Geological Strain Rates Research Articles

Strain partitioning and deformation mode analysis of the normal faults at Red Mountain, Birmingham, Alabama

In a low-temperature environment, the thin-section scale rock-deformation mode is primarily a function of confining pressure and total strain at geological strain rates. A deformation mode diagram is constructed from published experimental data by plotting the deformation mode on a graph of total strain versus the confining pressure. Four deformation modes are shown on the diagram: extensional fracturing, mesoscopic faulting, incipient faulting, and uniform flow. By determining the total strain and the deformation mode of a naturally deformed sample, the confining pressure and hence the depth at which the rock was deformed can be evaluated. The method is applied to normal faults exposed on the gently dipping southeast limb of the Birmingham anticlinorium in the Red Mountain expressway cut in Birmingham, Alabama. Samples of the Ordovician Chickamauga Limestone within and adjacent to the faults contain brittle structures, including mesoscopic faults and veins, and ductile deformation features including calcite twins, intergranular and transgranular pressure solution, and deformed burrows. During compaction, a vertical shortening of about 45 to 80% in shale is indicated by deformed burrows and relative compaction of shale to burrows, about 6% in limestone by stylolites. The normal faults formed after the Ordovician rocks were consolidated because the faults and associated veins truncate the deformed burrows and stylolites, which truncate the calcite cement. A total strain of 2.0% was caused by mesoscopic faults during normal faulting. A later homogenous deformation, indicated by the calcite twins in veins, cement and fossil fragments, has its major principal shortening strain in the dip direction at a low angle (about 22°) to bedding. The strain magnitude is about 2.6%. By locating the observed data on the deformation mode diagram, it is found that the normal faulting characterized by brittle deformation occurred under low confining pressure (< 18 MPa) at shallow depth (< 800 m), and the homogenous horizontal compression characterized by uniform flow occurred under higher confining pressure (at least 60 MPa) at greater depth (> 2.5 km).

Scaling of Newtonian and non-Newtonian fluid dynamics without inertia for quantitative modelling of rock flow due to gravity (including the concept of rheological similarity)

Scale model theory for constructing dynamically scaled analogue models of rock flowing in the solid state has until now assumed that the natural and model flows were both viscous. In viscous flows, at the very low Reynolds numbers ( Re ⪡ 1) common in solid rocks, geometrical similarity is sufficient to achieve dynamic similarity between a homogeneous material (scale) model and its natural prototype. However, experiments on the rheology of natural rocks suggest that they flow predominantly as non-Newtonian strain rate softening materials at the characteristic geological strain rate 10 −14 s −1. Non-dimensionalisation of both the equation of motion and the constitutive flow law of non-Newtonian flows is carried out to investigate what criteria are required to achieve dynamic similarity. It is shown that dynamic similarity of non-Newtonian flows at low inertia (e.g., a rock with Re ⪡ 1 and its model analogue) can only be attained if the steady-state flow curves of the model materials and the various rocks in the prototype have mutually similar shapes and slopes, and if these flows operate on similar parts of their respective flow curves. We term this the requirement of rheological similarity. Dynamic similarity of low inertia flows ( Re ⪡ 1) in non-Newtonian continua is achieved if they are rheologically and geometrically similar. Additional criteria for dynamic similarity of low inertia flows in inhomogeneous media (with Newtonian or non-Newtonian subregions, or both) are formulated in section 5. Scaling of thermal properties is not included. Steady-state flow curves of common rocks are compiled in log stress-log strain rate space together with analogue materials suitable for modelling of solid state rock deformation. This compilation aids the selection of model materials with flow curves geometrically similar to those of rocks in the prototype. Laboratory scale models of rock flow should generally be constructed of materials which strain rate soften during flow at the convenient shear rate 10 −2 s −1.

Formula omitted] in quartz from subsolidus deformed granite

The slip behaviour of quartz from a granite and granitic veins during subsolidus high temperature conditions (700°–800°C) of deformation is studied by lattice preferred orientation (LPO) and microstructural techniques. LPOs with a point maximum of [ C] axes parallel to the shear direction, which is close to the stretching lineation, are presented and interpreted with the aid of light and electron microscopy in terms of [ C] as the dominant slip direction during plastic deformation. Microscopy of such samples reveals the presence of (0001) tilt boundaries and free [0001] Burgers vector dislocations in edge orientations. A change in LPO in a decreasing temperature environment from [ C] axes parallel to the shear direction to [ C] axes normal to the shear direction documents a fabric transition from the rare [ C] slip to the more common < a> slip fabric. It is concluded that conditions of high temperature and partial pressure of water are required to initiate dominant [ C] slip during deformation at geological strain rates.

A dynamical model of lithosphere extension and sedimentary basin formation

Convection in the upper mantle can give rise to normal stresses on the base of the continental lithosphere that may cause localized elevation of its surface and extensional deviatoric stresses. This possibility is investigated assuming homogeneous, biaxial strain in a continental lithosphere whose strength is governed by a combination of brittle failure and power law creep in the crust and by brittle, power law, or Dorn law behavior in the mantle. For a given geotherm and for rheologies based on current laboratory data, the lithosphere responds to convection‐induced uplift in one of three ways, depending primarily on the magnitude of the driving stresses. These regimes are as follows: (1) When the driving stress exceeds a threshold value, the resulting strain rates are high enough (greater than about 3×10−16 s−1) that the lithosphere strains almost isothermally, its effective rheology is strain thinning, and it undergoes accelerating extension. The magnitude of the dynamic uplift required to produce the threshold value of the driving stress depends on the geotherm (characterized here by the Moho temperature) and varies from about 1 km for a Moho temperature of 700°C to around 3 km for a Moho temperature of 550°C; an uncertainty of at least 100°C is attached to these temperatures owing to the inaccuracies in extrapolating laboratory data to geological strain rates. (2) At stress levels due to less than about half of the critical uplift, extensional strain is negligible. (3) At intermediate stress levels, moderate uplift produces extension that is bounded by strength increases due to cooling of the ductile portion of the lithosphere during extension.

Earthquakes in the ductile regime?

Pseudotachylytes from a crustal scale shear zone in Central Australia have developed in a cyclical manner: once developed, an individual pseudotachylyte is deformed in a ductile manner, only to be overprinted at a later stage by a new generation of pseudotachylytes. Such cyclic generation and deformation of pseudotachylyte has been interpreted in the past as representing conditions at the brittleductile transition; a different interpretation, however, is presented here. It is proposed that psuedotachylytes and associated ultramylonites can develop entirely within the ductile regime as ductile instabilities. Such instabilities are different in nature to those previously discussed at length in the geophysical literature but are identical in principle with the instabilities that develop for velocity-weakening frictional behavior in spring-slider systems. At a given strain rate a critical temperature,T c, is defined, at which the transient work hardening equals the product of stress relaxation due to a thermal fluctuation and the heat generated by shearing. A necessary condition for ductile instability at a given strain rate is that the temperature is belowT c; then the rate of change of stress with respect to strain is negative. An additional requirement is that this rate of change exceeds, in magnitude, the effective elastic stiffness of the loading system. Ductile instabilities are marginally possible at geological strain rates in quartzites but are possible at mid-crustal temperatures in other rock types. On the basis of these observations a new interpretation is presented for the base of the seismogenic zone in crustal regions.

Rock mechanics observations pertinent to the rheology of the continental lithosphere and the localization of strain along shear zones

Emphasized in this paper are the deformation processes and rheologies of rocks at high temperatures and high effective pressures, conditions that are presumably appropriate to the lower crust and upper mantle in continental collision zones. Much recent progress has been made in understanding the flexure of the oceanic lithosphere using rock-mechanics-based yield criteria for the inelastic deformations at the top and base. At mid-plate depths, stresses are likely to be supported elastically because bending strains and elastic stresses are low. The collisional tectonic regime, however, is far more complex because very large permanent strains are sustained at mid-plate depths and this requires us to include the broad transition between brittle and ductile flow. Moreover, important changes in the ductile flow mechanisms occur at the intermediate temperatures found at mid-plate depths. Two specific contributions of laboratory rock rheology research are considered in this paper. First, the high-temperature steady-state flow mechanisms and rheology of mafic and ultramafic rocks are reviewed with special emphasis on olivine and crystalline rocks. Rock strength decreases very markedly with increases in temperature and it is the onset of flow by high temperature ductile mechanisms that defines the base of the lithosphere. The thickness of the continental lithosphere can therefore be defined by the depth to a particular isotherm T c above which (at geologic strain rates) the high-temperature ductile strength falls below some arbitrary strength isobar (e.g., 100 MPa). For olivine T c is about 700°–800°C but for other crustal silicates, T c may be as low as 400°–600°C, suggesting that substantial decoupling may take place within thick continental crust and that strength may increase with depth at the Moho, as suggested by a number of workers on independent grounds. Put another way, the Moho is a rheological discontinuity. A second class of laboratory observations pertains to the general phenomenon of ductile faulting in which ductile strains are localized into shear zones. Ductile faults have been produced in experiments of five different rock types and is generally expressed as strain softening in constant-strain-rate tests or as an accelerating-creep-rate stage at constant differential stress. A number of physical mechanisms have been identified that may be responsible for ductile faulting, including the onset of dynamic recrystallization, phase changes, hydrothermal alteration and hydrolytic weakening. Microscopic evidence for these processes as well as larger-scale geological and geophysical observations suggest that ductile faulting in the middle to lower crust and upper mantle may greatly influence the distribution and magnitudes of differential stresses and the style of deformation in the overlying upper continental lithosphere.

Constraints on yield strength in the oceanic lithosphere derived from observations of flexure

Summary. The wavelength and amplitude of outer rises seaward of sub-duction zones and arches surrounding islands and seamounts are used to parameterize flexure profiles in terms of the moment and curvature at the first zero crossing. The data show the clear age dependence in the mechanical thickness of the lithosphere up to 60–100Myr. Saturation of moment at large curvature is interpreted in terms of a depth-dependent yield strength for the lithosphere using relations adopted from laboratory experiments of rock deformation. A comparison of theoretical curves with observed moments indicates that old oceanic lithosphere has no long-term strength below about 40 km depth, with no difference between 100 and 165 Myr old crust. Moderate axial loading forces (±200 MPa) can explain most variations in the moment/curvature observations, except in the case of the Kuril Trench which appears anomalous given the age of the crust. Regional tension causes greater variability in moment as compared to regional compression because of the greater slope in the brittle failure envelope under tension. The observations point to a lithosphere weaker than the prediction from experimental deformation of rocks. Of the possible weakening mechanisms, elevated pore-fluid pressure on faults does not predict the correct age dependence and is incompatible with earthquake focal mechanisms. Our favoured explanation is that the activation energy, Q, appropriate for ductile flow at geological strain rates is lower than the values derived from laboratory extrapolations of dry olivine data taken at high temperatures. If recent oceanic geotherms are reliable, Q in the lower lithosphere must be lower than 100kcal mol−1. The method used here is most appropriate for trench profiles with curvatures greater than 10−7m−1. For lower curvatures, such as along seamount profiles, small errors in the curvature estimate cause large changes in rheological parameters.

Constraints on geological strain rates: Arguments from finite strain states of naturally deformed rocks

A summary of known finite strain states is presented; longitudinal strains (1 + e) as measured in many rocks often range from 1 to 40 and 1 to 0.025. The time span available to produce such measurable strains in young orogenic zones seems to be less than 10 m.y., possibly less than 1 m.y., which constrains conventional strain rates into the range of 10−13 s−1 to 10−15 s−1. For both pure and simple shear (the most efficient way and a much less efficient way to accumulate incremental strains, respectively) the ellipticity of the finite strain ellipse increases in a nonlinear manner. Finite strain variations in adjacent layers, which give rise to features such as cleavage refraction, arise with only slight differences in the strain rates within these layers.

Long-term creep experiment of rock with small deviator of stress under high confining pressure and temperature : Tectonophysics, V68, N3–4, 1 Oct 1980, P183–198

Abstract Long-term creep tests of gabbro which have been performed with a maximum bending stress (20 bar) under a high confining pressure (1 kbar) and various temperatures, are described. Methods and techniques used in the experiment are mainly similar to those reported previously by the same authors (Ito and Sasajima, 1980) except for the application of high pressure and temperature. The techniques include the bending system, size and preparation of the sample, and the determination of its deformation by use of interference fringes of Na-D light. In order to measure a very small deformation of creep, intermittent breaks of the application of loading, confining pressure and temperature are necessary, and the creep curve is constructed from the intermittent advance of permanent deformation. The experiment has revealed two strange phenomena : one is a sinuous progress of the creep curve, and the other is that the deformation recovery shows strange behavior after the unloading. These results are discussed in close connection with the mechanism of the “turn back of creep” denoted by Ito and Sasajima (1980). The mean creep curves, at 25°C. 95°C and 150°C, obtained so far lead to viscosities of 1.6 · 10 20 , 1.9 · 10 19 and 4.8 · 10 18 poise, respectively and the maximum strain rates employed in the samples were 4.2 · 10 −14 , 3.6 · 10 −13 and 1.4 · 10 −12 /sec, respectively, which cover the geological strain rate. Although we have only three data points, the logarithm of viscosity is linearly related to the reciprocal of absolute temperature (see Fig. 7), and an activation energy for creep of gabbro is found to be 7.6 kcal/mol. It should be noted that viscosities obtained are considerably smaller than those estimated for the crust and mantle, and that the activation energy is surprisingly smaller than those obtained by high-pressure experiments of rock deformation, which have been carried out under a strain rate larger than 10 −8 /sec.

Long-term creep experiment of rock with small deviator of stress under high confining pressure and temperature

Long-term creep tests of gabbro which have been performed with a maximum bending stress (20 bar) under a high confining pressure (1 kbar) and various temperatures, are described. Methods and techniques used in the experiment are mainly similar to those reported previously by the same authors (Itô and Sasajima, 1980) except for the application of high pressure and temperature. The techniques include the bending system, size and preparation of the sample, and the determination of its deformation by use of interference fringes of Na-D light. In order to measure a very small deformation of creep, intermittent breaks of the application of loading, confining pressure and temperature are necessary, and the creep curve is constructed from the intermittent advance of permanent deformation. The experiment has revealed two strange phenomena : one is a sinuous progress of the creep curve, and the other is that the deformation recovery shows strange behavior after the unloading. These results are discussed in close connection with the mechanism of the “turn back of creep” denoted by Itô and Sasajima (1980). The mean creep curves, at 25°C. 95°C and 150°C, obtained so far lead to viscosities of 1.6 · 10 20, 1.9 · 10 19 and 4.8 · 10 18 poise, respectively and the maximum strain rates employed in the samples were 4.2 · 10 −14, 3.6 · 10 −13 and 1.4 · 10 −12/sec, respectively, which cover the geological strain rate. Although we have only three data points, the logarithm of viscosity is linearly related to the reciprocal of absolute temperature (see Fig. 7), and an activation energy for creep of gabbro is found to be 7.6 kcal/mol. It should be noted that viscosities obtained are considerably smaller than those estimated for the crust and mantle, and that the activation energy is surprisingly smaller than those obtained by high-pressure experiments of rock deformation, which have been carried out under a strain rate larger than 10 −8/sec.

Stress corrosion and the rate-dependent tensile failure of a fine-grained quartz rock

Pre-cracked double torsion specimens of Arkansas Novaculite were deformed (1) in the load relaxation mode, and (2) at a fast cross-head speed using an Instron deformation machine to obtain stress intensity factor ( K I)-crack velocity ( v) data for stress corrosion in liquid water. The fracture toughness ( K Ic) was found to be 1.335 ± 0.075 MN m −3/2. At temperatures from 20°C to 80°C the stress corrosion index, n( v ∞ K n I was 25.1 ± 1.5 and the activation enthalpy for crack propagation was 69.5 ± 1.7 kJ mole −1. The K I-v data at 20°C were used to generate a diagram predicting the influence of strain rate on tensile fracture stress. These predictions were in good agreement with the fracture stress determined by bend experiments in liquid water at 20°C. Both the predictions and the experimental results are consistent with a monotonie reduction in tensile fracture stress from approximately 72 MN m −2 to 39 MN m −2 as strain rate is reduced from 6 · 10 −5 s −1 down to 10 −10 s −1. At strain rates faster than approximately 6 · 10 −5 s −1 stress corrosion does not influence the tensile fracture stress. It is unlikely that Novaculite will exhibit a fundamental fracture stress during deformation at even the slowest geological strain rates.

Shear heating at the Olympos (Greece) thrust and the deformation properties of carbonates at geological strain rates

An example of thermal gradient inversion below a major thrust is described from the carbonates of the Olympos autochthon in northeast Greece. On the basis of several hundred probe analyses, temperatures have been determined across 3 km of structural height using calcite-dolomite geothermometry. The inversion is interpreted in terms of shear heating accompanying the Tertiary emplacement of the overlying metamorphic sheet. Significant heating is restricted to the uppermost 1 km of the Olympos platform, where the carbonates have been deformed partly by steady-state flow. A simple heat-conduction calculation gives an estimate of about 0.6 m.y. for the duration of the shear heating, and geological constraints suggest that the minimum Tertiary movement on the thrust is 15 km, equivalent to a strain rate of 10 −12 s −1 during overthrusting. More detailed numerical modeling shows that the high rates of movement implied by this strain rate are essential to the generation of the inferred thermal profile. An additional requirement of a shear stress of several hundred bars at the thrust suggests that a horizontal compressive stress was necessary to maintain the movement. The shear strength behavior deduced for the Olympos carbonates is in good agreement with the extrapolation to geological strain rates of Heard9s and Heard and Raleigh9s experimental data for the Yule marble.

High-temperature flow of wet polycrystalline enstatite

Previous experiments by Raleigh et al. (1971) have shown that at strain rates of 10 −2.sec −1 to 10 −7.sec −1 only slip occurs in dry enstatite at temperatures above 1300°C and 1000°C, respectively. The present experiments have been conducted on polycrystalline enstatite under wet conditions in this regime where enstatite only slips, polygonizes and recrystallizes. Slip occurs throughout the whole regime on the system (100)[001] and at strains greater than 40% the system (010)[001] is observed. Polygonization and intragranular recrystallization begin at about 1300°C and 10 −4.sec −1 and the orientation of these neoblasts is host-controlled. At lower strain rates intergranular neoblasts develop and their fabric is one of [100] maximum parallel with σ 1 and [010] and [001] girdles in the σ 2 = σ 3 plane, similar to those in natural enstatite tectonites. Dislocation substructures of experimentally deformed enstatite have been examined by transmission electron microscopy. The samples were deformed within the field in which slip polygonization and recrystallization are the dominant deformation mechanisms. Samples within this regime have microstructures that are characterized by stacking faults and partial dislocations. Under the conditions of steady-state flow in olivine, these microstructures inhibit the operation of recovery mechanisms in enstatite. Other samples deformed within the polygonization and recrystallization field have microstructures that confirm the optical observations of intragranular and intergranular growth of neoblasts. It is suggested that the former result from strain-induced tilt of subrains, whereas the latter may result from bulge nucleation into adjacent subgrains. Mechanical data from constant strain-rate experiments at steady state, stress relaxation and temperature-differential creep tests are best fit to a power-law creep equation with the stress exponent, n~3 and the apparent activation energy for creep, Q~65 kcal/ mole. Extrapolation of this equation to a representative natural geologic strain rate of 10 −4. sec −1, over the temperature interval 1000–2000°C, gives an effective viscosity range of 10 20–10 18 poise and stresses in the range of 7-0.1 bar, respectively. Comparison with corrected wet-olivine mechanical data (Carter, 1976) over the same environment indicates that olivine is consistently the weaker of the two minerals and will recrystallize whilst enstatite will only slip and kink, thus accounting for the different habits of olivine and enstatite in ultramafic tectonites.

Viscosity of the upper mantle as non-Newtonian fluid.

The problem of isostatic recovery of incompressible and highly viscous fluid is considered for the case of non-Newtonian fluid which satisfies the following relation between the strain rate e and the stress difference τ:e∝τn (n>1). Because of nonlinearity of the equations of motion, it is impossible to solve them analytically. In this paper, therefore, the variational method is applied and a relation between the relaxation time of isostatic recovery τr and the wave length λ is obtained approximately. The case when the top surface is free and the bottom surface is rigid is considered. From the theoretical results and the postglacial uplife data of Fennoscandia and Laurentide, the upper mantle can be understood as a non-Newtonian fluid in which the strain rate is approximately proportional to the third power of the stress difference (n=3). This is in accordance with the results of WEERTMAN (1970), STOCKER and ASHBY (1973) and so on. The effective viscosity of the upper mantle is found to be η=5×1011e-2/3 poises, where the unit of e is sec-1. For the geological strain rate, say 10-15sec-1, the apparent viscosity is 5×1021 poises. This value is of the same order as the results of previous workers.

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.

Pressure solution and Coble creep in rocks and minerals: a review

A brief review of research on pressure solution is given. The mechanisms of pressure solution and Coble creep are discussed. Deformation by diffusive mass transfer processes is generally accompanied by grain boundary sliding and this will have important effects on the textures and microstructures produced during deformation. Experiments using relaxation testing seem promising in allowing access to the slow strain rates necessary to observe pressure solution phenomena. The thermodynamics of non-hydrostatically stressed solids is discussed and an analysis of possible diffusion paths in rocks is presented. Evaluation of theoretical rate equations for pressure solution and Coble creep indicates that pressure solution in fine-grained quartz and calcite rocks may give rise to geological strain rates at temperatures from 200–350°C. Coble creep is expected to give rise to geological strain rates in fine-grained galena at low temperatures and also in fine-grained calcite rocks at temperatures around 350°C. The chemistry of natural rock pressure solution systems is expected to have significant effects and needs further detailed study. Further research is needed to elucidate the nature and role of grain boundaries during diffusive mass transfer. Pressure solution phenomena are important in the compaction behaviour of some petroleum reservoir rocks and perhaps in some faults where sliding is accommodated by pressure solution.

Stress in the lithosphere: Inferences from steady state flow of rocks

Mechanical data and flow processes from steady state deformation experiments may be used to infer the state of stress in the lithosphere and asthenosphere. Extrapolations of flow equations to a representative geologic strain rate of 10−14/sec. for halite, marble, quartzite, dolomite, dunite and enstatolite are now warranted because the steady state flow processes in the experiments are identical to those in rocks and because the geotherms are reasonably well established. More direct estimates are obtained from free dislocation densities, subgrain sizes and recrystallized grain sizes all of which are functions only of stress. Using the last of these techniques, we have estimated stress profiles as a function of depth from xenoliths in basalts and kimberlites, whose depths of equilibration were determined by pyroxene techniques, from four different areas of subcontinental and suboceanic upper mantle. The results are similar and indicate stress differences of about 200 to 300 bars at 40 to 50 km, decaying to a few tens of bars at depths below 100 km. These stresses are reasonable and are in accord with extrapolations of the mechanical data provided that allowance is made for a general increase in strain rate and decrease in viscosity with depth.

Discussion of rates of deformation

D r . I. R. Q ureshi writes the following comments on the recent paper by Price (this Journal 131, 553–75): 1. On the average geological strain rate of 3.10 −14 S −1 , a strain of 95% would be produced in a period of one million years and not 10% as is suggested on p.554. I am also concerned that a strain of 10% is considered ‘almost infinitesimal’ by the author. 2. Figures given in Table 2 show that energy varied as the cube of the diameter rather than ‘the diameter varied as the cube of the explosive energy’ (p. 559). D r N. J. P rice and the editors are grateful to Dr Qureshi for drawing their attention to these two errors: (1) In lines 1–3, p. 554, the quoted strain-rate would produce a 10 per cent strain in approximately 10 5 years and not 10 6 years as stated. The correct time for such a strain to develop at the corresponding strain rate is correctly given in Table 1 of the paper. (2) Lines 6–7 from the bottom of p. 559 should read “the diameter varies as the cube-root of the explosive energy”. With reference to his comment and surprise that I should say that 10 per cent strain is “almost infinitesimal” .... I deliberately used this provocative phrase to indicate that a 10 per cent strain is, geologically speaking, very small. However, one could also point out that one of the assumptions of infinitesimal strain theory is that de × de is

Steady state flow of rocks

Experimentally determined steady state flow properties and processes of important rock‐forming materials are reviewed in reference to those of metals and ceramics and to physical conditions in the earth's crust and upper mantle. Dislocation motion controls the creep rate over a wide range of steady state conditions in the experiments, and the observation that the same processes have operated during natural deformations permits extrapolations of the mechanical data. Under these conditions, strain rate is related to stress raised to the power 2–9, depending on the material and conditions, and the resulting flow stresses and equivalent viscosities are compared at a representative geological strain rate of 10−14/s. The results are applied in brief discussions of diapirism, growth of folds, and flow in the upper mantle.

Experimental deformation of natural chalcopyrite at temperatures up to 300 degrees C over the strain rate range 10 (super -2) to 10 (super -6) sec (super -1)

Natural chalcopyrite from two localities was experimentally deformed in compression under 1.5 kilobars of confining pressure at temperatures up to 300 degrees C over the strain rate range 10 (super -2) to 10 (super -6) sec (super -1) . At 25 degrees and 100 degrees C the stress-strain behavior was relatively independent of temperature and strain rate and the deformation proceeded predominantly by intragranular and grain-boundary fracturing (microfracturing). From 150 degrees to 300 degrees C strength decreased with increasing temperature and decreasing strain rate, and the dominant mode was intragranular slip and deformation twinning. The higher temperature behavior of the two different experimental materials was similar in spite of differences in impurity and grain size. The low-temperature microfracturing strength, however, was higher in the finer grained, less pure chalcopyrite.Extrapolation of the experimental data for steady state plastic flow to representative geological strain rates indicates stress differences in the order of 250 to 1,000 bars at 100 degrees C, 80 to 500 bars at 200 degrees C, and 30 to 300 bars at 300 degrees C. These values are not expected to vary with confining pressure. Syntectonic recrystallization might lower these stress differences even further.Chalcopyrite is expected to flow plastically in the crust except for very shallow conditions where low confining pressures and temperatures and relatively high stress differences prevail.In etched polished sections evidence of naturally deformed chalcopyrite can be provided by slip lines, deformation twins, subgrains, high-energy serrated grain boundaries, distorted twin boundaries, and elongation (straining) of grains. Such evidence may be partially or wholly obliterated by subsequent recrystallization.