Density Of Free Dislocations Research Articles

A dislocation network model of recovery-controlled creep

A new model of recovery-controlled creep deformation, based on the jerky glide motion of dislocations between obstacles, is proposed. A three-dimensional distribution of dislocation links is visualized such that only links which attain a certain threshold size,λ a, through recovery can glide rapidly until they are again arrested at the next obstacle. The rate of mobilization of arrested dislocations is shown to be directly proportional to the annihilation rate, ϱa. The strain rate, γ, during transient creep is related to the annihilation rate, the obstacle spacingL and the Burgers vectorb of the dislocations according to the expression $$\gamma = \alpha _1 \psi (t)\dot \varrho bL$$ where α1 is a geometrical constant and ψ(t) is a time-dependent parameter whose value is determined by the instantaneous (free) dislocation density as well as some salient features of the dislocation distribution. At steady state, ψ(t) translates into a constant which is stress and temperature independent. The average effective dislocation velocity is also shown to be directly proportional to the annihilation rate. The model is used to rationalize the familiar creep transients which are usually observed when the stress is altered abruptly during recovery creep.

The effect of dislocation density on the aqueous solubility of quartz and some geologic implications: A theoretical approach

The internal energy associated with dislocations is calculated in quartz as a function of dislocation density. These calculations show that at dislocation densities of 109, 1010, 1011, and 1012 cm dislocation/cm3 the energy stored per mole of quartz is 2.2, 19.7, 170, and 1426 J, respectively. The density of free dislocations in natural quartz rarely exceeds 109 line cm/cm3, and the resulting increase in free energy is probably too small to affect any geochemical processes significantly. This applies to the overwhelming volume of rocks in the earth's crust. The density of dislocations in tangles may exceed 1011 line cm−2 which is significant, but the volume of quartz containing tangles is a very small fraction of most quartz grains. Nevertheless, where fluid/rock ratios are low, the aqueous activity of SiO2 may be significantly increased by the dissolution of quartz containing dislocation tangles. Such dissolution could be geologically significant in active greenschist facies fault zones and mylonites where repeated cold working would produce a sustained source and large population of dislocation tangles. In such a setting the locally high internal energies of quartz containing dislocation tangles would lead to strain solution. The resulting high activity of aqueous silica would enhance the stability of feldspars and would establish chemical potential gradients of SiO2 which would drive the diffusive mass transfer of SiO2 out of the fault zone.

Structural changes during hot deformation of austenite in alloy steels

In austenite of alloy steels, intensive strain hardening takes place during hot deformation to strains of 0.07–0.1. These processes lead to the formation of a hot-worked substructure which is characterized by a high density of dislocations, distributed uniformly or forming a cell-like substructure. With an increase in the degree of deformation (up to ε max , corresponding to the setting up of a dynamic equilibrium between the processes of strengthening and softening), the processes of dynamic polygonization develop, although net strengthening still prevails. Oriented polygonal subboundaries are formed, and with an increase in the strain, the volume fraction of polygonized regions increases, as does that of the equiaxed subgrains. The subgrain boundaries become more perfect, and the density of free dislocations decreases. During steady-state flow, a stable equiaxed polygonized substructure is formed, whose parameters do not change on further increases in strain. The structural changes occurring during hot deformation by compression or by rolling under comparable conditions are similar. The structures formed during rolling at ϵ ̇ g3′ > 1 s −1 correspond to the unsteady stage of hot deformation. The relatio established between the flow curve and the structural changes taking place during the hot deformation of austenite in alloy steels makes it possible to choose optimum conditions for the high temperature thermomechanical treatment of industrial alloys which soften by dynamic polygonization.

Analysis of dislocations in some naturally deformed plagioclase feldspars

Dislocations in intermediate plagioclase feldspars, which were deformed under granulite facies conditions, have been analysed. The study reveals extensive ductile deformation by intracrystalline slip and by twinning. Six out of the seven possible Burgers vectors were identified: \(b = \left[ {001} \right],\tfrac{1}{2}\left[ {110} \right],\tfrac{1}{2}\left[ {1\bar 10} \right],\left[ {101} \right],\tfrac{1}{2}\left[ {112} \right]and\tfrac{1}{2}\left[ {1\bar 12} \right]\). Most, perhaps all, dislocations are dissociated by up to 200 A. The microstructure is dominated by [001] screw dislocations, most of which appear to be dissociated in (010). The dominant slip system appears to be (010) [001]. Large grain-to-grain variations in the density of free dislocations indicate that the plastic strain in individual grains depended upon the Schmid factor for (010) [001]. The microstructure suggests that the rate-controlling step for high-temperature creep of plagioclase is cross-slip of extended [001] screw dislocations. The rheological contrast between feldspar and quartz is partly due to a difference in stacking fault energy.

軟鋼薄板材の疲労き裂近傍における転位構造の実験的考察

The Sheet specimens of mild steel were fatigued at room temperature by plane bending stressing. The dislocation structures during the process of fatigue crack initiation and near the tips of fatigue cracks were observed using a transmission electron microscope and the dislocation density and the size of cell structure were obtained quantitatively. The relationship between the dislocation structure and the plastic deformation zone near the crack tips was examined.The main results obtained are as follows:(1) During the process of crack initiation, the total dislocation density ρt increased to a saturation with progress of fatigue. The dominant structure at high stress amplitude was cell structure, and that at low stress amplitude was loop patch structure. The cell width lw (or the bundle spacing ls) and the free dislocation density ρf in the cell structure decreased gradually during this process.(2) From the observation of dislocation structure near the crack tip, the mean size of cell structure lm and the free dislocation density ρf in the cell structure were found to decrease with approaching the tip. They showed almost the same distribution in all directions from the crack tip, and this influence of decreasing lm and ρf extended to the distance of about 1000μm from the crack tip.(3) The plastic deformation region near the crack tip determined by Vickers hardness tests was larger than the area where the mean cell size lm was found to be below about 4μm.

Effect of the substructure created during hot deformation on the strength of Fe-Ni-C austenite

1. The high strength of austenite (σb and σ0.2) resulting from preliminary hot deformation depends on the total contributions to strengthening of the subboundaries, the high density of free dislocations, and the reduction in the grain size resulting from partial or complete dynamic or static recrystallization. 2. The formation of a polygonized substructure as the result of hot deformation leads to a change in the susceptibility of austenite to strain hardening — higher resistance to plastic deformation (σ0.2), lower rate of strain hardening in the even-deformation section (increase of ductility) with retention of higher resistance to substantial plastic flow up until failure.

Stress dependence of recrystallized-grain and subgrain size in olivine

New experiments on Mt. Burnet dunite have been carried out to evaluate the effects of important physical parameters on recrystallized-grain size and subgrain size in olivine deforming under steady-state conditions. The experiments, done under both wet and dry conditions in a Griggs solid-pressure-medium apparatus, were conducted in constant strain rate, constant stress and stress relaxation modes at 10 kbar confining pressure, temperatures from 1000°C to 1300°C, strain rates from 10 −4 to 10 −8/sec and stress differences of from 0.5 to 10 kbar. For dunite deformed under wet conditions, recrystallized-grain size is slightly temperature-dependent but under dry conditions it is only stress-dependent with D = 137 σ −1.27 for D in μm and σ in kbar. Subgrain sizes also depend only on stress; for the dry experiments d = 28 σ −0.62 and for the wet ones d = 15 σ −0.69 . Subgrain sizes decrease with increasing stress but do not increase with decreasing stress and hence record only maximum stress levels. Recrystallized-grain sizes adjust to both increasing and decreasing stress levels, at minimal strains and times, and thus record the stress history. Because of this and of the inherent stability of recrystallized grains, this technique is regarded as more reliable than the subgrain size and free dislocation density and curvature methods for estimating stress magnitudes in tectonites having deformed in the steadystate.

The influence of second phase particles on the free dislocation density during creep of stainless steel

The free dislocation density was measured in a γ′-hardened stainless steel (A-286). The dislocation density is smaller in specimens which contain particles with a smaller interparticle distance provided the specimens were crept at equal stresses. The decrease of the dislocation density may be considered as supporting the view that particle hardened materials behave like pure materials subjected to a smaller stress.

The effect of pressure on the rate of dislocation recovery in olivine

Samples cut from single crystals of olivine which had been deformed in the laboratory were annealed for 1 hour at either 0.1‐MPa or 500‐MPa gas pressure to study the effect of pressure on the kinetics of dislocation recovery in olivine. After an anneal the dislocation structure was examined by transmission electron microscopy and compared with the dislocation structure in an unannealed ‘reference’ sample from the same deformed single crystal. For the range of annealing temperatures used, 1525–1675 K, the density of free dislocations decreased by dislocation‐dislocation annihilation. The activation volume and activation energy for this dislocation recovery process were obtained from an analysis of the decrease in dislocation density as a function of temperature, for the two hydrostatic pressures, in terms of second‐order kinetics. This analysis yields V = 11 ± 1 cm3/mol and Q = 300 ± 15 kJ/mol.

Differential stress determined from deformation‐induced microstructures of the Moine Thrust Zone

The dislocation structure, recrystallization, and elongation of quartz grains in tectonites from three localities along the Moine thrust fault have been analyzed by transmission electron and optical microscopy. The dislocation density, 5×108 cm−2, and the grain size after recrystallization, 15 μ, in the basal quartzite unit at the Stack of Glencoul are independent of distance from the fault, to the maximum sampling distance of ∼100 m. The differential stress level determined from the deformation‐induced microstructures is on the order of 100 MPa. The magnitude of the differential stress at the fault decreases by a factor of 2 from Knockan Crag to Loch Eriboll, a distance of 50 km. At the Stack of Glencoul, grains in the basal quartzite are progressively elongated and recrystallized approaching the fault, corresponding to a progressive increase in strain. At 100 m from the fault, the aspect ratio of relict quartz grains is ∼1:1; at 0.01 m it is 85:1. A quantitative estimate of the strain, based on the aspect ratios of the relict quartz grains, as a function of distance from the fault has been used to calculate strain rate and temperature profiles. For a creep activation energy of 0.19 MJ mol−1 the temperature decreases away from the fault with a gradient of 7.5×10−3 °C cm−1. For a differential stress of 100 MPa, a steady state thrust sheet velocity of 11 cm yr−1 would be required to produce this gradient. At 100 m from the fault, 5% of the quartzite is recrystallized from 1‐mm to 15‐μm grains; at 0.01 m it is 100% recrystallized to 15‐μm grains. This small grain size probably favored grain boundary deformation mechanisms over grain matrix mechanisms and thus helped to concentrate the strain at the fault. Systematic changes in the elongation and recrystallization of quartz grains in Lewisian Gneiss and Moine Schist are obscured by the constraints imposed by other mineral phases. The small size of the grains after recrystallization, highly serrated grain boundaries, and large densities of free dislocations suggest that very little static recovery followed the plastic deformation event.

Microstructure and transient creep in an austenitic stainless steel

Abstract The dislocation substructures associated with normal and inverted transient creep in annealed and prestrained type 304 austenitic stainless steel were investigated using transmission electron microscopy. Normal primary creep was accompanied by subgrain formation, a process which was accelerated by pre-straining. A prolonged accelerating creep stage was observed under certain test conditions. The associated microstructures revealed that this type of transient creep was also accompanied by subgrain development and a reduction in the free dislocation density. It is concluded that knowledge of the evolution of the dislocation microstructures during transient creep cannot be used to predict whether creep is accelerating or decelerating.

T. E. M. investigation of chromites from New-Caledonia

A T.E.M. investigation on chromite from New-Caledonian ophiolites has been undertaken in an effort to elucidate the origin of structures in chromite ore bodies. These bodies have a podiform shape and internally the chromite ore and its olivine matrix are strongly deformed. It is a question with important economical bearings to decide whether these structures were directly obtained in a magma chamber during the course of a turbulent magmatic sedimentation of chromite and olivine or if they result from plastic deformation postdating the magmatic event. This plastic deformation is registered in the surrounding peridotites and in the olivine matrix of the chromite ore. It occurred around 1200° C for stresses lower than a few hundred bars. Chromites consist in large grains with a very low density of free dislocations and well organized sub-grain boundaries. Stereographic analysis of some of these subgrain boundaries indicate that a large amount of climb occurred because in most cases, the constitutive dislocations no more lie in the usual glide planes of the spinel structure. These features are characteristic of a temperature well above 1/2 TMj that is probably higher than the 1200° C estimated for plastic flow conditions. Optical observations of thin sections show that during this plastic flow chromite grains have accommodated strain by brittle fracture andT.E.M. observations at the tip of the cracks show that the zone which has been plastically deformed at the front crack does not exceed some microns. These remarks are in agreement with the mechanical properties of other spinels which begin to be correctly known. All seem to have a very high elastic limit, even at 1/2 TM. These observations suggest that the dislocation structure in this chromite has not been produced by the plastic deformation observed in surrounding olivine bearing rocks but is possibly due to its magmatic history.

Experimental annealing of a natural dunite

Samples cut from a natural dunite were annealed at 1,100-1,700° C for o., 1-2,000 hours, at atmospheric pressure and under controlled oxygen fugacity. The evolution of free dislocation density and (100) tilt walls spacing was studied. Several recovery mechanisms have been observed. The mean ascent velocity of kimberlitic magma is expected to be 1 to 1.5 km/h, from the analysis of the dislocation microstructure in peridotite nodules.

Effect of deformation of austenite during HTMT on the stability of high-carbon martensite during low-temperature tempering

1. Hot plastic deformation of austenite affects the kinetics of biphase decomposition of martensite during low-temperature tempering. The lattice constant of temper martensite depends on the extent of biphase decomposition of martensite. 2. As a rule, HTMT accelerates self-tempering during quenching and has different effects on biphase decomposition of martensite during subsequent low-temperature tempering, depending on the hot deformation conditions of austenite. When an imperfect polygonization structure with high density of free dislocations is formed during deformation of austenite, the biphase decomposition of martensite is accelerated during low-temperature tempering; after HTMT producing a perfected regular structure of polygonal subboundaries in austenite (and inherited by martensite), biphase decomposition of martensite is slowed down.

Dislocation substructure of mantle-derived olivine as revealed by selective chemical etching and transmission electron microscopy

Cleaved and mechanically polished surfaces of olivine from peridotite xenoliths from San Carlos, Arizona, were chemically etched using the techniques of Wegner and Christie (1974). Dislocation etch pits are produced on all surface orientations and they tend to be preferentially aligned along the traces of subgrain boundaries, which are approximately parallel to (100), (010), and (001). Shallow channels were also produced on (010) surfaces and represent dislocations near the surface that are etched out along their lengths. The dislocation etch channel loops are often concentric, and emanate from (100) subgrain boundaries, which suggests that dislocation sources are in the boundaries. Data on subgrain misorientation and dislocation line orientation and arguments based on subgrain boundary energy minimization are used to characterize the dislocation structures of the subgrain boundaries. (010) subgrain boundaries are of the twist type, composed of networks of [100] and [001] screw dislocations. Both (100) and (001) subgrain boundaries are tilt walls composed of arrays of edge dislocation with Burgers vectors b=[100] and [001], respectively. The inferred slip systems are {001} 〈100〉, {100} 〈001〉, and {010} 〈100〉 in order of diminishing importance. Exploratory transmission electron microscopy is in accord with these identifications. The flow stresses associated with the development of the subgrain structure are estimated from the densities of free dislocations and from the subgrain dimensions. Inferred stresses range from 35 to 75 bars using the free dislocation densities and 20 to 100 bars using the subgrain sizes.

Dislocation structure of Ni-20Cr-2ThO 2 after high temperature deformation

The development of the dislocation structure during high temperature deformation of coarse grained polycrystalline Ni-20Cr-2ThO 2 has been investigated by means of transmission electron microscopy. The samples were deformed in compression at temperatures of 700, 900 and 1100°C. The stress and strain dependencies of the subgrain size, L, and of the density of free dislocations, ρ, which are not associated with subgrain boundaries, were measured. While ρ reaches an almost constant value after ϵ = 0.15 ( T = 900° C, σ = 145 MPa), the development of a steady state subgrain size in the entire volume of the samples requires larger plastic strains. The stress dependencies of ρ and L which have developed after strains of 0.15–0.30 are similar to those for single phase metals and can be described by L ~ σ −1 ρ ~ σ 1.6. The observation that the stress dependence of the deformation rate for dispersion strengthened metals is large and increases with decreasing stress is often attributed to the existence of a threshold stress which has to be overcome before plastic deformation can occur. Studies of the ThO 2 particle distribution showed that the threshold stress probably does not coincide with the Orowan stress in the present case. The observation that the dislocations, subgrain boundaries and twin boundaries, present in the as received material are very stable during annealing, suggests that these structural features might to the threshold stress.

Deformation mechanisms in alpine-type ultramafic rocks from new zealand

An electron microscope study has been made of mylonitized ultramafic rocks from Milford Sound, New Zealand. In the olivine porphyroclasts, substructural arrays of dislocations with Burgers vector b = [100] were observed. These substructures are similar to those observed in olivines deformed experimentally under creep conditions. Superimposed on the substructures was a variable density of free dislocations, b = [001], ranging from 10 7 cm −2 to 2 × 10 9 cm −2. The olivine grains in the matrix, while containing ordered arrays of dislocations, had relatively high densities of free dislocations, up to 5 × 10 9 cm −2. The orthopyroxene, as both porphyroclasts and matrix, contained fine-scale lamellae of clinoenstatite. The occurrence of the clinoenstatite suggested a low temperature fast strain rate phase of deformation. Although the metamorphic and tectonic histories of the region have been interpreted in terms of three phases of deformation under conditions of decreasing metamorphic grades, at least two of these phases have been verified by the crystallographic defects associated with these phases of deformation. It is proposed that the microstructural development of the ultramafic rocks occurred during the crustal deformation that overprinted the substructural evidence for the upper mantle origin of these rocks.

Effects of shock loading and cold rolling on the structure and high temperature creep properties of Fe-3.75 Pct Si

The effects of shock loading and cold rolling on the dislocation substructure and high temperature creep properties of Fe-3.75 pct Si at 923 K and 7000 psi (4.82×107 Pa) have been investigated. We find the primary creep transients of this alloy to be “normal” (\((d\dot \varepsilon /dt< 0)\) for the annealed contidtion and to change with increasing prestrain by rolling, becoming “inverted” ({ie1615-2}) for prestrains greater than about 11 pct. It is shown that both shock loading to about 70 kilobars (7×109 Pa) and cold rolling 25 pct produce a fine subgrain size and an inverted creep transient with a minimum creep rate about one third of the steady state creep rate. During the inverted creep transient both the free dislocation density and the subgrain size increase and approach the steady state values. These structural changes are opposite to those observed for normal creep transients. Also it is found that the strengthening effect of shock loading is less stable than that produced by cold rolling. It is suggested that this difference is due to the greater instability of the shocked substructure as compared to the cold rolled substructure. Some effects of partial recrystallization are also discussed.