Jul 10, 1993 - Kronenberg and Shelton, 1980; Van der Molen and Paterson,. 1979; Tullis, 1990]. ...... pictures. Greg Hirth, William Durham, and an anonymous.
JOURNAL OF GEOPHYSICAL
RESEARCH, VOL. 98, NO. B7, PAGES 11,921-11,933, JULY 10, 1993
Brittle and SemibrittleDeformationof SyntheticMarbles Composedof Two Phases G•o•o D•sm,• • AND B•u,• Ev•s DepartmentofEarth, Atmospheric,andPlanetarySciences, Massachusetts Instituteof Technology
To investigatethe influenceof rigid, second-phase particleson the strengthof marble in the semibrittle deformationregime,we performedconventional triaxial mechanicaltestson syntheticsamplesformed by hot
isostatic pressing two-phase aggregates of5 fine-grained calcite and5-20wt % of eitherSiC,A1203,orSiO2. The 1
samplesweretestedat strainratesof 10' s' and at roomtemperatureover a rangeof pressures from 5 to 300 MPa. Microstructureswere studied using optical microscopy,scanningelectron microscopy(SEM), and transmission electronmicroscopy(TEM). Adding rigid inclusionswith incoherentmatrix/particleinterfaces increased the rangeof pressureoverwhichthe transitionbetweenlocalizedbrittlefailure and crystalplasticflow occurred. The strengthof the puremarbleswasinverselyproportional to porositybetween0 and 8%. In the brittle field,two-phaseaggregates are generally50 MPa weakerthanpuremarblesof similarporosity.Secondphasesand associated cracklikeporositytendto distributebrittledeformation in our samples.Aggregates with 20% inclusions showstablecataclastic flow at 5 MPa confiningpressure.At the samepressure,pure samplesfail catastrophically alonga distinctfault. At higherpressurein the semibrittlefield, the strengths of pure and two-phaseaggregates converge.The deformation resistance of the materialcontainingparticlesis consistently higherthanthat of the pure samples. TEM observations alsosuggest an additionalcontribution to the deformation resistance andhardeningrate by interactions betweenthe dispersed particlesandcrystaldefects. INTRODUCTION
empirical method based ondeformation ofporous metals. Such
rely on volumeaveragingof the properties The theologyof polyphaserockscan be very complex,[e.g., boundingtechniques Kronenbergand Shelton, 1980; Van der Molen and Paterson, of the phases;they do not attempt to model details of the 1979; Tullis, 1990]. From the viewpointof structuralgeologists, interactionsamong the second-phaseinclusions or between inclusionsand defectsin the matdx. But, they do a better understandingof the average flow properties of second-phase demonstrate the importanceof relativeproportions, shape,size, polyphasematerials is particularly important in interpreting deformationin rock masses,which inevitablyhave significant strength,and orientationsof the constituentgrains.Recently, spatialvariationsin mineralogy.Yet, there are few experiments Tullis et al. [1991] simulated two-phaseflow with a finite investigatingthe effect of secondphaseson brittle, semibrittle, elementmodel utilizing the Voigt and Reuss boundsand the and plastic flow. Owing to the large variety of petrologic individual flow laws of the two phases.In their model, the strengthis mainlyaffectedby volumefractionand,less textures,chemistries,mineralogies,and pore structureswhich aggregate occur naturally, many uncertaintiesremain in extrapolating importantly,by the geometryof the components. Quantitativemicromechanical modelsof dispersionhardening laboratory constitutive data to natural tectonic situations duringplasticflow of metals [Ashby,1970; Fischmeisterand [Paterson,1987; Tullis et al. , 1991]. The flow propertiesof polymineralicaggregatesmay be Karlsson,1977;Humphreys,1985] suggestincreasedhardening grouped into three general classes:(1.) mixtures of weak ratesas straingradientsnear the particlesdevelopincreasingly inclusions,including porosity, in a strong, load-supporting large internal stresses.Secondarygrain boundarydislocations framework;(2.) rockswith two phases,bothdeforming,but with may also be generatedat the matdx/particle interface and differentstrengths;and (3) aggregates composed of a relatively contributeto hardening[Humphreysand Kalu, 1987; 1990]. weak, deforming matdx with rigid second-phaseparticles Hardeningratesare predictedto increasewith increasingvolume [Handy,1990]. In this paper, we study the effect of dilute proportionof hard particles and with increasingratio of the and dispersionsof rigid second-phase particleson deformationof strengthsof the inclusionto that of the matrix [Fischmeister fine-grained,syntheticmarblesin the brittle and semibrittlefield Karlsson,1977]. at roomtemperatureoverthe rangeof pressures of 5-300 MPa. Detailed experimentalstudiesof the mechanicsof polyphase Extensive work has been done to understand the elastic moduli rocksare still relativelyfew (for a review see Tullis, [1990]). of aggregates.The averageelastic propertiesof homogeneous Somerecentexperimentalstudiesof plastic flow have utilized mixturesof two phasescan be estimatedby computingHashin- syntheticrockspecimens to producesampleswhichvary only in Shtrikmanbounds,averagingwith Voigt-Reuss-Hillsystematics, relativeproportionof the two phases[Jordan,1987, 1988;Ross or using self-consistent methods.See reviewsby Simmonsand et al., 1987, Burg and Wilson, 1987; Hitchings et al., 1989; Wang[1971], Wattet al. [1976], andHudsonand Knopoff [1989] Durham et al., 1992; D. L. Olgaard,personalcommunication, and papersby Walsh [1965], O'Connelland Budiansky[1974], 1993];mostshowa strong,nonlinearreductionof strengththat is Budianskyand O'Connell[1976], and Watt[1988]. a functionof the volumeproportionof the weak phase[Jordan, Boundingmethodsmay also be appliedto nonlinearcreep 1987; Ross et al. 1987]. Further complexity in mechanical [Chen and Argon, 1979], and Tharp [1983] has discussedan behavior arises when the dominant deformation mechanism changes[Xue and Raj, 1990; Farquhar et al., 1990], when the frameworkof a strongmatdx breaks down with progressive l,Nowat' GeoForachungs Zontrum Potsdam, Germany strainand concomitant formationof foliation[Gottschalket al., 1990], or when the relative strength of the componentsis Copyright1993 by theAmericanGeophysical Union. reversedas conditionschange [Tullis, 1990; Handy, 1990]. Metamorphicreactionsmay introduceyet moreintdcaciesin the Papernumber93JB00697. 0148-0227/93/93 JB-00697505.00 mechanical behavior[Rubie,1983;BrodieandRutter, 1986]. 11,921
11,922
DRESENANDEVANS:DEFORMATION OFTWO-PHASEMARBLES EXPERIMENTAL METHOD AND STARTING MATERIAL
keV. For SEM and TEM observation,polishedthick sections were milled in an argon ion thinner and carboncoated.The SamplePreparation porosityof the samplewas determined by weighingthe sample We wishedto test samplesin which the mineralogy,second dryandimmersedin distilledwater.Cracksurfaceareaper unit phase particle size, and matrix grain size were controlled volume,anisotropy of crackorientation, andtotal porositywere separately.To this end, we preparedsyntheticmarblesby hot- alsoestimatedfrom the opticaland SEM micrographs using isostatic pressing (I-]•) mixtures ofreagent-grade CaCO3powder quantitativestereology techniques[Underwood,1970, pp. 66with grain size of 5 [xm, and varying amountsof dispersed 71]. secondphases.The second-phase powdershaddiametersvarying The porositiesof the samplescovarywith the amountof from 200 [xm,andwere addedto comprise5, 10 or 20 second phaseandvaryslightlyfromnm to rim, butwereusually wt % of the samples.Severaldifferentmaterialswith widely lessthan6%. Poresresidedonthreesites:as sphericalinclusions varyingparticlesize and thermo-elastic moduliwere chosenas within calcitegrains,as sphericalinclusions or cracksalong second phases: SiC, A1203or SiO2. SeeTable1 for particle calcite/calcite interfaces,or as largerporesin the intersticesof diameters,densitiesand elasticconstants. particle agglomerates(Figure 1). Sphericalpores occur as After weighing,the powderswere dispersedin distilledwater inclusions withinthe matrixgrainsor as bubblesalonggrainor or methanol, and mechanically mixed for 4 hours. The interphase boundaries in boththe pureandtwo phasemarbles; supematant liquid was decantedand the resultingslun-ydried. theseporesprobablyresultfrom densificationduringthe The dried powderwas die-pressed at roomtemperatureto form process.Cracklikeporosityis formedalonginterfacesbetween green bodies with densities around 60% theoretical. Final two calcitegrains,or alonginterfaces betweencalciteandsecond densification was donein oneof threeplaces.The first samples phasegrains.Thesecrackslikely ariseduringthermalquenchor preparedwere either pure calcite or calcite/SiCmixturesand depressurization owingto differingelasticmodulior coefficients were hot isostaticpressedfor 1 hour at 200 MPa pressureand of thermalexpansion of the abuttinggrains.Finally, largepores 600øC in the servo-rig at the MassachusettsInstitute of maybe includedwithinagglomerations of second phaseparticles Technology.Most of the material,however,was processedin whenthere are disruptionsof the packingof the matrix near the large volume batches, either at Eidgenossische Technische inclusionsin the greenbody,or when voidsare shieldedwithin Hochschule,Zarich, Switzerland(20 hoursat 200 MPa, 600øC) particleagglomerates during• [Langeet al., 1991]. or IndustrialMaterialsTechnology, Andover,MA (2 hoursat 200 Variationsin pore shapestronglyinfluencethe elasticmoduli MPa, 600øC). of solids[e.g., Walsh,1965];cracklikeporositywith largeaspect ratiostend to closeat muchlower pressures than more equant Characterizationof theSyntheticMarbles voids.Since,in the two-phaseaggregates, the aspectratiosrange Grain sizeandmineralogy.The grainsizeof the calcitematrix from very high, e.g., cracksat the matrix/particleinterface,to variesslightly,dependingon the amountof secondphase.Pure very low, e.g., bubblesincludedwithin grains,variationsin the sampleshavematrixgrainsabout16 p•min diameter,while those elasticmodulicanbe usedto determinevariationsin crackshape in mixtureswith 20 wt % secondphaseare about 9 [xm. The fromonesampleto another[Walsh,1965]. spreadin the sizeof individualgrainsis greaterin the two-phase We measuredthe bulk modulus,the Young'smodulus,and aggregates thanin purecarbonates, andlikely resultsfrom grain Poisson's ratio as a functionof pressurefor a selectednumberof boundarypinningeffects[OlgaardandEvans, 1986].Thereis no samplesand show sometypical hydrostatsfor pure and twoevidenceof exaggeratedgrain growth (see Figure 1). Grain phasesamplesin Figure2. The curvesexhibita smallhysteresis, boundariesare slightly curved and are sometimescuspateor but the permanentporosityreductionis only a smallfractionof lobate.Somegrainsare twinnedor showundulatoryextinction. the initial porosity. Thus, these mechanicaldata show little Althoughthe temperatureand pressureconditionsare closeto evidencefor grain crushing[Zhanget al., 1990a,b]. Similarly, the stabilityfield of wollastonite,theyare still belowthe reaction the SEM micrographsshow abundantcracksalong grain and curve[Deer et al., 1973]. We couldfind no evidenceof reaction interphase boundaries, but little clearevidencefor porecollapse. The actual values of the elastic moduli are a function of the betweenquartzandcalcitewith the scanning electronmicroscope (SEM) or with X-ray diffractionanalysis. sample porosity and of the second-phase content. Volume Porosity,pore microstructure,and elastic moduli. Samples averagingschemes predictthatthe elasticmodulishouldincrease were examined in reflected and transmittedlight, with the when an increasingamountof rigid secondphaseis added.For Japanese Electron Optics Laboratory (JEOL) superprobe example,the lowerHashin-Shtrikman boundsfor the respective operatingasa SEM in backscattered mode,andwith a JEOL200 aggregatesare given in Table 2 [Simmonsand Wang, 1971]. CX transmissionelectronmicroscope(TEM), operatingat 200 However,the two-phaseaggregates actuallyshowa decreasein TABLE1.Ph•,sical Properties Material
Particle Size,
CaCO3 AI203 SiO2
2.71+
80+
0.2-1.1•
4.2
3.98*
380*
2.7-4.2*
7.2-8.6*
6.6
2.65+
0.3-1.7•
30.3-17.6õ
Density,, g/cm •
Young's Modulus, Fracture Toughness, GPa MPam•
78.7+
Thermal Expansion, 10'6/øC -3.9-31.8õ
15 25
sic
50-250
* Ceramic Source, 1988.
• Atkinson andMeredith, [1987] 0Skinner, 1966 + Simmons andWang,[1971]
3.22'
410'
5-7*
4.3-5.6*
DRESENAND EVANS:DEFORMATION OFTWO=PHASE MARBLES
11,923
Fig.1.Backscattered SEM micrographs ofUndeformed two-phase aggregates. (a)CaCO 3+20wt%SiO 2.Thedispersion ofparticles isfairly homogeneous. Noteporesthatareassociated with largerparticlesor agglomerates. (b) Quartzinclusions areoftenbroken,and the matrix/particleinterfaces seemcracked.Many poresare locatedonthe interfaceor in interstices betweenparticles.(c) Large SiC inclusions showa lesscoherentmatrix/particleinterface.(d) Aluminaparticleembedded in the calcitematrix. The particle/matrix interfaceseemsclosed;note,however,thereareminorpores.
300 ;
/ Pure Calcite
200
/
;
20% AI,_O //
,,.,' _//
.
elastic moduli with increasingsecondphase abundance,even whenthe total porosityincreasesonly slightly.This fact suggests that secondphasecontentand crackporosityare correlated,in agreementwith the SEM observationsthat matrix/particle interfacesare often cracked(Figure 1). Table 2 givesthe bulk modulus,the porosity,and the Hashin-Shtrikmanboundsfor selectedsampleswith differentcompositions. Data from the hydrostatsmay be usedto infer the amountof cracklikeporesand equantvoidsin the pure samples.The effect of sphericalporeson the compressibility is
ß
/
5%
....:...-
. 31-v r/]
fl• =fl 1¾- .
2 1-2v
0.0
(1)
::::::::::::::::::::::::::::::::: where [5•ff is the effectivecompressibility, [5 is the
SiO
--
l-r/
i
0.5
1.0
1.5
Volumetric Strain (%)
compressibility of the solidmaterial,q is the porosity,and v is Poisson'sratio [Walsh, 1965]. The effective bulk modulus calculatedfrom (1) andthe Reussaveragefor the bulk modulus of calcite(Table 2) agreeswell with the modulusmeasuredat higherpressures. Some samplesshowednonlinear elastic moduli up to 300 MPa, the highestpressures in the hydrostats,suggesting that a rangeof crackaspectratios is present.The measuredmoduli of
Fig. 2.Representative hydrostats ofpure synthetic calcite and two-phase theaggregates arealsoconsiderably smaller thaneffective aggregates. The curvesgenerallyshowa smallhysteresis; the bulk modulus ' of the aggregates is inverselycorrelated with particleabundance. The change in the moduluswith increasing strainmay be relatedto the closingof cracks introducedalong particle/matrixinterfaces.Such cracksform to relieve stresses aris•ing frommismatchin thermalexpansion duringHIP.Thethermal expansion coefficient of quartzis largerthancalcite,thatof aluminais lower. The fracturing associatedwith quartz particlesleads to an aggregate compressibi!ity which is larger than that of the aggregatescontaining alumina.
moduli calculatedassumingthat all porosityis spherical.SEM observations confirmthat a rangeof pore shapesare present.In particular, many of the larger voids at the matrix/particle interfaceand in the agglomerates are not spherical(Figure 1). The volume fractionof porositythat was closedat 200 MPa pressurewas estimatedfrom the hydrostatsusing a procedure describedby Walsh[1965] andis alsogivenin Table 2 for a few
11,924
DRESENANDEVANS:DEFORMATION OFTwo=PHASEMARBLES
TABLE2.Porosity_ andBulkModuli Calculated
Sample
Composition
Porosity, vol. %
Ca20T Ca9T
Pure Pure
5%A1203
1.6
Z31 Z32 Z33 Z35
20%A!203 20%A1203 20%AI203 20%AI203
2.7 2.5 2.2 4.1
IR3 IR2
IBL4 IBL2 IBL1
vol. %
GPa
5%SIC 20%SIC
4.6 4.7
5%SiO2 a 5%SiO2 a
2.2 2.7
5%SiO,,a
3.6
100-300
65.4
72.1 72.1
0.25
51.4
74.5
0.5
32.7
82.8
50-195
0.54
28.6
82.8
25-195
0.57
27.9
82.8
25-195
0.48
34.3
82.8
40-!95
32.2
74.9
0-50
28
84.2
0.44
35.7
69.8
100-200
0.6
43.1
69.8
200-300
O.37
50
69.8
200-300
0.32
48.6
69.8
200-300
0.21
46.3
69.8
100-200
1.2
5%SIO2, 5%SiO2•
MPa
GPa
49.2
3.1 2.1
Z14
Ca19 CalSB
CrackPorosity% BulkModulus, BulkModulus +, ConfiningPressure,
0-25
100-200
0-50
IB4 IB1
20%Si•* 20%SiO•*
4.6 5.0
25.4
63.3
0-100
32.8
63.3
200-300
63.3
200-300
20%SIO2õ
4.9
36.4
Z62
7.4
21.1
63.3
100-250
5.8 5.7 5.5 5.8
45.3
100-200
45.9
100-200
IG2 S1 S2 S3 S4
20%SiO2 • Solnhofen Solnhofen Solnhofen Solnhofen
41.5
0-350
45.3
100-200
'15 Basedon Walsh[1965].
õ6 lam. 25 gm. LowerHashin-Shtrikman bound,basedon dataof Simmonsand Wang[1971].
samples.Althoughthe highaspectratio cracksaccountfor onlya verysmallfractionof the measuredtotal porosity,their number appearsto be correlated with second-phase content.
400
Mechanical
3OO
Tests
Once the syntheticmarbleswere prepared,they were cored and groundpreciselyto give samplesof 12.7 mm diameterand 25.4 mm length.Beforetesting,the sampleswere vacuumdried for severalhoursat 80'C. All experimentswere performedat roomtemperaturein a stiff triaxial apparatusat strain-ratesof
•
i
i
I
i
i
200
10-5 s-1 withmaximum strain of press•e on crack smbili•tion. •e of •e several 50 MPa andIx= 0.5 forPc< 50 MPa fromourdatato calculate complexties •ssing from •e model •d present in •ese the hardeningmodulus. Both the calculated and measured staples may be •e presenceof asphehcalporosi• which may hardeningmoduli increasewith increasingconfiningpressure sere asa nucleation sitefor dilamt cracks.Suchporesmi•t be and decreasingdilatancycoefficient,but the predictedcritical presentinitially or be producedduhng pore collapse[Wong, hardeningmodulusfor incipientlocalizationis overlynegative, 1990]. as previouslynotedby Rudnicla'and Rice [1975]. For all the parameterswe measuredfrom our experiments,strainsoftening Localizationas a MacroscopicInstabili• is predictedfor localization;strain softeningoccurredonly in • alternativeapproachto s•ain l•ali•tion in press•eexperiments at Pc=5MPa wherelocalization was actually sensitivematehals is based on •e view of rapture as a observed in the post-failuresamples.For samplesIR3 andIIM (5 constimtive instability [Rudnicki and Rice, 1975; Rudnicki, and20 wt % quartzat 5 MPa, Table 4), and for thosedeformed 1977]. •is •alysis •co•orates •e internal•ction coefficient, in the semibrittle field at 300 MPa, the calculated critical g, the dilamncyfactor,•, the hardeningmodulus,h, and •e hardeningmodulisuggestthat localizationshouldnot occur,also elastic she• •d bu• moduli, G •d K, res•ctively. •e consistent with our observations.
nomalizedmticalh•de•ng modulus, h•r,for •e inception of s•a•
localization
is
Effectof lnclusionsat High ConfiningPressures
- 90 v) h,,. 1••. -
l•v( ••)2 3
Our microstructural
observations show that microcracks were
(4) still formedat 300 MPa, but the sampleswere compacting. Edmondand Paterson[1972] suggested that the "incrementof
whereN equals 1N3 foraxisymmetric compression [Rudnickiwork neededper incrementof deformation"might be a better and Rice, 1975]. For most stressstates,the model predicts
measure of the deformation resistance than the differential
stress
DRESENAND EVANS:DEFORMATtON OFTWO=PHASE MARBLES
11,931
TABLE4: Constitutive Parameters andPredicted CriticalHardening Coefficients Sample
Composition
Confming Pressure, MPa
her/G*
htan+
b•
5
-1.47
-7440
-0.47
6.4
ZI 1
5%A1203
5
-8.42
-507
1.48
9.67
IBLI
5%SiO2 n
5
-1.27
-343.1
0.66
1.67
IR3
5%SIO2*
5
-0.67
59.7
0.63
0.44
IG3
20%SiO2 n
5
-2.31
-677
1.12
2.5
IB4
20%SIO2*
5
-1.25
44.8
0.71
1.5
ZI7
5%A1203
50
-0.87
114
0.45
300
-0.30
1029
0.013
0.5
0.43
2Ca9T
Ca20T
Pure
Pure
1.04
Z14
5%A1203
300
-0.25
733
-0.08
IBL4 IR2
5%SiO2 n 5%SIO2*
300
-0.19
1318
-0.2
0.4
300
-0.23
1125
-0.11
0.37
IG2
20%SiO2 n
300
-0.21
1445
-0.17
0.39
IBI
20%SIO2*
300
-0.17
1444
-0.23
0.35
15
•25 Normalizedcriticalhardening coefficient.
Measured post-yield hardening coefficient. Dilatancy coefficient. IncrementalPoisson's ratio.
[see also Rutter and Hadizadeh, 1991]. In this view the
deformation resistance owis a, =
de,
6OO
=
,, P,.
de,
(5)
o• is thedifferential s•ess,Pcis •e co••g pressure, ev is ß e volmeMcs•ain•d e• is •e a•al s•ain.h Fig•e 13 we plot•e defo•ationresismceow asa hnctionof a•al s•ain fora number of representative two-ph•eaguegates; ow of •e •o-phase aguegateswas consistently hiker •an •at of •e p•e •ples. •e fomer also e•ibited a •eater h•deMng coefficientup to about 2% a•al s•aM. •e difference in hardeningof •e pure •d •e second-phase materialwas much less pronounced• •e differencein s•eng•, as expected, because the defomation
resismce
is co•ected
flow •c•s
=00MPa
20% SiO 5% SiO
500
400
Pure Calcite
300 200
100
for volmeMc
changes.•e optical •d •M obse•ations suggest•at dislocationglide •d •mng •e increasMglyimpoaant at hiker confiningpressures, and •e Mgher dislocationdensities closeto •e matfi•paaicle interface(Fig•e 11) suggest•at dispersionh•dening may have conMbutedto •e increasein defomationresistance•d •e h•dening rates of the secondphasematerial. • •e Mcrea• M defomation resis•ce of •e •o-phase aguegatesin •e se•bfittle field also •c•s for hlly plastic defomation,•en •e •sition •om se•bfiRle to hlly plastic flow •11 • s•Red to •• press•es • for a s•gle-phase material; additionally,consti•tive laws ba•d on s•gle phases •11 probably•derest•ate •e s•en• [cf. Tullis et al., 1991]. F•ally, •e• ex••ents suggest•at •e press•e for •e •sition •om l•al•ed fail•e to se•bd•le (ductile)•havior •11 • lowered relative to s•gle-phase r•ks. •us, adding second-ph•eswouldprobably•crease •e press•e r•ge •der whch se•bd•le
I
• •e E•.
It is •po•t to real•e •at s•dies • of •e ca•clastic defo•ation of •rous r•ks [Edmondand Paterson,1972,High and Tullis, 1989, Rutter and Ha•izadeh, 1991] •d of •e defomationof a we• ma•x con•ing a s•onger•cond ph•e [Jordan, 1987, Ross et al., 1987] •dicate •at •e mech•ical response c• show•sients relatedto spatialre•gements of
I
T
I
2
4
6
Axial Strain (%) Fig. 13. Deformation resistanceas a function of axial strain. The deformation resistance of two-phaseaggregates is consistently higherthan of the pure syntheticcalcitesamples.Note alsothe increasedwork hardening with increased abundance of secondphaseparticles.
the systemcomponents which occurover large strains(>10%). Thus,multi-phaserocksmight showa particularlyrich behavior in naturalsituations, e.g.,alonga faultor mylonitezone. CONCLUSIONS
Many aspectsof the mechanicalbehaviorof the two-phase, syntheticsampleswere similarto earlierexperimentsin natural limestonesand silicates [e.g., Heard, 1960; Edmond and Paterson, 1972; Rutter, 1974; Fredrich et al., 1989]. In these experiments, localized faulting, as observed from the macroscopic appearanceof the sample,only occurredat low pressure(5 MPa); was alwaysassociated with net dilatancyand strainsot•ening;and occurredunderconditionswherethe critical hardeningmoduluspredictedfrom the post-peakmoduli was negative, agreeing with Rudnicki and Rice [1975]. With
11,932
DRESENANDEVANS:DEFORMATION OFTWO-PHASEMARBLES
increasingconfiningpressurein the semibrittle(ductile) field, the total crack surface area (Table 3) and the dilatancy coefficient(Table 4) at a given strain were greatly reduced; crystalplasticdeformation mechanisms seemedto accomodate a largerpercentage of strainaspressure increased. In other ways, the mechanicalpropertiesof the two-phase sampleswere systematically differentfrom the pure, synthetic samples. Dispersed rigid inclusions with incoherent matrix/particleinterfacestend to delocalizebrittle failure, and reducestrength.Becausethe amountof porositytendedto covary with the secondphasecontent,we cannottell unambiguously whetherthe delocalizationwould occurin a samplewith rigid second-phase particles,but no associated porosity.The difference betweenthe two sets of samplesis reducedas the confining pressureis increased, suggesting thatporestructureis important, but the factthat the two-phasesampleswere consistently weaker than pure sampleswith the same total unconnectedporosity suggests thatthe weakeningis not dueto porosityalone. At higher confiningpressures(300 MPa) the deformation resistanceof the two-phaseaggregates was consistently greater than that of the pure, syntheticmarbles.Observationsof the microstructure suggestan additionalcontributionto hardening andstrengththroughthe addedsecondphaseparticles,similarto that observedin metals.The net effect of delocalizingbrittle failureandincreasing plasticflow stresswouldbe to increasethe rangeof conditions underwhichsemibrittleflow occurs. Acknowledgements.We thank JoanneFredrich for numerous helpful discussions and sharingunpublisheddatawith us. Dave Olgaardkindly allowedus to usethe hot isostaticpressat ETHZCtrich.
Steve
Recca
and Mike
Jercincovic
took
the
SEM
particulateson the rheologyof water ice at planetaryconditions,J. Geophys.Res.,97, 20,883-20,897 1992. Edmond,J.M., and M.S. Paterson, Volumechanges duringthe deformation ofrocksat highpressures, lnt. J. RockMech.Min. Sci., 9, 161-182, 1972. Evans,B., J. T. Fredrich,and T.-f. Wong, The brittle-ductiletransitionin rocks:Recentexperimental andtheoreticalprogress, in TheBrittle-Ductile Transitionin Rocks,Geophys.Monogr. Ser., vol. 56, editedby A. G. Duba, W. B. Durham,J. W. Handin, and H.-f. Wang, pp. 1-20, AGU, Washington,D.C., 1990. Farquhar, D.S., R. Raj, and S.L. Phoenix, Fracture and stiffness characteristics of particulatecomposites of diamondin zinc sulfide,J. Am. Ceram. Soc., 73, 3074-3080, 1990.
Fischer,G. J.,andM. S. Paterson, Dilatancyduringrockdeformation at high temperatures andpressures, J. Geophys.Res.,94, 17,607-17,618,1989. Fischmeister,H., and B. Karlsson, Plastiziffttseigenschat•en grobzweiphasiger Werkstoffe,Z. Metallkd., 65, 311-327, 1977. Fredrich,J. T., B. Evans,and T.-f. Wong,Micromechanics of the brittleto plastictransitionin Cartaramarble,J. Geophys.Res., 94, 4129-4145, 1989.
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(ReceivedApril 26, 1992; revisedFebruary8, 1992; accepted March 15, 1993.)
