Plastic Flow In Crystals Research Articles

Strain accommodation about strike-slip fault discontinuities in granitic rock under brittle-to-ductile conditions

Brittle and ductile structures adjacent to fault terminations and echelon fault steps of left-lateral strike-slip faults in the Lake Edison Granodiorite of the central Sierra Nevada, California are related to stress perturbations caused by fault slip. The structures associated with fault terminations change from dilatant splay fractures only, to splay fractures and ductile fabrics on opposing sides of the fault, to ductile fabrics ahead of the fault with decreasing distance from a younger neighboring pluton and, presumably, with increased temperatures. The distributions of deformation mechanisms correlate with the inferred local magnitudes and spatial distributions of the maximum tensile stress, the mean stress, and the maximum shear stress. Displacements along the faults are transferred across echelon stepovers by mineralized dilatant fractures in extensional steps. To accommodate slip transfer across contractional steps, rock apparently was squeezed vertically out of the step by ductile flow; concentrations of mobile and immobile elements indicate that diffusive mass transfer was not significant. Increased mean stress in contractional steps apparently enhanced crystal-plastic flow of quartz. A flow law that includes a pressure effect through correlation with pressure-dependent solidus temperatures is more successful than other experimentally derived flow laws in predicting the observed distribution of ductile fabrics.

Preferred crystallographic orientation development during the plastic and superplastic flow of calcite rocks

Grain-size sensitive flow of fine-grained rocks, such as are often found in mylonitic shear zones, is commonly inferred to be accomplished by grain-boundary sliding, so that no preferred crystallographic orientation is expected to develop, pre-existing fabrics are supposed to weaken and grain shapes to remain equant. However, many fine-grained mylonites commonly exhibit marked preferred crystallographic orientation, whilst displaying a stable but weak grain-shape fabric. We have examined preferred crystallographic orientation and shape fabric development during the flow of synthetic, ultrafine-grained (<10 μm), hot-pressed calcite rocks, Solnhofen limestone and Carrara marble. Samples were deformed experimentally both in extension and compression, under conditions encompassing the transition from grain-size insensitive crystal-plastic flow to grain-size sensitive superplastic flow (300– >700°C). The strong crystal-plastic fabric develops more slowly but is not eliminated through the broad transition into true superplastic flow. This is interpreted to reflect an important role of intracrystalline plasticity in the accommodation of grain-boundary sliding. From experiments designed to investigate the extent of survival or modification of an initial twinning fabric through recrystallization and subsequent hot working, it was shown that although the microstructure could be totally annealed, the early formed fabric survived even subsequent high-temperature crystal-plastic or superplastic flow. This may explain the frequent occurrence of strong, low-temperature fabrics in calcite ultramylonites.

Fluid-melt-rock interaction in mafic eclogites and coesite-bearing metasediments: Constraints on volatile recycling during subduction

The question as to whether the metasomatizing-slab agent needed to form island-arc magmas is an aqueous fluid or a hydrous melt requires a knowledge of fluid-melt-rock interaction during high-pressure low-temperature metamorphism. In the Western Alps, typical “anhydrous” mafic eclogites (Monviso Massif) and coesite-bearing metasediments (Dora-Maira Massif) have experienced a prograde P- T path characteristic of a mature (cold) subduction zone. Microstructural, petrologic, geochemical and fluid inclusion studies show that fluid flow was limited during eclogite and high-grade blueschist facies metamorphism. Most of the fluids were driven off the rocks at pressures lower than 1 and 1.6 GPa, respectively. With increasing pressure and temperature, the remaining fluid phase was released during crystal plastic flow processes or devolatilisation reactions but retain the host rocks to form veins, partial melts or dense hydrous silicates. Tectonic erosion at modern convergent margins delivers large amounts of terrigenous sediments (KMASH system) in subduction zones. In contrast to the basalt and peridotite systems, the KMASH system is characterized by a wide range of pressure-sensitive reactions which allow the reconstruction of dehydration/hydration depths in the subducted slab. Independently of the thermal structure of subduction zones, terrigenous sediments will begin to melt at pressures < 2 GPa. The melt phase can absorb tremendeous quantities of water and represent major sinks for devolatilisation fluids. Dense hydrous silicates will form in any subducted sediments at all depths. These silicates can store significant amount of water in their structure. In the subducted oceanic crust and upper mantle, heterogeneous distribution of fluids inherited from hydrothermal alteration at mid-ocean ridges will cause contemporaneous dehydration and hydration reactions on a local scale rather than large-scale fluid infiltration in the overlying mantle wedge. The situation where a cold, competent and fluid-rich subducted slab is bounded above by a hot, relatively weak and anhydrous material is likely to act against buoyant rise of devolatilisation fluids by forcing the fluids to flow downwards. At sub-arc depths (50 ± 10 to 80 150 km ) and for any geothermal gradient, continuous internal buffering of volatile activities will retain the fluid phase in the slab. This is in contrast with shallow, sub-forearc depths (20 to 50 ± 10 km), where tectonic vein arrays, localized thrust faults, serpentine diapirs, mud volcanoes and boninite magmas attest to the release of large volume of fluids into the overriding mantle wedge.

Brittle and semibrittle deformation of synthetic marbles composed of two phases

To investigate the influence of rigid, second‐phase particles on the strength of marble in the semibrittle deformation regime, we performed conventional triaxial mechanical tests on synthetic samples formed by hot isostatic pressing two‐phase aggregates of fine‐grained calcite and 5–20 wt % of either SiC, Al2O3, or SiO2. The samples were tested at strain rates of 10−5 s−1 and at room temperature over a range of pressures from 5 to 300 MPa. Microstructures were studied using optical microscopy, scanning electron microscopy (SEM), and transmission electron microscopy (TEM). Adding rigid inclusions with incoherent matrix/particle interfaces increased the range of pressure over which the transition between localized brittle failure and crystal plastic flow occurred. The strength of the pure marbles was inversely proportional to porosity between 0 and 8%. In the brittle field, two‐phase aggregates are generally 50 MPa weaker than pure marbles of similar porosity. Second phases and associated cracklike porosity tend to distribute brittle deformation in our samples. Aggregates with 20% inclusions show stable cataclastic flow at 5 MPa confining pressure. At the same pressure, pure samples fail catastrophically along a distinct fault. At higher pressure in the semibrittle field, the strengths of pure and two‐phase aggregates converge. The deformation resistance of the material containing particles is consistently higher than that of the pure samples. TEM observations also suggest an additional contribution to the deformation resistance and hardening rate by interactions between the dispersed particles and crystal defects.

結晶の塑性流動と転位過程

結晶の塑性流動と転位過程

Enrichment of CO 2 in fluid inclusions in quartz by removal of H 2O during crystal-plastic deformation

Ductile strain-induced leakage of H 2O from mixed CO 2 + H 2O fluid inclusions in quartz is proposed as a mechanism for producing occurrences of pure CO 2 fluid inclusions in metamorphic rocks. The H 2O needed for hydrolytic weakening of quartz under stress may be provided by the H 2O in fluid inclusions. With dislocation creep, as dislocations nucleate on the walls of fluid inclusions or intersect them, H 2O can be transported with the dislocations from the inclusion to the grain boundaries. The process should continue so long as there is stress on the host quartz and the inclusion contains H 2O. The H 2O taken to the grain boundaries would, due to its wetting properties, be wicked out along the grain boundaries. If the H 2O is totally removed from an inclusion by a flux of dislocations through the quartz during the crystal-plastic flow, then a residual inclusion bearing components other than water should remain. A mixed CO 2 + H 2O inclusion would, as a consequence of the process, become a pure CO 2 fluid inclusion. During dynamic recrystallization, the CO 2 would collect at grain boundary triple junctions and, following grain boundary migration, would become incorporated into the recrystallized quartz as fluid inclusions. This mechanism of generating pure CO 2 inclusions could result in CO 2 fluid inclusions having densities appropriate for the pressure—temperature conditions during deformation. Using estimates of temperature of deformation, the total confining pressure during deformation could be determined from the density of the CO 2 fluid in these inclusions.

An attempt at a soliton approach to plastic flow of crystals

In order to eliminate the discrepancy between theoretical and experimental data on the low-temperature dependence of the strain rate sensitivity in copper single crystals, a rough quantum-mechanical approach is proposed. Its general idea consists in that the dislocation kinks are discussed in terms of solitons and the steady state of plastic flow is considered as a soliton gas governed by Bose-Enstein statistics. Particularly, in order to apply this approach to the plastic flow of fcc crystals both a very simplified soliton mechanism for partial dislocation construction and a very simplified quantum-mechanical approach to the formation of the jog on the gliding dislocation are proposed. The calculations results obtained from the simple model are in quite good agreement with those obtained experimentally by Basinski.

The mechanisms of plastic relaxation in single-crystal deformation

Plastic flow in crystals is never quite uniform. Plastic strain gradients develop and internal stresses build up as deformation progresses. In the last few years it has been suggested that specific dislocation mechanisms of plastic relaxation relieve these stresses and create the microstructure. These mechanisms are described here. The first mechanism to operate is cross-slip, which lays down the framework of dislocation cells. The second mechanism is secondary slip, which completes the formation of relatively stress-free dislocation cells and subdivides the crystal into mutually misoriented regions. The third mechanism, which operates when the microstructure contains cells, is local slip within dislocation-rich load-bearing cell walls. Depending on the orientation of the cell walls, this third mechanism produces either work hardening or dynamic recovery.

The concepts of latent hardening and strain hardening in metallic single crystals

Starting from the rate independent theory of the single crystal plasticity (Schmid law), one here tries to both give the most realistic description of the concept of intracrystalline latent hardening—or hardening anisotropy—through the analysis, at the microstructural scale of the dislocation densities, of various and complementary experimental data, and to underline the excessive restriction introduced by the classical assumption of pure strain hardening in the determination of the most general single crystal hardening variation law for the wider range of loading processes. These developments about the microstructural features of single crystal hardening, involving mobile and nonmobile dislocation density evolutions (multiplications) and interactions, are correlated at the macroscopic scale of the slip systems with a strain and load process and orientation hardening law which is shown on few examples to give a better fit with observed behaviour than pure strain hardening. A third part shows that, even starting from a rate dependent assumption for the single crystal plastic flow, the present analysis of latent hardening remains basically unchanged. It shows too that the load process and orientation effect on hardening, which is implicitly present in such approaches although introduced according to specific assumptions on the correlations between slips and dislocation densities, is one of the most significant features in the single crystals hardening evolution during plastic deformation, whatever the theoretical frame is chosen.

Structural levels of translational-rotational deformation of crystals in a complex stress state

A theory of deformation is developed on the basis of the concept of the multilevel development of plastic flow of crystals, with the participation of rotation. The influence of the loading conditions on the complex trajectories in stress space and in time on the crystal deformation is analyzed. The rheological properties of the material in active deformation over two-element loading trajectories with an orthogonal discontinuity are investigated. Considerable attention is paid to the investigation of the influence of various loading trajectories on the creep in isothermal conditions.

Conference Report

Report of meeting held by the Tectonic Studies Group at the Department of Geological Sciences, University of Birmingham on 3 November 1982. The transition from fracture-dominated deformation at high levels in the crust to flow-dominated deformation as temperature and confining pressure increase with depth is a concept familiar to all geologists. Nevertheless, the nature of this transition, and the ways in which ‘brittle’ and ‘ductile’ processes interact and compete at different levels in the lithosphere, are still poorly understood. The ten papers presented at the meeting addressed these difficult issues and included experimental and theoretical approaches as well as a number of carefully documented field and petrographic studies. The meeting attracted about 80 participants. Murrell opened the meeting with a wide-ranging review of experimental rock deformation but made the point that, in spite of the wealth of experimental data, a detailed understanding of the conditions under which brittle processes are superseded by crystalplastic processes is lacking. Rutter argued that the entrenched ‘brittle’-‘ductile’ terminology should be replaced by a 4-fold classification of failure mode based on deformation mechanism (cataclastic or crystal-plastic) and on whether or not the failure is localized. He illustrated this scheme with examples from experimentally and naturally deformed rocks, and drew attention to apparent scale differences. Both Murrell and Rutter emphasized that fracture-dominated deformation involves dilation and is therefore very sensitive to effective confining pressure but rather insensitive to temperature and strain-rate; crystal-plastic flow, on the other hand, is very sensitive to temperature and strain-rate but insensitive to

On the equivalence of the relaxed Taylor theory and the Bishop-Hill theory for partially constrained plastic deformation of crystals

The classical Taylor and Bishop-Hill theories for the plastic flow of crystals are equivalent to each other. This can be demonstrated by the duality theorem of linear programming. This proof is developed in detail, showing in addition that the Bishop-Hill stress states can be obtained with a negligible additional effort when the Taylor theory is solved using linear programming. A similar proof is then given for the equivalence between the relaxed Taylor theory and the Bishop-Hill theory with mixed boundary conditions. These are two theories designed to treat cases of partially constrained deformation, when some of the components of the strain tensor describing the deformation of the crystallites are not prescribed a priori. It is believed that such models give a better description of the behaviour of polycrystals containing very flat grains or cells in the case of cold rolling.

Examination of the stress-strain state and selection of criteria for the optimum design of bolted joints with interference fit

I. A. L. Bement, R. G. Hoagland, and F. A. Smidt Jr., ~Fracture mechanisms and irradiation defects," in: Fracture, Vol. 3, Academic Press, New York--London (1971)~ pp. 535'587. 2. V. F. Zelenskii, V. E. Ivanov, B. V. Matvienko, et al. nSimulation and examination~ with the aid of charged particle beams, of certain phenomena taking place in materials of nuclear and thermonuclear reactors," in: Problems of Nuclear Science and Technology, Physics of Radiation Damage and Radiation Materials Science [in Russian], No, i~ (1975), pp. 8-25. 3. R. I. Garber, Zh. I. Dranova, I. M. Mikhailovskii, et al., "Autoion microscopic examination of lattice defects in tungsten by irradiation with high-energy electrons," Fiz. Tverd. Tela, 13, No. 2, 406-410 (1971). 4. I. A. Gindin and I. M. Neklyudov, Physics of Programmed Hardening [in Russian], Naukova Dumka, Kiev (1979). 5. A. Sato, T. Mifune, and M. Meshii, "Irradiation softening in pure iron single crystals= ~ Phys. Status Solidi, 18, No. 2, 699-709 (1973). 6. J. Nagakawa, M. Meshii, and B. Zoomis, "Effect of electron irradiation on the low-temperature deformation of niobium," Scr. Metall., 13, No. 4, 241-244 (1979). 7. G. G. Maksimova, V. G. Azbukin, R. P. Krylov, et al., "Aging of 15Kh2MFA steel at temperatures of 500 and 550~ '' Fiz. Khim. Mekh. Mater., No. 3, 122-124 (1978). 8. A. Sato and M. Meshii, ~Solid solution softening and solid solution hardening, 'v Acta Metall., 21, No. 6, 753-768 (1973). 9. I.A. Gindin, V. I. Kovalenko, V. S. Okovit, et al., "Equipment for measuring low-fre10-1100 K," quency internal friction and elasticity moduli in the temperature range ~ ~ Zavod. Lab., No. ii, 1397-1399 (1970). i0. M. A. Krishtal and S. A. Golovin, Internal Friction and Structure of Metals [in Russian], Metallurgiya, Moscow (1976). Ii. A. H. Cottrell, Dislocations and Plastic Flow in Crystals, Oxford Univ. Press (1953) o 12. I. A. Gindin, L. A. Chirkina, and V. S. Okovit, "Effect of the type of deformation and irradiation on the parameters of the dislocation structure of silicon iron," Fiz. Met. Metalloved., 49, No. 3, 1280-1290 (1972).

Experimental high temperature and high pressure faults

Deformation experiments on Hale albite rock have produced faults at 5 to 15 kb confining pressure and 700° to 1125°C, when hydrolytic weakening is suppressed by either the absence of water or by low pressure. The faults are characterized by: 1) an angle of about 45° to σ1, 2) very little gouge, and 3) several percent permanent strain before failure. Temperature dependent friction is believed to allow frictional sliding and faulting at stresses below those predicted by the Coulomb failure criterion, but above those of hydrolytically weakened crystal plastic flow. High confining pressure, low friction and reduced tensile stress concentrations may allow the fault to propagate as a shear rather than a tensile crack.

Dislocations in metals: the Birmingham school, 1945-55

Cottrell, Sir Alan. Born Birmingham 1919. Lecturer and Professor of Metallurgy at Birmingham until 1955. Atomic Energy Establishment, Harwell 1955—8. Professor of Metallurgy at Cambridge 1958-65. Scientific advisor to British Government 1965-74. Master of Jesus College, Cambridge, from 1974. ViceChancellor, University of Cambridge, 1977-9. Author of several books and papers on metallurgy and plastic flow in crystals.

Dynamics of dislocations and plastic shear in crystalline solids

1. A comparative calculation based on dislocation dynamic properties is made of the initial portions or Fe+3.25% Si crystal deformation curves, both allowing for the crystal elastic deformation, using formula (1), and neglecting it, using formula (2). In contrast to the approximate formula (1), allowance for elasticity leads to a predicted lower upper yield point and yield “tooth.” 2. An analysis of the effects of the important physical parameters (temperature, deformation rate, original dislocation density) on the initial crystal plastic flow stages, shows that the lower yield point is practically independent of the original dislocation density for the given temperature range and for N0<107 cm−2. 3. The calculated temperature dependence of the lower yield point agrees with that derived experimentally for Fe+3.25% Si single crystals from the temperature dependence of the “frictional” strains in the lattice of Fe+3.27% Si polycrystals, although no allowance was made in the calculation for the effects of temperature on the dislocation multiplication process. 4. The Hall-Petch formula was used to generalize the obtained results to polycrystals. A comparative analysis is made of the sensitivity of the lower yield point to the deformation rate, predicted by the calculation, and constructed on the basis of the many experimental results available in the literature.

Principal Stress Directions from Plastic Flow in Crystals

Methods for determining orientations of principal stress axes in deformed rocks involve dynamic analysis of twin-gliding and of extinction bands produced by inhomogeneous translation gliding in crystals. The methods, beginning with Turner9s (1953) technique for dynamic analysis of calcite twins, have been developed using as guides the results from experiments under controlled laboratory conditions. Structures induced by intragranular flow in calcite, dolomite, quartz, micas, orthopyroxenes, clinopyroxenes, olivine, and other common rock-forming materials, may now be used to derive orientations of principal stresses causing the deformation. The various methods, some new, are discussed in detail and examples of their application to tectonites are given. The usefulness of such studies is illustrated by evaluating the observed orientations of principal stresses around folds in light of new data from a theoretical analysis of large amplitude folding of viscous layers in a less viscous matrix. Other areas of research in structural geology in which these methods should prove useful have also been outlined.

On size effects in polycrystal plasticity

Two cumulative ‘size’ effects are responsible for the increased strength of a polycrystalline aggregate above the single crystal strength at low temperatures : a ‘specimen size’ effect and a ‘grain size’ effect. The ‘specimen size’ effect occurs when few grains are present in a specimen cross-section (say less than twenty), and this effect is due mainly to the orientation dependence of crystal plastic flow. The ‘grain size’ effect occurs when many grains are in a specimen cross-section (say more than twenty), and this effect results because, in addition to the orientation dependence of plastic flow within grains, internal concentrations of stress are necessary at grain boundaries to cause bulk yielding and subsequent plastic flow of the polycrystalline aggregate.

Dislocations and Plastic Flow in Crystals

Dislocations and Plastic Flow in Crystals