Dislocation dynamics in cyclic plastic deformation

The paper presents a theoretical investigation of the slip avalanches (so-called strain bursts) which occur in single-glide-orientated face-centered cubic or hexagonal close-packed metals during stress-amplitude-controlled cyclic plastic deformation. The study is based on a model of the dynamics of dislocations that has been developed in a companion paper (Part I). It is shown that this model allows for a quantitative treatment of the strain-burst phenomenon. In particular, the scaling relations between different strain-burst-characteristic parameters which have been found by experiment are connected to the evolution of the dislocation microstructure and thus find a natural explanation.     

The evolution of persistent slip bands in copper single crystals

The transformation of the so-called matrix structure into persistent slip bands (PSBs) during the fatigue of copper single crystals has been investigated by transmission electron microscopy (TEM). By cyclic pre-deformation a saturated, hard matrix structure was established which is not capable of further hardening. A sudden increase of the applied amplitude of the resolved plastic shear strain initiated the transformation of the matrix structure into PSBs. The number of deformation cycles with enlarged amplitude of resolved plastic shear strain was increased from experiment to experiment in order to obtain crystals with PSBs in consecutive stages of evolution. Surface observations indicated strain localization well before first fragments of the typical ladder-like dislocation pattern of PSBs could be identified in the bulk. From our experiments, we conclude that the transformation from the matrix structure into PSBs very likely starts from the centers of the veins which exhibit small dislocation-poor, soft areas. These areas are enclosed by a harder shell, where a high dislocation density is maintained and which may develop into first dislocation walls. During the evolution of PSBs the frequency distribution of the wall spacings narrows. This indicates that a shift of dislocation walls (1–2 nm/cycle) plays an important rôle in establishing the typical regular ladder-like dislocation pattern of well-developed PSBs.     

Stochastic dislocation patterning during cyclic plastic deformation

A dislocation dynamical theory is developed for the formation of dipole dislocation patterns during cyclic plastic deformation in single glide. The stochastic dislocation dynamics adopted is suitable to account, in terms of a fluctuating effective medium, for the effects of long-range dislocation interactions on a mesoscopic scale. The theory can explain the occurrence of a matrix structure and persistent slip bands as a result of evolutionary processes, it gives the intrinsic strain amplitudes and the characteristic wavelength of these structures, and it allows for an interpretation of the structural changes associated with changes of the deformation conditions. Quantitative results are in good agreement with experimental observations.     

On the foundations of stochastic dislocation dynamics

A stochastic approach to dislocation dynamics is proposed that starts off from considering the geometrically necessary fluctuations of the local stress and strain rate caused by long-range dislocation interactions during plastic flow. On a mesoscopic scale, a crystal undergoing plastic deformation is thus considered an effective fluctuating medium. The auto- and cross-correlation functions of the effective stress and the plastic strain rate are derived. The influences of dislocation multiplication, storage and cross slip on the correlation functions are discussed. Various analogies and fundamental differences to the statistical mechanics of thermodynamic equilibrium are outlined. Application of the theory of noise-induced transitions to dislocation dynamics gives new insight into the physical origin of the spontaneous formation of dislocation structures during plastic deformation. The results demonstrate the importance of the strain-rate sensitivity in dislocation patterning.     

Temperature-induced rearrangement of the dislocation pattern of Persistent Slip Bands in copper single crystals

Experimental investigations are reported on mechanisms by which dislocation arrangements of Persistent Slip Bands (PSBs) respond to changes of the deformation temperature. Copper single crystals orientated for single slip were cyclically deformed well into saturation at 300 K at an applied resolved plastic shear-strain amplitude, , such that the plastic strain became localized in PSBs. The spacings of the dislocation walls in these PSBs are about 1.4 m. After the temperature had been lowered to 77 K, cyclic deformation was continued with unchanged . A transformation of the dislocation pattern started. A certain fraction of the PSBs produced at 300 K finally showed a mean wall spacing of about 0.7 m which is typical for PSBs formed at 77 K. The remaining PSBs did not finish the transformation and became obviously inactive. In the state of cyclic saturation reattained at 77 K 50% of the PSBs, which had been formed at 300 K, show the dislocation pattern characteristic of 77 K. It is concluded that the amplitude of the resolved plastic shear strain localized in a PSB, , must be twice as large at 77 K as at 300 K. In an additional series of experiments crystals were cyclically deformed at constant temperatures of 430 K, 300 K, 190 K, and 77 K. In the temperature range covered by these experiments, the amplitude of the saturation flow stress, _S, appears to be proportional to the intrinsic amplitude of the PSBs, .     

Microstructural instabilities: dislocation substructures with pronounced mechanical effects

Microstructure evolution is largely dominated by the internal stress fields that appear upon the appearance of inhomogeneous structures in a material. The hardening behaviour of metals physically originates from such a complex microstructure evolution. As deformation proceeds, statistically homogeneous distributions of dislocations in grains become unstable, which constitutes the driving force for the development of a pronounced dislocation substructure. The dislocation structure already appears at early stages of deformation due to the statistical trapping of dislocations. Cell walls contain dislocation dipoles and multipoles with high dislocation densities and enclose cell-interior regions with a considerably smaller dislocation density. The presence and evolution of such a dislocation arrangement in the material influence the mechanical response of the material and is commonly associated with the transient hardening after strain path changes. This contribution introduces a micromechanical continuum model of the dislocation cell structure based on the physics of the dislocation interactions. The approximation of the internal stress field in such a microstructure and the impact on the macroscopic mechanical response are the main items investigated here.     

Spatio-temporal aspects of low-temperature thermomechanical instabilities: A model based on dislocation dynamics

The occurrence of plastic instabilities which are accompanied by a significant heat release is a typical feature of the plastic behaviour of metals deformed at sufficiently low temperature. This phenomenon may be studied within the framework of a dislocation-dynamical model. The influence of the heat which is released by the deformation process on the dislocation velocity, and thus on the deformation dynamics, is taken into account. In particular, the influence of the spatial coupling which arises from heat conduction on the spatio-temporal behaviour of the deformation process is studied.     

Temporal dissipative structures in cyclically deformed metallic alloys

cyclically deformed metallic alloys. The model employs quasi-chemical reactions of multiplication, annihilation and positive feedback among the populations of mobile, immobile, and Cottrell-type dislocations [1]. Three major types of loading have been simulated, namely, pure sinusoidal, “creep fatigue”, and ramp loading. Computer movies of the temporal evolution of stress serrations and dislocation densities have been produced as an aide for analysis and illustration. It has been demonstrated that the model successfully reproduces strain bursts and stress serrations in fatigued metallic alloys in terms of the underlying dislocations mechanisms, thus establishing the fundamental connection between micro- and macromechanics of cyclic deformation. Received: 20 June 1996/Accepted: 6 October 1996     

Mechanism of Strain Rate Effect Based on Dislocation Theory

Based on dislocation theory, we investigate the mechanism of strain rate effect. Strain rate effect and dislocation motion are bridged by Orowan＇s relationship, and the stress dependence of dislocation velocity is considered as the dynamics relationship of dislocation motion. The mechanism of strain rate effect is then investigated qualitatively by using these two relationships although the kinematics relationship of dislocation motion is absent due to complicated styles of dislocation motion. The process of strain rate effect is interpreted and some details of strain rate effect are adequately discussed. The present analyses agree with the existing experimental results. Based on the analyses, we propose that strain rate criteria rather than stress criteria should be satisfied when a metal is fully yielded at a given strain rate.     

Scanning probe microscopy on superconductors: Achievements and challenges

A dislocation dynamical model of the reaction-diffusion type is used to describe the spatio-temporal dynamics of Lüders band propagation in polycrystals. The diffusive nature of dislocation glide is traced back to the random crystallographic orientation of the active slip systems. The role of pile-ups in dislocation multiplication is accounted for by a dynamical generalization of the Hall-Petch law. It is argued that Lüders bands in polycrystals are related to a bistable dynamics of mobile dislocations. Further results obtained cover the dependences on material parameters and deformation conditions of (1) the occurrence, (2) the strain, propagation velocity and width of Lüders bands, and (3) the upper and lower yield stresses. These results are in good agreement with experimental findings.     

Strain Rate Sensitivities of Face-Centred-Cubic Metals Using Molecular Dynamics Simulation

We use dislocation theory and molecular dynamics （MD） simulations to investigate the effect of atom properties on the macroscopic strain rate sensitivity of f cc metals. A method to analyse such effect is proposed. The stress dependence of dislocation velocity is identified as the key of such study and is obtained via 2-D MD simulations on the motion of an individual dislocation in an fcc metal. Combining the simulation results with Orowan＇s relationship, it is concluded that strain rate sensitivities of fcc metals are mainly dependent on their atomic mass rather than the interatomic potential. The order of strain rate sensitivities of five fcc metals obtained by analysing is consistent with the experimental results available.     

Climb via vacancy diffusion of edge dislocations in 2D dislocation microstructures

The prevention of strength degradation of components is one of the great challenges in solid mechanics. In particular, at high temperatures material may deform even at low stresses, a deformation mode known as deformation creep. One of the microstructural mechanisms that governs deformation creep is dislocation motion due to the absorption or emission of vacancies, which results in motion perpendicular to the glide plane, called dislocation climb. However, the importance of the dislocation network for the deformation creep remains far from being understood. In this study, a climb model that accounts for the dislocation network is developed, by solving the diffusion equation for vacancies in a region with a general dislocation distribution. The definition of the sink strength is extended, to account for the contributions of neighbouring dislocations to the climb rate. The model is then applied to dislocation dipoles and dislocation pile-ups, which are dense dislocation structures and it is found that the sink strength of dislocations in a pile-up is reduced since the vacancy field is distributed between the dislocations. Finally, the importance of the results for modelling deformation creep is discussed.     

Magnetic studies of the dislocation structure of iron single crystals deformed at 195K and 77K

Measurements of the coercive field, the initial susceptibility and the reversible susceptibility in the approach to ferromagnetic saturation show that during low-temperature deformation of iron single crystals mainly screw dislocations are created. Long-range internal stresses are found to be significantly smaller than in crystals deformed at room temperature. Macroscopic slip occurs on several slip systems. In the parabolic region of the work-hardening curves at 195 K the relation is valid, where τ isthe shear stress andN is the dislocation density. In the region of saturation of the shear stress the dislocation density further increases. After room-temperature prestrain the relation appears to hold for 77K-deformation also. Exhaustion hardening of edge dislocation is found at the beginning of the low-temperature deformation.     

The role of thermally activated processes in the formation of magnetosensitive point-defect complexes in NaCl: Eu single crystals

The formation of magnetosensitive point-defect complexes in NaCl: Eu crystals is investigated. It is shown that the formation of intermediate metastable magnetosensitive point-defect complexes and their subsequent spontaneous transformation into relaxation products are thermally activated processes and do not depend on the diffusion mobility of impurity-vacancy dipoles. It is revealed that the magnetic field induces a transition of the magnetosensitive point-defect complexes to a new state that cannot occur in the absence of a magnetic field. A variation in the heat treatment temperature makes it possible to enhance the magnetoplastic effect significantly (by a factor of three) and to create the appropriate conditions for the existence of magnetosensitive complexes in the crystal over a long period of time.     

New aspects of the plastic deformation of silicon – prerequisites for the reshaping of silicon microelements

New shapes of silicon microelements which can be partially situated outside the wafer plane can be created by the combination of wet anisotropic etching and plastic deformation at high temperatures. Therefore new applications become possible. In order to characterize the plastic behaviour of the silicon microelements bending tests in the 3-point manner were carried out at monocrystalline, differently orientated beams with variation of temperature, bending rate and maximum bending. Additionally the fracture strength at room temperature of deformed and undeformed beams was determined. The dislocation content introduced during the deformation was analysed by the etch pit technique. The deformation is characterized by the formation of dislocations, a pronounced yield point effect, and an orientation-dependent strengthening. The yield points depend strongly on temperature. Because of the strong dependence on the deformation parameters it is possible to create the same amount of irreversible deformation at different stages of the stress–bend diagrams resulting in different dislocation contents and therefore different properties. The analysis of the fracture strength values by means of the Weibull statistics shows a slightly decreased average fracture strength of the deformed material in comparison to the undeformed silicon but a strongly increased Weibull modulus. Received: 22 September 1998 / Accepted: 29 January 1999 / Published online: 28 April 1999     

TEM investigation of the interaction between dislocation and nitride precipitates in deformed high manganese-chromium austenitic steels

The interaction between dislocations and nitride precipitates during high-temperature creep deformation of high manganese austenitic steels has been investigated by transmission electron microscopy. Most of the dislocations activated by applied stress were dissociated into Shockley partials. The fine TiN precipitates are pinning and/or incorporating the bow-type moving dislocations and they turned out to be more effective than the coarser TaN in disturbing the dislocation movement.     

Dislocation emission from an elliptically blunted crack tip with surface effects

The explicit expressions for critical stress intensity factors are derived for edge dislocation emission from an elliptically blunt crack with surface effects under mode I and mode II loadings. The influence of surface effects on dislocation emission criterion is analyzed. The result indicates the impact of the surface stress becomes remarkable for nanoscale blunted cracks and some particular materials, which cannot only affect the value of the critical stress intensity factors for dislocation emission, but also alter the emission angle.     

Dislocations in deformed and annealed Fe-3 wt.% Si single crystals

Changes of the dislocation arrangement during isothermal anneal in the temperature range 593 K–823 K of Fe-3 wt.% Si single crystals previously deformed 40% in tension are studied by TEM. From the observed decrease in dislocation densities it is concluded that bundles of dislocations which are the main component of the dislocation arrangement consist predominantly of edge dipoles of primary dislocations. The maximum height of the dipoles is about 16 nm.