### №1-2019

https://elibrary.ru/contents.asp?id=37244687

**Kazarina S.A., Movchan A.A., Sil’chenko A.L.**

## The influence of inelastic deformations on the reverse thermoelastic transformation start temperature in shape memory alloys

The first part of the article presents experimental data indicating that the temperature of the onset of reverse martensitic or rhombohedral phase transformation in titanium nickelide in the absence of stresses increases with increasing initial phase-structural deformation of the material. This effect can not be described in the framework of the known model of nonlinear deformation of shape memory alloys in phase and structural transformations, since according to the constitutive relations of this theory, the change in the temperature of the onset of the reverse transformation is proportional to the convolution of stress deviators and initial phase-structural deformations, which turns into zero at zero stress. This effect is not described in the framework of most known phenomenological models of SMAs thermomechanical behavior.In this paper, to describe the effect under consideration, it is proposed to add to the expression for the Gibbs potential of the SMA a nonadditive term that is a function of the invariant of the phase-structure deformation deviator. According to this assumption, using the formalism adopted in rational thermodynamics, as a consequence of the first and second laws of thermodynamics, expressions were obtained for the temperature of the onset of an inverse thermoelastic phase transition containing a term that does not vanish at zero stress. The question of the sign of this term is analyzed.The formulation of the coupled energy balance equation taking into account the change in the expression for the Gibbs potential is also obtained. By comparison with the experimental data, the sign of the Gibbs potential additional term derivative and the values of the additional constants of the proposed model are determined. The question of the effect of the proposed change in the model on the values of the characteristic temperatures of direct thermoelastic phase transformation is discussed.

**Afanasyeva E.A., Antyufeeva N.V., Guseva M.A., Khaskov M.A.**

## Study of the blending process of epoxy oligomers with polyarylate

In the present paper, the methods of rotational viscometry and differential scanning calorimetry (DSC) studied the compatibility of PV-1 polyarylate with various epoxy resins. Of particular interest is this thermoplastic as a modifier due to the increased heat resistance. Materials based on it are obtained with higher heat-resistant and wear-resistant properties. The inter-solubility of the components requires attention, since this process greatly affects both the properties of the polymer composite material (PCM) and the method of obtaining the finished product. With poor compatibility of thermoplastics with reactoplastics, dispersion can be formed and uneven completion of exchange processes during processing, which can affect the structure and properties of the finished PCM. Due to the unpredictability of the initial factors, it is rather difficult to predict the behavior of the thermoplast, therefore, such issues are solved mainly in practice. The article investigated the behavior of mixtures of epoxy oligomers ED-20, UP-637, EN-6 and EHD, depending on the concentration of thermoplastic, as well as when comparing relative to each other. According to test results, it was found that, like other thermoplastic modifiers, PV-1 is dissolved in epoxy resins. However, unlike polyarylsulfones, the temperature range of this process shifts to higher temperatures due to the increased heat resistance of the thermoplastic compared to polyarylsulfones. A linear dependence of the thermoplastic dissolution temperature on its content in the mixture was found, as well as differences in the rheological behavior depending on the composition. It is shown that the regions of thermal effects on the DSC curves, which coincide with the regions of viscosity increase as they are heated, observed on the rheological curves, are not related to the chemical interaction, but to the process of dissolution. In addition, it was found that as a result of the combination, a gradual increase in viscosity occurs, especially at high temperatures.

**Berezin A.V., Zhirkevich V.J.**

## Estimation of process stability deforming the defects-contained media

Examples of the estimation of the moment of loss of stability of the deformation process, which is defined as the time of the beginning of deformation with decreasing applied stress under monotonic loading, are considered. Two examples of processes are considered: the necking in sample during the uniaxial tensile testing and the riveted joint of the fuselage of the aircraft. In the second case, in addition to the above method for estimating the moment of loss of stability, we also considered the possibility of applying the criterion derived from the results of finite element modeling, related to the ratio of effective stresses, defined as the tensile force divided by the cross-sectional area of the cross-section of the model still retaining its integrity, to effective deformation, defined as the maximum displacement of the ends of the stretched sample divided by the initial length of the unloaded model. When these two methods are used, fairly close results are obtained, what is demonstrated in obtaining for both cases similar estimates of the calculated values of the number of loading cycles, which is necessary for the crack in the aluminum 2024-T3 used in manufacturing the fuselage skin, to reach the critical length. Due to the variety of load levels and loading methods, the need for obtaining from the corresponding experiments a significant number of dependencies, required for the calculation, is noted. The method of acoustic emission is recommended as the main method for determining the starting moment of the motion of the fatigue crack. The need to refer to experimental methods for determining the laws of crack growth and the material parameters responsible for this is due to the dependence of the growth of microdefects on a wide range of external conditions: type of environment, temperature, pressure, etc. When using the proposed criteria, a methodology can be developed for assessing the onset of a critical state of parts used in various engineering areas that contain defects and are exposed to external loads. This will allow time to predict the time of their possible failure.

**Kalmykov P.N., Lapichev N.V., Mikhaylov I.A., Myagkov N.N., Pyrikov M.D., Salnikov A.V., Shumikhin T.A.**

## Morphology of damages to thick witness-plates produced by fragments of high-velocity projectiles made of different materials

The experimental study of the fragmentation of projectiles at high-velocity impact perforation of thin bumpers is not rich with technologies for in-situ observation. One of the reliable methods for the retrieving of data characterizing the fragment clouds produced by the impact is the analysis of the damage of witness plates situated in the path of the moving fragments at some distance from a bumper. In this work we performed a comparative analysis of the morphological features of the damages on the witness-plates produced by the fragments of projectiles made of different materials: polyethylene, aluminum alloy and caprolon embrittled by embedding of glass microspheres. The experiments were performed in the range of impact velocities from 2900 m/s to 7000 m/s. The tested bumpers were of three types: continuous bumpers (aluminum plates), steel meshes, and sets of steel strings (string bumpers). The analysis showed that at similar experimental conditions in tests with string bumpers the polyethylene projectile could reveal lower degree of fragmentation than embrittled caprolon material. The sufficient part of initial kinetic energy remains in the rear part of the polyethylene projectile without transition into other projectile parts or transformation into the energy of fracture. The projectile of caprolon keeps the tendency to generate jets from the frontal part similar to the case of non-brittle polyethylene. These jets produce linear chains of craters on the witness-plate surface. The fragmentation of a polyethylene projectile on a continuous bumper provides a formation of a fragment cloud containing chunky fragments and threadlike fragments as well. The threadlike fragments can combine into closed structure. This type of fragment clouds was observed in experiments with continuous bumpers and soda-lime glass projectiles. It is remarkable that the distribution of thread like craters formed by the fragments of the polyethylene projectile is similar to the distribution of the ensemble of small craters produced by the fragments of aluminum projectiles. There exists significant morphological similarity between a pair of experiments: in the first one the projectile was made of polyethylene and the bumper was a steel mesh, in the second there were an aluminum projectile and a mesh bumper made of tungsten wires. It seems that the parameter that controls the similarity in these experiments is the ratio of the projectile density to the bumper density.

**Gorbachev V.I., Solyaev Y.O.**

## Comparison between mori-tanaka and gorbachev-pobedrya methods in the problem of determinination of the effective properties of composites with piezoelectric spherical inclusions

The problem of prediction of the effective characteristics of composite materials with polymeric isotropic matrix filled with piezoactive transversely isotropic ceramic particles is considered. Within the framework of the spherical inclusion model, three methods of averaging are compared. Firstly, the Mori-Tanaka method is used, which allows one to obtain analytical estimates of effective properties based on the Eshelby problem solution for an isolated inclusion. Secondly, the Gorbachev-Pobedrya method is considered, which is based on an integral representation of solutions for problems of deformation of a heterogeneous medium and requires numerical solution of auxiliary problems for determining of the so-called structural functions. The predictions obtained in the framework of these methods are compared with the results of numerical modeling of representative fragments of composites, for which effective characteristics are determined as the ratio of the corresponding averaged values of stress, strain, electric field and electric displacements. As a result of the calculations, it was established that the considered methods may lead to different predictions of the properties of piezocomposites. The greatest difference is realized for piezoelectric constants: up to 150-200% with a volume content of inclusions 30-40%. The highest predictions for the elastic tensile moduli and dielectric constants are obtained by using Gorbachev-Pobedrya method and the lowest – by using Mori-Tanaka method. In opposite, the highest shear moduli are predicted by Mori-Tanaka method, while the smallest ones are followed from the finite element simulation.

**Kutsbakh A.A., Muranov A.N., Semenov A.B., Semenov B.I.**

## Investigation of free shrinkage of the main types of powder- polymer mixtures used for manufacturing parts from analogues of 38khma (42crmo4) steel by the mim-method

The paper discusses one of the advanced technologies of powder metallurgy, effective for serial and mass production of both metal and ceramic small-sized precision parts with a complex geometric configuration – the technology «Powder Injection Moulding» (PIM), based on the use of powder-polymer mixture (feedstock) for injection molding under high pressure. When using PIM technology, the quality of the final sintered metal or ceramic part in successive technological stages depends on the quality of the initial molded semi-finished product – the casting from the particulate filled polymer composite material. The dimensional accuracy of a molded composite semi-finished product is largely determined by its uncompensated shrinkage upon cooling and extraction from the mold, in turn, the value of this shrinkage is determined by the value of the coefficient of thermal expansion, which for feedstock primarily depends on the composition and properties of the polymer binder used. In this paper, we briefly consider theoretical methods for calculating the thermal expansion of powder-polymer mixtures (feedstocks). It was noted that for materials with a complex structure and weakly deterministic properties of components, such as, for example, feedstocks with a binder in the form of a polymer blends, definitive tests remain one of the most reliable means of studying effective thermomechanical characteristics. For feedstocks used for manufacturing parts made from analogues of 38KHMA (42CrMo4) steel with the two most common types of polymeric binder the temperature dependences of the average coefficient of linear thermal expansion were determined by linear dilatometry in the temperature range from minus 20 to plus 125C. The obtained experimental data, supplemented by an accurate pycnometric measurement of the density of the materials under study, made it possible to carry out for each of them an estimate calculation of the temperature dependence of the specific volume. As a result, based on the calculated dependencies, a comparative assessment of the values of free non-compensated shrinkage of feedstocks of compared types was made.

**Egorov S.A., Volkov A.E.**

## Change of the enthalpy of the reverse martensitic transformation in titanium nickelide at thermocycling under a load

There was fulfilled a study of the effect of stresses applied to a specimen during the direct and reverse transformations in titanium nickelide shape memory alloy on the enthalpy of these transformations. A series of experiments realizing the martensitic transformations on cooling and heating under a constant shear stress (in torsion mode), same for both the direct and the subsequent reverse transformations has been carried out. Simultaneously were made the measurements of the shear strain and the differential thermal analysis, the methodology of which allowed obtaining estimates of the amounts of heat release and absorption. It was found out that with an increase in the stress from 0 to 100 MPa the enthalpy of the reverse transformation decreases by a factor of 2.5. It was noted that if the direct transformation is carried out under a stress, and the subsequent reverse transformation is performed after the specimen is unloaded, the heat absorbed during the reverse transformation decreases with the same stress change from 0 to 100 MPa only 1.3 times. A theoretical explanation for this phenomenon has been proposed. For this various factors affecting heat absorption during the reverse transformation are considered, such as the energy of the boundaries separating the orientation variants of martensite, the work produced by the applied stress on the phase deformation and the elastic energy stored in the material due to incompatibility of the phase deformation of the martensite plates. Evaluation of the elastic energy is based on the representation of a shape memory alloy, as a composite consisting of differently oriented martensite plates, and on taking into account the equilibrium conditions of stresses and the compatibility of the total strain. Comparison of the elastic energy stored due to the formation of martensite in the absence of stress and under the action of a stress of 100 MPa shows that its value corresponds to the change in the heat released during the reverse transformation. It is noted that the contributions of other factors listed above that affect the enthalpy of reverse transformation is much smaller and, moreover, cannot explain its decrease with increasing stress, since these contributions are directed only towards its increase.

**Filimonova T.V., Shishkin A.A., Trutnev N.S.**

## About selection of the rational wall thickness of a liner high pressure metal compound cylinder

The design features of lightweight metal-composite cylinders are considered, the main requirements for pressure vessels are formulated. The principal part of them are include strength and resistance to cyclic pressure change. On the basis of the analysis of requirements, it has been established that the main factor preventing the achievement of mass perfection is the metal sealing shell – liner. Since the main load is perceived by the composite material, to weight savings, it is necessary to minimize the thickness of the wall of the liner, that is limited by technological possibilities. In addition, the presence of metal requires an increase in the amount of the composite layer to eliminate the fatigue failure of the liner. When calculating the design of the cylinder, the basic boundary criteria are taken: the strength and the admissible strains, which prevents the metal from falling into the plastic state. As a result of the analysis of the technological cycle of fabrication and testing of the metal-composite pressure vessel, the additional technologies stresses that affect the final range of strains are established to arise in the structure. Based on the known approaches to the calculation of combined cylinders, a calculation technique which takes into account the influence of technological stresses is proposed. The refined calculation made from the cylinder from the strength conditions and the absence of plastic strains in the metal for different combinations of materials at different wall thicknesses of the liner. It is established that in most cases the limiting factor is the requirement to limit metal strains. The account of technological stresses has a significant effect on the estimated mass of the cylinder, because in some cases, the thickness of the liner has a positive effect on the strains of the combined pressure vessel. The ration of metal and composite which ensure the minimum mass of the balloon are obtained. It is established that the correlation between the mass of the vessel and the thickness of the liner has a nonlinear character and in certain combinations of materials the tendency to minimize the metal is inexpedient.

Pages: 97-109 Elibrary

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**Firsanov Vic.V.**

## Сomputational model of axisymmetric bending of a round plate with accounting for its incompressibility

Incompressible isotropic elastic materials have a maximum Poisson ratio of 0.5. In the process of loading and deforming the structural elements of such materials their shape changes, while the volume of the structure remains unchanged. The property of incompressibility is a consequence of the physical relations of a linearly elastic material, in which the Poisson’s ratio is assumed to be 0.5, and the physical modulus characterizing the resistance of a material to a change in volume tends to infinity, as a result of which the physical relations of Hooke’s law turn into so-called «Neohooke» relations, in which normal stresses contain a common power function having the dimension of stresses. It replaces in physical relations the uncertainty with and where is the volume related modulus , and is the deformation of the change in volume. The unconditional fulfillment of the condition of the invariability of the volume, which relates linear deformations, substantially changes some classical models of mechanics of solid deformable body based on various hypotheses. The bending of thin plates with small deformations is described by the defining relations based on Kirchhoff’s hypotheses about the absence of shear deformations in the plane and transverse linear deformation in relation to a round axisymmetric plate. The fulfillment of the incompressibility condition leads to the necessity of abandoning these hypotheses, in particular, from the hypothesis of the absence of shear deformations. For plates with one boundary rigidly fixed contour or with two also rigidly fixed contours, there is no transverse linear deformation, which is a consequence of the invariability of the volume of the plate in the process of its deformation. In some problems in order to obtain simple and easily solvable equations for a round axisymmetric plate, the radial displacement can be specified as a linear function along the transverse coordinate. And at the same time, it is not necessary to go over to the integral characteristics of the stress state, which are the bending moment and the shear force. In the classical theory of plate bending, such a transition allows to eliminate the transverse coordinate; however, for some problems of bending plates of a material with an unchanged volume, this transition leads to serious errors.

Pages: 110-121 Elibrary

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**Rybakov L.S.**

## Linear elastic analysis of spatial thin-walled rod system with orthogonal structure

A linear elastic analysis of a regular spatial thin-walled rod system of orthogonal structure is presented. The system is formed from three mutually orthogonal families of straight homogeneous rods and thin rectangular plates of constant thickness located between them. According to the assumption, the rods work only for tension-compression and in the plates a state of uniform pure shear is realizable. For the elastic analysis of such systems, a strict discrete linear theory of elasticity constructed using the gluing method is proposed. In accordance with its procedure, the thin-walled rod system was divided into elements (rods, plates and nodes – intersections of elastic rod lines). The given external and unknown internal forces were applied to them and a linear analysis of the mechanical behavior of isolated elements was carried out taking into account the geometric conditions of their conjugation. The theory is formulated in terms of nodal displacements, the generalized strains (full rod elongations and shifts of the plates and their rod frames) and the generalized internal forces (initial rod forces and tangent force flows). All these variables are functions of integer parameters used for numbering system elements. The complete closed system of defining relations of the theory consists of geometrical and physical dependences, static relations and equations of compatibility of generalized deformations. Geometric relationships express generalized deformations through nodal displacements, and physical relationships represent a linear dependency between generalized internal forces and deformations. The role of static relations, establishing a connection between the given external and the unknown internal forces are the equilibrium equations of free nodes. With the help of all these dependences, two statements of discrete boundary value problems are given: one in nodal displacements and shifts of plates, another in generalized internal forces. The latter formulation is illustrated by the example of an arbitrarily loaded one-closed caisson of any finite length for which an exact analytical solution in Chebyshev polynomials is constructed.