The process of deformation and fracture of structural alloys under low-cycle fatigue in conditions of uniaxial loading with axial strain control under complex cycle shape and block loading has been studied. The obtained results of experimental studies of structural alloys were used to assess the possibility of using the nonlinear Marco - Starkey damage accumulation model. The processing of the nickel alloy cyclic tests results with a simple and complex form of the cycle has been carried out. A combination of exponents included in the non-linear Marco - Starkey model was selected which for the case of low-cycle fatigue with a complex M-shaped cycle made it possible to predict durability which is in good agreement with experimental test data. The main problem of using the nonlinear Marco - Starkey model for predicting cyclic durability with an M-shaped cycle is the presence of many combinations of exponents that allow predicting cyclic durability with the same accuracy. To determine the uniqueness of the solution it is proposed to carry out a set of tests under simple and block loading. Experimental results have been obtained on the processes of deformation, fracture of D16T aluminum alloy under low-cycle fatigue conditions under simple cycle forms with constant parameters, and block loading with variable cycle parameters in tests for uniaxial loading with axial strain control. Based on the obtained experimental results according to the new method combinations of the m degrees coefficients were selected, which was carried out in the range of exponents from 0.2 to 10 with a step of 0.2. Comparison of the forecasting results for blocks consisting of three groups made it possible to find several combinations of general exponents m for two groups that are present in all blocks. The final choice of a pair of coefficients was carried out on the condition that the predicted damage is close to unity in the first (test) block. The selected values of the coefficients made it possible to predict the durability under block low-cycle loading using the nonlinear Marco - Starkey model.

The article presents the results of experiments on cyclic loading of samples with an annular V-shaped notch and their mathematical modeling. The tests were carried out on specimens of the BrKh08-Sh alloy with a cyclic change in the tensile load from 0 to a given value. Under such loading, the material in the groove area is subjected to cyclic elastoplastic deformation, which leads to failure due to low-cycle fatigue. When testing samples using the digital image correlation method, the deformation of the material on the surface of the undercut was measured, which made it possible to determine the nature of the change in its range from cycle to cycle. Mathematical modeling of experiments is carried out according to the finite element method. For this purpose, models of elastic-plastic deformation and accumulation of material damages are introduced into the SIMULIA Abaqus software package. The plasticity model is based on the theory of flow under combined hardening. The damage accumulation model is based on the energy strength criterion. The article presents the basic equations used to calculate the models. The material parameters are determined and verified based on the results of a basic experiment on cyclic tension-compression of a smooth cylindrical sample under asymmetric rigid loading. Based on the results of the calculation, cartograms of stresses, deformations, and accumulated damages were constructed. It is shown that when the sample is unloaded, in the area of stress concentration close to the annular groove, compressive stresses arise, the values of which are close to the values of tensile stresses at the moment of application of the maximum load. The results of mathematical modeling are compared with the experiment. A comparison of the results was carried out in terms of the range of axial deformation of the material on the surface of the undercut and the number of cycles before failure.

In this paper, the problem of studying the dynamics of transverse vibrations of plate, taking into account the elastic dissipative characteristics of the hysteresis type in conjunction with a liquid section dynamic absorber under the influence of kinematic excitations. In the differential equations of motion, the elastic dissipative characteristics of the plate material of the hysteresis type are taken into account by means of harmonic linearization coefficients based on the Pisarenko - Boginich hypothesis. The amplitude-frequency characteristic of the vibrating plate and the analytical expressions of the transfer function were determined using a differential operator from a system of differential equations of motion depending on the system parameters. In order to perform numerical calculations, the coefficients of the first three terms of the logarithmic decrement expression were found. In the amplitude interval, the function representing the vertical deviation of the amplitude-frequency characteristic decreases and the function representing the energy dissipation in the plate material increases. It has been shown that the efficiency of the liquid section dynamic absorber in quenching harmful plate vibrations at low frequencies can be evaluated based on the results of numerical calculations to ensure that the displacements of the plate point reach minimum values. Amplitude-frequency characteristics for plate points at different parameters were constructed for the distributed parametric system using the developed model and method. Recommendations for the selection of parameters of the system depending on the elastic dissipative and inertial properties are given.

The problems on in-plane and anti-planar steady-state vibrations of an isotropic elastic strip with delamination at the lower boundary has been investigated. The goal of the study is to analyze the stress-strain state in the crack tips areas and to construct a crack opening function being the main mechanical characteristics in the crack theory problems. The problems under study have been solved in the framework of the nonclassical gradient elasticity theory (GET) on the basis of the one-parameter model proposed by Aifantis. The boundary integral equations (BIE) are obtained with respect to crack opening functions or their derivatives. The analysis of BIEs is carried out, regular and irregular parts are distinguished, the obtained BIEs with singular (e.g., with hypersingular, with cubic singularity) integrals are solved via collocation methods, approximating Chebyshev polynomials, quadrature formulas for singular integrals. For the in-plane problem solution, the simplified Ru-Aifantis method has been applied. The Ru-Aifantis method allows to divide the initial boundary value problem into two sub-problems - the classical linear elasticity theory (LTE) problem and the simplified boundary value problem for finding the gradient solution which includes the solution found via the classical theory. For each of the problems, semi-analytical expressions for the functions of crack opening have been constructed, and the analysis of the stress-strain state in the area of crack tips has been carried out. The problems have also been solved in the case of a crack with small relative length, the analysis of BIE depending on small parameters ratio has been carried out, and explicit expressions for the crack opening functions have been obtained. Numerical calculations have been performed; the applicability conditions for the asymptotic method are determined, and a comparative analysis of the results obtained on the basis of GET and LTE models, depending on the values of the gradient parameter and the delamination length, is realized.

A dynamic statement and a method for numerically solving the buckling problems of elastoplastic shells of revolution with filler in axisymmetric and non-axisymmetric shapes under quasi-static and dynamic loading are presented within the framework of two approaches. In the first approach, the problem of elastic-plastic deformation and buckling of shells of revolution with an elastic filler under combined axisymmetric loading with torsion is formulated in a two-dimensional (generalized axisymmetric) formulation based on the hypotheses of the shells theory of the Timoshenko type and the Winkler foundation. The constitutive relations are written in the cylindrical system of Euler coordinates. For each shell element, a local Lagrangian coordinate system is introduced. Kinematic relations are recorded in the current state metric. The distribution of the displacement velocity components over the shell thickness and strain rate tensors in the local basis is written as the sum of the momentless and moment components, which, in turn, are written as the sum of the symmetric and asymmetric parts in the local and in the general basis. The elastoplastic properties of the shell material are taken into account within the framework of the theory of flow with nonlinear isotropic hardening. To take into account non-axisymmetric forms of buckling, the desired functions (both displacements and forces, moments, contact pressure) are expanded into a Fourier series in the circumferential direction. The variational equations of shell motion are derived from the general equation of dynamics. The contact between the shell and the deformable filler is modeled based on the conditions of non-penetration along the normal and free slip along the tangent. The variational equations of shell dynamics for axisymmetric and nonaxisymmetric processes are interconnected through the physical relations of the theory of plasticity. They take into account large axisymmetric shape changes and the instantaneous stress-strain state of the shell. At the initial stage of the nonaxisymmetric buckling process, the deflections are small; therefore, the equations of nonaxisymmetric buckling are obtained as linearized with respect to nonaxisymmetric forms. To initiate nonaxisymmetric buckling modes, initial nonaxisymmetric deflections are introduced. To solve the defining system of equations, a finite-difference method and an explicit time integration scheme of the “cross” type are used. The second approach is based on continuum mechanics hypotheses and implemented in a three-dimensional setting. Both approaches make it possible to simulate the nonlinear subcritical deformation of shells of revolution with an elastic filler, to determine the ultimate (critical) loads in a wide range of loading rates, taking into account geometric shape imperfections, to study the processes of buckling in axisymmetric and non-axisymmetric shapes under dynamic and quasi-static complex loading by tension, compression, torsion, internal and external pressure. The results of numerical simulation are compared with experimental data on the torsion of steel cylindrical elastoplastic shells ( R / h = 1.45) with an elastic filler.

The problem of deformation of a DCB sample, which is a composition of bodies bound by an adhesive layer of finite thickness, is considered. Based on the variational equilibrium equation containing the layer thickness as a linear parameter, a finite element solution of the problem of loading the layer with a normal discontinuity in the plane strain state is constructed. The stresses averaged over the layer thickness are related to the stresses along the layer boundary by the equilibrium equations. The boundary stresses of the layer form the boundary conditions for the mating bodies. In the layer, along with shear stresses, stresses orthogonal to shear are also taken into account. The constitutive relations in the layer are represented in terms of average stresses. With a significant difference in the Young's moduli of the adhesive and mating bodies, the convergence of the value of the J-integral with a decrease in the layer thickness is shown. To find the J-integral, its representation is used as a product of the specific free energy at the end of the layer and its thickness. It has been established that the Poisson's ratio of the bodies affects the value of the J-integral, and the Poisson's ratio of the adhesive layer has almost no effect on the value of the J-integral. Using the theory of plates Mindlin - Reisner at zero Poisson's ratio of the adhesive, an analytical representation of the J-integral is obtained. The representation includes energy terms related to the pull-off stress and the axial stress in the layer. In this case, the term associated with the axial stress in the layer is proportional to the square of the ratio of the Young's moduli of the adhesive layer and the bodies mating with it. From the solution obtained, it follows that the mechanical properties of the adhesive layer with a small thickness compared to bodies do not affect the value of the J-integral if the elastic modulus of the adhesive layer is significantly less than the elastic modulus of the mating bodies. Thus, the use of replacing the adhesive layer with a layer of zero thickness is correct under these restrictions.

The paper presents a comprehensive analysis of the deformation and thermal states of the Waspaloy alloy billet heated to different initial temperatures of 1100°C and 1150°C and subjected to free upsetting to an average diameter of ~1060 mm at the deformation rate of 100 mm/s. The thermodynamic forces acting on the billet trigger the process of dynamic recrystallization, which is associated with the appearance and growth of low-defect nuclei of new grains instead of the deformed ones. To describe the material microstructure evolution, the phenomenological approach implemented in the DEFORM-2D/3D software package was applied. The simulation was based on the modified Johnson - Mehl - Avrami - Kolmogorov (JMAK) model, whose equations allow calculating the volume fraction of recrystallized material and describing the grain structure transformation of metal alloys. The results of solution of the non-stationary temperature problem are used to construct the temperature fields in the Waspaloy alloy billet during its transportation through air from the furnace to the deforming equipment within 45 seconds and during the subsequent upsetting process. For the latter, the force and strain characteristics, including the force required to complete this process, are determined in the framework of the plastic flow theory, and the characteristics of the grain structure of the nickel alloy, such as the average size of recrystallized grains and their volume fraction, are determined in the framework of the JMAK model. The results obtained by numerical simulation make it possible to substantiate an optimal selection of parameters of billet deformation ensuring the formation of the required material structure.

The problem of temperature stresses is solved in the work. The process of electric arc welding with guaranteed penetration of steel plates of various thicknesses is simulated. The possibility of reducing residual stresses formed as a result of welding by applying heat removal from the surface of the near-weld region of a steel plate is being investigated. The temperature distribution is determined by solving a non-linear heat equation, in which the specific heat and thermal conductivity depend on temperature. The heat source is modeled using the double ellipsoid method proposed by John A. Goldak. The horseshoe-shaped heat sink follows immediately after the anode spot and is set by the heat flux in such a way that the main temperature of the plate does not decrease below its initial temperature. This limitation reduces the level of the temperature gradient, thereby reducing the stresses in the metal plate. To illustrate the effect of active heat sink, the temperature distribution in the top layer at the moment of termination of welding is compared with and without active heat sink. The material is assumed to be elastoviscoplastic, the deformations are small and consist of reversible and irreversible ones. Reversible deformations are related to stresses by the Duhamel - Neumann law. Irreversible strains increase when the von Mises plastic flow condition is satisfied, in which there is a plastic strain rate component responsible for the plastic flow viscosity. The elastic moduli (Young's modulus, Poisson's ratio) and the yield strength are assumed to be temperature dependent. The solution of the mechanical part of the problem is found by the method of simple iterations. For plates with different thicknesses, diagrams of residual stresses are given, located in the center of the plate from the seam to the periphery. As a result of the work, according to the obtained distributions of residual stresses in the plate material, it is concluded that the use of an active horseshoe-shaped heat sink from the near-weld zone when welding thin steel plates reduces residual stresses, therefore it is recommended to use in the welding process. The use of an active heat sink on the reverse side of the plate leads to an increase in the stress level, therefore it is not recommended for use.