J. H. P. De Bresser

On dynamic recrystallization during solid state flow: Effects of stress and temperature

A hypothesis is advanced that dynamic recrystallization of Earth materials undergoing solid state flow may represent a balance between grain size reduction and grain growth processes occurring directly in the boundary between the dislocation and diffusion creep fields. Accordingly, the recrystallized grain size (D) and flow stress (σ) at steady state will be related by the equation delineating the field boundary, which in general is temperature dependent. Creep experiments on a metallic rock analogue, Magnox, yielded D=10 1.12 exp[29.3/RT]σ 1.2:3 and demonstrated that D (μm) decreases with increasing σ (MPa) and increasing temperature (T) in a manner which is in agreement with the field boundary hypothesis. If the model applies to rocks, the widely accepted idea that dynamic recrystallization can lead to major rheological weakening in the Earth may not hold. Moreover, empirical D-σ relations, used in paleo-piezometry, will need to be modified to account for temperature effects.

Strength characteristics of the r, f, and c slip systems in calcite

Abstract Numerical modelling of crystallographic preferred orientation or texture development in plastically deformed materials requires specification of all potential slip and twinning systems and their relative strengths or critical resolved shear stresses (CRRS). It is widely believed that the most important intracrystalline deformation systems in calcite are twinning on e{ 1 018}〈40 4 1〉 + , slip on r{10 1 4}〈 2 021〉 ± and slip on f{ 1 012}〈2 2 01〉 ± , the superscripted signs indicating slip sense. It is these systems which have been used in modelling texture development in calcite polycrystals to date. However, modelling has been limited by insufficient and partly conflicting data on the (relative) strengths of the various slip and twinning systems in calcite. Deformation experiments on calcite single crystals, performed by us in recent years, taken together provide new data for a more complete and consistent quantification of the strength properties of the calcite glide systems. In our experiments, single crystals of calcite were compressed in both the [4041] and [2243] orientations, at temperatures and constant strain rates in the range 300–800°C and 3 × 10−4−3 × 10−8 s−1, respectively. The stress-strain curves obtained mostly show two yield points. Slip line analysis shows that these yield points are related to the onset of macroscopically observable slip, first on an r〈 2 021〉 ± system and then on an f〈10 1 1〉 ± or c〈a〉 system. The latter two systems dominate at higher temperature (>600°C at strain rate 3 × 10−5 s−1) and have not been taken into account in any texture modelling so far. With increasing absolute temperature (Tabs>), calculated CRSS values (τC>) for the r, f and c systems decrease in a manner which can be described by empirical power law functions of the type τC = A(Tabs)b, where b r〈 2 021〉 and f〈10 1 1〉 systems. The yield stresses for r〈 2 021〉 + and f〈10 1 1〉 + slip were found to be rather insensitive to strain rate, with conventional power law stress exponents > 12. Comparing the present results with previous data, we conclude that two regimes of slip system activity exist, namely a low-temperature regime involving e twinning, slip on r〈 2 021〉 ± and on f〈2 2 01〉 − (positive direction not reported), and a high-temperature regime with r〈 2 021〉 ± , f〈10 1 1〉 ± and c〈a〉 slip. This slip system transition occurs at T ∼ 400°C at strain rate 10−4−10−5 s−1, and is expected to be associated with one or more texture transitions. The results point to a clear need for renewed texture modelling of calcite polycrystals.

On estimating the strength of calcite rocks under natural conditions

Abstract Field studies of calcite mylonites often document microstructures produced by dislocation creep. In contrast, flow laws derived from experiments predict that calcite rocks should deform mostly by diffusion creep during tectonic processes. To investigate this apparent discrepancy, we compare stresses estimated by microstructural piezometers to those obtained by extrapolation of experimentally derived flow laws. Considering shear zones from different geological settings, a clear trend is observed of increasing recrystallized grain size with increasing temperature. However, there is a large spread in grain size and associated stress. Because separate flow laws have been defined for various different marbles and limestones, the strengths predicted for a given set of conditions differ significantly. The stress estimates based on the piezometers and strength extrapolated from the various experimentally derived dislocation creep flow laws agree qualitatively, but no single flow law predicts all the palaeostress estimates. Even if experimental data are disregarded, the field observations are not consistent with a hypothetical law for Coble creep; they are consistent with a power law for dislocation creep, but only if the material constants are different from those currently determined in laboratory experiments.

Slip systems in calcite single crystals deformed at 300–800°C

In an attempt to resolve questions recently raised regarding the principal high-temperature slip systems in calcite, optical quality single crystals have been uniaxially compressed at 300–800°C and at a constant strain rate of ∼ 3×10−5 s−1. In addition, a single strain rate cycling test was performed at 650°C. The tests were all carried out with the compression direction parallel to [224⁻3], which lies at ∼30° to the c axis and makes angles of 52° and 23° with the poles to two rhombohedral (r) planes. Axial strains of 5–16% were achieved in the tests. The stress-strain curves obtained showed three-stage hardening behavior, while the strain rate cycling data showed flow stresses to be rather insensitive to strain rate with empirical power law fits yielding a conventional stress exponent of 22–30 at strains ≥ 5%. The active glide systems were identified by slip line analysis. Slip on r in the so-called negative sense was found to be an important deformation mechanism across the entire range of temperatures investigated, while slip on a single f system in the negative sense became important at 650°C and above. The active f slip direction was of type, confirming the existence of a new set of f slip systems, namely, f , as opposed to the generally accepted f systems. In addition, clear evidence was found for significant slip on the basal (c) plane at temperatures above 600°C, probably in the 〈a〉 direction. By comparison with earlier data on crystals from the same batch, no evidence was found for significant strength asymmetry on the r and f slip systems in the positive and negative senses. Notably, the presently observed f and c sup systems have not been taken into account in previous modelling studies of plasticity and texture (i.e., crystallographic preferred orientation) development in calcite rocks, and r slip is usually taken as stronger in the positive than negative sense. Our results therefore imply a need for renewed modelling work on calcite, particularly regarding texture development at relatively high temperatures.

Steady state dislocation densities in experimentally deformed calcite materials: Single crystals versus polycrystals

The theoretical relationship between dislocation density ρ and applied stress σ of the type σ ∝ ρ0.5 is an essential part of many microphysical models for dislocation dynamics and creep. Thus, application of these microphysical models requires demonstration of this relation. In an attempt to determine the relation between ρ and σ for calcite, uniaxial compression tests were carried out on optical quality single crystals, at temperatures of 550–800°C and strain rates of 3 × 10−4–3 × 10−8 s−1. The tests were performed with the compression direction parallel to [4041] (i.e., parallel to the intersection of two cleavage rhombs). Earlier data on crystals from the same batch already showed that, at the imposed conditions, steady state flow occurs by slip on the r- and f-glide systems, hence well within the dislocation creep regime. Dislocation densities measured by transmission electron microscopy achieved steady state values by ∼2% strain. The steady state dislocation density can be related to the flow stress according to the empirical relation σ = 10−6.21(±0.86) ρ0.62(±0.07) (σ in MPa, ρ in m−2) in close agreement with the theoretically expected relation. Dislocation densities measured in experimentally deformed calcite polycrystals (previous and present studies) match the single-crystal data at high stress (>40 MPa) but deviate from them toward low stress. The deviation appears to be more pronounced if the polycrystal has a smaller grain size. This can be explained using a theory of nonhomogeneous deformation in which strain incompatibility at grain boundaries is accommodated by “geometrically necessary dislocations”. The contribution of these dislocations to the internal stress of the material (hence to the applied stress required for deformation at a given rate) is significant if the grain size is small. Consequently, a comparison of dislocation creep behavior of calcite materials with microphysical models based on dislocation dynamics should take into account the possible influence of grain size if stress levels are relatively low.

The influence of dynamic recrystallization on the grain size distribution and rheological behaviour of Carrara marble deformed in axial compression

Abstract Strain localization and associated rheological weakening are often attributed to grain size reduction resulting from dynamic recrystallization. Most studies investigating rheological changes due to dynamic recrystallization regard recrystallized grain size as a single value that is uniquely related to stress during steady-state deformation. However, rock materials invariably exhibit a grain size distribution with distribution parameters that may be altered by dynamic recrystallization during transient deformation, affecting the rheological behaviour. This study aims to investigate the effect of deformation conditions on the evolution of grain size distribution and rheological behaviour during dynamic recrystallization in the approach to steady state. To study this, we have deformed Carrara marble to natural strains of 0.15–0.90 in axial compression at temperatures of 700–990°C, stresses of 15–65 MPa, strain rates of 3.0 × 10−6–4.9 × 10−4 s−1 and a confining pressure of 150 or 300 MPa, and analysed the grain size distribution of each sample. The results show that during dynamic recrystallization, grain size distributions evolve by a competition between grain growth and grain size reduction. The relative importance of grain-size-sensitive creep increases as the average grain size is reduced with strain. Minor weakening is observed, which is probably insufficient to cause strain localization in nature.

Current issues and new developments in deformation mechanisms, rheology and tectonics

Abstract We present a selective overview of current issues and outstanding problems in the field of deformation mechanisms, rheology and tectonics. A large part of present-day research activities can be grouped into four broad themes. First, the effect of fluids on deformation is the subject of many field and laboratory studies. Fundamental aspects of grain boundary structure and the diffusive properties of fluid-filled grain contacts are currently being investigated, applying modern techniques of light photomicrography, electrical conductivity measurement and Fourier Transform Infrared (FTIR) microanalysis. Second, the interpretation of microstructures and textures is a topic of continuous attention. An improved understanding of the evolution of recrystallization microstructures, boundary misorientations and crystallographic preferred orientations has resulted from the systematic application of new, quantitative analysis and modelling techniques. Third, investigation of the rheology of crust and mantle minerals remains an essential scientific goal. There is a focus on improving the accuracy of flow laws, in order to extrapolate these to nature. Aspects of strain and phase changes are now being taken into account. Fourth, crust and lithosphere tectonics form a subject of research focused on large-scale problems, where the use of analogue models has been particularly successful. However, there still exists a major lack of understanding regarding the microphysical basis of crust- and lithosphere-scale localization of deformation.

High-temperature deformation of calcite single crystals by r+ and f+ slip

Abstract Optical quality calcite single crystals have been uniaxially compressed at constant strain rates and temperatures (T) in the range 3 × 10−4 to 3 × 10−7 s−1 and 550–800°C respectively. The tests were performed with the compression direction parallel to [4041], i.e. parallel to the intersection of two cleavage rhombs. At strains above 1% strain, steady state flow was observed at T ≥ 600°C. The flow stresses at these temperatures were found to be rather insensitive to strain rate, and can be empirically described by a power law creep equation with a stress exponent ranging from c. 13 at 600°C to c. 9.5 at 700–800°C. The active glide systems were identified by slip line analysis. The crystals were found to deform by e-twinning at T < 600°C, and by slip on a single r<2021> system plus a single f system in the so-called positive sense at T ≥ 600°C. The effective slip direction on the active f-plane was of <1011> type rather than the <0221> type reported previously. The observed creep behaviour in the slip dominated regime has been compared with microphyical models. The deformation behaviour seems best explained by cross slip or glide-controlled creep models, or a combination of these.

Electron backscattered diffraction as a tool to quantify subgrains in deformed calcite

In this work, we investigated processing methods to obtain subgrain sizes from electron backscattered diffraction data using samples of experimentally deformed calcite (CaCO3) polycrystals. The domain boundary hierarchy method, based on area measurements of domains enclosed by boundaries larger than a given misorientation angle, was applied to these calcite samples and was found to be limited by: (i) topological problems; (ii) undersampling of large grains; and (iii) artefacts caused by nonindexing. We tested two alternative methods that may reduce the problems: (i) the measured linear intercept hierarchy method, based on measurements of linear intercept between boundaries having larger misorientations than a given minimum angle; and (ii) the calculated linear intercept hierarchy method, based on the total length of boundaries having misorientations larger than a given minimum angle. The measured linear intercept hierarchy method was found to produce results more representative for the microstructure than the calculated linear intercept hierarchy method, because the calculated linear intercept hierarchy method has a significant uncertainty related to the grid‐based nature of the measurements. Preliminary results on calcite suggest that the measured linear intercept hierarchy method is related, in a complex way, to deformation conditions such as stress, strain and temperature as well as to the characteristics of subgrain rotation and grain boundary migration processes.

Influence of deformation conditions on the development of heterogeneous recrystallization microstructures in experimentally deformed Carrara marble

Abstract Recrystallized grains are potentially useful as indicators of palaeostress in naturally deformed rocks, providing that well-calibrated relationships (palaeopiezometers) exist between the recrystallized grain size and stress. Rocks can exhibit microstructures that are heterogeneous, that is, containing recrystallized as well as deformed grains, and showing subgrains within grains that differ in size and character from the grain core to the mantle. Previous studies on palaeopiezometers only rarely took into account such heterogeneous microstructure. We used electron backscattered diffraction (EBSD) to accurately quantify the heterogeneous microstructures in experimentally deformed Carrara marble (flow stress 15–85 MPa, temperature 700–990 °C and natural strain 0.15–0.90). The sizes of bulges, recrystallized grains and deformed grains have been measured. We found that the overall character of the microstructures varies as a function of deformation conditions. In heterogeneous samples showing core-mantle microstructures, the sizes of the bulges and recrystallized grains are independent of strain and show an inverse dependency on stress. The recrystallized grains have been found to nucleate at grain boundary bulges. Our study illustrates that very different microstructures may develop in relation to the complexity of the recrystallization mechanisms. We therefore suggest that piezometers should be calibrated and applied for a single type of overall microstructure.