Plasticity and strength of solids

This article reviews research conducted over the past 15 years at the intersection of the physics and mechanics of a deformable solid on the basis of the concept that plastic deformation and failure represent the evolution of shear-stability loss of a loaded material at various scale levels. This research has led to the founding of a new scientific discipline: the physical mesomechanics of materials, in which a deformable solid is regarded as a multilevel self-organizing system. The development of mechanisms and stages of plastic deformation at different scale levels conforms to the principle of scale invariance. This qualitatively changes the methods of describing the plastic deformation and failure of solids. The most pressing areas of research in the physical mesomechanics of materials are noted; these will determine the basic trends in research on the strength of solids in the next decade. Institute of Strength Physics and Materials Science, Siberian Branch, Russian Academy of Sciences. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 7–34, January, 1998.     

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.     

Relationship of a gauge model of an elasto-plastic medium to the Mindlin theory

We examine the relationship between the simplest gauge model of a material with the Mindlin theory that takes into account microstructure in linear elasticity. We establish a connection between the dynamical equations for the two models. The connection allows us to relate an unknown material constant in the gauge Lagrangian to the inertial properties of the structural elements. We obtain an estimate of the unknown constant and the corresponding characteristic frequency for the dimensions of elements with different structural levels of deformation.Institute of Strength Physics and Materials Research, Russian Academy of Sciences, Siberian Branch. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 44–48, April, 1994.     

Scale invariance of plastic deformation of the planar and crystal subsystems of solids under superplastic conditions

The theory of structural transformations in the planar sybsystem (surface layers and internal interfaces) of solids under plastic deformation is developed. The theory is based on a consideration for local curvature of the crystal lattice, with new structural states arising in its interstices, responsible for plastic distortion. To satisfy the superplastic condition, such high-rate mechanisms should develop in both planar and 3D crystal subsystems. In a translation-invariant crystal, this condition is met by concentration fluctuations. The multiscale criterion of superplasticity is formulated based on the scale invariance of plastic deformation of the planar and crystal subsystems in a deformable solid. Beyond the criterion, superplasticity passes to the creep mode with restricted plasticity of the material.     

Computer modeling of the dynamics of high-velocity impact and accompanying physical phenomena

Some results of mathematical modeling of high-velocity collisions of solid deformable bodies are presented. A model is presented of a porous elastoplastic medium whose matrix undergoes a polymorphic phase transition during deformation, and approaches to the calculation of dynamical failure are examined. Finite-difference methods for solving boundary-value problems are briefly reviewed. The interaction of projectiles, having different shape, with different targets (semiinfinite, two-layer, separated) is investigated and the process of spall failure in porous media and media undergoing a polymorphic phase transition is examined on the basis of mathematical modeling.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 8, pp. 5–48, August, 1992.     

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.     

Fatigue failure mechanism of polycrystalline materials at the mesoscopic level

Systematic studies of the mesoscopic mechanisms of deformation of polycrystalline materials of lead and its alloys have been carried out under conditions of sign-alternating bending at room temperature. It has been shown that fatigue failure is due to the evolution of vortices of mesoscopic substructures. Multiple slip separated in adjacent grains is the basis for this kind of deformation. This causes extremely strong localization of the displacement in individual favorably oriented grains and self-organization of these grains in agreement with regular structural levels of deformation. In polycrystalline lead, the mesoscopic substructure has a block character, with each block containing several grains. The elements of such substructures are nucleated in stress mesoconcentrator zones which arise at the grain boundaries under conditions of intense grain boundary slippage. In the course of cycling they gradually propagate through the whole transverse cross section of the sample, which completes its failure. Alloying substantially changes the character of the mesoscopic substructures which are formed. We have considered the different types of vortex mesoscopic substructures and studied their connection with cyclical endurance of the alloy. Recommendations for increasing the fatigue endurance of plastic polycrystalline materials are given. Institute of the Physics of hardening and Materials Science, Siberian Section, Russian Academy of Sciences. V. D. Kuznetsov Siberian Physicotechnical Institute at Tomsk University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 6, pp. 40–57, June, 1996.     

Variation of apparent creep activation energy in plastic deformation of molybdenum in diffusion contact with nickel

The variation of the apparent creep activation energy as a function of the state of grain boundaries is investigated in the deformation of molybdenum in the presence of diffusion fluxes of nickel at the grain boundaries. It is shown that this energy varies in the same way as in the plastic deformation of classical superplastic materials.Physics Institute of Strength and Materials Science, Siberian Branch, Russian Academy of Sciences. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 110–113, May, 1993.     

Influence of nonhydrostatic stresses on the development of martensitic transformations and inelastic strains at various levels in Ti(Ni-Cu-Fe) polycrystalline intermetallic compounds

The levels of inelastic martensitic strain of polycrystals during a thermoelastic martensitic transformation under a load are discussed. The example ofTi(Ni-Cu-Fe) alloys with the B2 structure was used to study the role of microlevel and mesolevels in inelastic martensitic deformation during cooling of polycrystals under a load and loads in different initial structural states. V. D. Kuznetsov Siberian Physicotechnical Institute at Tomsk State University. Institute of Physics of Strength of Materials and Materials Science, Siberian Branch of the Academy of Sciences of the USSR, Tomsk. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, p. 35–46, January, 1998.     

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.     

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.     

Transition from a kinetic to a nonlocal hydrodynamic description for a nonrelativistic gas

Using a method that differs from the Chapman-Enskog, Grad, and Hilbert methods [1–4], we derive equations of linear hydrodynamics from a linearized kinetic equation. Noa priori assumptions are made as to the magnitude of the dissipative terms, the spatial gradients, or the interaction integral. The equations obtained for macroscopic hydrodynamic quantities are exact in the sense that the exact solution of the linearized kinetic equation can in principle be reconstructed from any solution of those equations. The constitutive relations of the model are nonlocal in time and space. As a direct consequence of the kinetic equation limitations are obtained at the corresponding kernels of nonlocality, which are associated with reversibility at the microlevel (analog of the Onsager relations) and the dissipativity.Institute of Terrestrial Physics, Russian Academy of Sciences. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 95–99, February, 1995.     

Structural changes in TiC-TiNi alloys on deformation

The deformation of a composition material with a binding phase of shearing-unstable alloy, namely, titanium nickelide, is considered. X-ray structural analysis and electron—positron annihilation methods are used to investigate the structural changes in the composite material as a function of the degree of deformation. It is shown that the deformation produces the structural phase transition B2 B19, which is confirmed by x-ray structural investigations and electron positron annihilation.Institute of Strength Physics and Materials Science, Siberian Branch, Russian Academy of Sciences. Translated from Izvestiya Uchebnykh Zavednii, Fizika, No. 4, pp. 100–103, April, 1994.     

Topological dislocation-type defects and mechanisms of plasticity and failure of nanostructured and amorphous materials

Possible mechanisms of plastic deformation and failure of nanostructured and cluster amorphous materials have been considered. It is shown that the most probable carriers of plastic deformation in these materials are macrodislocations—linear topological defects of the regular nanocrystallite packing in the nanostructure or cluster packing in amorphous materials. Continuum models are proposed to describe the processes of plastic deformation and failure of nanostructured and cluster amorphous materials. Original Russian Text ? L.S. Vasil’ev, S.F. Lomaeva, 2009, published in Izvestiya Rossiiskoi Akademii Nauk. Seriya Fizicheskaya, 2009, Vol. 73, No. 1, pp. 128–131.     

Electron form factors of deformable nuclei

Using the smallness of the deformation parameter of the nucleus, we obtain simple explicit expressions for the form factors of electroexcitation of the low-lying rotation-vibration states of light, deformable, even-even nuclei. The expressions satisfactorily describe the experimental data on the excitation of collective nuclear states by the inelastic scattering of fast electrons.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 62–66, September, 1987.     

Energy balance in deformation mechanics of solids at low temperatures

The model of a solid in the form of an ensemble of independent anharmonic oscillators arranged in a uniform stress field has been considered to analyze the energy balance during adiabatic mechanical loading of a solid at low temperatures. Oscillator elongation is determined as the average over the ensemble, and a part of its energy is matched to this quantity. This part has the physical meaning of the mechanical energy of sample deformation and becomes a part of the energy balance upon deformation. After averaging, the uniform force field is replaced by the resultant force associated with the average deformation. Another component of the balance at low temperatures is the energy of zero-point vibrations of oscillators. Thus, upon mechanical deformation of a solid, the energy exchange occurs between two scale levels: the atomic vibration energy at a microlevel and the macroscopic deformation energy of the sample as a whole.