The effect of porosity on the strength of quartz aggregates experimentally deformed in the dislocation creep regime

97

Tectonophysics, 200 (1991) 97-110 Elsevier Science Publishers B.V., Amsterdam

The effect of porosity on the strength of quartz aggregates experimentally deformed in the dislocation creep regime Greg Hirth ’ and Jan Tullis ~e~rt~ent

of Geological Sciences, Brown University, Providence, RI 0291.2, USA

(Received November 22,199O; revised version accepted June 21, 1991)

ABSTRACT Hirth, G. and Tullis, J., 1991. The effect of porosity on the strength of quartz aggregates experimentally deformed in the dislocation creep regime. Tectonophysics, 200: 97-110. The presence of porosity results in significant although transient strengthening of quartz aggregates experimentally deformed in the dislocation creep regime. Experiments were conducted on four quartz aggregates with porosities of < 1 to _ 8%, at 1073 K, 10-“/s, and 1.5 GPa con~ning pressure. Opticat and transmi~ion electron microscopy show that non-porous quartzite deforms at these conditions by climb-a~mmodated disl~ation creep with rec~tailization by progressive subgrain rotation; steady state flow is achieved at _ 10% strain. In the porous aggregates, very high densities of tangled dislocations develop around the pores when the samples are taken to run pressure and temperature. When sample shortening begins, strain is accommodated dominantly in the non-work hardened material away from the pores; the increased effective strain rate produces an increased flow stress. After - 10% strain the work hardened regions soften by grain boundary migration recrystallization, resulting in a lower effective strain rate and flow stress in the sample. After _ 30% strain the initially porous sampies have the same flow stress and microst~~ures as the non-~rous samples. The results of this study have important implications for the experimental determination of flow law parameters, and possibly for the strength of rocks naturally deformed at metamorphic conditions where pores form in the presence of non-wetting fluids.

Introduction Many physical properties of geologic materials are strongly influenced by the presence of porosity. For example, the values of electrical resistivity (Keller, 19831, permeability (Doyen, 1988), and compressibili~ (Walsh, 1965) are dependent on the porosity of a rock. In addition, the presence of porosity has been shown to dramatically reduce the strength of rocks experimentally deformed in the brittle field <(Paterson, 1978). The weakening results from the stress concentrations that develop around the pores (e.g., Hirth and Tullis, 1989) or at point loads between grains (e.g., Zhang et al., 1990). In this paper we illustrate how the presence of intergranular porosity

’ Present address: Dept. of Geological Sciences, Univ. Minnesota, Minneapolis, MN55455, U.S.A. 0040-1951/91/$03.50

leads to significant although transient strengthening of quartz aggregates e~rimentally deformed in the dislocation creep regime. This strengthening is opposite to the effect that microscopic water inclusions (or clusters) have on the flow stress of experimentally deformed single crystals of synthetic quartz O%Laren et al., 1989). It is also opposite to the effect that porosity has on the creep rates of hot pressed ceramics (e.g. Coble and Kingexy, 1956; Spriggs and Vasilos, 1964) and the strength of ductile metals (e.g. Haynes, 1971; Griffiths et al., 1979). To investigate the processes responsible for strengthening of porous quartz aggregates in the dislocation creep regime we have experimentally deformed samples with different initial porosities. In this paper we first compare the strengths of porous and non-porous quartz aggregates deformed at the same conditions, showing that the porous aggregates are significantly stronger. Then,

0 1991 - Eisevier Science Publishers B.V. All rights reserved

by contrasting the relationships between microstructural development and mechanical behavior for both porous and non-porous aggregates we illustrate the processes responsible for the strength difference. Finally, we discuss the implications that these results have for the experimental determination of flow law parameters, and for the strength of porous aggregates deformed in the earth. Experimental details starting materials

Experiments were conducted on cylinders (6.3 mm diameter, 14 mm length) cored from three orthoquartzites and one novaculite (all > 98% quartz). The initial grain size, porosity and water content of these materials are listed in Table 1. In this paper we describe the microstructures produced during experiments on two of these materials, Heavitree quartzite and Arkansas novaculite. Optical observations of Heavitree quartzite show equant grains with slight undulatory extinction (Fig. la). At the transmission electron microscope (TEM) scale, the grains exhibit variable dislocation densities (10’0-10’“/m2); a representative microstructure is shown in Fig. Ib. Heavitree quartzite has been used in several other experimental deformation studies (Mainprice and Paterson, 1984; Kronenberg and Tullis, 1984;

TABLE 1 Characteristics of starting materials Material

Heavitree quart&e Black Hills quartzite Oughtibridge ganister Arkansas novaculite

Porosity a (%) <1 - 4 - 7 - 8

Grain size

Water content ’

tfirn)

(wt.%)

ZOO 100 100 50

0.1-0.15 0.1-0.15 - 0.1 0.07-0.1

a Measured by linear intercept method (Gifkins, 1970; eqn. 2., p. 172). b Sample weight Iost after vacuum drying at 1073 K for 10 hrs, assumed to be dominandy H,O (see Kronenberg and Tullis, 1984; Kronenberg and Wolf, 1990).

Hirth and Tullis, in press). Optical observations of the Arkansas novaculite show equant grains with straight extinction and equant intergranular pores with an average diameter of N SO pm (Fig. ICI. Some of the pores are rhombohedral in shape (see arrow in Fig. lc), indicating that they probably formed as a result of dissolution of a carbonate phase. Density measurements on the Arkansas novaculite indicate that the pores do not contain a fluid phase. Thus any fluid which was present at metamorphic conditions must have escaped via grain boundary cracks after the novaculite reached the surface. TEM observations of the grains in the novaculite show a lower (10”’ to lO’*/m’) initial dislocation density than present in the Heavitree quartzite (Fig. Id). ~p~rim~ntal procedures

Samples were jacketed in a 0.25 mm thick sleeve of Ag, then mechanically sealed “as-is” using Pt end discs. Axial compression experiments were conducted in a modified Griggs-type apparatus using solid NaCl as the confining medium. All experiments were conducted at a confining pressure of 1.5 + 0.05 Gfa (includes up to 100 MPa cell and piston friction inherent to the solid medium apparatus), 1073 K, and a constant displacement rate of 1.9 x 10-s m/s (equal to an average strain rate of 1.5 X 10-‘/s>. The procedures for increasing and decreasing pressure and temperature are described in Hirth and Tullis (in press). Differential stress versus axial strain curves were calculated using the force measured with a standard external load cell assuming that the samples remained cylindrical with no volume change. Observed sample strengths were reproducible to k.50 MPa. Due to limitations of the solid medium apparatus we were unable to measure volume changes during an experiment. The assumption of no volume change may lead to underestimation of differential stresses for the porous samples, since some shortening is accommodated by compaction. Thus the difference in flow strength observed for the porous and nonporous samples may actually be larger than illustrated here. The differential stresses for all sam-

EFFECT

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ON STRENGTH

OF QUARTZ

99

AGGREGATES

ples may also include up to 100 MPa piston friction inherent to the solid medium apparatus (Green and Borch, 1989). This systematic error should be the same for all experiments, and thus not affect any of our interpretations. Samples were subjected to varying amounts of axial strain (up to a maximum of 60%) in order to relate microstructural evolution to mechanical behavior. Deformed samples were impregnated with epoxy, cut in half longitudinally, and several thin sections were prepared. Microstructural observations were made using a standard petrographic microscope and a Phillips EM420 transmission electron microscope.

Results All three of the porous quartz aggregates are stronger than non-porous quartzite deformed at the same conditions (Fig. 2). However, this contrast is only transient; after N 30% strain all of the samples achieve approximately the same flow stress (Fig. 2). In this section we first illustrate the microstructures developed in the non-porous Heavitree quartzite with increasing strain. Then we illustrate the microstructures associated with the higher yield stress and subsequent strain weakening shown for the porous aggregates (Fig. 2). Only Heavitree quartzite and Arkansas novac-

Fig. 1. Microstructures of starting materials. Widths of optical micrographs are given in parentheses. Scale bars are 1 pm for TEM micrographs. (a) Optical micrograph (2 mm) of Heavitree quartzite. fbf TEM micrograph of Heavitree quartzite showing typical dislocation density. (c) Optical micrograph (0.3 mm) of Arkansas novaculite. A rhombohedral pore is indicated by the arrow. Cd) TEM micrograph of Arkansas novaculite showing typical dislocation density.

100

ulite samples are described in detail, because they show the largest contrast in strength and microstructural development. Microstructural observations Non-porous Heavitree quartzite

At the conditions of these experiments the non-porous Heavitree quartzite deforms by climb-accommodated dislocation creep (regime 2 of Hirth and Tullis, in press). The microstructure of the Heavitree quartzite does not change significantly when the samples are taken to run conditions. However, at low strains (- 10% shortening) the original grains exhibit sweeping undulatory extinction and deformation lamellae (Fig. 3a). Observations at the TEM scale show that the original grains have relatively low dislocation densities (up to a maximum of - 5 X 10’3/m2). The dislocations are often curved and arranged into low energy subgrain boundaries (Fig. 3b), indicating the effectiveness of climb. At higher strains (- 60% shortening) the original grains become homogeneously flattened and continue to exhibit sweeping undulatory extinction, optically visible subgrains, and deformation lamellae (Fig. 3~). In addition, extensive recrystal-

Porosity 0 8% +

7%

. 4% .
o+ 0

,

,

I

10

20

.

, 30

.

, 40

,

, so

, 60

Axlal Strnln (X) Fig. 2. Differential stress versus axial strain curves for samples of the four quartz aggregates deformed “as-is” at 1073 K, IO-‘/s, and confining pressure of 1.5 GPa. The aggregate with the highest initial porosity (N 8% in Arkansas novaculite, indicated by open circles) shows the greatest peak stress, followed by the Oughtibridge ganister (7%, plus symbols), the Black Hills quartzite (4%, filled squares), and the Heavitree quart&e ( < l%, filled circles). After - 30% strain all of the samples achieve approximately the same flow stress.

lization (20-30% of the sample) occurs along the grain boundaries (Fig. 3c) as a result 01 strain gradients which develop between grains (White, 1976). In this regime of dislocation creep, recrystallization occurs dominantly by the progressive rotation of subgrains (Hirth and Tullis, in press). Evidence for this mechanism of recrystallization is best illustrated at the TEM scale. The recrystallized grains, which are usually about the same size as the smallest subgrains (compare Fig. 3d to 3b), are bounded partly by subgrain and partly by high angle grain boundaries. In addition, all of the recrystallized grains show a similar and low dislocation density, indicating that the driving force for grain boundary migration is low (Fig. 3d). Since the dislocation density of the recrystallized grains is similar to that of the original grains from which they formed, this mechanism of recrystallization is not expected to result in strain weakening. Porous Arkansas nouaculite

Unlike the non-porous Heavitree quartzite, the microstructure of the porous novaculite samples changes significantly when the samples are taken to run conditions. These changes are illustrated by the microstructures produced in a sample of Arkansas novaculite which was annealed at 1.5 GPa and 1073 K for 8 hours (the time required for the deformation piston to hit the sample after the drive motor is engaged). Optical observations of this sample show that the pores remain open, and that the grains adjacent to the pores exhibit a non-uniform patchy extinction in an annulus which extends - 30 pm away from the pore (see arrow in Fig. 4a). We believe that the concentric microcracks which are observed around the pores formed during unloading. At the TEM scale the region of patchy extinction around the pores correlates to an extremely high density of tangled dislocations (Fig. 4b). The dislocation density is too high to measure accurately because individual dislocations cannot be resolved, but we estimate it to be > 1015/m2. Away from the pores the dislocation density is much lower (10’0-10’3/m2, Fig. 4~). After 20% shortening all remnants of the original grains in the novaculite exhibit the patchy

EFFECT

OF POROSITY

ON STRENGTH

OF QUARTZ

AGGREGATES

extinction representative of work hardened material with a very high dislocation density (Fig. 4d). At this strain the pores are observed to be closed, and the material which used to surround the pores is recrystallized (see R in Fig. 4d). In addition, recrystallized grains are observed along grain boundaries which were not adjacent to pores (see arrow in Fig. 4d). The recrystallized grains are often too small to resolve with the optical microscope; however, using TEM we observe microstructures which indicate that the recrystallization in both regions occurs by strain-induced grain boundary migration. For example, in Fig. 4e

101

the dislocation-free grain appears to have been migrating into the heavily work hardened original grain. After 55% strain the microstructures of the Arkansas novaculite are very similar to those of the non-porous Heavitree quartzite. The remnants of the original grains are homogeneously flattened, and they exhibit a sweeping undulatory extinction as well as optically visible subgrains (compare Fig. 4f to 3~). These microstructures indicate that after strain weakening begins, the remnants of the original grains are able to recover by dislocation climb. The effectiveness of

Fig. 3. Microstructures produced in non-porous Heavitree quartzite. The shortening direction is vertical for all optical micrographs. The optical micrographs are 0.8 mm wide. (a) Optical micrograph of a sample shortened 10% showing sweeping undulatory extinction and deformation lamellae. (b) TEM micrograph (scale bar is 0.5 pm) of the 10% strain sample showing a low density of curved dislocations, subgrain boundaries and subgrains. Cc)Optical micrograph of a sample shortened 60% showing homogeneously flattened original grains with sweeping undulatory extinction, deformation lamellae and optically visible subgrains. Cd) TEM micrograph (scale bar is 1 pm) of a recrystallized region in the 60% strain sample. The recrystallized grains all have similar dislocation densities, and are bounded partly by subgrain boundaries and partly by high angle boundaries.

dislocation TEM

climb after 55% stram is confirmed

observations

low densities original

of subgrain

of curved

within

quartzite,

the same flow stress

that the dominant

nism of recrystallization

the

sample gressive

after the porous

we observe

and

grains.

Also at 55% strain, achieves

boundaries

dislocations

by

novaculite

as the non-porous

grains

from

grain

svbgrain are bounded

grain boundaries,

changes

boundary rotation.

throughout

migration The

the

to pro-

recrystallized

by both high angle similar

mecha-

and sub-

to those observed

in the

EFFECT

OF POROSITY

ON STRENGTH

OF QUARTZ

AGGREGATES

non-porous Heavitree quartzite sample (Fig. 3d) shortened _ 60%. In addition, all of the recrystallized grains have similar and low dislocation densities, indicating that the driving force for grain boundary migration is low. Discussion Mechanism for strengthening of porous aggregates

Microstructural observations indicate that the greater strength observed for the porous aggregates is associated with the formation of high dislocation densities around the pores. The dislocations nucleate in response to stress concentrations which develop around the pores under the influence of the confining pressure. The observation of extremely high dislocation densities indicates that the rate of dislocation climb is insufficient to accommodate recovery during the deformation associated with the compression of pores when the samples are taken to run conditions. An estimation of the magnitude of the stress concentration around the pores can be obtained from the expression for the stresses around a spherical pore in a linearly elastic material. The maximum hoop stress (a) at the surface of a pore is given by: u = P,/2 - 3PJ2

(1)

(Timoshenko and Goodier, 19511, where Pf is the fluid pressure and PC is the confining pressure. Thus, assuming that Pf is negligible in our experiments (density measurements indicate that the pores are empty), the magnitude of the hoop stress at a confining pressure of 1.5 GPa is 2.25

103

GPa. However, dislocations are nucleated around the pores when the temperature is raised, indicating that the porous novaculite is viscoelastic; thus the magnitude of the stress concentration derived from the elastic solution is a maximum value. Numerical modelling of the deformation around fluid inclusions in viscous materials has been done using a steady state power law creep rheology (e.g. Wannamaker and Evans, 1989); however, the dislocation microstructure around the pores in the novaculite indicates that the quartz was work hardening. The strengthening exhibited by the porous aggregates can be attributed to an increase in the effective strain rate experienced by the samples once shortening begins. In the porous novaculite, pores with a diameter of N 50 pm constitute N 8% of the volume. After going to pressure and temperature, an annulus N 30 pm thick of high dislocation density material develops around each pore. Thus, a maximum of 84% by volume of the quartz is work hardened before sample shortening begins. This value is a maximum because the work hardened regions around some pores overlap if the pores are closer than w 60 pm apart. When sample shortening begins, further deformation in the work hardened regions around the pores is very difficult, and the strain is accommodated dominantly in the non-work hardened regions away from the pores. Thus while the externally imposed strain rate is 1.5 x 10p6/s, the strain rate in the non work-hardened regions, which make up as little as 16% of the sample, is as high as 9 X 10e6/s. This analysis indicates that the difference in strength observed between the porous and non-porous samples results from the

Fig. 4. Microstructures produced in porous Arkansas novaculite. The shortening direction is vertical for all optical micrographs. The optical micrographs are 0.3 mm wide. Scale bars are 0.5 Frn for all TEM micrographs. (a) Optical micrograph of a sample annealed at run conditions for 8 hours. The grains which surround the pores (the pores are indicated by PI exhibit a patchy undulatory extinction which extends up to - 30 pm away from the pores (see arrow). (b) TEM micrograph of the annealed sample showing an extremely high density of tangled dislocations in a region adjacent to a pore. Cc) TEM micrograph of the annealed sample showing a relatively low dislocation density in a region away from a pore. fd) Optical micrograph of a sample shortened 20% showing patchy undulatory extinction in the remnants of the original grains, recrystallized grains in the regions which used to be pores (indicated by R), and grain boundary recrystallization (see arrow). The horizontal microcracks formed during unloading. (e) TEM micrograph of the 20% strain sample showing evidence for grain boundary migration recrystallization. (f) Optical micrograph of sample shortened 55% showing flattened original grains with sweeping undulatory extinction, deformation lamellae, and optically visible subgrains.

12w 1000

1

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Non-porous, 1O-5&

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400-

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0

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a 3

0 .

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Porous, 1o.6/s

Non-porous. 1O-6/s

mO-O.

04 0

O@

.

,

(

,

,

,

10

20

30

40

60

(

60

Axial Strain (%)

Fig. 5. Differential stress versus axial strain curves comparing the strength of non-porous Heavitree quartzite deformed at a strain rate of 10d5/s (plus symbols) to that of porous Arkansas novaculite deformed at 10e6/s (open circles). The curve for non-porous Heavitree quartzite deformed at 10V6/s (dots) is also shown for comparison.

The magnitude of the strengthening effect in the porous aggregates depends on the amount ot porosity in the sample. This follows since the volume of work hardened material which forms around the pore depends on the number and the size of pores in a sample. In this study the aggregate with the highest initial porosity (- 8% in Arkansas novaculite) shows the greatest difference in strength from the non-porous quartzite, followed by the Oughtibridge ganister (7%) and the Black Hills quartzite (4%) (Fig. 2). The microstructures observed in the Oughtibridge ganister and the Black Hills quartzite are consistent with the explanation that strengthening results from the formation of high dislocation densities around the pores. Mechanisms for gates

strain rate dependence of strength for quartz aggregates deformed at these conditions. The value of 9 X 10P6/s is obtained by assuming that the work-hardened regions are rigid, and thus represents the maximum possible increase in effective strain rate. The actual increase may be less due to the requirements of strain compatibility. To illustrate the effect of the increased effective strain rate in the porous samples we can compare the strength of the non-porous Heavitree quartzite deformed at 10-‘/s to that of the porous novaculite deformed at 10V6/s (Fig. 5). The maximum strength of the porous novaculite approaches that of the non-porous quartzite deformed at an order of magnitude faster strain rate. At this point in the experiment the rate of dislocation climb is insufficient to accommodate recovery in the porous novaculite (regime 1 of Hirth and Tullis, in press). Thus the portions of the original grains which were not affected by the pores during pressurization work harden and develop extremely high densities of tangled dislocations. However, with increasing strain the porous novaculite weakens due to the effect of grain boundary migration recrystallization. The details of the weakening are discussed in the next subsection.

weakening in the porous aggre-

Microstructural observations indicate that recovery in the porous novaculite samples is initially accommodated by grain boundary migration recrystallization. The recrystallization initiates in the regions adjacent to the pores and along the original grain boundaries at - 10% strain. The grains which form by this mechanism are strainfree and thus able to undergo increments of dislocation glide at lower stresses (Tullis and Yund, 1985b). The strain weakening which is associated with grain boundary migration recrystallization occurs because as a greater percentage of the sample becomes recrystallized, a correspondingly greater percentage of recovered grains is produced (as described for feldspar by Tullis and Yund, 1985b). The initiation of grain boundary migration recrystallization also leads to a change in strain partitioning in the porous novaculite samples. When shortening begins, the strain is partitioned dominantly in regions away from the pores, due to the high dislocation densities which develop around the pores when the samples are taken to run conditions. However, the regions away from the pores quickly work harden, due to the increased effective strain rate that they experience. When recrystallization initiates in the regions around the pores and along the grain boundaries,

EFFECT

OF POROSITY

ON STRENGTH

OF QUARTZ

AGGREGATES

the strain is p~itioned domin~~y in the grain boundary regions, This change occurs because the strain-free recrystallized grains which form along the grain boundaries are weaker than the work hardened remnants of the original grains. In additive, since the rec~stall~ed grain bounda~ regions are weaker than the interiors of the grains, it is possible that pore closure occurs partly by rigid grain translation along grain boundary shear zones. Our microstruc~ral obse~ations also illustrate that at high strains the remnant original grains, which were work hardened at low strain, are able to recover by dislocation climb. The enhancement of dislocation climb with increasing strain is promoted by the strain partitioning associated with the initiation of grain boundary migration recrystallization. During the strain increments where weakening initiates, the cores of the remnant original grains are not deforming at as high a rate because the strain is partitioned dominantly in the rec~staIlizing grain bounda~ regions. Thus the rate of dislocation production is lowered in the core regions, and the high densities of dislocations which were produced at low strain are reduced by dislocation climb. The combinati~~ of initial grain boundary migration recrystallization and subsequent recovery via dislocation climb results in the removal of all of the high dislocation density material by 55% strain. Thus the porous novaculite eventually achieves the same fIow stress as the non-porous quartzite deformed at the same strain rate. An alternative explanation for the behavior of the poraus aggregates

It is possible that the strengthening exhibited by the porous aggregates results partly from an effect of fHZo. The addition of a trace (- 0.1. wt.%) amount of water has been shown to strongly reduce the flow stress of quartz aggregates deformed in the disl~ation creep regime (e.g. Kronenberg and Tuftis, 19&Q;Mainprice and Paterson, 1984; Koch et al., 1989). The weakening effect is more pronounced at higher confining pressures, indicating that it may be closely related to fHZo (Tullis and Yund, 1989; Paterson, 1989).

105

Thus it is possible that the greater initial strength exhibited by porous aggregates is due to a Iower f H20which results from the greater pore volume (e.g., Luan and Paterson, in press). As the porosity is reduced the f;lZo will increase, which could lead to weakening of the sample if some of the H,O in the pores is driven into the crystal structure. The effectiveness of the fH20 mechanism depends on the pa~itionin~ of the water in the aggregate, and the ability of water in the pores to co~unicate with the grain centers (in order to react to changes in fr&. Thus it is strongly affected by the solubihty and diffusivity of the water-related species responsible for hydrolytic weakening in quartz aggregates (see review by Paterson, 1989). Experimental studies indicate that the solubility of water in quartz at 973 K and 800 MPa is on the order of 50 to 100 H/106 Si (Cordier and Doukhan, 1989). This value is in qualitative agreement with the solubili~ calculated using theoretical arguments (Paterson, 1986, 19891, The Iow solubility of water in quartz suggests that the majority of water present in the quartz aggregates which we deformed (0.1 wt.% = 6000 H/lo6 Si) resides in the pores or along grain boundaries. E~erimental measurements show that diffusion of water in quartz is relatively slow (Kronenberg et al., 1986; Cordier et al., 1988). For example, at 1073 K, DH20 = 2.3 x 10-l’ m*/s according to the relationship determined by Gordier et al. (1988). Thus, in the time during our experiments between the initiation of sample shortening and the point where the samples achieve a low flow stress (* 30 hrs), water would only diffuse N 2 ,um. The experimental results on water diffusivity indicate that a fast or short-circuit diffusion path must be available to allow water residing in pores and grain boundaries to communicate with the grain centers. Recent studies on single crystals of Brazil quartz indicate that the weakening observed at high con~ning pressures (e.g., Griggs and Blacic, 19641 is probably a result of water entering the crystal via microcracks (Kronenberg et al., 1986, Fitz Gerald et al., 1991). However, this does not account for the rapid weakening of non-porous quartz aggregates (TuIlis and Yund,

1985a). In our porous aggregates, where stress concentrations produce extremely high dislocation densities around the pores, it is possible that water is transported to the grain centers by dislocation-assisted diffusion. There are no data for quartz, but if we use the data for dislocation-assisted diffusion of oxygen in feldspars (Yund et al., 19891, the diffusivity of water could be enhanced as much as three orders of magnitude in the high dislocation density material around the pores in the novaculite. This value was calculated using a ratio of the pipe diffusion rate to the lattice diffusion rate D,/D, = lo5 (Yund et al., 1981) and a dislocation density p = 10’6/m2. While dislocation-assisted diffusion may allow water transport between pores and grain centers in the times of our experiment, there is also a problem with the solubility of water. The effectiveness of the fi,,o mechanism depends strongly on the water being partitioned dominantly into the pores. However, FTIR measurements indicate that the water content within individual grains of a hydrolytically weakened sample of Heavitree quartzite is - 4000 H/lo6 Si (Kronenberg and Wolf, 1990). This is similar to the total amount present in our porous novaculite, but one to two orders of magnitude higher than the solubility determined by Cordier and Doukhan (1989). Thus it is not clear whether increased fHzo actually allows more water to dissolve in the crystal structure. Further work needs to be conducted to determine the equilibrium (or saturation) limit of water required to induce hydrolytic weakening, and how this limit is related to the experimentally measured solubility of water in quartz. In conclusion, while we still believe that the high dislocation densities which form around the pores result in a transient increase in strength, it is possible that the difference between the strength of the novaculite and the Oughtibridge ganister (which have close to the same porosity) results partly from differences in their initial water content and/or water distribution. Comparison with other experimental studies

The strengthening we observe for the porous aggregates is opposite to the effect that micro-

scopic water inclusions (or clusters) have on the flow stress of experimentally deformed single crystals of synthetic quartz (McLaren et al., 1989). In both our experiments and those of McLaren ct al. (19891, stress concentrations around pores result in the nucleation of dislocations. However, the two materials exhibit opposite behaviors due to differences in the size (and thus D/o sample volume) of the pores, and the nature of the stress concentration around the pores. McLaren et al. (1989) found that prismatic dislocation loops nucleate in response to the internal pressure associated with microscopic “water” clusters. After they nucleate, the prismatic loops grow by dislocation climb, and interact with other dislocations to produce glissile loops. When a dislocation density of N 1 x 10i2/m2 was achieved (the same density we observe in the non-work hardened regions away from the pores), the water inclusions appeared strain-free, indicating that the internal pressure was relieved. McLaren et al. (1989) concluded that it is the nucleation of these glissile dislocation loops which results in the low flow stresses observed for “wet” synthetic quartz; dry natural crystals are strong because they have no initial dislocations nor any defects to nucleate them (however, see Tullis and Yund, 1989; Paterson, 1989). In contrast to McLaren et al. (1989), we observe that high densities of tangled dislocations form in response to the stress concentrations which arise around large ( * 50 pm) intergranular pores. This observation indicates that the stresses around the pores are so great that dislocations are produced faster than climb can accommodate recovery. At a confining pressure of 1.5 GPa, the maximum hoop stress at the surface of the pores in our experiments is 2.25 GPa (calculated using the elastic solution given in eqn. cl), and neglecting the effects of fluid pressure). Our results on the effect of porosity on the creep strength of quartz aggregates also contrast with those observed for the effect of porosity on the creep rates of hot pressed ceramics and the strength of metals. Again, the apparent discrepancy may be due to the greater magnitude of the stress concentrations around the pores in our

EFFECX OF POROSITY ON STRENGTH OF QUARTZ AGGREGATES

107

samples, due to the higher confining pressures of our experiments. Creep rates measured during hot pressing of ceramics show a positive dependence on porosity. Similar results have been observed during hot pressing of fine (- 10 pm) quartz powder (Evans and Lockner, 1989). This effect is attributed to an increase in effective stress which results from the load being supported by a smaller cross sectional area (e.g., Spriggs and Vasilos, 1964). In addition to this effect, enhanced ductility in porous metals is attributed to the stress concentrations around pores (e.g., Haynes, 1971). These factors will only enhance deformation rates if the stresses are low enough for climb to allow continued crystal plastic deformation. Our microstructural observations indicate that these factors do not dominate in our samples because the stress concentrations around the pores are so great (due to the high confining pressure and negligible fluid pressure) that dislocations are produced faster than climb can remove them. Thus, instead of enhancing the ductility of the aggregate, the stress concentrations result in work hardening. It is important to emphasize that the strengthening we observe for the porous aggregates occurs because dislocation creep is the dominant deformation mechanism. If deformation occurred by grain boundary diffusion creep, the presence of porosity would enhance the creep rate by increasing the effective stress, and by providing short-circuits for grain boundary diffusion (e.g., White and White, 1981; Cooper and Kohlstedt, 1986).

demonstrate that the flow stresses represent steady state behavior. The results of this study show that steady state flow in the porous quartz aggregates was not achieved until N 30% strain, due to the high dislocation densities which initially formed around the pores. This illustrates the importance of making microstructural observations in conjunction with measuring flow stresses from experimentally deformed samples. In addition, it shows the value of conducting experiments to high strain. If we had only conducted experiments to 15% strain, the transient strengthening exhibited by the porous quartz aggregates would not have been correctly interpreted. When collecting rheological data for the determination of flow laws, it is advantageous to use aggregates which are as chemically pure as possible. Because even the purest naturally occurring rocks contain impurities, many researchers have begun measuring flow laws for synthetically prepared aggregates (e.g., Cooper and Kohlstedt, 1986; Karat0 et al., 1986). However, since it is difficult to produce theoretically dense synthetic aggregates, care must be taken to characterize the effect of initial porosity on the mechanical behavior of these materials. For minerals such as olivine and calcite (for which steady state crystal plasticity can be induced at relatively low pressures), stress concentrations which result in strengthening can probably be avoided. However, for the determination of flow laws for quartz and feldspar aggregates, where high pressures are required to induce steady state crystal plasticity at experimental strain rates (Tullis and Yund, 1977), it appears important to use non-porous aggregates.

Implications Determination of flow laws

One of the principal goals of experimental rock deformation is to provide mechanical data in the form of fIow laws relating strain rate to stress and temperature. Flow laws can be used to model a wide range of geologic processes (e.g., Parrish et al., 1976; Zuber et al., 1986; Christensen and Yuen, 1989), provided that extrapolation to geologic conditions is warranted. When collecting rheological data for flow laws, it is important to

Possible implications for the strength of naturally deformed rocks

The effect of porosity on the strength of naturally deformed aggregates depends on whether significant porosities t 7 3%) are present in rocks at metamorphic conditions, and on the magnitude of the stress concentrations which arise around the pores. Isolated pores will form at metamorphic conditions in the presence of non-

(i.

Fig. 6. SEM micrograph (scale bar is 0.25 mm) of Black Hills quartzite showing the geometry of pore\.

wetting fluids. In our experiments the pores were empty, but in the earth they would probably be filled with a fluid phase. The existence of isolated pores is thermodynamically favored when nonwetting fluids, such as CO, and H,O for calcite (Hay and Evans, 1988) or CO, for quartz (Watson and Brenan, 19871, are present. We have shown that a porosity of N 4% is sufficient to result in strengthening of Black Hills quartzite (Fig. 2). In addition, while the pores in the Arkansas novaculite appear to have formed by dissolution of a carbonate phase, the pores in the Black Hills quartzite show many features similar to those illustrated for quartz aggregates experimentally annealed in the presence of H,O and CO, fluids (compare Fig. 6 to fig. 4a from Watson and Brenan, 1987). This suggests that the pores in the Black Hills quartzite were present at metamorphic conditions. The possibility that strengthening occurs for porous aggregates in the earth depends on whether the stress concentrations around pores are great enough to produce work hardened regions. The magnitude of the stress concentrations around pores is significantly lowered by the presence of pore pressure (see eqn. 1). If the pores are not interconnected, the fluid pressure becomes equal to the lithostatic pressure. In this case it is unlikely that the stress concentrations around the pores will be great enough to produce

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the high density of dislocations necessary to promote strengthening. In addition, it is possible that dislocation climb is sufficiently rapid at geologic time scales to accommodate the rate of dislocation production which is caused by the stress concentrations. Thus, it appears more likely that the presence of porosity at metamorphic conditions leads to weakening in a manner analogous to what is observed during the hot pressing of ceramics and the deformation of porous metals. While it is unclear whether the strengthening we observe is important in the earth, the processes which control the mechanical behavior of the porous aggregates may be analogous to effects that hard inclusions have on the strength of two phase aggregates (Tullis et al., 1991). In this case the effective strain rate in the matrix material will also be increased. However, unlike the work hardened regions in the porous quartz aggregates, the hard inclusions will not be removed at high strains. Acknowledgments Supported by National Science Foundation Grant EAR-8708356. We thank R. Yund, J. Farver, and G. Gleason for helpful discussions, and T. Tullis and B. Evans for reviewing a preliminary version of the manuscript. We thank M. Paterson and an anonymous reviewer for their reviews, which stimulated the discussion of the effect of fH20, and for providing a pre-print (Luan and Paterson, in press) of unpublished results. References Christensen, U.R. and Yuen, D.A., 1989. Time-dependent convection with non-newtonian viscosity. J. Geophys. Res., 94: 814-820. Cable, R.L. and Kingery, W.D., 1956. Effect of porosity on physical properties of sintered alumina. J. Am. Ceram. Sot., 39: 377-385. Cooper, R.F. and Kohlstedt D.L., 1986. Rheology and structure of olivine-basalt partial melts. J. Geophys. Res., 91: 9315-9323. Cordier, P. and Doukhan, J.-C., 1989. Water solubility in quartz and its influence on ductility. Eur. J. Mineral., 1: 221-237.

EFFECT

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OF QUARTZ

AGGREGATES

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