Mervyn S. Paterson

The experimental deformation of dunite

Deformation experiments have been carried out on two dunites (Anita Bay, of 100 μm grain size, and Aheim, of 900 μm grain size) at strain rates from 10−3 to 10−6 s−1 and temperatures from 1000°C to 1300°C in a gas-medium deformation apparatus at 300 MPa confining pressure. Most of the tests were under “wet” conditions defined by the presence of small amounts of water from hydrous minerals initially present. Constant strain rate and relaxation experiments, covering ranges of flow stress down to about 70 MPa and 7 MPa, respectively, show that there is a change in flow law in going below about 100 MPa differential stress, and that the coarser-grained rock is stronger than the finer-grained one. Power law parameters above the transition are n = 4.48 ± 0.31 and Q = 498 ± 38 kJ mol−1 for Aheim dunite and n = 3.35 ± 0.17 and Q = 444 ± 24 kJ mol−1 for Anita Bay dunite, while below the transition relaxation tests on Anita Bay dunite give n = 2.44 ±0.18 and Q = 386 ± 27 kJ mol−1. It is concluded that there is a weakening effect of water, that this effect is mainly in the grain boundaries and that grain boundary sliding is probably a significant deformation mechanism at the lower stresses under wet conditions.

Superplastic flow in finegrained limestone

Creep of Solnhofen limestone at temperatures between 600° and 900° C was found to fall into three different flow regimes: regime 1 with an exponential stress-dependence of strain rate, regime 2 with power-law creep and n ~ 4.7 and finally a superplastic regime 3 with n ~ 1.7. Within the superplastic regime the creep behaviour is strongly grain-size dependent, the strain rate increasing markedly with decrease in grain size at a given stress. Microstructural observations indicate that in regimes 1 and 2 intracrystalline plasticity is dominant whereas the superplastic regime is characterized by grain-boundary sliding. The crystallographic preferred orientation within the superplastic regime is weaker and of different geometry when compared with that in flow regimes 1 and 2. In a discussion on the deformation mechanisms it is suggested that flow regimes 1 and 2 are regimes of dis location creep in which the rate controlling step is diffusion assisted; for the superplastic regime existing models of grain-boundary sliding are compared with the observations Finally, the tectonophysical importance of superplasticity is discussed and by extra polating the observed creep behaviour to geological strain rates it is found that super plasticity in rocks is to be expected under a wide range of conditions, particularly at smal grain sizes.

High temperature flow and dynamic recrystallization in carrara marble

Abstract Specimens of Carrara marble have been experimentally deformed at temperatures between 600° and 1050° and at strain rates between 10−2 and 10−6 sec−1. No single empirical flow law could be found for the whole range of experimental conditions covered. Instead it was found that three deformation regimes, each with its characteristic microstructural imprint, can be established. Above 1000 bar differential stress a relatively low strain rate sensitivity of the flow stress is observed and twinning is predominant (regime 1). Regime 2 extends down to 200 bar flow stress and exhibits the unusually high stress exponent n = 7–8 in the power law creep equation earlier found by Heard and Raleigh (1972) in Yule marble. The original grains exhibit a “core and mantle” structure. Only in regime 3 below 200 bar differential stress does one find lower values for n of around 4, and now a mosaic of equi-axed subgrains occupies entire grains. Extensive recrystallization and grain boundary migration was found at the higher temperatures. The grain size produced by dynamic in-situ recrystallization was found to be inversely proportional to the applied flow stress. Scanning electron microscopy observations on split cylinders suggests substantial amounts of grain boundary sliding in the low Stress region. The unusually high dislocation densities at low flow stresses as measured under the transmission electron microscope are interpreted to arise through strains induced during cooling under pressure after the deformation experiment. In view of the fact that the different calcite rocks so far investigated under elevated temperatures and low flow stresses exhibit rather different flow laws, caution is indicated when extrapolating such empirical flow laws to geological conditions. The size of dynamically recrystallized grains may directly lead to a paleostress estimate at the time of recrystallization. A subsequent work softening effect through a change in mechanism induced by syntectonic recrystallization may play an important role in the formation of shear zones and mylonite layers.

Rock deformation tests to large shear strains in torsion

Abstract Experiments performed to high strains in simple shear are necessary to resolve many important problems in rock deformation, including the simulation of non-coaxial deformation, the exploration of the influence of strain on rheology, and the development of mineral segregation, dynamic recrystallisation, and other aspects of microstructure. Using a new torsion system we are able to simulate both the high strains and the simple shear style commonly observed in naturally deformed rocks, and to make accurate measurements of shear stress, strain and strain rate at high temperatures and pressures. The torsion system, which is described briefly, is based on a standard gas-medium high-pressure high-temperature triaxial deformation machine to which has been added an additional module allowing rotary shear of a cylindrical specimen. In this paper, we discuss procedures for carrying out torsion tests and we analyse the mechanics of torsional deformation. We show how to extract information about the rheological parameters from the torque–twist data, and how to deal with the problems posed by the variation of strain within a cylindrical specimen. Procedures for microstructural studies are also set out. Finally, some results on calcite rocks are given to illustrate the application of torsion tests.

The simulation of fabric development in plastic deformation and its application to quartzite: The model

Abstract The Taylor-Bishop-Hill model for polycrystalline deformation has been applied as the basis of a computer program for simulating the development of preferred crystallographic orientations in deforming rocks in which the predominant mode of deformation is dislocation glide within the grains. The model assumes homogeneous deformation on the scale of the grains and rigid-plastic flow obeying Schmids critical resolved shear stress law for the glide systems. The input data for the simulation are the initial orientation distribution, the set of possible glide systems and their relative critical shear stresses, and the details of the deformation including its path, which can involve non-coaxial deformation histories in the general case. The analysis is applied to model quartzites in which four possible choices of glide systems and their critical resolved shear stresses are considered, for three different deformations. Some of the simulated fabrics bear close similarity to observed fabrics, suggesting that fabric development as a result of rotation of crystal axes during dislocation glide is potentially an important geological process, and that the Taylor-Bishop-Hill model is suitable for analyzing it. From the profound influence of deformation history on the simulated fabric and the sensitivity of the fabric to the choice of glide systems and their relative critical shear stresses, important possibilities are suggested for gaining information about geological environment and deformation history from the analysis of natural deformation fabrics.

Problems in the extrapolation of laboratory rheological data

Abstract The many types of variables and deformation regimes that need to be taken into account in extrapolating rheological behaviour from the laboratory to the earth are reviewed. The problems of extrapolation are then illustrated with two particular cases. In the case of divine-rich rocks, recent experimental work indicates that, within present uncertainties of extrapolation, the flow in the upper mantle could be either grain size dependent and near-Newtonian or grain size independent and distinctly non-Newtonian. Both types of behaviour would be influenced by the present of trace amounts of water. In the case of quartz-rich rocks, the uncertainties are even greater and it is still premature to attempt any extrapolation to geological conditions except as an upper bound; the fugacity and the scale of dispersion of the water are probably two important variables but the quantitative laws governing their influence are not yet clear.

A theory for granular flow accommodated by material transfer via an intergranular fluid

Abstract A new model has been developed for the deformation of granular material such as porous rock, based on a mechanism of relative movement of grains (granular flow) controlled by the rate of solution transfer involved in accommodating intergranular interferences. Distinction is made between control of the strain rate by: (1) the rate of diffusion of the dissolved granular substance in the pore fluid (fluid diffusion control); (2) the rate of dissolution or precipitation at the sources or sinks in the solution transfer process (reaction control); and (3) the rate of diffusion within the “islands” of the assumed “island and channel” structure of the grain interface (source/sink diffusion control). Using an analogy with particulate flow in soil mechanics to derive a flow equation for constant-volume flow and combining this with calculation of the rate of porosity reduction, general flow laws are derived for axisymmetric non-hydrostatic conditions. Application to the cases of quartz and rocksalt porous aggregates, with water as the pore fluid, suggest that, under geological conditions, source/sink diffusion control will tend to predominate where granular flow occurs.

The influence of room temperature deformation on porosity and permeability in calcite aggregates

Changes in permeability and porosity during shortening deformation of Carrara marble and hot-pressed calcite aggregates were measured under high pressure at room temperature using argon as pore fluid. At effective pressures of 30 and 50 MPa, the permeability of Carrara marble increased by up to 2 orders of magnitude with less than 2% strain during which the connected porosity increased by only 0.005. The permeability increased more slowly with further strain up to 18%, during which the connected porosity increased by a further 0.05 to 0.06. At effective pressures of 100 MPa to 200 MPa, these effects were much less marked. In hot-pressed calcite aggregates, deformed at an effective pressure of 50 MPa, the permeability increased by about 2 orders of magnitude after about 12% strain and an increase in connected porosity of about 0.03. Microstructural studies indicate that, in the coarse-grained Carrara marble specimens, both transgranular and grain boundary cracks are present after room temperature deformation. For a given strain, the average length and the linear density of transgranular cracks decrease with increasing effective pressure. In fine-grained, hot-pressed calcite aggregates, dilatancy is mainly due to opening of grain boundary cracks. The very marked increase in permeability with small strain at low effective pressure can be correlated with the proliferation of connected microcracks of relatively large apertures, deduced on the basis of theoretical models.

Porosity and permeability evolution during hot isostatic pressing of calcite aggregates

Porosity, permeability, and storativity were measured during isostatic hot-pressing of fine-grained calcite aggregates at temperatures of 633 to 833 K, confining pressures of 200 to 300 MPa, and argon pore pressures of 100 to 250 MPa. The progressive changes in total porosity were measured in situ by monitoring the sample length changes. The connected porosity and the permeability and storativity were measured in situ by incrementing and oscillating pore pressure techniques, respectively. In a given test, there was a decrease with time in the rate of reduction of porosity, the rates being higher at higher temperature and effective pressure. The permeability k was nonlinearly related to the total porosity ϕ in the form k ∝ ϕn. The exponent n was approximately equal to 3 and thus consistent with the prediction of the “equivalent channel” model, in the range of porosity from 0.18 down to 0.07. Below 0.07, n became much larger (around 14), an effect that can be attributed to loss of connectivity and which is qualitatively similar to that observed by Bernabe et al. [1982] in post-hot-pressing measurements. However, a cube law continues to apply below 0.07 total porosity if the permeability is related to the connected porosity itself. The storativity is also nonlinearly related to the porosity. Model analyses of the permeability and storativity results indicate both that the pore apertures decrease and that the pore shapes become more equant as the porosity decreases. The marked downturn in the permeability-porosity relationship at total porosities below 0.07 appears from microscopical observation to correspond to a change in pore geometry from largely connected, irregular pores between grains to isolated, tubular pores at junctions of several grains. Application of the “Swiss-cheese” continuum percolation model indicates a percolation threshold of about 0.04 porosity. Microstructural evidence, the apparent activation energy for densification, and the stress dependence of densification rate suggest that porosity reduction has occurred mainly by dislocation creep.

The simulation of fabric development during plastic deformation and its application to quartzite: fabric transitions

Abstract Fabric transitions can arise in materials such as quartz in which more than one set of symmetrically equivalent glide systems must be considered. The external conditions, such as temperature and stress, affect the relative ability of different mechanisms to operate. Adopting the Taylor-Bishop-Hill analysis allows an approximation to the resulting effects in the choice of critical resolved shear stress (CRSS) values for glide on the different dislocation systems. Different CRSS values may be appropriate to simulating fabric development in different deformational environments. For any specific set of CRSS values, for a particular deformation, a set of reorientation trajectories can be defined for differently oriented crystals with respect to the instantaneous stretching axes. There is a basic number of pattern types, and deformation leads to c -axes populating specific end-orientations. The CRSS values on different glide systems can vary smoothly relative to one another, but abrupt changes result in the deformation fabrics at critical CRSS ratios. Quartz fabrics may thus be used to delineate regions subjected to particular conditions of temperature and strain-rate in deformed metamorphic terrains, provided that allowance can be made for other factors such as trace impurity content of quartz.