The conditions of occurrence of acoustic stress resonances at the boundaries of an anisotropic layer are investigated. In general, under the action of an incident elastic wave, six elastic waves are formed in an anisotropic layer. The total effect of these waves determines the stressstrain state of the layer and is displayed in the spectra of waves scattered by the layer into the environment. The scattering spectra and acoustic stresses were modeled by solving the equations of motion of a continuous medium and the generalized Hooke's law. This system of differential equations is solved with respect to the components of the displacement vector and the stress tensor in the Cartesian coordinate system. The Peano-Becker method of solving a system of differential equations by means of a matrix exponential is used. The components of the displacement vector and the stress tensor at two opposite boundaries of the layer with thickness d are expressed through each other using a sixth-order transfer matrix T = exp(Wd), where matrix W is determined by the parameters of the layer under study. The method of scaling and multiple squaring is used. According to this approach, T = (exp(Wd/m))m. A method for selecting the scaling parameter m is proposed to estimate the errors of truncation and rounding when calculating exp(Wd/m). A guaranteed accuracy and the best efficiency of calculations of all elements of the matrix exponential of the sixth order, in comparison with other known methods, is provided by the use of the method of polynomials of the principal minors of matrix W. The modeling of elastic wave scattering spectra (conversion coefficients) and stress dependences on the angles of incidence for cubic crystal layers is given using the example of indium. The interpretation of resonances of acoustic stresses arising in the crystal layer under the action of a shear wave incident on the crystal is given.

In this paper, an experimental study of the strain fields at the fatigue crack tip was carried out. The strain fields were measured by an optical camera based on the digital image using the correlation method. Images were recorded using a Basler acA2440-75uc optical camera with a TC23007 OptoEngineering lens to achieve a spatial resolution of at least 3 μm. Recording frequency was 100 Hz. The possibility of using the solution of the linear singularity problem of elasticity theory to estimate the distribution of plastic strain at the fatigue crack tip was shown. Mechanical tests of uniaxial cyclic deformation with simultaneous registration of the strain field at the crack tip of different lengths were carried out on flat specimens of titanium alloys Ti Grade 2, Ti-1.1Al- 0.9Mn, Ti Grade 9. The specimens were loosened by means of a lateral semicircular notch in order to localize the crack. The solution of the problem of a specimen with a notch in the elastic formulation was carried out numerically in the finite element modelling package Comsol Myltiphysics. The peculiarity of the work is the use of the hypothesis of the functional relationship between real deformations and the elastic solution and the value of the secant modulus of the material to estimate the plastic deformation at the crack tip. The size of the zone of intense plastic deformations at the fatigue crack tip for different crack lengths was determined experimentally and numerically. By comparing the calculated and experimental data we showed the possibility of using the proposed dependence to estimate the distribution of the plastic strain field at the crack tip. The results obtained allow the analysis of the irreversible strain fields at the crack tip for mixed mode loading.

The paper considers new applications of the models, algorithms, software and methods developed by the authors to study shell structures of spherical shells (domes). For this type of structures, a method has been proposed to bypass the singularity at the top of the dome by choosing modified approximating functions. The mathematical model is geometrically nonlinear; it takes into account transverse shears, and is presented as a functional of the total potential strain energy. To reduce the variational problem to solving a system of algebraic equations, the Ritz method was used. The resulting system is solved by the method of continuing the solution using the best parameter with an adaptive mesh selection. The algorithm is implemented in the Maple analytical computing environment. A steel dome was estimated using different methods of border fixing, the values of the critical buckling load and the limit stress load were obtained. A graph of the load – deflection relationship and the deflection fields in the subcritical and supercritical stages were constructed. Fields are shown in the local and global Cartesian coordinate systems. The convergence of the Ritz method in terms of the critical load value is demonstrated. The methodology was verified by comparing the solution to the test problem with the known solution obtained by E.I. Grigolyuk and E.A. Lopanitsyn. The comparison results demonstrate the reliability of the data obtained. It was revealed that for the dome under consideration, the loss of strength occurs much earlier than the buckling, and therefore it can be recommended to select a steel grade with a higher yield strength for its design. A simply support border condition in this case gives a higher value of the maximum permissible load.

The paper deals with X-ray computed tomography results of a polyetheretherketone (PEEK) and a short carbon fibre reinforced by acrylonitrile butadiene styrene (ABS+CF). Individual carbon fibres and 3D printing defects (consolidated structures of interconnected fibres and densified resin clumps) are detected on an initial microstructure of the ABS+CF composite. The carbon fibres and the consolidated structures are densely packed with uniform sub-horizontal locations throughout in a sample volume. In the PEEK samples, the process-induced defects during the composite manufacturing process are visualised as tubular structures of a densified resin with internal voids. Significant changes in the structure of both composites are observed after five times pulsed laser shock peening. In case of a single pulse exposure and a surface treatment, no microstructural changes occur. In a test mode without a protective layer, a material evaporation to a depth of 0.3 mm and a structural degradation of the PEEK samples takes place, while the process-induced interlayer voids do not close. A single consolidated area with a porous spongy structure occurs due to melting of the carbon fibres in the ABS+CF composite. The results show that the laser shock peening has a significant effect on the surface microstructure. It is therefore necessary to carry out further experiments to select the optimum laser shock peening parameters and a protective layer material to eliminate the process-induced defects and improve the strength properties of the composites.

The paper investigates the process of local damages in the hip joint endoprosthesis (HJ) made of unidirectional carbon-carbon composite material (C/C composite) with pyrolytic carbon (PС) matrix. A mathematical model of deformation of the endoprosthesis from the C/C composite has been developed taking into account the processes of local damage. These damages are possible due to overloads, which may be caused by accidental circumstances during human movements. The developed model is a synthesis of an algorithmic model that takes into account the heterogeneity of the pyrocarbon matrix and composite, and an engineering computational model of the biomechanical endoprosthesis-femur system. The matrix algorithm solves the stochastic boundary-value problem of finding mesostresses in PС grains taking into account possible damages. The result of this algorithm is the probability distribution densities for meso-stresses in PС crystallites and the properties of the damaged matrix. The results of calculations based on the engineering model are the fields of macrostrains and macrostresses. At each step of loading of the endoprosthesis, the state of the matrix is monitored and the effective modules of the carbon composite are changed. This is implemented by a continuous exchange of data between the two algorithms, the recalculation of the properties of the composite, which are the input data for the engineering model. The continuous change in the effective properties of the C/C composite during deformation is replaced by a stepwise change. To do this, the volume of the endoprosthesis was divided into areas in which the properties become variable, starting with a certain loading step. The areas of change were determined based on the distribution patterns of macrodeformation fields. A nonlinear loading diagram of the endoprosthesis is constructed taking into account the damage. It is shown that the destruction of the carbon part of the prosthesis begins with local damage, which gradually engulfs the neighboring areas. Damage occurs when the standard load exceeds 1740 Newtons. The maximum force response of the prosthesis to an external load is equal to 2004 newtons. The deformation of the prosthesis at the stage of a critical reduction in load-bearing capacity exceeds the deformation at standard load by 16 %. The high reliability of the considered variant of the endoprosthesis was confirmed, the absence of catostrophic sharp decreases in load-bearing capacity under a significant excess of standard loads was confirmed.

Additive technologies, including laser powder deposition (a repair technology), enable a sequential deposition of powder layers. This process involves large temperature gradients and technological residual stresses, which can lead to shape violations and change mechanical and operational characteristics of products. To control and prevent residual deformations in the hardfacing body, it makes sense to carry out finite element modeling of the laser powder hardfacing using layer-by-layer activation technology or adding new finite elements to the surface of the hardfacing model. The Element Birth/Death method is the most suitable method for this problem. In this case the elements for the material to be created are deactivated (so not included in the solution area), and then gradually revived and included in the solution area. The material is built up discretely. At each sub-stage of the calculation, corresponding to the revival of the next sub-domain of dead elements, the coupled problem of thermal conductivity and solid mechanics is solved, and thus the result of the solution of the previous sub-stage serves as the initial conditions for the next one. A mathematical model and an algorithm for modeling warping during the deposition are developed, and calculations for the deposition of cylindrical specimens are carried out. During the calculations, the multilinear MISO plasticity model for the sample material and the BISO bilinear plasticity model for the filler powder were used. We verified the model based on the optical control results of changes in the geometry of the experimental samples after the deposition had been carried out. The error in warpage calculation did not exceed 5%.

Within the refined theory of bending, a coupled initial-boundary value problem of thermoelastic- plastic deformation of flexible circular cylindrical shells with arbitrary reinforcement structures is formulated. The tangential displacements of the shell points and the temperature along the thickness of the structures are approximated by high-order polynomials. This makes it possible to take into account, with varying degrees of accuracy, the weak resistance of fibrous sheaths to transverse shear and to calculate wave processes in them. From the obtained two-dimensional equations of the refined theory, in the first approximation, the relations of the traditional non-classical Ambartsumian theory are obtained. The geometric nonlinearity is modeled in the Karman approximation. The inelastic deformation of the components of the composition is described by the relations of the theory of flow with isotropic hardening. In this case, the loading functions of the materials of the composition phases depend not only on the strengthening parameter, but also on the temperature. For the numerical solution of the formulated nonlinear coupled two-dimensional thermomechanical problem, an explicit scheme of time steps is used. We studied the axisymmetric elastic-plastic deformation of flexible long cylindrical shells, which are reinforced in the circumferential and axial directions. Fiberglass and metal-composite structures from the inner front surface are loaded with pressure, which corresponds to the action of an air blast wave. It is shown that for an adequate calculation of temperature fields in the structures under consideration, it is advisable to approximate the temperature over their thickness with a 7th order polynomial. It has been demonstrated that at some points fiberglass shells can additionally heat up for a short time by only 10…11 C, so the thermal response can be disregarded in their calculations. Metal-composite structures can additionally heat up by more than 40 C. However, for their calculation it is also possible to use the model of elastoplastic deformation of the materials of the composition components. It is shown that when studying the dynamic inelastic behavior of both fiberglass and metalcomposite cylindrical shells, it is advisable to use the refined theory of their bending, rather than its simplest version, the Ambartsumian theory.