineinerralal pphhasaseess

olivine experiment

ChChapaptteerr 116:6: MMaaccrroscoposcopicic AspeAspeccttss ofof RoRocckk DeDefforormmatationion

ThThee ffloloww llawawss ccanan alsoalso bebe useusedd ttoo cconstonstrructuct ststrreenngtgthh eennvveeloloppeess tthhaatt dedescscrribibee tthehe ssttrreenngtgthh ofof tthhee ccrrusustt anandd mmananttllee witwithh dedeptpthh..

˙˙εε σσ n == AA (( diff)) ((ffO2 )) eexxpp [-E+[-E+PV/RPV/RTT]]

FFlowlow lalawwss araree dedetteerrmminineedd fforor:: e SSiningglele mmiinneerralal pphhasaseess e MMululttipiplele mmineinerralal pphasehasess

PARPARTT 22:: DDEFEFOORMRMATIATIOONN MMECECHANHANIISSMMSS

DDeeffoorrmmatationion mmeechchananiismsmss araree grgrainain ssccalalee prproceocesssesess tthhaatt ococcurcur inin rreespspoonnsese ttoo dedefforormmaattionion ofof aa rroocckk.. ThTheessee araree pprrococeesssseess tthhatat araree ococcurcurrriinngg atat tthhee mmicricrooscscooppicic scscaalele..

ChChapaptteerr 117:7: MMiiccrroscoposcopicic AspAspeeccttss ofof RoRocckk DeDefforormmatationion

UUpp ununttilil nnooww,, wwee cconsideonsiderreedd rrockock ddeefforormmaattionion ffrromom tthehe conconttinuuminuum ppoioinntt ofof vievieww,, wwhichichh assassumumeess tthathat tthhee rrocockk isis hhomomoogegeneneousous anandd hhasas nnoo disdisccononttiinnuituitiiees…s…

BButut…t…thhisis isis aa ququeeststionion ooff scalescale!!

RRocockkss aarree mmadadee ofof crycrystalstal graigrainnss whwhichich araree imimppeerrffeecctt inin tthhee mmicricroscoposcopicic scalescale.. ThTheessee crcrystystalal imimppeerrffeeccttioionnss ggiveive tthhee rrocockk avaveerrageage mmeechchananiiccalal pprropopeerrttiieess anandd ccononttrriibutbutee ttoo tthehe ovoveerrallall mmacracroscoposcopicic bebehhaviavioror ofof tthehe rrockock undeunderr ssttrreessss..

SSo…ifo…if wwee wanwantt ttoo ststudyudy tthhee mmacacrrososccopicopicalallyly dducucttiilele bbeehhavaviorior ofof rrocockks,s, wwee mmusustt zozoomom inin ttoo tthhee mmicicrro-o- aanndd ssubmubmicricroscoposcopicic scalescale..

ChChapaptteerr 117:7: MMiiccrroscoposcopicic AspAspeeccttss ofof RoRocckk DeDefforormmatationion

BByy eexaxamminininging rrocockkss oonn tthhee mmicricro-o- anandd subsubmmicricrososccooppicic ssccalalees,s, wewe willwill bebe aableble ttoo answeanswerr::

• What deformatioion mechaniisms permitit solliid rocks to fllow?

• Under what condititiions do these deformatioion mechaniisms operate?

• What rheollogy isis associaiated wiith each of these mechaniisms?

• What miicro- and submicicroscopiic structures can we ididentiify inin the rock that refllect the deformatiion mechaniisms that produced them?

• What can we iinfer from these structures about the condiitioions of deformatioion?

ChChapaptteerr 117:7: MMiiccrroscoposcopicic AspAspeeccttss ofof RoRocckk DeDefforormmatationion

IItt woulwouldd bebe mmosostt hheelplpffulul ttoo uunndederrssttanandd wwhhiicchh ddeefforormmaattionion mmeecchhanismanismss dodommininatatee fforor aa givgiveenn sseett ofof ssttrreessss anandd tteemmppeerratatururee ccoonnditditiiononss fforor aa parpartticicuularlar mmiinneerral.al. WeWe ususee aa dedefforormmatatioionn mmeecchhanismanism mmapap ttoo acaccomcomppllishish tthhisis ttasaskk..

DDeeffmm.. MMeechch.. SSttrreessss RRhheeoologylogy

• CatCataclastaclasticic fflowlow hhigighh

• DDislislococatationion ccrreeeepp hhigighh ttoo mmeed.d. PowePowerr-law-law ExpExpoonneentntial-lial-lawaw

• DDififffusiousionn ccrreeeepp mmeed.d. LLineinearar vviscousiscous

ChChapaptteerr 117:7: MMiiccrroscoposcopicic AspAspeeccttss ofof RoRocckk DeDefforormmatationion

LLeett’s’s rreeororganganiizeze tthheessee ddeefforormmaattionion mmeechchananisismmss anandd tthhee ssttrreessss ccoonnditditiiononss wwitithh whwhichich tthheeyy araree ttypicypicalallyly aassssocociaiatteed:d:

DDeeffmm.. MMeechch.. SSttrreessss RRhheeoologylogy

• CatCataclastaclasticic fflowlow hhigighh

• DDislislococatationion ccrreeeepp hhigighh ttoo mmeed.d. PowePowerr-law-law ExpExpoonneentntial-lial-lawaw

• DDififffusiousionn ccrreeeepp mmeed.d. LLineinearar vviscousiscous

ChChapaptteerr 117:7: MMiiccrroscoposcopicic AspAspeeccttss ofof RoRocckk DeDefforormmatationion

onon expeexperirimementalntal datadata..

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ChChapaptteerr 117:7: MMiiccrroscoposcopicic AspAspeeccttss ofof RoRocckk DeDefforormmatationion

SSomomee dedefforormmatatioionn mmeecchhaannismism mmapapss araree shshownown iinn tteerrmmss ofof tthhee hhomomologoologousus tteemmppeerratatururee,, soso tthhatat tthhee bebehhaaviorvior ooff difdifffeerreentnt

mmineinerralsals isis nnorormmalializezedd fforor tteemmppeerraattururee..

dif

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ChChapaptteerr 117:7: MMiiccrroscoposcopicic AspAspeeccttss ofof RoRocckk DeDefforormmatationion

NotNoticeice tthathat tthhee dedefforormmatationion mmeecchhaannismism mmapapss araree ccononssttrrucuctteedd fforor ccoommmmonon mminineerraalsls iinn tthehe ccrrusustt aanndd mmantantlele;; tthhisis isis hhowow wewe ttrryy ttoo

ununddeerrststanandd mmaatteerrialial fflowlow inin tthhee EarEartthh..

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ChChapaptteerr 117:7: MMiiccrroscoposcopicic AspAspeeccttss ofof RoRocckk DeDefforormmatationion

It isis iimportant to understand the micicroscopicic eviidence for a particicullar deformatioion mechanisism iin a naturalllly-deformed rock because itit allllows us to use these maps to see where our naturall data pllot. We can therefore callibibrate

our naturall data inin terms of temperature or strainin rate!

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ChChapaptteerr 117:7: MMiiccrroscoposcopicic AspAspeeccttss ofof RoRocckk DeDefforormmatationion

BByy eexaxamminininging rrocockkss oonn tthhee mmicricro-o- anandd subsubmmicricrososccooppicic ssccalalees,s, wewe willwill bebe aableble ttoo answeanswerr::

• What mechaniisms permitit sollidid rocks to fllow?

• Under what condititiions do these mechaniisms operate?

• What rheollogy isis associaiated wiith each of these mechaniisms?

• What miicro- and submicicroscopiic structures can we ididentiify inin the rock that refllect the deformatiion mechaniisms that produced them?

• What can we iinfer from these structures about the condiitioions of deformatioion?

ChChapaptteerr 117:7: MMiiccrroscoposcopicic AspAspeeccttss ofof RoRocckk DeDefforormmatationion

We wiillll now disiscuss these deformatiion mechanisisms and the structurall effects that these mechaniisms lleave inin the rocks.

We beginin wiith llow-temperature deformatioion mechanisisms that are higighlly sensititiive to the magnititude of confininiing pressure (briittlle deformatiion).

We wiillll then contininue wiith hiigh-temperature deformatioion mechanisisms that are sensiitivive to temperature, rather than confininining pressure (ductiille deformatioion).

ChChapaptteerr 117:7: MMiiccrroscoposcopicic AspAspeeccttss ofof RoRocckk DeDefforormmatationion

We beginin wiith llow-temperature deformatioion mechanisisms that are higighlly sensititiive to the magnititude of confininiing pressure (briittlle deformatiion).

• Ellastiic behavioior

When stress isis added, ioions are forced out of theirir llattiice posititioions and beginin to exchange posiitioions witith other iions iin the llatticice. The crystall llattiice wililll rellax when the stress isis removed.

ChChapaptteerr 117:7: MMiiccrroscoposcopicic AspAspeeccttss ofof RoRocckk DeDefforormmatationion

Thisis deformatiion mechaniism can occur at llow-temperature or midid-grade temperatures.

2. Sollutioion Creep, or pressure sollutioion

Durining sollutioion creep, mininerall graiins disissollve more readilily at faces under higigh compressivive stress. The disissollved components then diiffusioion through the flluidid phase on the graiin boundarieies and precipipititate on surfaces of llow compressiive stress.

dissolution

precipitation

ChChapaptteerr 117:7: MMiiccrroscoposcopicic AspAspeeccttss ofof RoRocckk DeDefforormmatationion

We wiillll then contininue wiith hiigh-temperature deformatioion mechanisisms that are sensiitivive to temperature, rather than confininining pressure (pllasticic deformatioion).

3. Diisllocatioion Creep

Thisis process occurs from the movement of diisllocatiions through the crystall llatticice allong a gllidide pllane. The crystall isis llititeralllly sheared allong the gllidide pllane. The bonds between atoms are broken for thisis to occur; thisis takes a LOT of energy, whicich isis why itit isis thermalllly activivated.

QuickTime and a Animation decompressor are needed to see this picture.

motion of dislocations initial finite

ChChapaptteerr 117:7: MMiiccrroscoposcopicic AspAspeeccttss ofof RoRocckk DeDefforormmatationion

MMacracroscoposcopicic fflowlow ofof rrocockkss cancan rreesultsult ffrromom aa nnumumbeberr ofof ddififffeerreenntt mmeecchhanismanismss,, mmostost ooff whwhicichh ininvvolvolvee eeitithheerr tthhee mmototionion ofof ppoinointt dedeffeectctss oorr tthhee mmototioionn ofof llinineeaarr ccrrysysttalal dedeffeeccttss ccalalleledd disdislocatlocationsions..

PoinPointt dedeffeeccttss

QuickTime and a Animation decompressor are needed to see this picture.

interstitial vacancy motion of point defects

ChChapaptteerr 117:7: MMiiccrroscoposcopicic AspAspeeccttss ofof RoRocckk DeDefforormmatationion

We wiillll then contininue wiith hiigh-temperature deformatioion mechanisisms that are sensiitivive to temperature, rather than confininining pressure (pllasticic deformatioion).

3. Diisllocatioion Creep

Witith inincreasining stress and temperature durining further deformatiion, more disisllocatioions are randomlly generated. Because the crystall llatticice isis such a regullarlly spaced and ordered structure, those diisllocatiions can onlly move allong certainin pllanes inin llimimiited dirirectioions witithinin the llattiice.

ChChapaptteerr 117:7: MMiiccrroscoposcopicic AspAspeeccttss ofof RoRocckk DeDefforormmatationion

We wiillll then contininue wiith hiigh-temperature deformatioion mechanisisms that are sensiitivive to temperature, rather than confininining pressure (pllasticic deformatioion).

3. Diisllocatioion Creep

These speciificic gllidide pllanes and sllipip dirirectiions together definine a sllipip system for a giiven mininerall. Each miinerall has a uniqique crystall llatticice, therefore dififferent minineralls have diifferent sets of sllipip systems.

b We wriite the slliip system for a mininerall iin the follllowining manner usining Miillller inindicices notatiion:

{crystall gllidide pllane} a {010} <001>

ChChapaptteerr 117:7: MMiiccrroscoposcopicic AspAspeeccttss ofof RoRocckk DeDefforormmatationion

We wiillll then contininue wiith hiigh-temperature deformatioion mechanisisms that are sensiitivive to temperature, rather than confininining pressure (pllasticic deformatioion).

3. Diisllocatioion Creep

There are severall mechanisisms of disisllocatioion creep; we wiillll examiine many of these inin the next llecture.

ChChapaptteerr 117:7: MMiiccrroscoposcopicic AspAspeeccttss ofof RoRocckk DeDefforormmatationion

We wiillll then contininue wiith hiigh-temperature deformatioion mechanisisms that are sensiitivive to temperature, rather than confininining pressure (pllasticic deformatioion).

4. Diiffusioion Creep

Durining dififfusioion creep, rock deformatiion takes pllace by the miigratiion of atoms Of the materiiall through the sollidid materiaiall iitsellf from areas of higigh compressivive Stress to areas of llow compressiive stress.

Diiffusiion may resullt from the dififfusiion of 1) poinint defects through the llattiice (calllled vollume dififfusioion), and 2) atoms or iions allong graiin boundarieies (calllled graiin boundary diiffusioion). Diiffusioion may greatlly enhance the rate of straiin by aididining the motioion of lliinear crystall defects, and by accommodatining the shape changes of minineralls requirired for grainin boundary sllididining.

ChChapaptteerr 117:7: MMiiccrroscoposcopicic AspAspeeccttss ofof RoRocckk DeDefforormmatationion

We wiillll then contininue wiith hiigh-temperature deformatioion mechanisisms that are sensiitivive to temperature, rather than confininining pressure (pllasticic deformatioion).

4. Diiffusioion Creep (Vollume Diiffusioion)

Vollume dififfusiion iis a thermalllly-activivated mechaniism that isis very sensiitivive to graiin siize. It operates at very higigh temperatures and llow stresses, and iis characteriized by the migigratioion of vacanciies.

QuickTime and a Animation decompressor are needed to see this picture.

motion of point defects interstitial vacancy (more common)

ChChapaptteerr 117:7: MMiiccrroscoposcopicic AspAspeeccttss ofof RoRocckk DeDefforormmatationion

We wiillll then contininue wiith hiigh-temperature deformatioion mechanisisms that are sensiitivive to temperature, rather than confininining pressure (pllasticic deformatioion).

4. Diiffusioion Creep (Graiin Boundary Dififfusioion)

Grainin boundary dififfusioion isis a thermalllly-activivated mechaniism that isis allso very sensititiive to grainin sizize. It isis characterizized by the movement of atoms allong graiin boundarieies, and operates at slligightlly llower temperatures than vollume dififfusioion.

interstitial vacancy

ChChapaptteerr 117:7: MMiiccrroscoposcopicic AspAspeeccttss ofof RoRocckk DeDefforormmatationion

We wiillll then contininue wiith hiigh-temperature deformatioion mechanisisms that are sensiitivive to temperature, rather than confininining pressure (pllasticic deformatioion).

4. Diiffusioion Creep

Both vollume and grainin boundary dififfusioion are very sensiitivive to grainin siize because the diiffusioion paths must be short. When the graiin siize remaiins smallll (<< 100 µm) durining deformatiion, then graiin boundary slliidiing may be a sigignififiicant mechaniism that accommodates strainin. Superpllastiic creep resullts from coherent grainin boundary slliidining inin whicich deformatiion occurs witithout the openiing of gaps or pores between adjjacent crystall grainins.

ChChapaptteerr 116:6: MMaaccrroscoposcopicic AspeAspeccttss ofof RoRocckk DeDefforormmatationion

IInn aa nnututshsheelll,l, hheerree’s’s hhowow ttoo rreelatlatee nnaattururalal andand eexxppeerriimmeennttaall dedefforormmatationion::

• ExamExamininee naturallnaturallyy ddeeffoorrmmeedd ssamamppllees,s, suchsuch asas mmylylononititeess • IIdedennttififyy rrhheeoologylogy-c-cononttrroollinllingg mminineerralal pphasehase(s)(s) σσ • DDeetteerrmmininee T,T, P,P, diff,, grgrainain sizsizee inin natnaturaluralllyy dedefforormmeedd samsamplepless • SSeelleecctt exexperiperimementalntal fflowlow lawlaw ffoorr samsamee mmineinerralal phphasease • UUsese expeexperirimentmentalal fflowlow lawlaw eeququatationion ttoo ffinindd ssttrrainain rraattee

˙ ε σ n = A ( diff) exp [-E/RT]

Rheology: Review

What physical properties control deformation ?

- Rock type - Temperature - Pressure - Applied Stress - Deviatoric (differential) Stress - Grain size - Others ? .  How are each of these processes related to “strain rate” () ? .  = A n/dm e-(E+PV/RT)

Rheology: Review

What are the different types of strain ? - Brittle Low T,P, Shallow - Elastic > - Plastic - Viscous > High T,P, Deep

Brittle/Plastic Transition

W here do these transitions occur in the Earth ?

- Upper/Lower crust - Lithosphere/Asthenosphere

Brittle deformation occurs above The friction limit (linear differential stress)

Plastic deformation occurs where differential stress is non-linear (exp-z)

Plastic Deformation

 In the plastic regime rocks deform by creep ?

 What is creep ?

 Diffusion creep: diffusion of atoms or vacancies through grains

- stress dependence for n is linear (n=1) - strong dependence on grain size dm (m = 2-3)

Plastic Deformation

 Dislocation creep: the motion of dislocations through grains

- stress dependence for n is nonlinear (n=3-5) - no dependence on grain size dm (m = 0) - strongly dependent on temperature

 What is a dislocation ? - imperfections in the crystalline lattice structure - All imperfections can be described with the superposition of 2 basic types: edge and screw dislocation

Plastic Deformation

 Dislocation creep: the motion of dislocations through grains

Edge Dislocation: the lattice structure is not uniform across the face of the atomic structure causing stress

Atoms are in compression above the plane of discontinuity

Atoms are in tension below

Plastic Deformation

 Dislocation creep: the motion of dislocations through grains

Screw Dislocation: the lattice structure is not uniform creating an “out of the plane” discontinuity in the atomic structure

 The atoms (solid black) are in a “second plane”

How Creepy is the Earth's Mantle ?

 The upper mantle: - both diffusion and dislocation creep are active - seismic anisotropy is only observed in dislocation creep regime

 The lower mantle: - dominated mainly by the diffusion creep regime

Brittle/Plastic Transition

Differential Stress in Continental and Oceanic plate

Brittle/Plastic Transition

Con tinental stress envelopes are “bimodal” -crustal rocks deform faster than mantle rocks -the lower crust deforms rapidly avoiding brittle failure

Continental lithosphere is “weaker” than oceanic lithosphere

- notice what happens at plate boundaries - which plate deforms more during collisions ?

Brittle/Plastic Transition .  = A n/dm e-(E+PV/RT)

What other factors effect viscosity of mantle material ?

- Depth (pressure) - Water content (addition or removal) - Temperature-dependence . - Partial melt content n m -(E+PV/RT)  = A  /d f ( + COH) e E = Activation Energy V = Activation Volume R = Gas constant  is melt fraction OH describes water concentration Temperature-Dependence of Viscosity

-(1/T - 1/Tr)  = r e

In “plastic flow” regime, viscosity can change with temperature

- For a temperature change of 100oC - Viscosity can change by factor of 10

Melting Temp (Tm increases with depth giving pressure effects)

Viscosity is not easy to determine in the Earth's interior

High pressure and temperatures are difficult to achieve in lab.

Also time scales of flow are long!

Deformation and Flow in the Earth's Interior

The Earth's mantle behaves as brittle material at shallow depths But behaves as plastic or viscous material at deeper depths We can consider the deep interior as a viscous fluid

over geologic time

The Composite Faililure Envellope: 3 parts

I: Tensile failure II: Coulomb failure III: von Mises criterion (deep crust)

σ s C φ 2θ τ σ σ 3 1 σ n

I II

III

Plastic Deformation

 In the plastic regime rocks deform by creep ?

 What is creep ?

 Diffusion creep: diffusion of atoms or vacancies through grains

- stress dependence for n is linear (n=1) - strong dependence on grain size dm (m = 2-3)

Plastic Deformation

 Dislocation creep: the motion of dislocations through grains

- stress dependence for n is nonlinear (n=3-5) - no dependence on grain size dm (m = 0) - strongly dependent on temperature

 What is a dislocation ? - imperfections in the crystalline lattice structure - All imperfections can be described with the superposition of 2 basic types: edge and screw dislocation

Plastic Deformation

 Dislocation creep: the motion of dislocations through grains

Edge Dislocation: the lattice structure is not uniform across the face of the atomic structure causing stress

Atoms are in compression above the plane of discontinuity

Atoms are in tension below

Plastic Deformation

 Dislocation creep: the motion of dislocations through grains

Screw Dislocation: the lattice structure is not uniform creating an “out of the plane” discontinuity in the atomic structure

 The atoms (solid black) are in a “second plane”

How Creepy is the Earth's Mantle ?

 The upper mantle: - both diffusion and dislocation creep are active - seismic anisotropy is only observed in dislocation creep regime

 The lower mantle: - dominated mainly by the diffusion creep regime