Dynamics of plastic deformation: Waves of localized plastic deformation in solids

Conclusions It has been shown here that a localized plastic deformation in structurally inhomogeneous media can be of a wave nature and can propagate in the form of nonlinear plastic waves, not only at the microscopic level but also at the mesoscopic level. It has been established that there is an interrelationship between this new effect and grain-boundary slippage (an effect which has been under study for a long time) and also with certain types of quasiviscous fracture in plastically deformable materials.We have discussed certain specific practical problems in the mechanics of plastic deformation, and for certain types of fracture. In the future, these problems will be discussed at a more profound level and in greater detail, because of experimental studies which are presently being carried out on the dynamics of deformation for various types of loading and fracture [17, 18, 31]. We hope that the approach proposed here for a theoretical study of the localization of deformation and fracture can be taken to study such effects as splitting off [31], the influence of defect fluxes on grain-boundary slippage [22], superplasticity [23], the behavior of tectonic faults and boundaries of various types [32], electroplastic and magnetoplastic effects, and high-temperature localization of deformation [25].The general nature of the approach proposed here results from the circumstance that a localization of deformation is present explicitly or implicitly during plastic deformation, and the behavior of this deformation plays a role of fundamental importance in the propagation of plastic deformation through a material.The author wishes to thank V. E. Panin for a constant discussion of this problem and I. O. Nedavnii for carrying out the numerical calculations.V. V. Kuibyshev Tomsk State University. Institute of Strength Physics and Materials Science. Siberian Branch of the Russian Academy of Sciences. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 19–41, April, 1992.     

Anomalous plastic deformation in nichrome

The temperature dependences of the properties of Kh20N80 Nichrome under tension have been found. Decarbonization of the alloy showed that there are two regions of anomalous strengthening, at 400–450 and 600–700 °C. The first region is attributed to order in the binary system, while the second is attributed to carbide aging. Correlation analysis of the oscillograms of the tension diagrams showed no local relationship between the load discontinuities and the intervals between them. The inadequacies of existing models for discontinuous flow are discussed.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 11, pp. 12–17, November, 1970.     

Universality and scaling of unstable plastic flow

The statistics of the jumplike plastic deformation of a Cu–Be alloy under the conditions of a low-temperature unstable plastic flow is studied experimentally. At a high strain rate, the parameters of the load jumps are found to be related by power laws, which corresponds to a scale-invariant behavior. A comparison with the data obtained for another mechanism of plastic instability, namely, the Portevin–Le Chatelier effect, points to the existence of universal laws governing the dynamics of a dislocation ensemble in the conditions of plastic instability.     

Relaxation waves in plastic deformation

Conclusion Experimental study of distortion fields of plastically deformed solids performed on a wide range of materials including fine- and coarse-grain body- and face-centered polycrystals, as well as amorphous alloys reveals that in these materials plastic deformation develops in the form of waves having translational and rotational components. This fact is in accordance with the currently developed theory of a turbulent mechanical field, which also has translational and rotational components.The plastic deformation waves are observable at a macroscopic structural level, and their spatial period (wavelength) is determined by the dimensions of the deformed object and dimensions of the basic structural elements (for a polycrystal, the grain size). The propagation rate of these waves is significantly less than the characteristic propagation rate of an elastic excitation and the velocity of previously described plastic waves which are produced by shock deformation, which latter speed is determined by the hardening coefficient.The character of plasticity waves depends on the form of the material's deformation curve, and on the stage of the hardening curve. The distribution of plastic distortion components changes especially significantly in prefailure regions, which allows detection of the latter long before formation of a macroscopic crack. The role of rotations in forming the failure process has been established.A synergetic interpretation of plasticity wave formation has been proposed, based on synchronization of relaxation acts occurring at stress concentrators during the deformation process.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 19–35, February, 1990.     

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 inhomogeneity of plastic deformation

Considerable local strain differences occur in single crystals as a consequence of slip bands. A significant contribution to this phenomenon is the effect of the deformation rate on the inhomogeneity of its distribution. In polycrystalline materials the plastic deformation is affected by grain boundaries and their vicinity as well as by various orientations of single grains in onephase metals and alloys, and by various component properties in multiphase materials. In some cases it has been possible to describe these phenomena by means of micromechanics. Valuable information has also been acquired by means of three-dimensional stereology.     

Surface effects in plastic deformation of metals

It is now accepted that the appearance of slip bands on the surface of a plastically deformed metal is evidence that the deformation is not homogeneous but is concentrated on relatively few atomic planes. Recent microscopical experiments have suggested that this conclusion is only valid in the later stages of deformation and that the first fractional per cent of strain is much more nearly homogeneous. Theories to account for both these stages of deformation are examined in the light of microscopical evidence.

The validity of conclusions about internal processes based on experiments on the surface is discussed; it is shown that the surface finish affects not only the appearance of internal processes but also the processes themselves.

In cases where the deformation is not homogeneous the balance of evidence is that it is also not continuous in time: instead, slip on an active slip plane tends to a limit which is reached either gradually or suddenly depending on the nature of the metal and the conditions of stress. The same processes which stop slip on the active planes produce general hardening of the metal. However, slip can restart on or near to former slip planes as a result of mechanisms activated by temperature and stress, and can, in favourable cases, continue until fracture. Therefore slip bands, the sources of hardening, are also places of weakness.     

Modern aspects of plastic deformation in metals

After a historical survey of crystal plasticity the rôle of dislocations in plastic deformation of metals is outlined. The theory of plastic deformation in metal single crystals before the impact of transmission electron microscopy is described. Recent experimental results on glide and workhardening in single crystals of b.c.c. metals are reviewed and explained by a simple dissociation model of the screw-dislocation cores. A relative success of this explanation together with calculations of atomic structure of dislocation cores support the conclusion that different structures of screw dislocation cores are responsible for both differences and similarities between plastic behaviour of f.c.c. and b.c.c. metals. Further developments in the field of metal crystal plasticity by modern experimental techniques (transmission electron microscopy of deformed crystals in the stress-applied state, magnetic studies of dislocations in ferromagnetic crystals) and by atomic calculations of defect configurations are discussed.Na Slovance 2, Praha 8, Czechoslovakia.Invited paper presented on a plenary session of the First European Conference on the Physics of Condensed Matter organized by the Board of the Condensed Matter Division of E.P.S., in Florence on 14–17 September 1971 (Chairman: Prof. S. F. Edwards; Schuster Laboratory, University of Manchester).     

Physical nature of stages in plastic deformation

Conclusion In summary, the transition from one stage of plastic deformation to another is due to the phase transformations in the subsystem of deformation defects. These transformations are controlled by an internal parameter of the system, viz., the scalar dislocation density, whose value is determined by both the external force and processes retarding the shear and annihilation. The main structural level controlling this process is the level of the dislocation subsystem.We express our thanks to associate professors L. A. Telyakov, Yu. P. Sharkeev, and V. A. Starenchenko, Candidates G. V. Daneliya, D. V. Lychagin, and I. A. Lapsker, and scientific associates S. P. Zhukovskii, L. I. Trishkina, A. V. Paul', and T. S. Kunitsyna, with whose collaboration part of the results reported in this review were obtained.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 89–106, February, 1990.     

Nowcasting Avalanches as Earthquakes and the Predictability of Strong Avalanches in the Olami-Feder-Christensen Model

Nowcasting earthquakes, suggested recently as a method to estimate the state of a fault and hence the seismic risk, is based on the concept of natural time. Here, we generalize nowcasting to a prediction method the merits of which are evaluated by means of the receiver operating characteristics. This new prediction method is applied to a simple (toy) model for the waiting (natural) time of the stronger earthquakes, real seismicity, and the Olami-Feder-Christensen earthquake model with interesting results revealing acceptable to excellent or even outstanding performance.     

Avalanches and Self-Organized Criticality in superconductors

We review the use of superconductors as a playground for the experimental study of front roughening and avalanches. Using the magneto-optical technique, the spatial distribution of the vortex density in the sample is monitored as a function of time. The roughness and growth exponents corresponding to the vortex `landscape' are determined and compared to the exponents that characterize the avalanches in the framework of Self-Organized Criticality. For those situations where a thermo-magnetic instability arises, an analytical non-linear and non-local model is discussed, which is found to be consistent to great detail with the experimental results. On anisotropic substrates, the anisotropy regularizes the avalanches.     

Mesoscale plastic deformation of aluminum polycrystals

A study is made of the mechanism of plastic deformation at the mesoscale level in flat specimens of aluminum polycrystals. The mechanism is examined with the use of high-resolution optical-television system TOMSC-1. It is shown that a multilevel mesoscale structure is formed in the specimen as it is deformed. The formation of this structure leads to the appearance of two types of stationary waves 120 μm and 4.8 mm long. The results are interpreted within the framework of a hierarchy of mesoscale levels of deformation and are linked with the decisive role of surface oxide films in the formation of the mesoband structure and stationary waves associated plastic flow. Institute of the Physics of Strength and Materials Science, Siberian Branch of the Russian Academy of Sciences. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 31–39, January, 1997.     

Current pattern of plastic deformation stages

A review of current concepts of strain hardening stages in metallic materials upon active deformation is presented. By now, five stages of the stress () — strain () dependence reliably have been identified. These stages differ by the strain hardening coefficient = d/d. There are also some data on stage VI. In the paper, the role of substructural transformations in the change of strain hardening stages is discussed, the factors complicating the deformation stage pattern are analyzed, and the effect of grain size on stages of strain hardening is examined.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 8, pp. 90–98, August, 2004.     

Microstructure evolution during severe plastic deformation

Radiotracer diffusion studies of severely deformed, ultra-fine grained materials have revealed the presence of ultra-fast transport paths, which include “non-equilibrium” grain boundaries and free volume. Under some experimental conditions, percolating porosity is produced even in pure copper. Micro-cracks may form in metals, if the local maximum shear stress exceeds the shear yield stress. However, their growth and propagation is postponed till late in the deformation process owing to the ductility of metals, the hydrostatic component of the stress system and/or dynamic recovery/recrystallization. In other words, crack growth and propagation is present only when the scope for further deformation is highly restricted. Using this approach, the load required for equal channel angular pressing, the change in the slope of the Hall–Petch plot with decreasing grain size and the theoretical limit for the smallest grain size attainable in a metal in a severe plastic deformation process are predicted and validated by experimental results. Experimentally successful prevention of percolated crack formation by the superposition of a hydrostatic pressure is also accounted for using this model.