Motion Of Screw Dislocations Research Articles

Polarity of the screw-dislocation motion in InSb crystals

Polarity of the screw-dislocation motion in InSb crystals

The analytical solution of a growing steady-state mode III crack in an elastic perfectly plastic solid through an electrical analogy

An approximate analytical solution is found of a quasi-static growing steady-state mode III crack in an elastic perfectly plastic solid. The analysis makes use of a close analogy between the mode III crack problem and the problem of the thin electrical conducting plate that is embedded in a medium of finite conductivity through which electrical current flows. Plastic strain is calculated from the motion of nonredundant infinitesimal screw dislocations. Screw dislocations are Eshelby’s analogue of lines of electrical charge. Calculation of the dislocation crack tip shielding can be used to check the analysis. The plastic zone is a combined Dean & Hutchinson (DH) type unfocused fan plastic zone and a Chitaley & McClintock (CM) type focused fan plastic zone. The asymptotic solution at the crack tip is the CM one. The plastic zone found differs significantly in size and shape from the DH and the CM plastic zones. Novel features in the analysis are the use of a (dislocation density required) stress gradient boundary condition and the introduction of a shifting centre cylindrical coordinate system.

An analysis of incident wave behavior required for screw and edge dislocation emission from cracks

Exact transient solutions for the motion and arrest of screw and edge dislocations at a crack subjected to the diffraction of, respectively, plane sinusoidal SH-waves and plane sinusoidal SV-waves are developed. These are then examined in view of a dislocation force-based criterion for emission. It is found, first, that, unless deceleration is allowed, dislocation arrest may be temporary. Then, expressions for the instant of emission and the arrest distance are obtained, and found to depend on properties such as dislocation speed, yield stress, and a dimensionless variable related to the size of a zone of attraction at the crack edge. Study of these expressions indicate that the edge dislocations are emitted in minimum times at particular finite speeds, while the screw dislocations achieve minimum emission times in the zero speed limit. Order-of-magnitude estimates of the expressions show that emission occurs on a micromechanical scale, that the incident wave frequencies required for emission may be in the MHz range, and that emission time varies directly with incident wavelength. A study of the dynamic stress intensity factors then shows that purely brittle fracture is more difficult to achieve than dislocation emission for a given incident wave.

An exact transient analysis of dislocation emission and fracture

D islocation-crack interaction studies have led to the development of criteria for fracture in terms of dislocation emission from crack edges, and to consideration of crack edge shielding effects due to dislocations. These studies have generally been quasi-static. To illustrate, therefore, the extension of the basic concepts involved to dynamic situations, three exact analytical results are presented. These involve screw dislocation motion near a crack which may be growing, and which may be subjected to dynamic loading due to SH-wave diffraction. Study of these results allows some useful insights. In particular, fracture initiation and dislocation emission times and, thus, their order of occurrence, can be determined. Moreover, it is shown that crack edge shielding can be temporary, and that parameters such as the dislocation force and the distance traveled by an emitted dislocation prior to arrest can have pronounced dynamic overshoot effects. Finally, it is found that this arrest distance depends only implicitly upon the applied loading.

On Lorentz Symmetries in Solids

AbstractSoliton properties of kinks on dislocations allow a definition of natural standards for the measurement of length and time which are inherently related to the lattice structure. If dynamical processes such as wave propagation and the motion of screw dislocations are expressed in terms of standards of such a kind, Lorentz symmetries associated with sound propagation become evident.

II. Microscopic mechanism

Abstract In part I of this study, extensive evidence for glide on the non-compact plane (001) was obtained in [112] aluminium single crystals under creep conditions at high temperatures. In this part II the same single crystals are used to measure the critical resolved shear stress for (001) glide as a function of strain rate and temperature in constant-strain-rate tests. The observed dependence is in good agreement with the kink-pair mechanism, initially proposed for prismatic glide in hexagonal closepacked metals. The apparent activation enthalpy ΔH 001 for the dislocation glide on (001) is equal to 1.74eV. This model also applies to {110} glide with an apparent activation enthalpy of 1.40eV. The screw dislocation motion predicted by this model in the face-centred cubic structure is in good agreement with the slip-line observations and in situ experiments reported in part I. This model also agrees well with the other non-compact glide characteristics available, such as the activation temperatures of {11...

The low-temperature plastic deformation of α-titanium and the core structure of a-type screw dislocations

Abstract α-titanium single crystals, containing three different amounts of interstitial impurities, have been tested in compression at temperatures between 77 and 700 K. The mechanical behaviour is characterized by a strong temperature dependence of the yield stress for slip on the primary prismatic slip plane (1010)[1210], a strong dependence of the critical resolved shear stress on the orientation of crystal axis and the failure of the Schmid law, an anomaly at temperatures between 300 and 500 K which is associated with cross-slip into a first-order pyramidal plane, and the occurrence of two hardening stages on the deformation curves at low temperatures. Both conventional and in situ transmission electron microscopy examinations revealed that a large lattice friction opposes the motion of a-type screw dislocations at temperatures below 550 K. Since edge dislocations are found to be highly mobile, it appears that, at low temperatures, the yield stress of pure α-titanium is governed by a Peierls force act...

Plastic deformation in nonstoichiometric UO2+ x single crystals—I. Deformation at low temperatures

Single crystals of UO 2 + x (5 × 10 −6 ⩽ x ⩽ 10 −2) have been deformed in equilibrium CO CO 2 mixtures at 873 K in compression and at 300 K under microhardness indents. The primary glide plane is {111} under all conditions, and the yield stress is independent of x at 873 K but increases slightly with increasing x at 300 K. Dislocation substructures consist largely of screw dislocations, indicating that the motion of screw dislocations controls deformation; it is likely that dislocation mobility is controlled by interactions between dislocations and extrinsic defects.

Stress history during propagation of a lateral fold-tip and implications for the mechanics of fold-thrust belts

This paper evaluates the hypothesis of lateral propagation of fold-tip lines by comparing paleostress data from the lateral tip of a natural fold with a theoretical stress history at a moving screw dislocation. The fold is an asymmetric kink fold exposed in Ogden Canyon, Utah, where mapping revealed that a cylindrical anticline-syncline pair changes along strike into a noncylindrical termination. Quartz deformation lamellae data from this fold indicate that the stress history in the fold tip was relatively simple with a general pattern of layer parallel compression perpendicular to the fold axis and layer parallel extension subparallel to the fold hinge line. In contrast, data from the cylindrical part of the fold are complex, regardless of the position within the fold. The latter is significant because although the symmetry of the cylindrical fold implies a plane-strain deformation, the paleostress data indicate that the strains were actually three-dimensional; an observation that is easily explained if the fold propagated laterally (along strike) during fold growth. To test this hypothesis, we consider a simple stress model where the non-cylindrical fold-tip is treated as a moving screw dislocation. We conclude that although a broad range of models are allowable, this simple model can account for most of the complexities of the data. Thus, we conclude that the fold has propagated laterally during its growth. Recent studies of two fold-related earthquake series (the 1980 El Asnam earthquake and the 1983 Coalinga sequence) lend support to models that call on lateral propagation of fault-related folds. Thus, these active fold-thrust systems as well as our study of an ancient system are consistent with the concept that folding is a three-dimensional process rather than a simple plane-strain deformation. Clearly, further word is needed to thoroughly test the fold-propagation models. Nonetheless, the recognition of lateral propagation of folds is important because it supports Elliot's “macroscopic creep” concept for development of fold-thrust belts where propagation of fracture tip-lines is a least-work process analogous to dislocation creep in crystals.

A study of (001) glide in [112] aluminium single crystals

Abstract [110](001) slip has been studied in [112] aluminium single crystals deformed in creep. Metallographic and microstructural observations were performed. At 150°C, the two primary {111} planes in a symmetrical orientation are activated. At 180-200°C, (001) starts being activated in some areas of the sample. The corresponding wavy slip traces indicate that slip is unstable on (001) and frequent cross-slip occurs between this plane and two {111} slip systems with low Schmid factors. In situ experiments in this temperature range show that screw dislocation motion on (001) is difficult. At 400°C and above, (001) slip becomes easy and straight traces are clearly visible. Two distinct dislocation substructures correspond to these different deformation modes. It is shown that (001) glide does not originate from the recombination of Lomer-Cottrell barriers, but dislocation multiplication takes place on this non-compact plane. The microscopic mechanism associated with (001) glide, and the importance of this ...

Dislocation behaviour during cyclic deformation of niobium single crystals

Dislocation structures formed during cyclic deformation of niobium single crystals have been studied. Single crystals of both [321] and [110] orientations have been cyclically deformed in tension-compression under strain control. Moreover, the mechanical property data are supplemented by the direct observation of dislocation arrangements by transmission electron microscopy. In the case of [321] orientation single crystals the hardening curve can be divided into three stages, i.e. first, rapid-hardening and saturation stages associated with various dislocation structures. In the first stage the dominan features of the dislocation configurations are high density networks and debris loops. In the rapid-hardening stage the main feature is the formation of dislocation bundles. In the saturation stage the characteristic features are the dislocation bundles and the screw dislocations between bundles. The imposed strain is accomodated mainly by the motion of screw dislocation travelling to and fro between the bundles. For the [110] orientation single crystals the hardening curves are similar to those of the [321] orientation except that dislocation bundles of more than one direction appear during the first few cycles. Three-dimensional cell, two-dimensional cell and bundle structures are summarized as the saturated dislocation structures of b.c.c. metals.

Thermal activation of glide in InP single crystals

The study of the plasticity of undoped indium phosphide between 573 and 1023 K by means of uniaxal compression (ϵ ∼- 10 −4 s −1), stress relaxation and transmission electron microscopy shows t the deformation is controlled by the motion of screw dislocations in the stress field of the lattice according to a thermally activated Peierls mechanism. Between 573 and 673 K, this mechanism is pure; it is assisted by the internal stress between 673 and 1023 K and the lattice friction has no effect on the screw dislocations above 1023 K: the deformation is then controlled by the forest mechanism. To move freely in the crystal, a screw dislocation needs an energy below 2.8 eV.

Brownian motion of screw dislocations in the hexagonal Blue Phase

By quickly decreasing the electric field, we observe a transition from the two-dimensional hexagonal Blue Phase (BPH 2D ) to the three-dimensional hexagonal Blue Phase (BPH 3D ) and the appearance of screw dislocations in some crystallites. After more or less long time, some of these dislocations may escape from the crystallites. We analyse the phenomena through the Brownian motion and consider the influence of the electric field on the diffusion time En diminuant rapidement le champ electrique, la transition de la phase bleue hexagonale bidimensionnelle a la phase bleue hexagonale tridimensionnelle fait apparaitre des dislocations vis dans certains cristallites. Certaines de ces dislocations s'echappent des cristallites en des temps plus ou moins longs et l'on analyse ce phenomene en terme de mouvement brownien en regardant l'influence du champ electrique sur le temps de diffusion

Shear wave-front motion from a nonuniform dislocation

The model of a nonuniformly moving screw dislocation in an unbounded elastic medium is employed to analyze the shear wave-front motion. The elastic motion near the shear wave-front is obtained by inversion to the time domain of the dominant high frequency term. The displacement discontinuity of the dislocation considered is of the form Δu z = U(x)ƒ(t − t R(x)) . Necessary and sufficient conditions for the functional dependence of U( x), ƒ(t) and t R ( x) are established for the existence of a nonsingular velocity field.

The plastic deformation of potassium single crystals at low temperatures

The yield stress of potassium single crystals was measured in the temperature range of 1.5 to 30 K for a wide range of orientations. The effects of nobs itutional solutes (sodium and rubidium) on the yield strength of potassium single crystals were also investigated. The Schmid law of critical resolved shear stress for slip is invalkid in the temperature-dependent region of yield stress, and the orientation dependence of yield stress is in agreement with the Peierls mechanism for screw dislocation motion. The validity of the Schmid law may be questionable even in the athermal region, as suggested by the observations at 30K. Alloy softening is observed in the temperature-dependent region of yield stress by adding substitutional solutes to potassium.

Transient dynamic Green’s functions for a cracked plane

Closed-form solutions for the transient dynamic problems of a suddenly applied anti-plane concentrated force and concentrated impulse near a crack are obtained. The various wave signals comprising the solutions are identified, and their behavior noted. The concentrated force solution is then employed as a Green’s function to solve the important problem of arbitrary screw dislocation motion near a crack edge.

Effects of External Shear Stress on the Smallest Double Kink Nucleation Process in Si

A tight-binding type electronic theory (molecular approximation) is used to calculate the formation energy of the double kink E d k for a 1/2[110](1\bar11) (perfect glide set) screw dislocation in covalent semiconductor Si. Effects of external shear stress on the double kink nucleation process are investigated in detail. It is shown that the calculated stress dependence of the E d k is in good agreement with the experimental results of the activation energy for the screw dislocation motion in Si.

The dynamic stress intensity factor for a crack due to arbitrary rectilinear screw dislocation motion

The dynamic stress intensity factor for a stationary semi-infinite crack in an elastic plane due to the rectilinear motion of a screw dislocation is obtained analytically. The intensity factor is studied for its dependence on the (initial) dislocation position, orientation and speed. The speed is subsonic and possibly non-uniform. The position and orientation are arbitrary, so that crack-dislocation intersection is considered. It is assumed that a dislocation traveling toward the crack surface arrests upon arrival. It is found that, in general, dislocation motion initiation and arrest cause discontinuities in the intensity factor. In the latter instance, the factor takes on a constant value and, in the case of arrest on the crack surface, this value depends only on the initial dislocation position.

The Dynamic Stress Intensity Factor Due to Arbitrary Screw Dislocation Motion

The dynamic stress intensity factor for a stationary semi-infinite crack due to the motion of a screw dislocation is obtained analytically. The dislocation position, orientation, and speed are largely arbitrary. However, a dislocation traveling toward the crack surface is assumed to arrest upon arrival. It is found that discontinuities in speed and a nonsmooth path may cause discontinuities in the intensity factor and that dislocation arrest at any point causes the intensity factor to instantaneously assume a static value. Morever, explicit dependence on speed and orientation vanish when the dislocation moves directly toward or away from the crack edge. The results are applied to antiplane shear wave diffraction at the crack edge. For an incident step-stress plane wave, a stationary dislocation near the crack tip can either accelerate or delay attainment of a critical level of stress intensity, depending on the relative orientation of the crack, the dislocation, and the plane wave. However, if the incident wave also triggers dislocation motion, then the delaying effect is diminished and the acceleration is accentuated.

The work-hardening behaviour of hydrogen-charged high purity iron single crystals at temperatures between 296 and 200 K

Three-stage work hardening is observed when high purity iron single crystals of single-slip orientation are tested in tension during hydrogen charging between 296 and 200 K. The effects of hydrogen on the deformation behaviour, i.e. the temperature and orientation dependence of the stress-strain curve, the slip lines, the dislocation structures and the rotation of the specimen axis during deformation, were investigated. Hydrogen causes marked softening, and stage I′ proceeds with single slip by the motion of primary screw dislocations. After overshooting, stage II′ sets in with the long-range motion of secondary screw dislocations. The length of stage I′ increases with the distance of the initial specimen orientation from the double-slip boundary and with decreasing temperature down to 225 K. The results are discussed in terms of the variation in the difference between the mobilities of edge and screw dislocations due to the hydrogen. Hydrogen charging increases the uniform elongation of the crystal because it results in a long stage I′. The fracture is of a semi-brittle nature in contrast with the complete ductility in specimens without hydrogen.