The stress-strain state and duration until fracture are calculated for a two-stage behavior of a rotating disk with a hyperbolic surface shape under creep. The first stage is the damage accumulation and beginning of fracture in a certain body’s area where the accumulated damage reaches a critical value. The second stage is the fracture front spreading and a complete destruction of the body. It is assumed that the fracture front propagates axisymmetrically, the fracture is brittle. The calculation method consists in the fact that the unsteady creep problem is reduced to a similar problem within the assumption of a steady material creep. In order to obtain a valid solution, it is necessary to multiply the known solution of the steady creep by some functions of the coordinates and time. To find these functions, we obtain the corresponding system of equations. We investigate the duration of stages depending on the creep kinetic theory version in the statement of Yu.N. Rabotnov and L.M. Kachanov. According to the calculations, the dependence of the second stage duration to the first stage duration can be from tenth to several tens of percent depending on the applied load, the surface shape and the size of the inner hole of the disc. With a decrease in the radius of the disc’s inner hole, the second stage duration can be comparable with the first one. In all the studied cases the first stage duration in the Rabotnov’s model is higher than on the Kachanov’s one; the dependence of the second and the first stage duration in the Rabotnov’s model is smaller than in the first stage of the Kachanov’s model. The analysis of the fracture front movement showed that the main time of the second stage (about 75-85 % according to the Kachanov’s model and 85-90 % according to the Rabotnov’s model) is 20 % of the working part of the disk radius.

Fiber-optic sensors are used to monitor the state of structures in various industries. The best solution for monitoring deformations in the products made of polymer composite materials are fiber Bragg gratings (FBGs). In this paper, we consider the possibility of studying the stress-strain state (SSS), tracking structural changes in the construction with the help of FBGs, using the example of a "U" -shaped composite frame of an aircraft engine. Based on the revealed regularities and peculiarities of the FBGs operation, the main control points have been determined. In the course of the research, we created a three-dimensional computer model of an aircraft propulsion system composite frame which was used for the analysis of the stress-strain state under various loading conditions. The developed model makes it possible to perform a layer-by-layer analysis of the composite frame structure to estimate the normal and shear interlayer stresses, which determine the destruction of the structure. Numerical modeling of this problem was carried out by the finite element method (FEM) in the software package ANSYS Workbench. Numerical results were compared with the experimental data obtained in laboratory tests of a composite frame segment equipped with fiber-optic sensors. The tests were carried out on the equipment of the unique scientific installation "Unique scientific and technological complex of automated computation" using the Zwick servo-hydraulic machine and the Astro X327 interrogator. The results obtained will be used to determine the size of the effective "sensitive zone" for embedding fiber-optic sensors (FOS) based on Bragg gratings into the construction of a composite frame. The main goal of this work is the development of a methodology for detecting and identifying various types of damage and the maximum load during the working lifespan of the structure.

The paper presents the experimental and numerical results of elastoplastic deformation of specimens with a cylindrical working part and specimens with a stress concentrator made of 09G2C steel under monotonic kinematic tension-torsion loadings prior to failure, taking into account large deformations and inhomogeneity of the stress-strain state (SSS). A complete system of equations describing generalized axisymmetric torsion problems is written in a cylindrical coordinate system. Kinematic relations are formulated at speeds in the metric of the current state, which makes it possible to describe large deformations. The equation of motion of a continuous medium follows from the equation of the balance of virtual capacities. Since we consider active loading processes close to proportional ones, we describe the elastoplastic properties of materials by the flow theory with nonlinear isotropic hardening. The system of equations, supplemented by kinematic boundary and initial conditions, is solved by the finite element method in a combination with an explicit integration scheme of the "cross" type. On the basis of the experimental-calculation method, true deformation diagrams for tension and torsion were constructed to supplement the plasticity model with material functions. These diagrams differ significantly with deformations of more than 15 %, which is caused by the sensitivity of the plastic properties of the test material to the form of the stressed state. To describe the tension-torsion, the dependence of the deformation diagram on the form of the stressed state is introduced. The refined deformation diagram is a linear combination of tension and torsion diagrams, which coefficients depend on the parameter of the form of the stressed state, the parameter of the stress triaxiality or the Nadai-Lode stress parameter. There is a good correspondence of the numerical results with the experiment on the integral characteristics (axial force from axial displacement and torque from the twist angle). The analysis of the SSS parameters in the neck and circular concentrator is performed. The estimated the peculiarities of the mutual influence of tension and torsion on the localization of deformations and destruction of cylindrical samples and samples with a stress concentrator.

Based on the concept of the interactive layer (IL), the paper considers the deformation of a body with a thin deep notch in a linearly elastic formulation. The stress state in the interactive layer is determined on the basis of the constitutive relations of the Prandtl bonds type. The proposed formulation of the task explicitly includes a linear parameter (LP). Based on the analytical solution of the task in the beam approximation, the dependence of the wedge force on the thickness (IL) is obtained. The use of the classical strength criteria in this dependence leads to a zero critical force at zero thickness IL, which contradicts the Griffith-Irvin criterion. We use it as a universal criterion for the destruction of the energy product (EP), as a product of a linear size and an increase in the specific free energy of the layer is shown. A relationship is established between the dimensions of the sample and the critical force, which ensures independence with a given degree of accuracy of the critical force from the thickness IL. By comparing the solution obtained and the classical solution for the notch in the form of a mathematical cut, the assumptions under which EP criterion and the Griffith's criterion (GC) coincide are determined. By using the Neuber-Novozhilov approach, the structural volume of the material with averaged characteristics of the stress-strain state (SSS) is identified. This volume is considered as a representative volume for determining the increment of еру average free energy that controls the state of pre-destruction. The product of the increment of the average free energy and LP determines the average EP. The expression for the average EP is determined on the basis of the obtained analytical solution. It is shown that the transition to the averaged value of the EP on a square Neuber cell does not lead to an increase in the margin of error in determining the critical force. It has been established that starting with a certain value of LP, which depends on the geometric characteristics of the damaged body, the convergence of the average EP in the pre-destruction zone to the GC takes place with a specified degree of accuracy.

The paper presents a set of mathematical methods and its computer implementation aimed at studying the real change in mechanical characteristics (elastic modulus) and the geometry of deformable solids based on scanning. Later these data will be used in constructing the finite element (FE) models and analyzing the stress-strain state (SSS). The presented research is important for deformable solids of complex (individual) geometric shapes and pronounced properties of inhomogeneity of the material mechanical characteristics. The scanning of the deformable solids is carried out by a computer tomography (CT). As a result of this work we prepared a package of raster images of sections of the investigated body. The further stage of the investigation is determined by analyzing the pixel color characteristics of the resulting raster images for the construction of an individual geometry of deformable solids and the distribution of mechanical characteristics in it. The contour of the external geometry and geometry of the internal structure of deformable solids in the cross-section is constructed based on two stages. The first stage is the preliminary one; and is necessary for the determination in the sections of the domain, both of the body itself and of the regions in it with pronounced changes in the mechanical characteristics. At the second stage, the geometry of the contours is refined, formed based on the method of studying the gradients of the change in the pixel color indices. The determination of the field of the change in mechanical characteristics is carried out by calculating the weight coefficients obtained on the basis of two parameters: the mathematical expectation of a change in the pixel color index in the package of sections of deformable solids; as well as the results of a full-scale test on the tensile (compression) of standard samples, that is, the averaged data on the mechanical properties of the material of deformable solids. We studied the deformable solids from bone tissue, in the form of a fragment of the femur, a human tooth in the jaw and a tooth with a composite seal in the jaw. The presented choice of deformable solids is not principled, but is caused by the following circumstances: a high degree of heterogeneity of bone material and its geometry, as well as a high level of development of CT scanning technology in medicine and engineering. The analysis results of the SSS of the obtained FE models of real deformable solids, obtained taking into account the inhomogeneity of the mechanical characteristics of the material and the individuality of the geometry, allow us to reach a higher level realization of the mathematical finite element model with respect to the real object, and also prove efficiency and accuracy of the presented technology in real working conditions (design and manufacturing) of structures.

Vibration diagnostics is one of the most promising approaches for the diagnostic of reinforced concrete structures integrity, which analyzes natural vibrations caused by impact loads. It concentrates on the propagation of the shock wave through the elements of the structure and the effect of defects on this process. An important element of the shock wave control system is a mathematical model of the structure. The mathematical modeling accuracy is ensured by a precise determination of the material elastic and dissipative characteristics. This aspect is essentially important for concrete since its characteristics may vary much. The paper presents a theoretical and experimental approach to determining elastic and dissipative characteristics of concrete. In the framework of the viscoelastic model, the deformation response of a concrete specimen to a localized shock impulse load is analyzed. A numerical solution of the initial boundary value problem is obtained by the finite-element method using the ANSYS software. Based on this solution, the structural scheme of experiments has been obtained. In the experiments, free vibrations of the specimen are excited using a striker equipped with a vibrometer. The deformation response at reference points of the sample is recorded with a laser vibrometer. A special iterative procedure ensuring the agreement between the numerical and experimental results is developed. The agreement is achieved by the correction of the mechanical characteristics of the material. The reliability and effectiveness of the proposed approach are demonstrated by considering the vibration processes in a concrete specimen. Model parameters are obtained for description of elastic and dissipative characteristics of concrete at frequency range of 5.6±0.5 kHz. The proposed algorithm can be used to identify the properties of concrete in any frequency range. It represents the possibilities for determining the frequency dependence of the elastic and dissipative properties of materials. The described approach can be used to identify the elastic and dissipative characteristics of other materials.

We consider the main features and equations of the applied theory of inelasticity relating to the class of flow theories with combined hardening. The applied theory of inelasticity is the simplest engineering version of the theory of inelasticity; and can be used for calculations of the worked out and residual resource of high-performance structural materials under repeated and long-term thermomechanical loads. The strain rate tensor is represented as the sum of the elastic and inelastic strain tensors, i.e. here there is no conditional separation of inelastic deformation by deformation of plasticity and creep. The elastic deformation follows the generalized Hooke’s law. A loading surface is introduced that isotropically expands or reduces and displaces during loading. For the radius of the loading surface (isotropic hardening), an evolutional equation is generalized to nonisothermal loading and restoration of mechanical properties during annealing. The displacement of the loading surface (anisotropic hardening) is described through the evolution equation with a three-member structure, generalized to non-isothermal loading and the back stresses removal (displacement) during firing. To determine the rate tensor of inelastic deformation, the associated (gradient) flow law is used. For rigid (given deformations) and soft (given stresses) loading regimes, expressions are obtained to determine the rate of the accumulated inelastic deformation. Conditions of elastic and inelastic states are formulated. To describe the nonlinear processes of damage accumulation, the kinetic equation of damage accumulation is introduced, where the energy equal to the work of back stresses on the field of inelastic deformations is assumed as the energy spent on creation of damages in the material. Here this kinetic equation is generalized to nonisothermal loading and processes of embrittlement and healing of damages. The material functions closing the applied theory of inelasticity are singled out; the basic experiment and the material functions identification method are formulated. An example of determining the material functions from the basic experiment results is considered and material functions for 12Х18H9 stainless steel in the temperature range from 20 °C to 650 °C are given. Further we give a list of experiments and structural steels and alloys on which the applied inelasticity theory was verified under plastic and inelastic (viscoplastic) deformations, isothermal and nonisothermal, simple and complex loadings. In conclusion, we discuss the application of the theory of inelasticity.

The work studies the fatigue life of metallic materials under various schemes of multiaxial non-proportional loading which lead to the occurrence of a complex stress-strain state. We present the results of the experimental study of the fatigue life of 40CrMnMo structural alloyed steel and 2024 aluminum alloy under biaxial cyclic loading. Cyclic tests were carried out on the Instron ElectroPuls E10000 biaxial electrodynamic test system under joint tension-compression and torsion of solid cylindrical corset-type samples. The methodological issues of conducting cyclic tests with a mixed modes loading are considered and the corresponding new experimental results are obtained. The experimental data are presented in the form of points on the graphs and corresponding approximating lines which reflect the dependence of the number of cycles to failure on the relative values of the constant components of the tangential and normal stresses. In all the tests, the specified values of the additional parts of the stress components did not exceed the values of the corresponding conditional yield strengths, which were previously determined in the quasistatic tensile and torsion tests for each material. Based on the test results, the influence of the constant component of tangential stresses on the fatigue life of the materials under cyclic tension-compression was evaluated, and the effect of the constant component of normal stresses on the fatigue life under cyclic torsion was considered. It is shown that because of the constant stress components, both under cyclic tension-compression and cyclic torsion, there is a decrease in the number of cycles before the specimens break. The obtained data demonstrate the necessity to estimate the allowable limits of the constant parts of the stress components, which will not lead to a significant reduction in the fatigue life of structures operating under cyclic loading conditions.

An axially symmetric elastic equilibrium problem is investigated for a continuously inhomogeneous space with a cylindrical cavity when Poisson’s ratio is being an arbitrary fairly smooth function with respect to radial coordinate while shear modulus is constant. For this case Young’s modulus is also variable with respect to the radial coordinate. A general solution is suggested which leads us to a vector Laplace equation and a scalar Poisson equation whose right-hand side depends on Poisson’s ratio. As a result, exact general solutions of the Laplace and Poisson equations are constructed in integral forms with the help of Fourier transformations. Then integral equations of two axially symmetric contact problems are derived on the interaction between the cavity surface and a rigid cylindrical insert fitted with interference. In the first problem the contact is supposed to be absolutely ideal, a singular asymptotical method is used here to solve the integral equation of the first kind with respect to the contact pressure, which is effective for fairly long inserts. In the second problem the mine surface is supposed to be rough simulated by an extra Winkler type, a collocation method is used for solving the integral equation of the second kind, which is effective for fairly short inserts. The contact pressure has typical square root singularities at end-points in the first problem while it takes finite values at those points in the second problem. For a homogeneous material, the integral characteristics of the contact pressures in both problems are close for small coefficients of roughness for some values of the insert relative length. It is shown that the rough surface distributes contact pressures more uniformly removing effect of nonhomogeneity. The calculations are made for the cases when Poisson’s ratio and Young’s modulus increase or decrease from the surface of the cavity.

The paper deals with predicting deformation and strength properties of metallic materials with defects uniformly distributed over the product volume in the form of gas bubbles under single and cyclic loadings. The proposed approach is based on the use of the corresponding characteristics of a defect-free material (stress-strain diagram, plasticity resource, curve of deformation in a cycle and cyclic deformation curve, and fatigue curve) and the results of numerical experiments on samples models with different volume fractions of defects (degree of porosity of the medium). We analyze the stress-strain state of the virtual samples using the finite element method in ANSYS. The moment of reaching the limiting state-discontinuities - was recorded with a monotonous loading using the deformation criterion of V.L. Kolmogorov. Under single loading, the elastic constants and stress-strain curves are determined up to the moment of destruction of the model medium simulating a material with different porosity (a possible change in the deformation mechanism due to distortion of the gas bubbles wall shape accompanied by plastic flow of the matrix material was not taken into account). The property of the central similarity of the stress-strain curves is noted. Under cyclic loading conditions, both deformation curves in a cycle representing the trajectory of the state point in “the stress ~ strain” space during the cycle and the cyclic deformation curve, i.e. the stress amplitude versus the strain amplitude, reflecting the hardening (weakening) of the material of various porosity degrees are obtained. The description of the fatigue curves characterizing the strength properties under these conditions was carried out using the local Manson-Langer type criterion. The results can be used to normalize the allowable defect size and density and to assign the reasonable safety factor for stress, strain and durability of a real porous medium.

In this paper, we consider the loading interaction problems that arise in fatigue life prediction. The brief overview of recently most popular models is presented. Most of them explain this phenomenona by the crack closure effect with different nature. At the same time, cycle-sequence sensitivity can be observed at high stress ratio in the absence of crack closure. This fact calls into question the adequacy of these approaches. A new physically based model which can adequately predict fatigue life in a wide range of crack growth rates (the Paris region, near-threshold) is proposed. This model is based on the suggestion of a brittle fracture nature of the crack propagation in the near-threshold region. As a result it is shown that the threshold stress intensity, ΔKth, is not a material constant, but a variable that is extremely sensitive to load history. A numerical technique is proposed to estimate the near-tip stress for an arbitrary loading sequence including random loading spectra. This method is based on the constitutive equations with the combined (isotropic-kinematic) hardening rule and linear rule for strain prediction. The combined hardening can be interpreted as a simple modification of Frederick-Armstrong law and Chaboche model. The numerical integration of constitutive equations based on the return-mapping scheme (implicit Euler method) is performed. The experimental procedure for adjustment of models and its verification is proposed. We show the comparison of the experimental and calculated data with a constant amplitude loading under a variety of overloads and underloads and under spectral loading. In all cases, a satisfactory compliance with a high correlation factor can be observed.

The optimization of dissipative properties of electroelastic bodies with external electric circuits suggests the selection of parameters for these circuits which can provide the most effective damping of vibrations at the prescribed frequency. Since the external circuits can be represented as a set of elements with concentrated parameters connected to the system with distributed parameters, solving the electroelastic problems for such systems using their full formulation requires high computational and time costs. In mechanics, there exist several approaches, which allow the representation of the mechanical systems with distributed parameters as discrete systems with concentrated parameters of the spring-mass-damper type. In this paper, an approach to the analysis of the dynamic behavior of electromechanical systems with external electric circuits is developed based on the equivalent electric circuits representing discrete electric systems with concentrated parameters. The above discrete systems are the analogues of the initial electromechanical systems in relation to frequency characteristics and electrical processes occurring in them. The solution to the problem on natural vibrations of electromechanical systems are the complex natural vibration frequencies, the real part of which defines the frequency of vibrations and imaginary part - the damping index. The present paper considers the problems of determining the magnitude of elements parameters of the equivalent circuit. The proposed approach made it possible to obtain the mathematical relations binding the limit values defining the dynamic characteristics of systems under consideration (boundaries of the frequency range for natural vibration frequencies change, maximal reachable damping index, the valued of resonant frequency of a system when the resistive external circuit is attached) with the values of natural vibration frequencies of the original structure with piezoelectric element operating in the open circuit and short circuit modes.