## No 4 (2021)

**Year:**2021**Articles:**15**URL:**https://ered.pstu.ru/index.php/mechanics/issue/view/153**DOI:**https://doi.org/10.15593/perm.mech/2021.4

DETERMINATION OF THE STRESS STATE AND THE FORCE OF DEFORMATION OF BALL-SHAPED BILLETS IN A CLOSED MATRIX

#### Abstract

At the present stage of development of science and technology, the problem of improving the quality of metal products by integrating methods of severe plastic deformation into existing technological processes is urgent. Intense plastic deformation makes it possible to obtain nanostructured metallic materials with improved quality and an attractive set of properties due to the saturation of the metal with nanoscale defects. Spherical billets with two ends along the edges are a common form of metal products. For the manufacture of such metal products, the effect of mutual influence of all-round compression and ECAP pressing in a device for the implementation of equal-channel angular pressing in a closed matrix was used. The purpose of this study is to develop a theoretical approach to determining the stress state and deformation force of spherical blanks in a closed matrix. To achieve this goal, an integrated approach was used to determine the stress state and deformation force by the method of slip lines and computer simulation in the Deform-3D software package. Analysis of the results of the stress state of the workpieces obtained by the slip line method showed that a uniform stress state is formed with a predominance of the maximum compressive stresses. The combination of the latter with angular metal extrusion into the lateral channels of the matrix predicts the production of workpieces with sub-ultrafine-grained and/or nanostructure. By the method of joint solution of differential equations of equilibrium and plasticity conditions, as well as computer modeling, the deforming force of the blanks at the final stage of deformation, when the metal flows out into the lateral channels of the matrix, is determined. The analysis of the obtained results shows that the value of the deformation force obtained by the two methods is comparable with a difference of up to 2 %, which confirms the correctness of the obtained values.

**PNRPU Mechanics Bulletin**. 2021;(4):5-12

Composite materials in aircraft engine blades

#### Abstract

The article investigates the strength of the propeller blades made of a multilayer composite material, subjected to centrifugal and gas loads with various combinations of fiberglass and carbon fiber and orientation of the material base. The finite element method is used as a research method. A propeller blade used in turbines of jet engines and compressors, made of composite materials, is considered as a naturally twisted rod, provided that the hypothesis of flat sections across the thickness of a multilayer composite package is valid under conditions of rigid contact at the boundary of layers. The propfan blade model is modeled by four-node finite elements of natural curvature with forty-eight degrees of freedom, taking into account the compression of the normal. The applied method for calculating the strength makes it possible to assess the strength of an arbitrarily reinforced blade in sections and layer by layer. The blades of hydrodynamic engines of the first and second stages were considered under the action of centrifugal and gas loads. The stress was determined at 17 points of 21 cross-sections in layers. As a result of the study, the strength parameters of the blades with different ratios of the dissimilar materials of the layers of the multilayer composite material were obtained. Conclusions are drawn, based on the fact that the blades made of composite material have significant advantages in terms of strength and weight characteristics compared to blades made of materials traditionally used in technology in the manufacture of propfans.

**PNRPU Mechanics Bulletin**. 2021;(4):13-18

Simultaneous identification of mechanical properties of functionally graded plates under the Kirchhoff and Tymoshenko models

#### Abstract

The paper presents models of deformation of functional-gradient round plates in the framework of the hypotheses of Kirchhoff and Timoshenko. Based on the equations of oscillations and boundary conditions obtained earlier using the Hamilton - Ostrogradsky variational principle, the formulations of problems in a cylindrical coordinate system are written, taking into account the variability of the functions of cylindrical stiffness and density along the radial coordinate. The plates was considered rigidly clamped along the edge. The case of steady-state vibrations caused by a load applied to the surface was considered. A scheme for solving direct problems calculating vibrations of plates based on the Galerkin method is constructed. An analysis of the influence of the functions of cylindrical stiffness and density on the amplitude-frequency characteristics (AFC, acoustic response) was carried out, which revealed that both functions significantly affect the AFC, and the greatest influence is observed in the vicinity of resonant frequencies. The results of the analysis made it possible to formulate new inverse problems of simultaneous identification of the functions of cylindrical stiffness and density of an inhomogeneous circular plate using additional information about the acoustic response for both hypotheses. To solve them, a special projection technique was built, based on the expansion of unknown functions of mechanical characteristics, as well as dynamic quantities (functions of deflection and angle of rotation of the normal) in terms of some systems of linearly independent functions that satisfy the boundary conditions. The coefficients of these expansions are determined from the solution of special systems of linear and nonlinear equations obtained from the formulated weak statements of both problems. As a result, it is possible to identify the desired characteristics in the given classes of functions. The identification results are illustrated with a set of computational experiments for various functions.

**PNRPU Mechanics Bulletin**. 2021;(4):19-28

Crack root radius effect on stress fields under nonlinear

#### Abstract

The influence of crack root radius and plastic material properties on the crack tip fields was evaluated by strain gradient plasticity theory, and classical plasticity theory. A conventional mechanism-based strain gradient (CMSG) plasticity theory was used in the study. The stress fields in single edge tension specimen are investigated numerically for a wide range of the crack tip radius variations. Five values of the crack tip curvature radius ρ = 0 (mathematical notch); ρ = 25 nm, ρ = 30 nm, ρ = 60 nm and ρ = 100 nm were investigated. The strain hardening exponent varied from N = 0.075 to N = 0.4. A stress analysis by CMSG plasticity was performed for two values of the Taylor’s length parameter l = 1μm and l = 10μm. The boundaries of the local areas, where the influence of the crack tip radius is realized were determined for both HRR and CMSG plasticity. The sizes of the dominance area of the strain gradient plasticity were established and their approximation equations were presented. The influence of the plastic properties and the Taylor’s length scale parameter on the stress fields in the vicinity of rhe crack tip was estimated for the strain gradient plasticity.

**PNRPU Mechanics Bulletin**. 2021;(4):29-40

Theories of plasticity under complex loading along spatial trajectories of deformations

#### Abstract

Variants of theories of plastic flow with combined hardening, which are widely used in practical calculations of structures, are considered. A comparative analysis of variants of the theory under complex loading along the spatial trajectories of deformations of constant and variable curvature and torsion is carried out. The trajectories of large curvature and from medium to large torsion are considered. The analysis of the research results is carried out in the vector space of A.A. Il’yushin. The spatial trajectories of deformations in the form of helical lines of constant and variable curvature are considered. The calculation results are compared with the results of experimental studies on the response components of the stress vector and scalar properties along the deformation trajectory. Variants of the theory are considered: the Ishlinsky - Prager - Kadashevich - Novozhilov model (linear kinematic hardening and isotropic hardening); the Shabosh model with three evolutionary Armstrong - Frederick - Kadashevich equations; Themis model based on the invariant theory of plasticity; Bondar model with a three-term transformation of the evolutionary equation for kinematic hardening. Material parameters (functions) that close versions of the theory of plasticity are given. Satisfactory agreement with the experiment for all trajectories of deformations is achived when calculating on the basis of the Shabosh model - the difference between the results of calculations and experiments does not exceed 30 %. The best agreement with the experiment is achieved on the basis of the Bondar model - the difference between the results of calculations and experiments for all trajectories does not exceed 10 %. The Bondar Model is closed by three material parameters and one material function which are determined from simple experiments on uniaxial tension after preliminary compression (kink of the deformation trajectory by 180°). Bondar plasticity model has a generalization for non-isothermal loading, many features of cyclic disproportionate and proportional loading and describes the processes of damage accumulation (resource).

**PNRPU Mechanics Bulletin**. 2021;(4):41-48

Modeling of rubber-cord layers under quasi-static loading

#### Abstract

Modeling a pneumatic tire with a strong change in shape causes the problem of choosing an adequate model for rubber-cord plies. Generally, the classical method of asymptotic homogenization is not suitable due to physical and geometrical nonlinearity for the strain up to 15 %. The known models used for simulation the entire tire as well as rubber-cord plies are analyzed. A choice is made in favor of modeling the plies using the stress anisotropic potential, which is an anisotropic function of the strain tensor invariants. The relationship of such a constitutive law with a quasi-linear constitutive equation in terms of stress and strain differentials is indicated. A convenience of these two types of constitutive equations in terms of numerical implementation is also given. A modification of the effective properties definition for an inhomogeneous layer is explained. The difference from the standard effective moduli definition is clarified. The arrangement of the cords is supposed to be approximately periodic and all cords to be equivalent to the effective fiber. Two models of a rubber-cord plies are described under such assumption. These are a model of an orthotropic material and a model of a transversely isotropic material. Computational experiments, which make it possible to determine the material parameters of anisotropic potentials, are pointed out. Real tests with a sample of rubber ply under slow quasi-static loading were conducted. Significant hysteresis was detected. It is shown that an additive model combining a hyper elastic material with Maxwell viscoelastic model provides good accuracy in stress dependence on the strain rate. The numerical procedure developed to calculate solution to the quasi-static problem of tire deformation is described. It is implemented in home-made computer code. A numerical example on the tire simulation is given. That is so-called breaking test, in which strong deformation is achieved and the developed model is applied to.

**PNRPU Mechanics Bulletin**. 2021;(4):49-59

Investigation of the stress-strain state of a hollow cylinder with a coating based on the gradient model of thermoelasticity

#### Abstract

The study of the stress-strain state of a thermoelastic hollow cylinder with a homogeneous coating is carried out taking into account the scale effects. Aifantis' one-parameter gradient model is used to account for scale effects. Equilibrium equations and boundary conditions for a composite hollow thermoelastic cylinder are obtained on the basis of the Lagrange variational principle. In comparison with the classical formulation of the problem, additional boundary conditions and conjugation conditions are set for moment stresses and displacement gradients. The dimensionlessness of the task of thermoelasticity has been carried out. Solving the problem of uncoupled thermoelasticity begins with finding the radial temperature distribution of a layered cylinder on the basis of solving the problem of heat conduction in the classical formulation. The solution of the problem in displacements is presented as a sum of solutions in the classical formulation of the problem and additional boundary layer terms found on the basis of the asymptotic properties of the modified Bessel functions. Simplified analytical expressions are obtained for finding radial displacements, radial and circumferential Cauchy stresses, nonzero components of the tensor of moment and total stresses. On specific examples, calculations of the radial distribution of displacements and stresses of a composite cylinder in the case of both mechanical and thermal loading are carried out. The limits of applicability of the asymptotic solution of the problem are investigated. The difference between the radial distribution of displacements and stresses found on the basis of solutions to the problem in the classical formulation and in the gradient formulation is shown. It was found that the Cauchy radial stresses experience a jump at the boundary of the cylinder and the coating, which is explained by the continuity of radial displacements and their first derivatives. The components of the moment stress tensor either take on peak values or experience a jump at the interface. The moment stresses are proportional to the square of the gradient parameter, at small values of which they have values that are much less than the values of the total stresses. With an increase in the dimensionless scale parameter, the values of radial displacements and total circumferential stresses decrease, but moment stresses increase.

**PNRPU Mechanics Bulletin**. 2021;(4):60-70

Investigation of the features of crystallization of granules of high-strength aluminum alloys of the Al-Zn-Mg-Cu system at ultra-high cooling rates

#### Abstract

The article presents the results of studies of the process of obtaining granular materials from high-strength aluminum alloys of the Al - Zn - Mg - Cu system by centrifugation of the melt with ultra-high cooling rates of granules. The concept of a «steam jacket» is introduced, namely, a steam layer that occurs between the granule body and the cooling liquid, which prevents the intensity of heat removal and is an obstacle to increasing the crystallization rate due to the lower thermal conductivity of water vapor. It is established that the formation of a vapor layer always occurs due to the heating of the cooling liquid in contact with the melt drop to boiling temperatures and the transition of the cooler from the liquid phase to steam. The technology of increasing the rate of crystallization of granules due to the constant removal of the vapor layer is proposed. The removal (knocking down) of the vapor shell that occurs around the drop occurs due to the high speed of the drop movement in the cooling medium. Fundamentally important in the industrial implementation of this technology is not so much the design of the device for obtaining pellets by centrifugation of the melt, namely, the high required rotation speed of the spraying crucible of the device under consideration. The results of experimental data are presented to determine the necessary rotation speed of the perforated cup, which ensures the creation of a sufficient initial velocity of the drop movement, leading to a constant churning of the «steam jacket». It is determined that an increase in the rates of heat removal from the crystallized granules and, as a result, an increase in the crystallization rate leads to an increase in the strength characteristics of granular aluminum alloys of the Al-Zn-Mg-Cu system. In particular, in the production of pressed semi-finished products from alloys of the Al-Zn-Mg-Cu system, such as B95, B96c. the increase in the strength characteristics of the material of the press products is up to 15 % compared to the same granular materials obtained by traditional methods with industrial crystallization rates of melt droplets. It is established that this method, based on the removal of the vapor layer around the formed granule, is the only possible one for further increasing the cooling rate and, as a result, the crystallization rate. Reducing the size of granules to the size of powders leads to serious technological problems in the further consolidation of granules and, in fact, is a dead end branch of the further development of granulation methods.

**PNRPU Mechanics Bulletin**. 2021;(4):71-82

Multilevel model of polycrystals: application to assessing the effect of texture and grains misorientation on the critical deformation of the dynamic recrystallization initiation

#### Abstract

The current state of materials constitutive models and the computer technology development make it possible to numerically implement complex multilevel models that allow describing the material structure evolution. In this regard, it is possible to formulate optimal control problem for metal forming processes in order to create the required performance characteristics of finished products and their ingots. To solve this problem in this study, the effective multilevel modeling approach is used to describe the thermomechanical treatment of polycrystalline materials. The model is based on this approach with the introduction of internal variables, in which the carriers and physical mechanisms of the processes of hot intense plastic deformation are explicitly considered. At deformation temperatures order of 0.5 homologous and above, recrystallization process have a special effect on the formation and change of the grain and defect material structure. The paper considers the problem of determining the critical deformation of dynamic recrystallization initiation, that depending on the material texture and the mutual misorientation of neighboring grains. Numerical experiments of the multilevel model are used to simulate two stages of inelastic deformation for this purpose. At the first stage, cold inelastic deformation by simple shear and compression is considered, that leading to the formation of a corresponding texture. At the second stage, uniaxial hot tension deformation is considered. The initial distribution of crystallographic grain orientation is assumed to be uniform. Two variants of the grains mutual misorientation with the prescribed increased and decreased values of the average misorientation angles are considered. The recrystallization process is not explicitly modeled. The current model is intended to assess the recrystallization critical deformation. It is shown that the mutual misorientation of grains, rather than texture, has the most influence on the critical deformation. An increase in the angle of grains mutual misorientation contributes to an earlier start of the dynamic recrystallization process. The formation of a deformation texture leads to a decrease in the angle of mutual misorientation, and, accordingly, to a decrease in dynamic recrystallization intensity. Despite this, with an increase of deformation, the driving force of recrystallization (the average value of the difference of stored energy between neighbor grains) is increases, which leads to the implementation of dynamic recrystallization.

**PNRPU Mechanics Bulletin**. 2021;(4):83-97

The potential of using SWCNTs, MWCNTs and CNFs capable of increasing the composite material dimensional and technological stability as modifiers of a polymer matrix

#### Abstract

In this study, the effect of carbon nanofibers (CNN), single-wall carbon nanotubes (SWCNTs) and multi-wall carbon nanotubes (MWCNTs) on the warpage expected value and warpage dispersion of a plate made of a fibrous composite material are investigated. Laminates with fiber disorientation were considered as asymmetric and the model proposed by Dano and Hyer was used to evaluate the warpage. The results obtained confirm that the addition of carbon nanoparticles as a modifier to the polymer matrix of a fibrous composite material can increase the dimensional stability (the mathematical expectation of the standard deviation) and the technological stability of the reinforcement scheme (the variance of the standard deviation of the composite plate). Modeling of the warpage of plate, taking into account the possible disorientation of the fiber, showed a decrease in the warpage dispersion by 12.6 and 26.6 % with the modification of the SWNTs and MWCNTs, respectively. The coefficient of thermal extension (CTE) of a nanostructured polymer matrix with various fillers were experimentally determined. It was found that carbon nanomodifiers are more effective as compensators for the thermal expansion of the polymer matrix in composite laminates reinforced with carbon fibers than the polymer matrix without macrofibers. The addition of 0.05 % SWCNTs, 1 % MWCNTs to the epoxy resin reduces the CTE by 9.7 and 15.4 %, respectively. At the same time, the addition of a similar amount of nanoparticles to the epoxy matrix of the fiber composite reduces the CTE in the transverse direction by 15.56 and 35.8 %, respectively. On the basis of the obtained results, the dependences of the transverse CTE of the polymer composite material, the mathematical expectation of the standard deviation, and the variance of the standard deviation of the composite plate form accuracy on the concentration of the modifier were constructed. According to the obtained data, it can be concluded that in order to reduce the mathematical expectation and the variance of the warping of the composite material, there is an effective concentration, the increase of which is impractical, despite the further decrease in the transversal CTE.

**PNRPU Mechanics Bulletin**. 2021;(4):98-110

Anti-icing indicator polymer coating with built-in fiber-optic PEL-sensor for indication, location and de-icing of aerodynamic surfaces

#### Abstract

A mathematical model was developed and a numerical modal analysis of the anti-icing mode of operation of the new indicator polymer coating with an integrated optical fiber piezoelectroluminescent (PEL) sensor for icing indication, location and self-cleaning from icing of aerodynamic surfaces was given. The fiber optic PEL-sensor is located in the plane of the coating. Receiver-analyzer of informative integral intensities of light signals is installed at output from optical fiber of sensor. Alternating voltage generator is connected to outputs of two control electrodes of sensor. The anti-icing function of the polymer coating is carried out automatically by thermo-mechanical actuation of the PEL-sensor on the appeared ice layer (on the ice crust of the coating) and only in those local areas of the coating where the thickness of the attached ice layer has reached a given critical value. Quality of cleaning from icing of surface of anti-icing coating is controlled by algorithms of digital processing of informative light signals at output from optical fiber of PEL-sensor. As a result, improved efficiency and control of de-icing on aerodynamic surfaces is achieved, especially for extended surfaces. The energy efficiency of the anti-icing polymer coating is increased due to the locality and self-control of the icing process. The modal analysis was carried out in an ANSYS finite element analysis package based on a numerical solution of the electrical-elasticity boundary value problem of stationary electromechanical oscillations of the representative cell of the anti-icing indicator polymer coating in the absence and presence of an ice layer of different thickness. Results of calculation of natural frequencies and forms of oscillations of representative cell of anti-icing coating, amplitude-frequency characteristics of mechanical stresses at coating/ice boundary for different values of thickness of attached ice layer for case of action of harmonic "force" in form of control electric voltage on electrodes of built-in PEL-sensor are presented.

**PNRPU Mechanics Bulletin**. 2021;(4):111-121

Influence of the stress-strain state on the jerky flow effects and kinetics of the strain bands nucleation in Al-Mg alloy (A 95456)

#### Abstract

The aim of the work is to develop a technique on the experimental study of inelastic deformation of structural metal materials in various types of stress-strain state. A technique is proposed based on the use of original samples of specialized complicated geometry, in the working zone of which a controlled biaxial stress state is realized, and the use of a contactless 3D digital image correlation measurement system Vic-3D for recording displacement and deformation fields. The authors proposed the use of original samples of variable thickness in the form of plates located inside a rigid circular rim and a rim of reverse curvature. Under uniaxial tension of these samples in the central area of the plate (working part of the sample), the plane stress state is realized with principal stresses of different signs, depending on the shape and rigidity of the rim. In the working part of the plate with a ring-shaped rim, tensile forces in the longitudinal direction and compressive forces in the transverse direction are realized due to the curvature of the circular rim and its narrowing in the transverse direction. In a plate with a rigid rim of reverse curvature, biaxial tension is realized in the working section. High efficiency of the proposed experimental technique has been shown to solve problems in the mechanics of solids, in particular, to study the processes of macroscopic localization of plastic flow in Al-Mg alloys (AlMg6) under the conditions of the Portevin - Le Chatelier effect. Using a video system, experimental data of the realized ratio of the deformation components (longitudinal and transverse deformations) in the working zone of the samples were obtained. The analysis of the kinetics of band formation and discontinuous yield strain occurring under conditions of a plane stress state has been carried out. The use of the Vallen Amsy-6 system made it possible to obtain data on the occurrence of acoustic emission signals accompanying the observed processes of inelastic deformation of the material. The graphs of the dependence of the energy parameter and frequency characteristics of acoustic emission signals on time have been constructed and analyzed.

**PNRPU Mechanics Bulletin**. 2021;(4):122-135

Analysis of stress fields at the crack tip and fracture resistance parameters under conditions of gradient plasticity

#### Abstract

This paper presents a numerical analysis based on previously obtained experimental data on crack growth for P2M and 34X steels, aluminum 7050 and titanium alloy Ti-6Al-4V compact samples (CTS) with a one-sided lateral incision, within the framework of the conventional theory of strain gradient plasticity (CMSG), based on the Taylor dislocation model. In this study, the initial points of the curved crack trajectory were considered for two classical states: plane strain and plane stress with normal separation and pure shear. The constitutional equations of material behavior for CMSGP theories were introduced into the finite element computational complex and new fields of stress-strain state parameters for the conditions of strain gradient plasticity were obtained. The results of FE calculations show a significant increase in the magnitude of the true stress fields at the crack tip, taking into account the plastic deformation gradients and the internal characteristic length of the material. The numerical results also show that the singularity in the crack tip region is different for the model of gradient plasticity of deformations and depends on the mode I/II. An important conclusion regarding the numerical results regarding the parameters of the material's fracture resistance is that the new plastic stress intensity coefficients for gradient plasticity differ for plane strain and plane stress, and also show significant sensitivity to the plastic properties of the material and to the scale parameter of the intrinsic material length, which is attractive from the point of view of practical application and further fundamental research.

**PNRPU Mechanics Bulletin**. 2021;(4):136-148

Elastic-plastic invariant of autowave plasticity

#### Abstract

It is shown in the work that plastic flow in solids develops always in localized manner. A macroscopic scale ~ 10-2 m characterizes the localization. The localized flow zones form the pattern of localized strain, which is the projection of the autowave processes of plastic flow, developing in the volume, on the observed surface of the tested specimen. One can observe the pattern with the help of speckle-photography method. The investigations of various materials allowed to establish that the pattern of localized deformation is the information source for a kinetics of deformation processes. A general characteristic of localized plastic flow in solids is the elastic-plastic invariant of deformation which couples the typical characteristics of localized plastic flow autowaves with the same for the elastic waves in crystal lattice. The quantity of the invariant ratio is defined for nearly forty various materials (BCC, FCC, HCP metals and alloys, alkali-halide crystals, ceramics, rocks) studied in the conditions of active elongation and compression at the temperature range 143-420 K. The physical considerations are presented to explain the invariant origination and its relation to other physical characteristics of crystal lattice, in particular, the Debye temperature. In the light of these considerations, it is possible to explain the meaning and the origin of the invariant, and to derive numerous consequences from them. In fact, the set of these consequences comprehend all the regularities of developed plastic flow processes and allows to consider the elastic-plastic invariant of deformation as the master equation for developing this day autowave approach to physical theory of plastic deformation.

**PNRPU Mechanics Bulletin**. 2021;(4):149-161

© ПНИПУ Numerical and experimental research of the evaluation of the mechanical behavior of carbon fiber reinforced polymerspecimens with an embedded Smart-layer

#### Abstract

Currently, scientists have paid special attention to the possibility of creating so-called Smart-structures that are capable of real-time self-diagnostics and/or functional changes. Within the framework of this work, the possibility of creating structures capable of diagnosing the deformation state in real-time is considered. When creating such Smart-structures, fiber-optic, piezo-, and strain-gauge sensors are usually used as control sensors. The use of such sensors is due to a number of their advantages, such as small size, the ability to integrate into a single measuring network, ease of use, a wide range of measured values, the ability to transmit data over long distances. However, when such sensors are embedded into the structure, several difficulties arise in installation/dismantling or implementation due to the fragility of the fiber, the difficulty of locating the sensitive element, ensuring the integrity of the fiber-optic sensors at the exit from the polymer structure. The team of the Scientific and Educational Center of Aviation Composite Technologies, PNRPU, has developed a prototype of a Smart-layer based on 3D-printing technology, capable of solving the problems described above. However, the influence of such an embedding on the structure of structures made of carbon fiber reinforced polymer (CFRP) remains open. Thus, this work aims to carry out computational and experimental studies to assess the mechanical behavior of CFRP samples with an embedded Smart-layer. Within the framework of this work, the technology and scheme for manufacturing a Smart-layer with embedded fiber-optic sensors, as well as a scheme for laying a Smart-layer into CFRP samples, are described. Since the properties of molded plastic specimens differ from those of printed specimens, mechanical tensile tests of printed specimens were carried out. The obtained values of the strength limit and the modulus of elasticity were used to identify the mathematical model. Within the framework of the experimental part, mechanical tests for tension, compression, and interlayer shear of CFRP samples with an embedded Smart-layer were carried out. When analyzing the obtained experimental results, it was found that the maximum percentage deviation of the physical and mechanical characteristics (PMC) is no more than 15 %, which lies within the spread of the PMC of carbon fiber in a prepreg roll. As a result, we can conclude that the embedded of such Smart-layers does not significantly affect the PMC of the final CFRP structure. According to the results of mathematical modeling of the tensile strength of a CFRP sample with an embedded Smart-layer, it was found that the maximum value of normal stresses in the sample reaches 540,28 MPa, which is 1,46 % higher than the maximum value for the statistical ultimate strength of the sample. The maximum values of the Mises stress for the Smart-layer do not exceed the ultimate strength, while for the epoxy binder there is a significant excess of the ultimate strength, on the basis of which one can make an assumption about its destruction during deformation.

**PNRPU Mechanics Bulletin**. 2021;(4):162-177