Operation Of Frank-Read Sources Research Articles

Some considerations on the contradictions of the theory of Frank-Read sources

Abstract The basis of the theoretical explanation of the plastic deformation of metals is the sliding of dislocations and the dislocation multiplication that takes place during the deformation. The best-known interpretation of this process is based on the operation of Frank-Read sources. The article tries to shed light on aspects and theorems that have been known for decades, which draw attention to quite a few contradictions in the theory of Frank-Read sources.

Temperature dependent phase field dislocation dynamics model

In this work, we present a three-dimensional phase field-based formulation for simulating the temperature-dependent motion of discrete dislocations in crystals. For demonstration, this thermal phase field dislocation dynamics method is applied to study pyramidal-type dislocations in three exemplar hexagonal close packed materials, Mg, Ti, and Zr. Pyramidal-type dislocations are well known for temperature sensitivity and influence on the yield strength of these metals. Calculations include the predictions of activation stress, dislocation velocity, and dislocation nucleation over temperature ranges from 0 K to up to half the melting temperatures of these metals. We show that pyramidal slip is glissile, but the activation stress and stacking fault widths are asymmetric with respect to forward/backward glide. The stress to initiate glide reduces logarithmically with homologous temperature. The role of temperature in Frank-Read source operation is shown to decrease the size and time of first loop formation. The analysis identifies a master inverse relationship for the dislocation loop nucleation rate with homologous temperature followed by all three metals.

Size-dependent yield stress in ultrafine-grained polycrystals: A multiscale discrete dislocation dynamics study

In this study, the effects of grain size and dislocation source properties on the yield stress of ultrafine-grained (UFG) polycrystals were examined using three-dimensional multiscale discrete dislocation dynamics (DDD). A polycrystal model containing multiple grains with randomly distributed orientations was constructed within a multiscale DDD framework. Grain boundaries (GBs) were assumed to be penetrable by dislocations, with two dislocation-GB interaction mechanisms, i.e., dislocation absorption at GBs and dislocation emission from GBs, being considered. The simulation investigated the dislocation source effect and demonstrated a non-monotonic dependency of flow stress on dislocation source length, where the lowest flow stress corresponds to a Frank-Read (FR) source length of d/4 where d is the grain size. When the length of a FR source in the polycrystalline sample exceeds this value, the simulated yield stress increases owing to the constraining effect of grain boundaries on dislocation movement. The grain size dependence of the yield stress shows deviations from the classical Hall–Petch relationship as the exponent in the Hall–Petch type relation ranges from about 0.91 to about 0.98, depending on the initial dislocation density in the samples. Detailed analysis indicates that the grain size dependence of the yield stress is mainly controlled by the effect of grain boundary constraints on dislocation activation. A secondary effect arises from grain size dependent dislocation accumulation and the resulting Taylor hardening. The activation and operation of FR sources were quantitatively examined to further understand the origins of source length and grain size effects. A theoretical model is proposed to account simultaneously for the effects of source length, grain size, and initial dislocation density on the yield stress of polycrystals in the UFG regime.

Frank-Read source operation in six body-centered cubic refractory metals

The Frank-Read (FR) source is a well-known intragranular dislocation source that plays an important role in size-dependent dislocation multiplication in metallic crystals. In this work, we extend a phase-field dislocation dynamics (PFDD) technique to study FR source operation on the {110}, {112}, and {123} slip planes in body-centered cubic (BCC) crystals. Here, the periodic lattice potentials for shearing across these planes used in PFDD simulations are provided by density functional theory (DFT) calculations for six BCC refractory metals, Cr, Mo, Nb, Ta, V, and W. The DFT calculations show that the group 6 elements (Cr, Mo, and W) have higher generalized stacking fault energies than the group 5 elements (Nb, Ta, and V). With PFDD, we focus on the effects of the GSFE curve shape, initial character angle, slip plane crystallography, and elastic anisotropy (measured by the Zener ratio, Ac) on the critical stresses to activate the FR source. For the same FR source of any character angle in the same metal, the critical stress on the {123} plane is lower than those on the {110} and {112} planes. It is also shown that elastic anisotropy decreases the critical stress when Ac < 1 and increases it when Ac > 1. We also find that in both Cr and Nb, which possess the lowest values of Ac among the six metals, elastic anisotropy causes the critical stress on {110} planes to achieve a local maximum for the mixed 45∘ oriented FR source.

Examination of Dislocations in Ice

Three techniques have been used to study dislocations in ice: etch pitting-replication, transmission electron microscopy, and X-ray topography (XT). Each is considered, and it is shown that the most useful is XT. This is because ice has low absorption of X-rays and can be produced with a low dislocation density, thus, allowing relatively thick specimens to be studied. The many useful observations that have been made with conventional XT are presented. However, the introduction of high-intensity synchrotron radiation showed that conventional XT observations are of dislocations that have undergone recovery. Thus, the important dynamic observations and measurements that have been made using synchrotron XT are also outlined. In single crystals, it has been shown that slip mainly occurs by the movement of screw and 60° a/3(1120) dislocations on the basal plane. In addition, the operation of Frank-Read sources has been clearly demonstrated, and dislocation velocities have been measured. In contrast, in polycrystals, dislocation generation has been observed to occur at stress concentrations at grain boundaries, and this completely overwhelms any lattice dislocation generation mechanisms. The nature of faulted dislocation loops has been determined in both polycrystals and single crystals.

Acoustic emission induced by dislocation annihilation during plastic deformation of crystals

A description of the dislocation annihilation component of acoustic emission (AE) during plastic deformation of crystals is presented. The annihilation of dislocation kink–antikink pairs during Frank–Read source operation is investigated within the framework of a dynamic model describing the interaction between dislocations and acoustic waves. This model consists of a d’Alembert wave equation nonlinearly coupled to a sine-Gordon equation. The AE by annihilating dislocation kinks is considered and both the emitted energy and the power spectral density of the emitted waves are calculated. It is shown that the lifetime of the generating event is inversely proportional to the square of the applied stress in agreement with existing measurements. The stress corresponding to maximum emission is calculated and is found also to be in agreement with existing experimental data. The obtained results support the hypothesis that the annihilation of dislocations can also be a source of considerable AE during plastic deformation of crystals. The proposed model, furthermore, provides a better physical insight to the emission mechanisms involved.

The operation of Frank-Read sources, yield stress reversibility and the strain‐rate dependence of the flow stress in the anomalous yielding regime of L12alloys

Abstract In the anomalous yield stress regime the strain-rate dependence β = (δτ/δ ln ∊) of the flow stress τ is proportional to (τ - τy), where τy is identified with the stress required to bow out edge dislocations to a near-critical Frank-Read source configuration, at a level equal to that needed for the dynamic propagation of screw dislocations. The conditions necessary for successful Frank-Read source operation are discussed. In the microstrain region the source dislocations are predicted to form loops elongated along the screw direction. Experiments on the ‘partial reversibility’ of the yield stress with temperature are described; it is shown that β is not reversible, but that the yield stress is instantaneously ‘partially reversible’. This is ascribed to the instability and ‘running back’ of some dislocation loops in the microstrain region, on unloading. The temperature dependence of β/τh is found to reflect different obstacles at different temperatures. The temperature and strain-rate dependences of the flow stress are formulated on a model in which the critical step is the operation of Frank-Read sources.

Acoustic emission during plastic deformation of crystals: A lattice-dynamics approach

A lattice-dynamics approach to acoustic emission during plastic deformation of crystals is proposed. First the dynamics of a dislocation interacting with transverse acoustic waves is investigated on the basis of a microscopic Frenkel–Kontorova model in which the rigidity of the substrate is relaxed. It is shown that the interaction can be described by a d’Alembert wave equation for the elastic displacement coupled to a sine-Gordon equation that governs the dislocation dynamics. Within the framework of this model and considering the soliton nature of dislocations, two basic mechanisms of acoustic emission are investigated both analytically and numerically: One is the accelerated motion of dislocations and the other is the annihilation of dislocation kink-antikink pairs during Frank–Read source operation. The results are discussed on the basis of existing experimental data.

Dislocation dynamics and acoustic emission during plastic deformation of crystals

A soliton approach to acoustic emission during plastic deformation of crystals is presented. The approach is based on a microscopic Frenkel-Kontorova model where the rigidity of the substrate is removed in order to establish the interaction mechanism between a dislocation and both longitudinal and transverse acoustic waves. It is shown that this interaction is described by a sine-Gordon-d' Alembert system. Within the framework of this system, two basic mechanisms of acoustic emission are investigated both analytically and numerically. One mechanism is related to nonstationary dislocation motion and the other one to the annihilation of dislocation kink-antikink pairs during Frank-Read source operation. In both cases, computer simulations are obtained which illustrate graphically the analytical considerations and model the acoustic radiation. The obtained results are in agreement with existing experimental data and may provide a better physical insight to the acoustic emission mechanisms during plastic deformation of crystals.

Acoustic emission technique for detecting micro- and macroyielding in solution-annealed AISI Type 316 austenitic stainless steel

The acoustic emission (AE) technique has been used to detect the microplastic yielding occurring during macroscopic elastic deformation in an AISI Type 316 stainless steel. It has been observed that selection of different resonant frequency sensors is essential to detect the AE signal with maximum sensitivity at different strain levels during tensile deformation. An attempt has been made to develop a theoretical model to predict the approximate frequency range of the AE signal generated from dislocation sources operating during pre-yield and near-yield tensile deformation. The frequency of the AE signal has been calculated from the event life time of the Frank-Read and grain boundary source operations. The model for predicting the frequency of the AE signal from Frank-Read source operation during pre-yield deformation has been verified by the experiments on a nuclear grade AISI Type 316 stainless steel. This model has also been extended to predict the frequency of the AE signal from the grain boundary source operation near the macro-yield region and its validity has been verified by considering the AE results obtained on aluminium, copper and AISI Type 316 stainless steel by different investigators. This study has shown good agreement between the theoretically estimated and experimentally observed values. This study has established a simple, but reasonably accurate model which could help in selecting the resonant sensors with suitable frequency for detecting both the microplastic yielding and macroyielding with high sensitivity during proof testing of pressure vessels and pipes and other components used in various industries.

Yield Stress Reversibility and the Operation of Frank-Read Sources in Li2 Alloys in the Anomalous Regime For (111) Slip

AbstractThe yield stress τy at small strains (≈ 0.01%) is strain rate independent, and has the same anomalous temperature dependence as that of the 0.2% strain. τy is considered to be the stress at which Frank-Read sources operate in a virgin crystal. For successful operation, τy must exceed the stress τs at which screws propagate dynamically through the crystal, and the source dislocation must pass rapidly through the unstable Frank - Read configuration. This can be achieved by the bowing edge dislocation overcoming local obstacles before reaching that configuration. Loops elongated along the screw direction are expected to be formed in the microstrain region. Under certain conditions such loops are unstable on unloading, thereby generating long edge dislocations which can operate successfully as sources at low but not at high temperatures, explaining the reversibility phenomenon.

The Effect of Room Temperature Prestrain on the Yield Stress of Single Crystals of γ’ in the Anomalous Regime

AbstractThe yield stress of a specimen prestrained at 294 K increases only slowly or is constant up to a temperature above which the yield stress of a virgin specimen is greater. Above that temperature, the yield stress tends to increase as for a virgin crystal. For sufficiently high prestresses, the yield stress anomaly disappears completely. The results are interpreted in terms of a model in which the operation of Frank-Read sources is rate controlling.

A new type of misfit dislocation multiplication process in InxGa1−xAs/GaAs strained-layer superlattices

Abstract A new misfit dislocation multiplication process has been observed for the first time in InxGa1−xAs/GaAs strained-layer superlattices (with x<0.20). Transmission electron microscopy reveals that this process is based on the occurrence of interactions between perpendicular 60° misfit dislocations with identical Burgers vectors and cross-slip events on the resulting dislocation configurations. The last stage of the process involves the operation of Frank-Read sources that emit glissile dislocations into the {111} planes; parts of the half-loops which develop towards the superlattice are parallel to the interface and are then new misfit dislocations.

Influence of electric current pulses on the mobility and multiplication of dislocations in Zn-monocrystals

The method of selective etching was applied to study the influence of electric current pulses with duration 2 × 10−4 s and current density more than 20 MA/m2 on the pyramidal dislocation mobility in Zn monocrystals at 77 and 293 K. It was established that the increase of dislocation mobility under the influence of current pulses is accompanied by multiplication of dislocations at current densitiesj > 102 MA/m2. The obtained results are discussed with the account of electron-dislocation interaction, heating and Frank-Read source operation under the electron wind influence.

Possibility of a soliton description of acoustic emission during plastic deformation of crystals

Two basic sources of acoustic emission (AE) during plastic deformation of pure crystals are discussed. One is related to nonstationary dislocation motion (the bremsstrahlung type of acoustic radiation), and the other to dislocation annihilation processes (the main component of the transition type of acoustic radiation). The possible soliton description of the bremsstrahlung acoustic radiation by oscillating dislocation kink and by a bound kink-antikink pair (dislocation breather) is considered on the basis of Eshelby’s theory [Proc. Roy. Soc. London A 266, 222 (1962)]. The dislocation annihilation component of the transition acoustic emission is considered only in relation to the Frank–Read source operation. A soliton model for this type of acoustic radiation is proposed and the simple quantum-mechanical hypothesis is advanced for the purpose. Both soliton descriptions are discussed on the basis of available experimental data on the AE intensity behavior during tensile deformation of crystals.

Observation of acoustic harmonics generated by long-range motion of dislocations

We report, for the first time, observations of the acoustic harmonics generated by steady-state vibration at amplitudes so large that long-range dislocation motion occurs. Most of the measurements have been made on the second and third harmonics A2 and A3. At low amplitudes the experimental results of Hikata and Elbaum et al. are confirmed, but there is some discrepancy with theory for A3. At amplitudes such that dislocation sources operate, the harmonic spectrum departs strongly from the Hikata-Elbaum predictions. The harmonic amplitudes do not always increase monotonically with strain; A2 occasionally shows a maximum, A3 sometimes, and A5 even more frequently, in a pattern sensitive to mechanical history. The spectrum depends on grain size and prestress, varying jointly with the modulus defect and internal friction as these indicators of dislocation motion vary. The results on strain dependence are in accord with a simplified model of dislocation breakaway and Frank-Read source operation proposed previously to account for the internal friction and modulus defect.

Steady State Deformation of Crystals Controlled by Motion of Screw Dislocations

To elucidate the relation between individual dislocation motion and macroscopic flow of crystals, the deformation process has been modelled for the case where the deformation is governed by the mobility of screw dislocations which can cross slip freely. The deformation process has been treated by taking account of the interrelating operation of Frank-Read sources randomly distributed in the crystal. The strain-rate of the steady state, which is brought about by the balance between the multiplication rate and the annihilation rate of dislocations, has been derived in an explicit form without any adjustable parameters; it is an increasing function of the source density, and for the same source density it is proportional to τ m +1∼ m +2 a , where τ a is the applied stress and m the stress exponent in the dislocation mobility equation.