Brian Evans and David L. Kohlstedt. 1. LABORATORY. MEASUREMENTS. 1.1. Strategy and Techniques. For a rock of given mineralogy and microstructure, the.
Rheology of Rocks
Brian Evans and David L. Kohlstedt
1. LABORATORY
MEASUREMENTS
1.1. Strategy and Techniques
For a rock of given mineralogy and microstructure, the variables important in determining strength are pressure, temperature, strain, strain history, strain rate, pore fluid pressure,grain size, fugacities of water and other volatiles, and chemical activities of the mineral components. Although earth scientistsmay now duplicate pressuresand temperaturesappropriate to the mantle and core in modern high pressureapparatus,they still cannot study mechanical properties under truly natural conditions. Time scales in the Earth are too long, and length scalestoo large. Sinceexact deformation conditions cannot be duplicated in the laboratory, the experimenter’sstrategy must involve determining the kinetic parameters of the appropriate processesat laboratory conditions and extrapolating to much lower strain rates [58]. Two convenient techniques are available to aid laboratory studies. Temperature and, hence,kinetic rates may be increased,or processesmay be studiedat smaller length scales[60]. Testing at high temperatures also imposes constraints. For example,maintaining chemicaland phasestability and
B. Evans,Massachusetts Institute of Technology, Department ofEarth, Atmospheric and Planetary Sciences, Cambridge, MA 02139-4307 D. L. Kohlstedt, University of Minnesota, Minneapolis, Department of Geology and Geophysics, Minneapolis, MN 55455 Rock Physics and Phase Relations A Handbook of Physical Constants AGU Reference Shelf 3 Copyright
1995 by the American
Geophysical
Union.
.48
producing accelerated deformation kinetics may be mutually exclusive goals. This conflict can be mitigated by testing single phaserocks or by fabricating synthetic rocks with speciallydesignedphasecompositions. The chemical fugacities of the mineral components and any volatiles, particularly water, must also be controlled. Unless the experimenter aims to investigate the properties of partial melts, eutectic melting needsto be avoided. Deformation at low strain rates can also be studied by reducing a length scale.For mechanismsprimarily limited by diffusion, the most important length scale is the grain size. Natural rocks with grain sizesof a few microns may be found, and synthetic aggregates of olivinc, calcite, feldspars, and quartz have been produced in a range of very small grain sizes. Such synthetic rocks can bc usedto understand the effect of variations of grain size, second phase abundance, or dissolved hydroxyl content on the physical properties of rocks. 1.2. Apparatus
Modem apparatus use a variety of loading schemes, including rotary shear, double block shear, conventional triaxial, full triaxial, diamond anvil, and large volume, opposedmulti anvil devices [60, 901. The most common loading geometry is the conventionaltriaxial configuration (Figure 1). Such machines have cylindrical loading symmetry with coaxial stress and strain. If the axial compressive stress, oa, is larger than the confining pressure,P,, then loading is triaxial compression;if o, < _-_---Localized ________-___-__~ >< ___________ plastic __-________ > < ____________ Brittle------------>3%----------->< ----------->5% -----------> Strain to Failure < > Work Softening > < StressDrops ----> < Loss in Cohesion Microcracking Dilatancy Acoustic Emission -I-___ < > Press.Dep. Strength ______________ ________________ >< ______-____ high ______________ _______________ > < ------------low Temp. Dep. Strength Distributed and Localized Distributed Microcracking Fully Plastic Deformation Mech. Local Plasticity Microcracking Macroscopic Appearance m-w--
------
With increasing confining pressure and decreasing dilatancy factor, h,, is predicted to increase. Experiments on a variety of rocks agree with the mechanical analyses, except that the hardening modulus critical for incipient localization is predicted to be overly negative as compared with the experimentalvalues. During cataclastic failure of rocks in compression, dilatant microcracks nucleate,grow, and coalesce[48]. For dilatant wing cracks growing from an inclined preexisting flaw, fracture mechanics models [55, 751 indicate that strain hardening occurs until the dilatant cracks interact elastically; at which point strain softening and localization occur. Although rigorous tests of the fracture mechanics models do not exist, the theories do provide rational explanations for several observations, including, for example, dependenceof fracture strength on the inverse of the square root of grain size. The models do not explain the empirical observationthat the friction law bounds the brittle-ductile transition, unless fracture toughness and plastic flow strength scalewith eachother.
(17)
6.2. Mechanics of Semibrittle
whereg is the shear modulus, v is Poisson’sratio, and N is l/J3 for axisymmetric compression.For most stress states, the model predicts negative h, for shear band formation, both for a yield vertex model and for isotropic hardening.
Deformation
Plastic flow mechanisms and brittle cracking can interact in a variety of ways. Cracks may be nucleated at dislocation pileups [97], intersecting twins, rigid second phases, or incoherent boundaries. Cavities may form during creepat sliding grain boundaries.Cracks may grow
162 RHEOLOGY
OF ROCKS
or blunt by creep processes [54, 681. Based on tensile failure experiments several broad classes of fracture mechanisms can be defined [2] depending on the partitioning of strain into rate independent plasticity, creep, and fracture processes: cleavage, intergranular brittle fracture, plastic void growth, and plastic rupture are low-temperature processes; intergranular creep fracture, creep void growth; and creep rupture are high-temperature processes. As with brittle fracture, semibrittle deformation may be treated by prescribing a nucleation criterion and predicting growth to failure according to a separate failure criterion, often involving a critical damage state. Then, contours of time or strain to failure may be plotted in differential stress-temperature space. Most work has concentrated on tensile loading, but some attention has been paid to compressive, multiaxial loading [1, 55, 751. In much the same way that confining pressure stabilizes the propagation of brittle wing cracks, an analysis of the Stroh
crack mechanism [97] shows that cracks nucleated by dislocation pileups propagate to a length which scales with the number of dislocations in the pileup, and with the difference between the resolved applied stress and the Peierls stress. Despite progress in understanding semibrittle failure, a satisfactov constitutive law does not exist. Because of the potential complexity of mixed deformation mechanisms, it is naive to expect one theory to represent semibrittle deformation over a range of conditions. In the same way that deformation maps are necessary to represent plastic flow, multimechanism maps will surely be needed to describe semibrittle deformation. Acknowledgments:
Funding
for this work was provided
by NSF
GeosciencesDivision by grants EAR91 18969 (BE), EAR901823 (DLK), and OCE920041 (DLK). We thank the editor and the reviewer for comments and forbearance, and apologize to the authors of many excellent papers which could not be cited, owing to space restrictions.
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