I.V. Alexandrov

• Ufa State Aviation Technical University

Goods made of beryllium bronzes got widespread use in the industry due to the complex of properties: high heat conductivity, strength, hardness, wear resistance, and corrosion resistance. They are not magnesium-based and do not spark on impact; therefore, they are essential for the production of non-sparking tools. The alloys of this system are use...

This paper presents the results of the microstructure and crystallographic texture investigations of the Cu-Zn alloys system with different stacking fault energies (SFE) subjected to severe plastic deformation (SPD) by equal channel angular pressing (ECAP) and subsequent flat rolling. It is shown that ECAP leads to the formation of an ultrafine-gra...

Within the framework of experimental investigations and computer modeling using the viscoplastic self-consistent (VPSC) model of a material plastic flow, the regularities of preferential orientations formation were established, the proportion of certain texture components was estimated, and existing slip systems (SS) and twinning systems (TS) were...

The effect of cold rolling with a reduction rate of 95% at room temperature and subsequent aging on the evolution of the microstructure, strength properties and electrical conductivity of the Cu-0.5Cr alloy (wt.%), which is widely used in the electrical industry in the form of strips and ribbons, has been studied. The cold rolling and aging of the...

The results of X-ray diffraction analysis aimed to reveal the features of the evolution of microstructure parameters as a result of equal-channel-angular pressing and subsequent flat rolling of the Cu-Zn alloys system with different Zn (10 and 30 wt. %) contents and, as a result, different stacking fault energies are presented.

The effect of equal-channel angular pressing (ECAP) on the strength and electrical conductivity of low-alloyed Cu-Cr-Zr alloys to identify conditions for the formation of states with high strength and electrical conductivity is considered. The increase in the content of alloying elements does not increase the strength of the alloys in the initial q...

Corrosion resistance of ultrafine-grained Ti processed by equal channel angular pressing with 3 passes was investigated. Results indicated that corrosion rate of ultrafine-grained Ti significantly reduced in comparison with coarse grain Ti. Furthermore, corrosion resistance of 3 passes ECAP sample had an obvious distinguish for different extraction...

The results of a study of the strength and conductivity of electrotechnical bulk nanostructured copper alloys obtained by methods of severe plastic deformation is presented. The contribution of the microstructure parameters to the formation of high strength while maintaining sufficient electrical conductivity is discussed.

The results of the analysis of the deformation behavior of nanostructured Cu-Zn alloys, obtained as a result of severe plastic deformation, implemented by the equal-channel angular pressing method, are presented. The role of structural factors responsible for increasing the strength characteristics and uniform elongation of the Cu-Zn alloys has bee...

In this paper, we use the scientometric approach based on the Web of Science Core Collection to analyze the data on publication activity in the area of nanostructured materials processed by severe plastic deformation (SPD) techniques on the following three main topics: ultrafine-grained materials, severe plastic deformation and bulk nanostructured...

The specific resistance of the nanostructured Cu-1.8wt.%Cr-0.8wt.%Zr alloy has been analyzed by means of analytical modeling. The contribution of different structural parameters to the specific resistance of the material has been estimated.

The results of studying the microstructure, mechanical and electrical properties of the UFG alloy Cu-0.5wt.% Cr, obtained by equal-channel angular pressing (ECAP), followed by cold rolling and subjected to aging, are presented. It was found that, as a result, the average size of the fragmented structure is 160 nm. The results showed that the tensil...

The results of investigation of the Cu–Zn system alloys with 10 wt.% and 30 wt.% Zn, the stacking fault energy (SFE) of which differs by a factor of 2.5, are presented. ECAP and subsequent flat rolling resulted in the refinement of the microstructure. Flat rolling with the reduction degree 95% resulted in the decrease of the concentration of nanotw...

The texture transition Cu {112}〈111〉 → S3 {123}〈634〉, untypical for the coarse-grained state, is discovered during the flat rolling of the ultrafine-grained (UFG) Cu-10 wt%Zn alloy. This fact is the evidence of a change in the deformation mechanisms which are related to the features of the UFG state produced by severe plastic deformation. Modeling...

The structural parameters ensuring high strength and low electrical resistance have been analyzed in Cu–Cr alloys exposed to severe plastic deformation (SPD) and aging. Specific resistance and strength characteristics have been modeled for a Cu–0.5 wt % Cr alloy with a nanostructure state caused by SPD. A comparison of modeling data with experiment...

This article investigates the effect of various contents of Cr and Zr on the microstructure and properties of the alloy of the Cu-Cr-Zr system. It has been defined that an increase in the content of Zr leads to a decrease in the grain size both in the initial state and after severe plastic deformation. The increase in the content of Zr significantl...

In this paper, we report on the microstructure characteristics and strength properties of the Cu-10 wt.% Zn alloy subjected to equal-channel angular pressing (ECAP) and subsequent flat rolling (FR), in order to form an ultrafine-grained (UFG) structure and enhance the strength properties. It is shown that the formed subgrain structure increases the...

In the present work, new possibilities of the X-ray diffraction for investigations of the phase composition, size, shape and volume fraction of particles in ultrafine-grained ferritic/martensitic steel and the Cu-Cr-Zr alloy have been demonstrated. For the first time, the method of X-ray diffraction in the transmission mode was used to identify par...

An ultrafine-grained (UFG) austenite Cr-Ni stainless steel was produced by equal-channel angular pressing. The UFG samples were irradiated in a research nuclear reactor up to damaging doses of 12 and 15 dpa at 350 °C and 450 °C, respectively. The post-irradiation examination featured in this work covers microstructural and mechanical property chang...

The mechanisms of high-speed deformation of ultrafine-grained copper produced during severe plastic deformation by equal-channel angular pressing were analyzed using numerical modeling in comparison with those in the case of coarse-crystalline copper. The activity of annihilation processes during nonconservative motion and double cross slip of disl...

The differences of effective stress, effective strain, velocity field, and the load-time curves between the spider isothermal and non-isothermal forging processes are investigated by making full use of 3D FEA, and verified by the production experiment of spider forging. Effective stress is mainly concentrated on the pin, and becomes lower closer to...

Cu-Al alloys with different stacking fault energy (SFE) were processed by equal channel angular pressing and rolling (ECAP + R) at cryogenic temperature with liquid nitrogen cooling. The effect of SFE on microstructure, effective grain size, dislocation density and tensile properties has been investigated. With decreasing of SFE during cryogenic EC...

Results are presented of experimental x-ray diffraction analysis of the microstructure of VT6 titanium alloy billets in ultrafine-grained (UFG) state subjected to flat rolling. The UFG state was formed by six cycles of isothermal multiaxial forging at 650°C. The regularities of changes of the structural parameters (the lattice parameter, coherently...

The microstructure and microhardness of joint welds formed with linear friction welding (LFW) of an Al-Cu-Mg alloy was investigated. Welds of two samples of rectangular shape do not show any macroscopic defects and are characterized by high strength. The substantial transformation of the microstructure occurs in the weld. The lattice parameter decr...

This investigation is on the properties of hardened layers, developed with the micro-arc oxidation method (MAO) on the surface of the ingots from an Al-Si alloy. It has been established that the properties (microhardness, thickness, porosity) of the generated surfaces depend on the structure of the alloy.

Microstructure and mechanical properties of a solid-phase joint produced by linear friction welding of AA2139 alloy samples have been studied. It has been shown that the weld formed as a result of LFW of two rectangular-shaped samples does not have macroscopic defects and has a high strength. It has been that the microstructure transforms significa...

This chapter summarizes the experimental data, and analyzes the models of severe plastic deformation (SPD). It reveals the tendencies, and establishes the methods for increasing the strength and electrical conductivity of bulk nanostructured Cu and copper (Cu)-based alloys produced by SPD. The influence of SPD and aging on the microstructure, stren...

Al-Si сплава. Установлено, что свойства сформированных поверхностей (микротвердость, толщина, пористость) зависят от концентрации компонентов электролита и микроструктуры материала основы. Увеличение концентрации жидкого стекла Na 2 SiO 3 и гидрооксида калия KOH приводит к образованию МДО-слоя с большей толщиной, повышенной микротвердостью и пониже...

T-shaped equal channel angular pressing (T-shaped ECAP) is a novel process of severe plastic deformation (SPD). The maximum effective strain per pass in the T-shaped ECAP is larger than that in the ECAP. Deformation models of the T-shaped ECAP have been proposed by a designed grids deformation experiment considering the deformation dead zone (DDZ)...

This paper presents the results of experimental studies on the evolution of structure, crystallographic texture and the anisotropy of strength properties in the volume of Ti Grade 4 billets subjected to continuous equal-channel angular pressing (ECAP). Continuous ECAP is performed at temperatures of 200° 400° and 450° with 1 to 8 passes, using rout...

For the first time, the possibility of radical reduction of the friction coefficient from 0.7 up to 0.3 with an increase in the strength from 950 MPa up to 1600 MPa was demonstrated for electrical Cu-0.5Cr-0.2Zr alloy as a result of the ultrafine-grain structure formation by equal channel angular pressing.

The presented work considers one of the promising ways of enhancement of strength in ultra fine-grained (UFG) metal materials produced as a result of application of severe plastic deformation techniques. Mathematical modeling showed that structure design in UFG Al and Ti alloys enabled significantly increasing their strength. By introducing impurit...

This work presents the results of experimental studies and computer modeling of the crystallographic texture evolution in the billets of titanium alloy VT6, subjected to plane rolling in the coarse-grained and ultrafine-grained (UFG) states. UFG state has been formed by the method of multiaxial isothermal forging at 650°С with the number of cycles...

The microstructure and mechanical properties of joint welds formed by linear friction welding (LFW) in in Al-Cu-Mg alloy was investigated. Joint welds of two samples of rectangular shape do not possess any macroscopic defects and are characterized by high strength. The substantial transformation of the microstructure occurs in the weld zone as a re...

The investigation studies the properties of hardened surface layers, developed with the microarc oxidation method (MAO) on ingots of a Al-Si alloy. It has been proved that properties of the developed surfaces (microhardness, thickness, porosity and corrosion properties) depend on the concentration of electrolyte components.

Al-Cu-Mg-Mn alloy samples were joined together with linear friction welding in two conditions, as is, without pretreatment, and after etching the welding interface. The effect of the welding interface condition was evaluated based on microstructure analysis, microhardness and tensile testing at room temperature. Also, the temperature distribution d...

The paper presents the results of studies of the properties of hardened surface layers formed by micro-arc oxidation on the workpiece surfaces of aluminum alloy Al-12Si-Mg-Cu-Ni. The authors attempted to determine the influence of micro-arc oxidation modes on the properties of the modified layers. Investigation of the adhesion strength of the surfa...

This work presents the results of computer modeling of crystallographic texture evolution in the volume of Ti Grade 4 billets subjected to continuous equal channel angular pressing (ECAP) at a temperature of 200 °С, with a number of passes from 1 to 8 via the ВС route. Regularities of preferred orientation formation have been stated, and the activi...

A model describing the behavior of elastic–plastic medium with account of kinetics of dislocations has been developed. A method for determining kinetic parameters of the model is described. The model allows analyzing the mechanisms of deformation behavior of metallic materials on the basis of the obtained information on evolution of the average gra...

The Al–5%Ti master alloy has been subjected to the equal channel angular pressing (ECAP) by route A at room temperature, and the grain refining performance of Al–5%Ti master alloy before and after ECAP with the use of an industrial purity Al has been evaluated. The effects of the ECAP on the size and the distribution of the TiAl3 particles, grain s...

Long-length ultrafine-grained (UFG) Ti rods are produced by equal-channel angular pressing via the conform scheme (ECAP-C) at 200 °C, which is followed by drawing at 200 °C. The evolution of microstructure, macrotexture, and mechanical properties (yield strength, ultimate tensile strength, failure stress, uniform elongation, elongation to failure)...

The composite filament structure was produced in the Cu-5.7%Cr and Cu-12.4%Cr as-cast alloy ingots by using equal channel angular pressing (ECAP) at room temperature. Optical and TEM microstructure, micro-hardness, tensile strength and electrical conductivity of ECAPed samples were investigated. The rotation and spreading of Cr particles took place...

The states and processes in grain boundaries of Cu, subjected to severe plastic deformation have been analyzed here. It has been shown that microstructure refinement in the process of severe plastic deformation leads to a hyper sensitivity of the processes occurring in the grain boundaries towards the applied hydrostatic pressure. The temperature a...

Bimodal microstructure consisting of ultrafine-grained (UFG) matrix with the embedded micro-size recrystallized grains has been developed in Cu due to equal channel angular pressing (ECAP) and subsequent high strain rate deformation (HSRD). Both high strength and high ductility are characteristic for this microstructure. High strength is achieved b...

Basing on the kinetic modeling, the quantitative evaluations of activity of mechanisms, affecting the strength properties to explain the deviations from the Hall-Petch law towards the greater side in the area of small grains, have been made. The income of each strengthening mechanisms has been evaluated. It has been shown that the grain size and th...

This paper presents the results of comparative analysis for the samples of austenitic AISI 321 (18Cr-9Ni) steel in the as-received state and the state after the equal channel angular pressing he ECAP-state) before and after he eactor adiaton on ast neutons BîR-60 up o maximum damage dose 5.3 dpa at 350° C. The results point out the mixed fragmentar...

The paper presents the results of the application of a newly developed method to study deformation and fracture processes in specimens produced by linear friction welding. This method combines mathematical modeling and experimental mechanical testing. By application of this method it has been demonstrated that during uniaxial testing of welded join...

The linear friction welding process of α+β titanium alloys VT6 and VT8M-1 has been studied and in particular the investigation of microstructure in the weld zone. The results of this investigation were used for development of a numerical model of LFW equilibrium stage using the ANSYS Mechanical software. The set of parameters used in this model all...

The effect of aging treatment on mechanical properties and electrical conductivity of Cu-5.7%Cr in situ composite produced by equal channel angular pressing (ECAP) was investigated here. The rotation and spreading of Cr particles was observed in Cu-5.7%Cr alloy during the ECAP, resulting in long thin in situ filaments. The equiaxed grains of the Cu...

This paper presents the research results of crystallographic texture and deformation mechanisms, which are characteristic of the ω-phase of Ti, subjected to high pressure torsion under pressure of 6 GPa at temperature 298K. The research has been carried out on the diskshaped samples with radius 20 mm and thickness 1.5 mm in an initial state (the as...

Twist extrusion (TE), a promising severe plastic deformation (SPD) technique for grain refinement down to ultrafine/nanocrystalline microstructures, was introduced as an attempt to provide large plastic deformation conditions similar to those in high pressure torsion while allowing large workpiece dimensions for industrial applications. As a relati...

This paper presents the results of the development and application of a dislocation-kinetic approach to the analysis of strength and ductility in metals and alloys. The influence of the temperature-strain rate conditions of deformation on the character of dislocation processes, taking place in some pure metals and alloys, has been investigated here...

The microstructures of ultrafine-grained nanostructured materials developed by severe plastic deformation are widely varied in their grain size and grain-size distribution; grain boundaries and their structures; lattice defects, especially dislocations; point defects; and impurities. All of these features can be influenced by the way severe plastic...

Microstructure, mechanical properties and electrical conductivity in Cu-0.73%Cr alloy after HPT process and the subsequent aging treatment have been investigated. Ultrafine grained structure with the grain size ~150 nm has been achieved after the HPT and the subsequent aging treatment. Ultrafine grains with some growth twins were preserved in the o...

Basing on the kinetic modeling, the role of microstructure peculiarities in formation of a revealed experimentally high-strength state of the nanostructured Al 6061 (Mg 0.8…1.2, Si 0.4…0.8, Cu 0.15…0.40, Cr 0.15…0.35, Mn 0.15, Fe 0.7, Zn 0.25, Ti 0.15 wt. %) alloy was analyzed, Possible strengthening mechanisms of the alloy subjected to high pressu...

Microstructure, mechanical properties and electrical conductivity of industrial Cu–0.5% alloy subjected to equal channel angular pressing (ECAP) by route A and cold rolling with and without aging treatment were investigated. The lamellar grains in thickness of 100nm were obtained after eight ECAP passes. They were not further pancake shaped, but fr...

This paper presents the research results of the grain refining effect on the ductile-to- brittle transition temperature (DBTT) of commercial purity tungsten. The as-received tungsten was subjected to eight passes of equal-channel angular pressing (ECAP) at decreasing temperatures from 1300 to 1150 °C. According to optical and TEM microscopy the ave...

This paper presents the results of experimental X-ray structural analyses of both the evolution structure and the crystallographic one in the volume of Ti samples, subjected to the Severe Plastic Deformation (SPD), realized by torsion under high pressure equal to 6 GPa at temperature 298 K. The investigations have been carried out on the disk-shape...

The composite filament structure was produced in Cu-5.7%Cr as-cast alloy ingots, subjected to equal channel angular pressing (ECAP) and cold rolling (CR) at room temperature. Microstructure, tensile properties and electrical conductivity before and after the severe plastic deformation (SPD) processing have been investigated here. The results point...

The initial and deformed states of austenitic stainless steel AISI 321 before and after neutron irradiation with a damage dose up to 5.3 dpa at reactor core temperature of 350 °С were comparatively investigated. Corrosion behavior, mechanical properties are analyzed in the temperature range of 20…650 °С. It is shown that radiation damage of the ste...

The high-strain-rate response of ultra-fine-grained (UFG) copper fabricated by equal channel angular pressing (ECAP) has been characterized by Split Hopkinson Pressure Bar (SHPB) test and quasi-static compression test has also been performed for comparison here. In the result of quasi-static tests a maximum yield stress equal to 432 MPa has been re...

A grain size is known to be one of the factors which define mechanical properties of metallic materials. At the same time the mechanisms which regulate the deformation behavior of bulk ultrafine-grained (UFG) metals produced by the severe plastic deformation method are still a subject for intensive study and fixed ambiguously. The report presents t...

The role of various microstructure parameters in developing the experimentally ultrahigh strength of nanostructured aluminum-magnesium Al 1570 (Al-5.7Mg-0.32Sc-0.4Mn wt.%) alloy has been analyzed here. It was demonstrated that the main factors, which determined the alloy strength, are the grain size, the dislocation density and the segregation of m...

Nanostructuring of metals and alloys by severe plastic deformation techniques is an effective way of enhancing their mechanical and functional properties. The features of the nanostructured materials produced by severe plastic deformation are stipulated by forming of ultrafine-sized grains as well as by the state of grain boundaries. The concept of...

Regardless of the origin of structure irregularities of materials, the recognition of their spatial distribution in a sample or constructing elements is a great research problem. One of the most effective and non-destructive tools used for this purpose is the X-ray diffraction technique, assisted by an appropriate experimental method and data proce...

High pressure torsion (HPT) is one of the most widely used severe plastic deformation methods which enable to obtain a crack-free ultra-fine grained bulk sample. In the process, a disk-shaped sample is pressed between two anvils and deformed via surface friction forces by rotating one of the anvils. The aim of this study is to nondestructively char...

The common feature of the technologies, such as the equal channel angular pressing (ECAP) is the use of a changeable deformation path, which changes the configuration (value and direction) of the acting forces that impose various directions of plastic flow. The changes destabilize a temporary dislocation structure as well as the spatial distributio...

The paper has viewed the manifestation of the paradox of severe plastic deformation (SPD), caused by the occurrence of preexisting deformation twins in ultrafine-grained Cu, which has been obtained by the combination of the SPD method, accomplished by an equal-channel angular pressing with the conventional methods of deformation-thermal treatment....

Rods of commercial-purity tungsten were subjected to severe plastic deformation by means of equal-channel angular pressing (ECAP). An ultrafine-grained (UFG) equiaxed microstructure with an average grain size of about 0.9 μm was developed. Microhardness measurements in a wide range of temperatures suggest a ductile-to-brittle transition at temperat...

High pressure torsion (HPT) is one of the severe plastic deformation methods, which can significantly refine the microstructure, improve the mechanical and physical properties. During the process, the strain can exceed the levels of hundreds and considerable residual stresses develop. The aim of this study is to nondestructively characterize the va...

The paper presents the results of modeling of tensile deformation behavior of bulk nanostructured Ti VT1-0 processed by different ways of severe plastic deformation. SPD has been implemented by means of combined deformation consisting of equal-channel angular pressing and both direct and alternating high-pressure torsion. A model for simulation of...

To effectively demonstrate the dependence of ductility improvement on the scheme of introducing bimodal structure into nanostructured materials, a three-step processing was adopted in hypo-eutectoid Cu–Al alloys to obtain controllable bimodal structure of micrometer-grained pre-eutectoid phase embedded on ultrafine-grained (UFG) matrix with eutecto...

Bulk nanostructured Cu samples with 20 mm in diameter and 1 mm in height were processed by HPT at a pressure of 6 GPa by 10 rotations. Measurements of texture by means of state-of-the-art XRD technique have been achieved in directions parallel and normal to the torsion axis. Local texture measurements were performed by a spot size of 500 -m in step...

In the current investigation, the dislocation model suggested by Zehetbauer was used to analyze the deformation behavior of pure Ti in the initial state and after 1 and 8 passes of equal-channel angular pressing along the route BC. Accounting of possible twinning was carried out on the basis of the law of two-component mixtures when counting the fl...

In the present investigation, a bimodal structured alloy with ultrafine-grained (UFG) eutectoid matrix embedded with micrometer-grained pre-eutectoid phase was introduced into the hypo-eutectoid Cu-10.8wt.%Al and Cu-11.3wt.%Al alloys by means of pre-pressing heat-treatment, equal-channel-angular pressing (ECAP) and subsequent annealing. Different s...

The results of a recent multiscale computer modeling are presented in this report. The conducted investigations are devoted to the processes, which take place in different metallic materials subjected to severe plastic deformation (SPD). It is presented that the developed models and approaches can be useful in the successful prediction and comprehe...

In this article we present the results of the experimental research and those of the processes developing the crystallographic texture of computer modeling in CP Ti in the process of 1-4 equal channel angular pressing (ECAP) passes along the route ВС. The goal of the research was to determine the active deformation mechanisms, depending on the stra...

In the present work high pressure torsion (HPT) was imposed on commercial purity (CP) tungsten at different temperatures of 450 °С and 490 °С to achieve different microstructures and grain boundary misorientation spectra (GBMS). After HPT at 450°С, ultrafine grained microstructure with an average grain size of ~150 nm was developed in the metal. HP...

A kinetic composite dislocation-based model of the deformation behavior of pure metals has been developed. The model incorporates the known approaches by M. Zchetbauer and M. Barnett and allows considering both dislocation activity and dislocation twinning in the process of plastic deformation. The model is employed to analyze the deformation behav...

The paper presents the results of experimental studies of the evolution of the homogeneity of the crystallographic texture and deformation behavior in bulk Cu and Ti billets subjected to the different numbers of equal-channel angular pressing (ECAP). It is found that the 1st pass during ECAP of pure Cu and Ti results in the formation of the pronoun...

The upgraded Estrin-Tóth model is presented to describe the deformation behavior of the materials subjected to severe plastic deformation. The model has been applied toward study of tension of the as-received Cu samples and the samples after the 1 st , 4 th , and 8 th equal channel angular pressing passes. The dislocation density evolution in the t...

The upgraded Estrin–Tóth dislocation model has been suggested to describe deformation behavior of materials, subjected to severe plastic deformation, which in its turn is realized under high imposed pressure of several GPa. The model was applied to study high pressure torsion of Cu samples. The dislocation density evolution has been studied in the...

Evolution of dislocation cell microstructures during severe plastic deformation was analyzed using a modified kinetic dislocation model based on the two dimensional approach by ETMB [Y. Estrin, L.S. Tóth, A. Molinari, Y. Bréchet, Acta Mater. 46 (1998) 5509]. The proposed model simulated decreasing dislocation density after a maximum point and incre...

The plastic flow of a copper billet calculated using 2D and 3D finite element modeling are compared during a single extrusion of equal-channel angular pressing. Both models predict deformation heterogeneity irrespective of material behavior, die geometry and friction conditions. On the symmetry plane where the numerical approaches can be compared,...

X-ray investigations revealed that the increase in the applied pressure during high pressure torsion (HPT) of commercially pure Ti leads not only to substructure refinement with an increase of the dislocation density and microstrain level but also to an α → ω phase transition at room temperature. The coexistence of both a and co phases, the latter...

In the investigation the 3D version of the Estrin-Tóth dislocation model was used to analyze deformation behaviour of pure Cu, subjected to high pressure torsion (HPT) under pressures equal to 0.8, 2, 5, 8 GPa. As a result of the computer simulation, the nature and reasons for strain hardening are analyzed, the dislocation density evolution versus...

The development of the crystallographic texture in copper subjected to severe plastic deformation (SPD) by means of high pressure torsion (HPT) and equal-channel angular pressing (ECAP) was experimentally investigated and analyzed by means of computer modelling. It was demonstrated, that the texture developed in HPT and ECAP Cu is characterized by...

Microstructure development during severe plastic deformation by simple shear is modeled using a disclination model for substructure formation incorporated into the viscoplastic self-consistent (VPSC) polycrystal model. The strain incompatibilities between a homogeneous effective medium and a grain calculated by the VPSC model are assumed to result...