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Along with the classical finite element method (FEM), other calculation methods for assessing crack resistance characteristics are currently being actively developed. This is due to the existing shortcomings of the FEM caused by the dependence of the calculation results on the density of the finite element mesh. One of the promising methods being developed in world practice is the extended finite element method (XFEM), which allows obtaining satisfactory calculation results while simplifying the crack modeling procedure and saving calculation time. In this paper, three problems are numerically modeled using the classical FEM and XFEM methods: calculation of a disc crack in a cube under uniaxial tension, calculation of the off-center tension of a compact CT specimen, and calculation of a cylindrical part of an NPP reactor vessel with a semi-elliptical crack under thermal shock. The obtained results showed that the extended finite element method gives sufficiently accurate results compared to analytical solutions and the classical FEM. At the same time, using the XFEM method does not require considering the singularity of stresses at the crack tip when building an FE model. Therefore, the minimum size of the FE can be increased by almost five times while maintaining the accuracy of the results. This greatly simplifies the procedure for constructing the FE mesh, reduces the total number of FEs in the model, and saves computational time. Thus, the XFEM method can be used to calculate the crack resistance characteristics and improve the efficiency of assessing the resistance to brittle fracture of structural elements. [ABSTRACT FROM AUTHOR]

The paper deals with the 3D printing process that is compatible with electrodynamic processing (EDP) of the printed layer in order to increase the density of the latter. Based on mathematical modeling, the influence of the impactor shape for EDP on the stress-strain state of the AMg6 aluminum alloy layer was studied. The formation of residual compressive stresses in the EDP zone was taken as a compaction criterion. The distribution of values along the thickness of the plate of the main parameters and components of the stress-strain state, in particular, the plastic deformation and stress zone dimensions, the depth and width of the contact interaction zone in the metal layer interacting with an impactor roller moving normal to the layer at speeds of 1, 5, and 10 m/s, was determined. The cylindrical impactor with a rounded end surface usage instead a straight quadrangular prism with a rounded side surface formed a higher-density layer, characterized by generation of compressive stresses up to the yield strength of the AMg6 alloy. This helps optimize the structure of the printed metal and increase its durability by forming compressive stress fields in the electrodynamic compaction zone. [ABSTRACT FROM AUTHOR]

In order to predict the temperature, humidity and deformation of the 3D gel-printing metal laminated green body during the drying process. This paper presents a mathematical model of solving the coupled temperature, moisture, and stress-strain fields during the drying process. This model was established on the Luikov's irreversible thermodynamics and material mechanics. It was numerically solved based on the discrete difference method, and it was implemented into numerical simulations through a combination of sequence and direct coupling method. The results have shown that, for the temperature field, green body temperature field approached to be steady in a short time during drying. For the moisture field, moisture migration exhibited between materials with different initial moisture contents. While for the stress-strain fields, obvious tensile stress state was experienced on the edges of green body longitudinal sides. The research carried out in this paper contributes to provide a comprehensive guide of the process planning of drying process of green body. [ABSTRACT FROM AUTHOR]

The paper deals with the dynamics of asymmetric three-layer hemispherical shells with the discretely symmetric lightweight, rib-reinforced filler under pulsed loads. Since the distances between the ribs are much larger than the dimensions of the rib cross-sections, the theory of independent static and kinematic hypotheses for each layer is applied. In asymmetric shells, the load-bearing layers are made of different materials and have various thicknesses. The equations of motion of asymmetric three-layer spherical shells and natural boundary conditions are obtained using the Hamilton– Ostrogradsky variational principle for the Timoshenko-type shell and rod theory model. This makes it possible to develop an adequate finite element model for asymmetric three-layer shells composed of several materials and obtain numerical results on the dynamic behavior of an asymmetric three-layer elastic structure using the finite element method. The influence of physical and mechanical parameters of asymmetric layers of hemispherical shells on the stress-strain state under axisymmetric internal pulse loading is investigated. New mechanical effects are revealed. [ABSTRACT FROM AUTHOR]

This paper proposed a modeling method of the thermo-fluid-solid coupling simulation for the hot water pipeline with the insulation layer outside in the nuclear reactor. The temperature and stress distributions are analyzed and compared with the tests; the effects of the insulation layer thickness and support interval are investigated. The maximum stress occurs at the support points. The maximum stress increases approximately linearly with the increase of the support interval. The maximum deflection occurs at the middle of the two supports. The maximum deflection increases rapidly with the increase of the support interval, which is approximately in a parabolic relationship. The axial elongation ratio increases with the insulation layer thickness. The simulation results agree with the test results very well with regard of both stress and temperature distributions. The simulation method can also be used for the stress and temperature analysis in various cases, such as chemical-vessel and gas-oil pipeline with various thermal fluids inside. [ABSTRACT FROM AUTHOR]

Recently, much attention has been given to developing numerical modeling methods for calculations of complex nodes of structural elements, especially for the equipment of the first circuit of NPP. The use of new methods increases the accuracy of the results and significantly reduces the calculation time. This is especially important when solving the problems of modeling the processes of crack nucleation and propagation in the material, in which, in particular, local thickening of the finite element mesh is necessary. In this paper, a description of the "submodeling" technique is given, which allows one to calculate individual components of structural elements, taking into account complex geometric shapes, contact conditions, and other factors that are difficult to take into account in calculations by conventional methods. The submodeling technique was used to calculate the stressstrain state in complex components of the pressure compensator of the WWER-440 reactor unit. For this purpose, a global simplified finite element model of the pressure compensator and a detailed submodel of the injection nozzle were built, taking into account the gap between the containment and the inner surface of the nozzle, as well as contact conditions. The results showed that the submodeling technique gives more conservative results when modeling complex assemblies. Hence, its application increases the reliability of the results obtained when assessing the strength of critical structural elements, particularly the equipment of the first circuit of NPP. [ABSTRACT FROM AUTHOR]

In this paper, reinforced thermoplastic pipes (RTP) were studied under various loads. A total of five groups of specimens were designed to study the mechanical properties of RTPs under internal pressure, bending, a combination of internal pressure and bending moment, external pressure, and tension. This study obtained the bursting pressure of RTPs under internal pressure, the minimum bending radius under the bending moment, and the failure pressure under external pressure. At the same time, the mechanical properties of RTPs under various loads were analyzed using the finite element analysis. Analytical results agree well with the experimental ones. The finite element model established in this paper can be used for further research on the mechanical properties of RTPs. [ABSTRACT FROM AUTHOR]

Special features of computational assessment of dimensional change of WWER-1000 reactor core baffle during the reactor operation are discussed. The paper gives results of computational analysis of a change in shape of core baffle, which was performed by applying up-to-date approaches of modeling the irradiation-induced swelling of constrained austenitic steels under the action of neutron irradiation and elevated temperatures. The results have been obtained by using median and conservative values of parameters of the temperature and dose dependence of free swelling of austenitic steel Kh18N10T. The authors have set out the fundamental principles of elastic-plastic stress-strain analysis of the reactor core baffle and core barrel, taking into account the irradiationinduced swelling deformation and contact interaction conditions. The finite-element analysis is based on a FEM mixed scheme that ensures a continuous approximation both for displacements as well as stresses and strains, thus providing a high-accuracy determination of the stress-strain state. The calculations were carried out in the two-dimensional definition for the baffle cross-section with the maximum damaging dose and irradiation temperature in the baffle height, assuming a generalized plane-strain deformation. The calculated results are given for the reactor full-power operation and scheduled shutdown for re-fueling at the end of the charge life. According to the calculation data, disregarding the irradiation-induced swelling deformation leads to an incorrect assessment of the change in shape of the core baffle during its operation, while the use of the accepted free swelling model gives too conservative results on the shape change, even within the designed lifetime. The influence of the mean normal stress on the irradiation-induced swelling of metal makes the principal contribution to the change in shape of the core baffle. During the reactor operation beyond the designed lifetime there occurs a local contact between the core baffle and the core barrel in the zone of the largest-diameter circular opening of the longitudinal cooling channel and the port channel for coolant flow between the baffle and the barrel. The paper gives results of the analysis of the change in shape of the baffle in modeling of the contact conditions taking into consideration the temperature re-distribution due to deviation from the design coolant passage conditions in the zone where the baffle is in contact with the barrel. In the case of using the median dependence of the free swelling, no loss of the nominal gap between the core baffle and the core barrel is observed within the designed lifetime. The computational assessment using the conservative parameters of the irradiation-induced swelling leads to a distinct decrease of the gap between the core baffle and the core barrel and a local contact between them at the end of the designed lifetime. The residual gap between the spacer grids of edge fuel assemblies and the baffle faces is ensured in the case of the median and conservative dependence of the irradiation-induced swelling. [ABSTRACT FROM AUTHOR]

The paper presents a methodology for determining the complete strain diagrams of materials in a complex stress state using the criteria of equivalence, which take into account the different behavior of the material under tension and compression. The proposed methodology is based on determining the relationship between the stress and strain surfaces. Since it is difficult to describe the deformation surface due to the volumetric influence of deformations, it is proposed to introduce the concept of "nominal strain." In this case, the general relationship between the stress and the nominal strain, for the case of a complex stress state, is defined as the relationship between the Euclidean norms of the stress and nominal strain tensors. The obtained dependences show the relations between the real values of stress and nominal strain, preserve the dynamics of change in the secant modulus, and, accordingly, allow comparison with other dependences obtained for a different stress state. The definition of the loading surface, as some geometric figure, is based on the fulfillment of differential conditions that are imposed on this surface and the possibility of determining a sufficient number of points for its construction. In this work, it is proposed to consider the loading surface in the form of a circular paraboloid. Under active loading, this surface expands to its limits – the fracture surface. To determine the characteristics of the above-mentioned surfaces and the law of their expansion, it is sufficient to conduct two basic experiments – for compression and for tension. The work provides a general methodology for determining the internal constants of the equation that describe the selected loading and nominal strain surfaces. [ABSTRACT FROM AUTHOR]

The paper presents the results of experimental studies of the possibility to assess the damage process of steels of different classes by using the LM-hardness method under cyclic loading at different cycle characteristics (stress amplitude, mean stress, loading frequency). Fatigue damage of metal under cyclic loading has been assessed by the method outlined in the PNAE standard. It is shown that the discrepancy between the recommended tabulated values and experimentally obtained values of mechanical characteristics of the material has a significant influence on the character of the calculated fatigue curve of the material, which increases with the number of cycles. Analysis of the dependence of stress ratio on the number of operation cycles shows that reduction of stress ratio decreases the durability of the studied material due to increase in the range of stresses in the cycle. It is obtained that increase of constant strain amplitude in the cycle relative to the established level by 10–15% corresponds to initial section of plastic deformation durability loss under cyclic loading. The homogeneity parameter determined in this case will characterize the limiting state of the material, which precedes its failure. Based on the analysis of experimental results, it is found that under conditions of realized loading, the damage kinetics curves for all investigated materials has a linear character. In different materials, the linear sections have different slopes. It can be assumed that the indicated slope of this curve characterizes the conditions of equilibrium between the processes of strain-hardening and softening of metal, achieved at the stage of steady creep. The presented results give grounds for using the homogeneity coefficient according to the LM-hardness method to assess the material condition of structural elements during the current monitoring of their condition. [ABSTRACT FROM AUTHOR]

Stress is one of the most important factors in metal-to-metal sealing. In this paper, two methods (theoretical and empirical) were adopted to calculate the normal stress of the brass sealing surfaces against different ultrahigh pressure liquid. The theoretical formula was derived in terms of force balance, and the empirical formula was obtained by polynomial curve fitting, which the fitted data were from simulated results; besides, the results calculated by using the empirical formula agree well with the results by theoretical formula. Meanwhile, the equivalent stresses of the brass seal, normal stress and contact stress on the brass seal surfaces were simulated by finite element method, and the simulated results indicated these stresses are increased with the increase of liquid pressure, and the maximum stresses always appear on the tip of the brass seal. [ABSTRACT FROM AUTHOR]

The geotemperature can reach 60°C at mining depth of 2000 m. The physical and mechanical properties of rocks will change with geotemperature, affecting the stress state of surrounding rock in deep excavation. In this paper, a thermodynamic model is applied to describe the stress and deformation process of rock material through the free energy function and dissipation equation, and yield surface, flow rule and plastic function are not considered in the elastic-plastic model, which greatly simplifies the calculation process. The developed finite element simulation program used to simulate the change of the stress between the rock and shaft wall. The temperature change induces thermal stresses between surrounding rock and shaft wall, especially at their interface. The results provide worthy support for the shaft failure and disaster prevention in deep engineering. [ABSTRACT FROM AUTHOR]

The paper presents the results of the application of the refined calculation guidelines to the analysis of the stress-strain state and fracture resistance of the equipment elements of the NPP primary circuit system with WWER reactor, in particular, the cylindrical part and the zone of the reactor pressure vessel inlet nozzle, coolant collector welded joint in a steam generator, baffle, and reactor internals' shaft under the operating and emergency modes of thermomechanical loading. The calculation methodology is based on the use of the modern models and methods of solution to the nonlinear boundary tasks of non-isothermal thermal viscoplasticity and tasks of fracture mechanics using the refined mixed schemes of the finite element method with increased accuracy. They allow one to obtain reliable solutions to the tasks considering the deformation history of thermomechanical loading, modern concepts of fracture mechanics and approaches to the modeling of brittle-viscous fracture defects, irradiation swelling and creep of metal, as well as as the structural elements, under the conditions of elevated temperature, intensive neutron irradiation and nonstationary modes of thermomechanical loading. The authors obtained and analyzed the calculation results for the cylindrical part and zone of the inlet nozzle of the WWER-1000 reactor pressure vessel, coolant collector welded joint in a steam generator, baffle, and reactor internals' shaft using the proposed guidelines. The results imply the possibilities of the proposed recommendations and make it possible to analyze some general tendencies and features of the application of the refined calculation models to justify the strength and life extension of the NPP structural elements under investigation. [ABSTRACT FROM AUTHOR]

The paper presents the results of an analysis of the correctness of constitutive equations of irradiation creep, which describe non-isothermal processes of inelastic deformation, taking into account the irradiation swelling and irradiation creep of material under the conditions of neutron irradiation, high temperatures, and damaging dose. Current models of irradiation swelling and irradiation creep, which take into account the damaging dose, irradiation temperature, and the effect of stress state and accumulated irreversible strain on the processes of swelling and creep of material, are considered. The conditions under which dissipation power and the power developed by additional stresses on additional deformations do not decrease during loading under neutron irradiation conditions have been studied. On the basis of the obtained energy inequalities, which generalize Drucker's postulate for the irradiated material, the conditions that ensure the correctness of the formulated creep equations have been determined. The results of an analysis of the correctness conditions for irradiation creep equations showed that taking into account accumulated irreversible strain in the confined swelling model contributes to the relaxation of restrictions on the possible swelling of the material and initial data, which ensure the correctness of the constitutive equations of irradiation creep. [ABSTRACT FROM AUTHOR]

In view of the problem complexity, numerical methods, mainly finite and boundary element methods, are fairly widely used in the calculation of the static deformation of composite shells. The paper presents a new approach to the calculation of the static deformation of composite cylindrical shells using potential theory methods, which made it possible to obtain a solution to the set problem in the closed analytical form. Longitudinally infinite cylindrical shells, which are sequentially rigidly joined together (by clamping the outer edges of the formed composite structure), are considered. Orthogonal curvilinear coordinates in the middle of each of the cylindrical shells have been chosen. The problem has been solved in displacements. The system of differential equations of the static deformation of each of the cylindrical shells being part of the compound body was written according to the Vlasov shallow shell theory. The composite structure was under the action of a normal surface load. The expressions for internal forces and moments are given in terms of the components of the vector of displacements and the corresponding derivatives of them. For the system of differential equations, an exact solution has been found. The problem was solved by the method of variation of arbitrary constants. To determine the integration constants, the rigid joint conditions of cylindrical shells (from physical considerations) and the generally known conditions of rigid clamping of the edges of a compound body have been formulated. A system of linear algebraic equations for the desired constants has been derived. As a result of solving the system and substituting the found constants into the expressions for displacement vectors, the final solution of the problem in the form of potential images has been obtained with the aid of constructed Green matrices for this problem. The calculation method is illustrated by some numerical results, which describe the stress state of the object under investigation, composed of two in-series connected sections, as a function of the wavelength of the cylindrical shells. Analysis of the stress state characteristics shows that both bending moment and transverse force increase with decreasing wavelength of the cylindrical sections. This can be accounted for by the way of joining the cylindrical shells in the composite structure. Deformation schemes of composite cylindrical shells (under unilateral normal load) are presented with a purely illustrative purpose as evidence of the capabilities of the proposed method. [ABSTRACT FROM AUTHOR]

The paper deals with the numerical stress calculation in the flexspline tooth rim of the harmonic drive. Due to the complex geometry of the toothed ring in the flexspline, the teeth were modeled as a ring, which height corresponded to the particular stress concentration in the teeth. To study the effect of type of wave generator on the stress distribution in the flexspline, the following models were elaborated: two-roller, four-roller, cam, and disk. The stress calculations were performed for the two cases: a zero torque load and the torque load value, corresponding to the true operation conditions of the hermetic harmonic drive. [ABSTRACT FROM AUTHOR]

Circular bars are widespread elements in building and mechanical engineering. They allow one to enhance the strength of the multilayer composite materials along with their weight reduction. However, their analytical modeling is developed rather poorly, which creates additional obstacles in their efficient design. The paper presents the results of the exact analytical solution to the plane bending task of elasticity theory for the multilayer beam with a circular axis under normal uniform loading on its longitudinal surfaces considering the cylindrical orthotropy of its layers' materials. The problem has been solved using the methods of linear elasticity theory based on the continual approach where the circular bar is considered as a solid with the elastic characteristics varying in the radial direction. The solution for the shear stresses is assumed using the known distribution in the cross section. Therefore, the solution to the problem is reduced to the determination of two unknown functions of stress distribution throughout the section height. The system of linear differential equations has been obtained for the determination of the sought functions and unknown functions of integration in the process of the solution to the equations of plane theory considering the variable elastic characteristics. General analytical solutions for uniform and discontinuous-nonuniform layers from cylindrically orthotropic and isotropic materials have been developed. The influence of transverse shear deformation and compression on the characteristics of the stress-strain state of a cantilever three-layer beam with a semicircular axis is theoretically investigated. The obtained relations allow us to predict the stress-strain state of circular multilayer beams, as well as to build applied methods for solving problems of strength, rigidity, and optimal design of such structural elements. [ABSTRACT FROM AUTHOR]

This paper proposes an analytical model for the stress-strain state in a welded joint with a hard single-V butt weld. Analytical expressions for the stress-strain state in both the hard weld and the mild main material subjected to elasto-plastic deformation are proposed. In order to verify the proposed expressions, a finite element simulation of the stress-strain state in a welded joint with a hard single-V butt weld was carried out and the results were compared to the analytical results obtained applying the proposed analytical model. The analytical solution was basically consistent with the finite element analysis results. The proposed analytical model can be used in design practice for assessment of the stress-strain state in welded joints. [ABSTRACT FROM AUTHOR]

The statistical analysis performed on the defectiveness of rails in the Kiev subway railway shows that the main cause of the occurrence of most defects is the contact fatigue of the rail material. The paper presents modern concepts of crack growth in the railhead. It has been found that one of the most promising directions of studying the stress-strain state of rails and the crack growth process is a numerical simulation, which results on the contact interaction between rails and subway rolling stock wheels are presented. During the simulation, the problem was solved in an elastic formulation. We considered R50, R65, and UIC60 rail profiles, standard railway wheels, and wheels whose tire profile was developed by the Minetek closed joint-stock company. The conditions for the rail–wheel interaction corresponded to train movement on the straight section of the track without slipping. The effect of the wheel tire profile on the contact stress level in rails of different types has been assessed. Comparison of the maximum equivalent stress levels for a different combination of rail and wheel types shows that the best combination (in terms of reducing the contact stress level) for the straight sections of the subway track is an R50 rail with a gradient of 1 in 20 and 1 in 10 taper wheel, whose profile corresponds to GOST 9036-88. When wheels with the profile developed by the Minetek company are used, the maximum equivalent stress level in the contact zone is over 1000 MPa for all rail types. It is higher than the yield strength of rail steel, which will accelerate wear and give rise to low-cycle fatigue cracks with subsequent formation of contact fatigue defects. [ABSTRACT FROM AUTHOR]

The paper presents the stress-strain state simulation of the compound technical structure - vulcanizer diaphragm. A set of working plates in the form of a circular plate with the thickness discretely varied in the radial direction is modeled. An algorithm to solve the contact problem is developed. The obtained calculation results are compared with the experimental ones to demonstrate their practical use. [ABSTRACT FROM AUTHOR]

The paper considers the results of determining the vibrodiagnostic indicators of the presence of various mode I breathing transverse cracks in rod elements of rectangular and circular cross section with different boundary conditions under longitudinal vibrations. Relative second harmonic amplitudes in the vibration spectrum at the main and superharmonic resonance of the first eigenmode of cantilever rods without mass and with a mass at the end and rods with the ends free for longitudinal displacements under forced and kinematic vibration excitation were taken as diagnostic indicators. To determine the above indicators, analytical and numerical bending vibration methods considered before are used. In the analytical solution, the nonlinearity parameter of the vibrating system is calculated using the corresponding values of stress intensity factors. The numerical solution is performed on the basis of eight-node finite element models with the representation of a breathing crack as a mathematical cut and the treatment of a contact problem in the formulation providing mutual nonpenetration between crack faces. Plots of the values of diagnostic indicators as a function of relative crack depth, crack location and the site of measurement of longitudinal displacements have been obtained. Comparisons of values of diagnostic indicators with the value of relative change in natural vibration frequency are presented. It has been shown that at the main resonance, the numerical solution confirms the pronounced effect of localization of diagnostic indicators in the crack region. It has been found that at the superharmonic resonance, the value of the vibrodiagnostic indicator is two orders of magnitude higher than that of the indicators at the main resonance, but the effect of their localization near the crack does not practically manifest itself. Some localization is observed for the absolute values of the second harmonic, and only for longitudinal strain, there is a strongly pronounced effect. A comparison of the obtained values of diagnostic indicators with the data for bending vibrations is given. It is noted that in spite of basically lower indicators under longitudinal vibrations, they have an advantage in terms of the possibility to diagnose symmetric both surface and internal breathing cracks. [ABSTRACT FROM AUTHOR]

In this paper, optimum test plans of step-stress partially accelerated life tests are developed using failure-censored data from Burr type-XII distribution. The maximum likelihood approach is applied to obtain the estimates of the acceleration factor and the parameters of the distribution. The minimization of the generalized asymptotic variance of the maximum likelihood estimators of the model parameters is used as an optimality criterion to develop optimum plans of the step-stress partially accelerated life tests. For illustrative purposes, simulation studies are presented. [ABSTRACT FROM AUTHOR]

For planning of thermal fatigue tests of materials and comprehensive analysis of their results, it is proposed to use the thermal cyclic test maps (TC-maps) that allow tracing the strain development in a thermal cycle. TC-maps illustrate the diagrams of the temperature-dependent elastic strain, which corresponds to the yield strength of the material, and the free strain variation under constraint conditions. This paper presents the procedure of thermal cycle test map compiling for some materials and their physical as well as mechanical properties. The useful information obtained from the TC-maps is exemplified by some heat-resistant alloys employed for the production of gas-turbine engine blades. [ABSTRACT FROM AUTHOR]

The paper provides the strength analysis performed for POLYITAN-2 nano-satellite under quasistatic overload conditions arising at the ascent stage. An efficient solid-state model together with its corresponding finite element model has been developed for nano-satellite. The numerical investigation of the stress-strain state of nano-satellite has been performed using the ANSYS software package. The maximum relative displacements of structural elements, as well as safety factors, have been determined. Different strength criteria were analyzed for the strength assessment of nano-satellite structural elements made of composite materials. It is found the considered POLYITAN-2 structure satisfies the critical strength and stiffness requirements. [ABSTRACT FROM AUTHOR]

The paper presents the numerical investigation on the stress-strain state of single- and two-layer spheres with spherically transtropic radially reinforced layers under a centrally symmetric internal explosion. A comparative analysis is made between two widely used methods of modeling the explosive loading. The influence of the reinforcing fiber volume fraction and the alternation of layers on the strength of shells is investigated. [ABSTRACT FROM AUTHOR]

Molecular dynamics simulation was employed to make the model of crack propagation for singlecrystal γ-TiAl alloy. The effects of the angle between a microcrack and loading direction on crack propagation were studied through the analysis of the atomic configurations and stress-strain curves in the paper. The results show that the time for the emission of first dislocation and the yield stress value decrease with the angle. The crack propagation occurs by the submain crack mechanism, which becomes more obvious as the angle increases and the number of stacking faults and stair-rod dislocations decreases. [ABSTRACT FROM AUTHOR]

The paper presents the analysis of analytical models to determine the stress state in the substrate-coating system, when a load is applied to the substrate. The results obtained with these models are shown to differ. It is noted that the advantage of the analytical methods as compared to the numerical analysis is the possibility to calculate stresses in the singularity region in the vicinity of the free edge of the coating. The character of the shear stress distribution is analyzed using the analytical models. Examples of using different approaches to determine the critical shear stresses that define the adhesive strength of coatings are given. The analysis of literature sources shows that both simple and more sophisticated analytical models are employed in the investigation of the adhesive strength of coatings. [ABSTRACT FROM AUTHOR]

The paper addresses some aspects of inclusion of loading history in the fracture strength analysis of reactor pressure vessels under thermal shock conditions. The strength assessment of a reactor pressure vessel and its lifetime extension are shown to essentially depend on reliability of results of elastic-plastic modeling of stress-strain kinetics and determination of design values of the fracture mechanics parameters. The present findings of the finite-element analysis demonstrate that the loading history must be taken into account in the determination of the temperature dependence of stress intensity factor for a postulated specified crack. It is shown that, in the fracture toughness analysis of a reactor pressure vessel, the temperature dependence of the stress intensity factor has to be derived from the results of the analysis of kinetics and mode of loading of metal at the crack tip under thermal shock conditions. For construction of the above dependence, we proposed approach, which accounts for the active loading and unloading processes occurring in the metal in the crack front vicinity. Incorporation of the loading history into the analysis of the temperature dependence of the stress intensity factor using the proposed approach forcan permit revealing some additional margin of strength during the substantiation of lifetime extension for a reactor pressure vessel under thermal shock conditions. [ABSTRACT FROM AUTHOR]

This paper presents results of the analysis of numerical simulation of rotary compression process of hollow ball forging. Numerical analysis is conducted based on the finite element method using the Simufact Forming software. The methods of hollow ball forming are discussed with presentation of the geometrical model applied in calculations and the obtained rotary compression process description. The simulation is conducted under three-dimensional strain conditions. Strain, stress and temperature distributions are determined. The diagrams of forces and rotary moments of the hollow forging compression process are given. The described results of the numerical analysis confirm the possibility of producing the hollow balls by means of rotary compression with the use of billet in the form of a pipe part. [ABSTRACT FROM AUTHOR]

The paper addresses the temperature and thermoelastic states of a single-crystal blade with a complex vortex cooling system and passages for cooling air outflow. The problem of determination of stress-strain state of the blade at hand under the action of temperature fields and centrifugal forces is solved by the finite element method. The authors study the influence of azimuth orientation of crystallographic axes on the distribution and magnitude of thermoelastic stresses in the blade volume. [ABSTRACT FROM AUTHOR]

In this paper, the extended finite element method has been used to evaluate the fatigue life of cracked specimens in presence of bi-material interfaces. The standard finite element approximation is modified by adding appropriate enrichment functions in order to take into account the effect of these discontinuities present in the domain. The level set method is used to track different discontinuities in the domain. The stress intensity factors are calculated by the interaction integral approach. Finally, several numerical problems are presented to demonstrate the effect of these bi-material interfaces on fatigue crack growth. [ABSTRACT FROM AUTHOR]

Accelerated life testing (ALT) is an effective way to assess the lifetime of a product. Due to the complex nature of its testing profile, it is difficult to carry out temperature cycling ALT. This paper establishes a modified Norris-Landzberg model as acceleration model, and proposes the optimum design method of temperature cycling ALT. First, the FEA method is used to study the influence of temperature cycling profile parameters on the thermal fatigue life of 63Sn-37Pb solder joints. Then, a modified Norris-Landzberg model is proposed by introducing ramp time and dwell time with an added weight value. Finally, the temperature cycling ALT is regarded as a special multi-stress ALT to study its optimum design method. The uniform design theory is used to determine the combined mode. The optimum model is established with the objective of minimizing the asymptotic variance of the estimation of median lifetime under normal use conditions, and the simulation example shows the workability of the proposed method. [ABSTRACT FROM AUTHOR]

This paper presents the experimental justification of the applicability of a rapid method for the life assessment of heat-resistant steels under cyclic loading in a multiaxial stress state with consideration of metal damage. [ABSTRACT FROM AUTHOR]

The paper presents a mathematical model of the non-localized fatigue damage accumulation process in rubberlike materials. A relation for the determination of the constants of the corresponding equation with allowance for known fatigue curve characteristics, in particular for their random spread, is proposed. Computational relationships for the determination of the probabilistic characteristics of damage have been derived. Experimental data for the determination of realization of the fatigue accumulation process in rubber specimens, which are in good agreement with theoretical results, are considered. [ABSTRACT FROM AUTHOR]

Based on the energy approach formulated earlier by the authors, the calculation model for determining the durability of a fiber-reinforced concrete beam under long-term pure bending and local creep was developed. The model relied on the first law of thermodynamics regarding the energy balance and the balance of rates of energy variations in the fiber-reinforced concrete beam with initial volumetric damage after such loading. The following provisions and assumptions were introduced. Matrix and fiber materials were homogeneous and isotropic. The process of cracking in concrete occurred after the stresses attained the strength value of concrete. Opening of the generated microcracks and pull-out of fibers from concrete was treated as the main mechanism of its creep. The tensile diagram of fiber concrete was taken as piecewise linear. For simplicity of calculations, the area of the tensile diagram corresponding to the second stage of deformation was approximately represented by a straight line, similar to the compression case. During long-term bending of the beam element, the loss of its carrying ability was determined mainly by the stress-strain state of the tensile zone. Its rheological characteristics in the first approximation were assumed to be equal to the compressed ones. Fibers (of the same circular section and length) in the tensile zone were evenly distributed in all directions and were subjected to tension only. There was a complete adhesion between the fibers and the concrete, so their strains were identical. To improve the computation efficience, we used the plane section hypothesis, simplified models of fiberreinforced concrete deformation under tension, compression, and bending, as well as the creep condition of its creep at fracture (loss of performance properties of the fiber-reinforced concrete beam). The model feasibility was proved by the durability assessment of a real fiber-reinforced concrete beam with specified characteristics from literature. [ABSTRACT FROM AUTHOR]

The paper presents results of an analysis of the gas-dynamic control of flow around the guide blades of axial compressor stage for the vibration intensity of rotor blades. It has been shown that gas-dynamic action on flow around blades equalizes the flow velocity field before the rotor and reduces the level of resonant stresses in blades in the case of their resonant excitation. [ABSTRACT FROM AUTHOR]

The possibility of increasing the survivability of the system of refueling combat vehicles during combat operations through the development of a new method that reduces refueling time and the use of new technical means to implement it is substantiated. The essence of the method of accelerated refueling of combat vehicles is to place an elastic fuel reservoir (EFR)under the combat vehicle wheel and run it over at low motion velocity, resulting in the fuel displacement from EFR to the fuel tank of the vehicle being refueled. The study results indicate the feasibility of accelerated refueling of combat vehicles by this method. A mathematical model for determining the pressure in the EFR run over a vehicle wheel was refined in this study. A mathematical model for determining the stress-strain state of an EFR loaded with internal excessive alternating pressure was proposed, allowing one to assess stresses arising in the EFR wall when refueling combat vehicles and optimize the EFR design. Experimental results on the of accelerated refueling of vehicles confirmed the efficiency of the proposed refueling method and the EFR design. [ABSTRACT FROM AUTHOR]

Formulation of a method for the strength design of a rubber cable stay with defects in its connection to a structure. Solving the model of interaction of discrete cables joined by rubber, taking into account the break in the continuity of the cables in the stay connection assembly and the nonlinearity of deformation of stay components. A method for the strength design of a rubber cable stay with a connection defect under the nonlinear deformation of its components. The stay in the structure is subjected to significant loads. It is mostly composed of a system of parallel pulling elements. These can be cables. In general, there can be several defects in the connection, but less than the number of cables. A defect in the connection of the stay to the structure is manifested in the redistribution of forces between the reinforcement elements – cables. A cable connection defect is considered to be a connection for which the cable load is zero (the maximum possible consequence of a single defect). A method for determining the stress-strain state of a stay rope with defects at which the loads of several cables in the connection cross-section are equal to zero. A break in the continuity of a stay cable significantly affects the stress state of adjacent cables and the material, interacting with it, over a limited length. The number of cables adjacent to the damaged ones affects the level of stress increase. At a smaller number, the stresses increase more. The nonlinear nature of the ratio of the shear modulus of the matrix material and the tensile elastic modulus of the cables practically does not affect the size of the zone of perturbation of the cable's stress state in the event of a break in cable continuity. The method allows taking into account the effect of the maximum deviation of the load force of an arbitrary cable from the design one on the pulling capacity of the stay due to a defect in the connection to the structure, taking into account the nonlinear deformation of its components, thereby increasing the reliability of the results of stay calculation and thereby increasing the reliability of the structure. [ABSTRACT FROM AUTHOR]

An approach to the determination of steady ratcheting strain rate under biaxial loading depending on the loading cycle geometry is proposed. Based on the data analysis, the microstructural investigation results, as well as the similarity detected between the microstructural formations after deformation at the stress- and strain-controlled modes of loading, it is proposed to use the cycle nonproportionality parameter to predict the ratcheting rate. It is shown that the geometric cycle parameters and basic experiments allow one to adequately predict the ratcheting rate for complex cyclic paths. [ABSTRACT FROM AUTHOR]

The problem of the cylindrical cavity under axisymmetric constraint under plane strain conditions is analyzed. The soil is considered an elastoplastic material. The physical properties of soil are described. A proposed constitutive equation is adopted to describe the stress-strain relationship for soil. The soil strength characteristics are described by the united strength for spatial mobilized plane and Lade strength criteria. The analytical solution of critical plastic pressure in the cylindrical cavity can be obtained by solving the analytical elastic equilibrium equation. The stress ratio and the relation between the critical radial stress and the volume strain corresponding to the peak stress ratio are analyzed quantitatively. The results show that the critical value of the radial stress decreases with the increase of the peak stress ratio corresponding to the volume strain in the soil with a small amount of shear dilatancy. The critical value of the radial stress decreases first and then increases with the peak stress ratio of the corresponding volume strain in the soil with an intermediate amount of shear dilatancy of the volume strain. However, for soil with a large amount of dilatancy and shear strain, the critical value of radial stress increases monotonically with the peak stress ratio corresponding to the volume strain. [ABSTRACT FROM AUTHOR]

The aim of this finite element stress analysis (FEA) study was to assess the effect of separated files (SF) that were broken at two levels (at apical 4 and 9 mm) on the biomechanics of premolars and to determine if removal techniques affect stresses. Six lower premolar teeth were screened on computerized microtomography (micro-CT), standard access cavities were prepared, working lengths were determined, and root canals were prepared (Protaper files, Protaper Universal, Dentsply, Switzerland). Notches were created on the final shaping-file F3 at points 4 and 9 mm from the file tips, inserted in the canals, and squeezed at the apical to break. The roots were rescreened, and SFs were removed by using a Masseran kit (MK; Micro Mega, France), ultrasonic tips (UT; Satelec, Acteon group, France), and the bypass (BP) technique. Final scans were obtained and converted into three-dimensional FEA models. The following conditions were then simulated: a) root-filled tooth with SF; b) root-filled tooth after removal of the SF by using MK, UT, or BP techniques. The models were loaded axially (from two directions) and vertically (300 N), and von Mises stresses were then analyzed. SFs increased the stresses within the root. Longer SFs cause higher stresses within the root and thus should be removed, while short SFs could be kept considering the other clinical factors. Removal via MK caused the highest stresses within the roots among the techniques used. Axial loading caused higher stresses at the cervical side, while the stresses moved toward the apical side under vertical loading. SFs increase the stresses within the root. Long SFs should be removed while short SFs can be left (considering other clinical factors that may affect the success of the treatment). Removing short SFs located at the apical side negatively affects the biomechanics of the teeth, and this effect is more dramatic with the MK technique. [ABSTRACT FROM AUTHOR]

The effect of the metallic layer thickness on the stress-strain state and strength of metal-composite cylinders of the total constant thickness under internal dynamic pressure produced by the explosion of a charge evenly distributed along its axis in air at the constant total-to-running charge mass ratio (ξ = 1.421 mm was numerically investigated. The strength of the cylinders was evaluated by the generalized Mises criterion. The strength of shells with a unidirectionally circularly reinforced outer composite layer for the composites of low tensile strength in the isotropy plane is shown to be mainly governed by the wave processes across the shell width. Under this condition, its dependence on radial and axial stresses is much higher than on the circumferential ones, which are usually much larger than the first two components of the stress tensor. The four composites and two designs of the cylinders: thin-walled and medium-thickness are examined. The cylinders are double-layered: the inner layer is steel (St20) and the outer layer is a circularly reinforced composite. At given (ξ and the total constant cylinder thickness H, the optimum in strength terms ratio (βopt of the metalliclayer thickness h to H is strongly dependent on H, a composite (i.e., its physicomechanical characteristics) and varies within 0.4–0.7 for thin-walled cylinders and 0.6–0.7 for medium-thickness ones. Irreversible plastic energy losses in the inner steel layer have a significant impact on the shell strength, as a result the shock wave travelling to the outer composite layer is of lower intensity and the strength of the object as a whole can be ensured. The inclusion of the plastic steel layer deformation in thin-walled cylinder calculations significantly changes the dynamics of objects qualitatively but insignificantly increases the strength quantitatively, the Mises strength function can be reduced by less than 5% compared to an ideally elastic calculation. If the plastic metal deformation is accounted for medium-thickness cylinders, it significantly changes the wave patterns both qualitatively and quantitatively, the strength function can be reduced by almost 50% compared to the elastic calculation. [ABSTRACT FROM AUTHOR]

This work is devoted to the determination of vibrodiagnostic indicators of the presence of symmetric and annular breathing cracks in cantilever beams at their nonlinear longitudinal vibrations. The results of determining the vibrodiagnostic indicators of the presence of cracks, namely, the relative change in the fundamental frequency of longitudinal vibration and the ratio of the amplitudes of the dominant harmonics at the fundamental and superharmonic resonances for different depths and locations of cracks, are presented. To carry out computational studies, various computational models were developed, namely, with concentrated and distributed parameters, beam and volumetric finite element (FE) models, and methods for their research. The use of the model with concentrated parameters consists of the analytical determination of the nonlinearity parameter of the system, which takes into account the change in the stiffness of the system in the presence of damage and is determined by changing the potential deformation energy of the beam due to the opening of the crack during oscillations. The determination of vibrodiagnostic indicators of the presence of a crack using a model with distributed parameters is carried out by solving the differential equation of forced longitudinal vibrations of the second order, where the crack is represented as a section of the beam with a reduced cross-sectional area. The numerical analysis of vibrations of the objects of study with a breathing crack is carried out using the developed beam and volumetric FE models. In the beam FE model, the breathing crack is modeled by a finite element with variable stiffness, and in the volumetric model, it is represented as a mathematical section with the setting of contact interaction conditions for its banks. The main dependences of vibrodiagnostic indicators of the presence of cracks on their parameters are obtained analytically using a model with concentrated parameters and numerically using a beam FE model. To confirm the reliability of the obtained dependences, their individual values are compared with the data obtained for the volumetric FE model, which obviously describes the stress–strain state in the vicinity of the crack most accurately among the proposed models but at the same time requires more computational resources. The obtained numerical dependences of the ratio of the amplitudes of the dominant harmonics of displacements at the main resonance from the place of vibration registration are characterized by fractures in the vicinity of the crack and therefore can be used to determine the location of the crack. According to the results of the analysis of the obtained dependences, it was found that it is practically impossible to determine the location of the crack in this case, since the results obtained for the relative location of the crack in the range from 0.1 to 0.5 are close in values, and the dependences of the vibrodiagnostic indicator on the place of registration of vibrations at superharmonic resonance are uniform and have no fractures. [ABSTRACT FROM AUTHOR]

The processes of creep of woven materials are investigated. An industrial fabric, which is made on the basis of polymer threads, is chosen as an object of investigation. By analogy with the investigations of threads performed earlier the regions of linearity of viscoelastic properties of woven material are determined, fulfillment of the condition of similarity between the isochronous curves is proven, and the instantaneous stress-strain diagram is plotted. The similarity of viscoelastic nature between the woven material and threads, which form it, is shown. The possibilities of use of linear and nonlinear models of viscoelastic deformation for the description of creep of polymer fabrics are analyzed. [ABSTRACT FROM AUTHOR]

The stress-strain state of a drill string during its compression in a horizontal borehole is considered. The function of the elastic axis of the drill string as a wave curve is obtained, which enables one to improve the analytical models: evaluation of decrease of axial force depending on the drill string elastic axis shape, determination of the force of pressing of the string to borehole walls, and calculation of normal stresses in the cross section of drill pipes. [ABSTRACT FROM AUTHOR]

Deformation of rectilinear elements of Du 200 pipeline made of 20 steel under cyclic loading with internal pressure has been studied experimentally. Tests were carried out on a pneumohydraulic bench under conditions close to plane stress state, room temperature, and cycle asymmetry under soft loading mode (stress control). Circumferential and axial strains were recorded at three points of a diametrical section located in the middle of the element under study. Two tubular elements were tested at different values of maximum and amplitude stresses based on 100 cycles of loading. Deformation curves (cyclic creep) of tubes in a circular direction have been obtained, the character of which is significantly non-uniform in comparison with deformation of laboratory specimens. It is shown that even a slight increase in maximum (by 4%) and amplitude (by 8%) stresses significantly (up to 50%) increases the cyclic creep strains in the circular direction. Such growth of deformations can be explained by a peculiarity of 20 steel, the deformation diagram of which in the elastoplastic transition area contains a yield point, which determines intensive deformation of the material. Fixed plastic deformations in the axial direction are more than an order smaller than circular ones, and with increasing loading cycles, they change insignificantly and coincide for the two studied tubular elements. [ABSTRACT FROM AUTHOR]

The effect of the creep of materials of a structure on the nature of the contact interaction between its elements during long-term operation is investigated. The problem of the stress-strain state of the rotor blade interlock for the medium-pressure cylinder of a steam turbine for ultrasupercritical steam parameters (over 240 at and 565°C) is solved using a finite element software package. As a model of creep, a modified model of creep with hardening is considered. The methodology for solving the thermal contact problem of interaction between the interlock elements under creep conditions is based on the application of a contact layer model. The calculation is made for the case of the total loads of the centrifugal forces of blades and the temperature field in which the structural element is operated. The results on the distribution of total strains, equivalent stresse,s and contact stresses during long-term operation are analyzed. The points of time, upon reaching which the permissible strength characteristics of the materials used were exceeded, were determined. A change in the nature and level of contact stresses on the bearing surfaces of interlock elements due to the redistribution of the stress-strain state of the structure as a whole is shown. The moments of the appearance of detachment and absence of contact stresses on individual contact surfaces were determined. The results obtained are compared with the data from the operation, during which the structure was damaged. [ABSTRACT FROM AUTHOR]

A mathematical model of hydrogen diffusion in structural elements near stress concentrators has been developed and experimentally confirmed. A finite-element algorithm for solving elastic-plastic and diffusion problems in the case of arbitrary geometry of the structure has been created. The study was performed on flat hydrogenated samples with a central crack. The calculations were performed for three materials: 20, 40Kh, and 65G steels. Experimental true stress–strain diagrams were used in the calculations of the hydrostatic stress. Distributions of hydrostatic stress and hydrogen concentration on the extension of the crack line for the above three steels under tension at the moment of ultimate equilibrium and after unloading were calculated. The results of hydrostatic stress distribution for steel 20, which were obtained experimentally by digital image correlation technique at the ultimate force, are also presented. For steel 20, a comparison of the calculated hydrogen concentration with the results of experimental studies obtained at the Paton Institute of Electric Welding of the National Academy of Sciences of Ukraine by mass spectrometry after complete unloading has been made. In this case, the results correlate well with each other. The correspondence between the distribution of hydrogen concentration and hydrostatic stress near the crack tip has been established. Similar to hydrostatic stress, the maximum value of the hydrogen concentration is reached at a certain distance from the crack tip. As the hydrostatic stress increases, the amount of hydrogen in the pre-failure zone increases. The concentration of hydrogen near the crack tip in the loaded sample is 2–3 times higher than the initial one; in the unloaded sample, it is 1.5–3 times lower than in the limit-equilibrium state. Plots of hydrogen concentration near the crack tip versus on the mechanical characteristics of the material were constructed, which can be used to estimate the hydrogen concentration near sharp stress concentrators in a hydrogenated metal with a given yield stress The empirical dependence of hydrogen concentration on the mechanical characteristics of the material was established, which can be used to assess the load-bearing capacity of structural elements. An engineering method for estimating the maximum hydrogen concentration near a notch is proposed. [ABSTRACT FROM AUTHOR]

To better explore the influence of friction stir jointing process parameters on temperature field distribution in the jointing process, the forces acting on the tool and the friction coefficient between the shoulder and tool and the changes of the internal materials of workpiece with the temperature were considered. A heat source model was established to simulate and analyze the variation of temperature field with the process parameters of friction stir jointing. The heat source model was established. The simulation results showed that the temperature in the advancing side was higher than that in the retreating side. The peak of heat cycle curve gradually decreased from the surface to the bottom of workpiece. The rotation speed on the peak of heat cycle curve effect was small, and the feed speed was large. The accuracy of the heat source model of the friction stir jointing was related to the accuracy of the subsequent simulation analysis of the residual stress distribution and deformation of the connection. Therefore, this study has important theoretical significance. [ABSTRACT FROM AUTHOR]

The authors have developed two approaches to investigating the thermal stress state of layered composite hollow shells. The face surfaces of the shell layers have zero torsional curvature, the variation in principal curvatures is neglected. The coefficients of the first quadratic form are assumed to be unity. It is assumed that the radii of curvature are much larger than the thickness of the structure, and its outer surfaces have the same curvature. The restrictions allow one to identify the curvilinear system of orthogonal coordinates with the planar system of orthogonal coordinates. Based on Hooke's law, the missing longitudinal components of the stress tensor are obtained. Using the Reissner variational principle, a system of integro-differential equations of equilibrium is written down (for the case of joint support in the temperature load distribution under the trigonometric law). Moreover, it is transformed into a system of ordinary differential equations for the distribution of required functions over the thickness of the hollow shell. This system is solved analytically, with the functions in the form of an exponent, searching for the roots of homogeneous algebraic characteristic equations and their eigenvectors. The integration constants are on the conditions on the outer surfaces of the layers. In compliance with the second approach, the polynomial approximation of the functions to be searched by the thickness of the hollow shell is applied. The peculiarity of this approach is the attribution of the unknown functions to the outer surfaces of the layers, which allows one to partition them into sublayers with a corresponding reduction of the approximation error. The convergence of the calculation results from the two proposed approaches can confirm their reliability. [ABSTRACT FROM AUTHOR]