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.     

Laws of electrical stimulation of plastic deformation of metals and alloys at various structural levels

The laws governing the electrical stimulation of plastic deformation at various structural levels are reviewed. The following topics are covered: the hierarchy of external current stimuli affecting plastic deformation; the variation of the mobility of individual dislocations in zones of thermally activated and quasiviscous motion associated with mechanical, electrical, and combined stimuli over a wide range of temperatures (microlevel); the evolution of defect structure in materials of various structural classes subjected to electrical stimulation over a wide range of strains (mesolevel); the ordered character of plastic deformation inhomogeneities; models of the stress — strain state in the presence of current stimulation (macrolevel) and their interpretation.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 3, pp. 66–96, March, 1996.     

Connection between hardness and stresses in the plastic region

In studying plastic deformation by measurement of hardness [1] it is necessary to use a hardness-stress calibrating graph plotted from the results of tests under the simplest stress conditions. For the use of these graphs in plastic deformation in general to be well-founded, it is essential to have experimental data confirming that the hardnessstress curve is common to various states of stress. However, [1–3] give this data from tensile, compressional and torsional tests only. Clarification of this problem is particularly important, because all the stress and deformation components for a number of cases of practical importance can be determined by reference to the stress intensities at various points in a body [4].The present work gives the results of experimental work on the connection between stresses and hardness under conditions of two- and three-dimensional stress.     

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.     

Plasticity limit of metals during hot plastic deformation

A model of plasticity limit has been derived in the condition of hot plastic deformation, where dynamic recrystallization takes place, through the ratio between the rate of grain boundary sliding and the overall deformation rate. If fracture occurs preferentially at the grain boundaries we can replace the grain boundary deformation through the energy needed to cause fracture and express the temperature influence on the deformation stress. The plasticity limit is then the function of Zener-Hollomon parameter and deformation stress, where the exponent of deformation stress has a value of –4·3.     

Method of movable cellular automata as a tool for simulation within the framework of mesomechanics

Conclusion The proposed MCA method is based on mesomechanics of heterogeneous media [4, 5, 9]. It is connected first with the ability to describe the material as a set of structural elements of deformation [9]. The role of the structural unit in the MCA method is played by the element (movable cellular automaton). The expressions of interparticle interactions used, as well as the rules of changing the state of the elements, allow us to simulate a wide range of phenomena including melting, chemical reactions, and phase transformations. The characteristic size of the element and its properties are defined based on the features of the model constructed in the framework of mesomechanics as described in [9]. Therefore the MCA method as a computational technique allows us to realize the principles of mesomechanics when simulating material response to external loading of different types. This method is highly recommended in computer-aided design of new materials.Institute of Strength Physics and Materials Science, Tomsk. North Carolina State University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 11, pp. 58–69, November, 1995.     

Influence of the temperature and structural state on the systematic features of plastic deformation in Mo-Re-based alloys

The salient aspects of the formation of a dislocation structure during plastic deformation of the alloys Mo-47 wt. % Re and Mo-47 wt. % Re-1 vol. % ZrO₂ at T=300 K in previously recrystallized and polygonalized structural states have been studied with an electron microscope. The studies revealed the systematic features of rotational modes of plastic deformation in these alloys under conditions of substructural hardening and high-temperature grain-boundary slip. An analysis is made of the effect that the substructure and highly dispersed particles of the oxide phase have on the plastic deformation and mechanical properties of Mo-Re-based alloys at T=300-1500 K.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 12, pp. 96–104, December, 1994.     

Role of solid-solution strengthening and interactions in the dislocation ensemble in the formation of flow stress in austenitic nitrogen steel

The paper reports on an experimental investigation of the role of structural levels of deformation in the formation of the flow stress of austenitic nitrided steel. The contributions to the yield stress and the flow stress from the structural levels of various scales have been determined and it has been found that small-scale levels make the main contribution to the strain resistance. A detailed study of the dislocation ensemble has shown that undergoes strong relaxation at different stages of deformation. The laws of solid-solution strengthening and its effect on substructural transformations are examined.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 3, pp. 33–56, March, 1996.     

Structural levels of translational-rotational deformation of crystals in a complex stress state

A theory of deformation is developed on the basis of the concept of the multilevel development of plastic flow of crystals, with the participation of rotation. The influence of the loading conditions on the complex trajectories in stress space and in time on the crystal deformation is analyzed. The rheological properties of the material in active deformation over two-element loading trajectories with an orthogonal discontinuity are investigated. Considerable attention is paid to the investigation of the influence of various loading trajectories on the creep in isothermal conditions.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 28–33, September, 1984.     

Structure,unelastic properties,and deformation behavior of ultrafine-grained titanium

The results of investigations into the structure, unelastic properties, deformation behavior, strength, and plasticity of ultrafine-grained titanium produced by equichannel angular pressing are discussed. Particlular emphasis has been placed on the grain-boundary unelasticity and the effects of external thermal and thermal-force actions on the deformation behavior and plastic deformation localization at the meso- and macroscale levels. The influence of cold plastic deformation of ultrafine-grained titanium on the grain-boundary unelasticity and temperature dependence of the mechanical properties is considered.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 33–43, September, 2004.     

The relaxation-element method in models of the plastic strain of structurally inhomogeneous materials

It is shown that it is possible to represent a continuous field of plastic strain with high gradients in local regions of a material by methods of the continual theory of defects. A practical method of constructing highly inhomogeneous fields of plastic strain in local regions of a solid under load is proposed, and the stress fields connected with them are determined. The method is used to propose a principle of a unique connection between the process of inelastic deformation and stress relaxation in local volumes of the material. This enables one to simulate the inhomogeneous fields of plastic strain and stresses connected with the external stress without discontinuities and singularities at the interfaces between the phases and crystallites.Institute of Physics of the Strength and Study of Materials, Siberian Branch, Russian Academy of Sciences. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 16–22, February, 1994.     

High-temperature operation of AlGaInAs/InP lasers1994

We discuss the design of uncooled lasers which minimizes the change in both threshold current and slope efficiency over the temperature range from–40 to +85°C [1]. To prevent carrier overflow under high-temperature operation, the electron confinement energy is increased by using the Al _x Ga _y In_1–x–y As/InP material system [1] instead of the conventional Ga _x In_1–x As _y P_1–y /InP material system. Experimentally, we have investigated strained quantum well lasers with three different barrier layers and confirmed that the static and dynamical performance of the lasers with insufficient carrier confinement degrades severely under high-temperature operation [2]. With an optimized barrier layer, the Al _x Ga _y In_1–x–y As/InP strained quantum well lasers show superior hightemperature performance, such as a small drop of 0.3 dB in slope efficiency when the heat sink temperature changes from 25 to 100°C [3], a maximum CW operation temperature of 185°C [4], a thermally-limited 3-dB bandwidth of 13.9 GHz at 85°C [2], and a mean-time-to-failure of 33 years at 100°C and 10 mW output power [5].     

Dislocation dynamics and thermal hardening of alloys with L12 superlattice

We studied the effect of superdislocation velocities on thermal hardening of alloys with the L1₂ superlattice. We estimate the activation energy for self-stopping of dislocations due to changes in the elastic field of moving dislocations as compared with immobile dislocations. We calculate the velocity of a dislocation loop element, taking into account interactions with dislocations. We show that, because of deformation stress, superdislocations can move at nearly the speed of sound. This, in turn, can help reduce the activation energy for self-stopping processes of superdislocations by a factor of 1.3 to 5.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 57–61, February, 1996.     

Evolution of the Structure and Carbon Atom Transfer in the Zone of Fatigue Crack Growth in Ferrite-Pearlite Steel

Structure and phase transformations in Fe–0.6C–1Mn–2Si steel subjected to multicyclic fatigue tests under normal conditions and with intermediate electrostimulation are investigated by the methods of metallography of etched microsections and scanning and transmission electron diffraction microscopy of thin foils and carbon replicas. It is demonstrated that fatigue failure under normal loading is preceded by complete dissolution of initial cementite particles with carbon localized on structural defects (dislocations, subboundaries, and boundaries), micropores, and microcracks. Electrostimulation, promoting the relaxation of stress concentrators through dissolution of particles localized on the grain boundaries and the state change of the interphase boundaries between the matrix and second-phase particle, causes the mean and maximum subcritical crack length to increase together with the thickness of the sample layer involved in the strain of the material and the zone of fatigue crack growth. This is accompanied by a significant increase in the operating lifetime of the material.     

A dynamic deformation model of an elastoplastic porous medium

A closed system of equations is obtained for dynamic deformation of an elastoplastic Prandtl-Reiss porous medium. The heterogeneous approach makes it possible to describe the properties of such media in a wide range of loading rates within the theory of plastic flow with the kinematic simplification. The hydrodynamic deformation theory of porous media [1, 2] has been first correctly generalized to the case of including the deviator components of the stress tensor of the medium. The well-known functions of the model are determined from analyzing the fundamental deformations of the corresponding spherical cells.Institute of Theoretical and Applied Mechanics, Siberian Branch, Russian Academy of Sciences. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 46–53, July, 1992.     

Variation of the ultrasonic velocity in al under plastic deformation

Variation of the velocity of ultrasound propagation in polycrystalline aluminum under plastic deformation is studied. The dependences of the velocity of ultrasound on the strain and the actual stress are found to consist of three distinct stages. The study of the complex shapes of these dependences allows one to reveal additional stages in the parabolic stress-strain curve of the plastic flow, these features being impossible to observe by conventional methods. The behavior of the ultrasonic velocity observed in the experiment is explained by the changes in the defect structure of the material under deformation.     

Wave phenomena during creep in macrocrystalline aluminum

A wave model of plastic flow, which has been theoretically substantiated and experimentally verified under the conditions of active quasistatic loading of diverse materials, is being developed on the basis of concepts of the autocatalytic nature of elementary acts of plastic deformation. Data from the study of the evolution of distortion fields during low-temperature creep of macrocrystalline aluminum are given in order to explain the tighter relation between the parameters of plastic-deformation waves and the characteristics of the elementary processes of plastic shear. The wave nature of this evolution is emphasized and a linear correlation is found between the creep rate and the velocity of the plasticity waves. The activation volumes of the processes controlling the velocity of the plastic waves and the creep rate are shown to be correlated.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 5–9, April, 1991.     

Periodic solutions for planar four-body problems

For Newtonian four-body problems with equal masses, we use variational minimizing methods to prove the existence of non-collision periodic solutions such that all bodies move on two symmetric trajectories with opposite orientation; here the methods and results are simpler and more general than those of Chen [K.-C. Chen, Action minimizing orbits in the parallelogram four-body problem with equal masses, Arch. Ration. Mech. Anal. 158 (2001) 293–318].