# Статьи журнала - Вестник Пермского национального исследовательского политехнического университета. Механика

Все статьи: 1033

A body failure model with a notch based on the scalable linear parameter

Статья научная

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.

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Статья научная

The stress concentration must often be examined at two levels while analyzing the stress condition of composite materials. The macroconcentration depends on the presence of holes, notches and other local areas of a construction. Typical dimensions of macroconcentration distribution areas are of the order of 0,01-0,1 m. Macroconcentration analysis is performed using the models of homogeneous material. Microstress concentration occurs in structurally inhomogeneous composites due to the structural heterogeneity of the composite. The sizes of concentration areas in regular structures are defined by the sizes of periodically recurring areas. In fibrous composites, such areas have the size of approximately 0,0001 m or less. This makes it necessary to use a two-level approach for the analysis of the stress concentration in the construction of composite materials. The aim of the present study was to compute the stress concentration in unidirectional reinforced composite plate with circular hole with respect to the volume ratio of the component materials in composite. The contour of the circular hole and its dependency on the structure of plates was calculated in order to study the behaviors of macro- and microstresses. The boundary conditions at a large distance from the hole are pressure, uniformly distributed on the plate. Also this problem is analyzed with the finite element method by package ANSYS. Macroconcentration is defined based on the solution of the plane problem of elasticity theory of the orthotropic material by the virtue of functions of a complex variable. The finite element method was used to investigate the stress distribution at microlevel. Boundary conditions that model the state of the specified two-dimensional representative cell in the composite structure were established. The results demonstrated the macro- and microstresses and behavior of the orthotropic plate with a circular hole calculated for two different structures.

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Characterization of low velocity local impact of sandwich panels

Статья научная

The present paper deals with analysis of local indentation and their energies in point loading of sandwich panel with thin orthotropic composite faces and honeycomb core as an introduction for low velocity impact loading and energy absorbing in sandwich structures. Energy is consumed in two stages: local indentation of sandwich panel skin and bending of sandwich panel. If the impact is located near support or clamping only first stage (indentation of sandwich panel) will be presented. Here the analytical model has been used assuming a rigid-perfectly plastic compressive behaviour of the honeycomb core and membrane behaviour of orthotropic skin for large indentation of sandwich panel. In experimental work were investigated two types of sandwich panels, which consisted of different laminated skins: cross-ply of unidirectional CFRP and AFRP (aramid fabric reinforced plastic) and core honeycomb materials (impregnated paper like Nomex and one layer of glass fabric reinforced plastic). Length of cell side is 2.5 mm. Skins were made with symmetrical lay-ups [0/90]s and [45/-45]s. For indentation test we used steel balls with radius 5-30 mm, speed of loading was 2 mm/min. The experimental results are in good agreement with the analysis. These results can be used in impact loading and energy absorption studies of laminated structures by integrating of “local load vs deflection” curve.

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Composite materials in aircraft engine blades

Статья научная

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

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Статья научная

The inapplicability of the reference formula for determining the convergence of two statically compressed parallel cylinders made of a homogeneous, isotropic and physically linear material has been proved due to a well-known logarithmic feature in the plane classical problem of mechanics of elastic solids. In the special case of the elastic interaction of a cylinder with a half-plane, when one of the radii has an infinite length, it has been found that the convergence also becomes equal to infinity. This paradoxical result contradicts not only the physical and mechanical meaning of the process under study, but also confirms the inadequacy of Flamant model of a simple radial stress state in determining displacements. The authors have proposed an algorithm for eliminating the contradictions based on the solution of Fredholm integral equation of the first kind. In the future, it can be considered as a new fundamental and applied problem of the theory of elasticity, which is of a great importance for a refined assessment of the contact strength and stiffness of the cylindrical parts of load-bearing structures taking into account the general and local deformations (cylindrical rollers, gears, road surfaces, when they are compacted with steel rollers, etc.) on the basis of a flat Flamant calculation scheme considering three stress components and the width of the cylinder contact area previously developed and mathematically approximated by the authors.

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Статья научная

Currently, modern CAE programs like ANSYS, LS-DYNA, ABAQUS, Simcenter 3D etc. are widely used to develop each engineering product. CAE reduces development costs and speeds up product launches. Computer modelling allows eliminating unsuccessful design options at early design stages and minimising or eliminating critical design changes at the prototype testing stage. Computer simulations are especially needed for the development of high-performance perfection designs like jet engines. The use of composites in the engines requires the availability of appropriate design tools to assess the mechanical behaviour of structural elements made of such materials under operational loads and in an emergency. Predictive modelling of the deformation and fracture of the composite fan blades and fan case subjected to dynamic loading cause considerable interest of engineers. As in the case of simulation of shock loading of metals, a model of a composite material must be verified. However, the problem is that the fibrous composite material itself is already a structure and can be modelled in various ways: without considering the layered structure (homogeneous approach) taking the mesostructure into account (at the ply-level or at the yarn-level) taking the microstructure into account (at the filament level). The requirements for the initial data, the number of parameters determined during the verification process, the complexity of creating geometric models will differ in each case. This paper briefly describes the main approaches to the numerical simulation of composite elements under high-velocity impact loading. The main advantages and disadvantages of these approaches are also considered. On the example of the meso-scale approach, the main parameters of the computational models that affect the results of calculations are shown. Based on the obtained data, the main recommendations were formulated on the validation of meso-scale models of composites.

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Статья научная

Работа посвящена исследованию эффективных упругих свойств пенообразных или ячеистых материалов, моделируемых массивами открытых ячеек Гибсона-Эшби регулярной и нерегулярной структуры. В настоящее время существует множество работ, в которых представлены результаты исследований ячеистых материалов теоретическими, численными и экспериментальными методами. Однако в этих работах рассматривались либо регулярные решетки, либо отдельная ячейка, либо модели представительных объемов, не основанные на моделях Гибсона-Эшби. В данной статье помимо регулярной решетки численно исследовались и нерегулярные структуры. Описана математическая постановка задачи гомогенизации, основанная на эквивалентности по энергии пенообразного материала и однородной среды сравнения. Приведены постановки шести краевых задач, решения которых в совокупности позволяют определить полный набор эффективных модулей жесткости для пен с произвольными типами физической и геометрической анизотропий. Все этапы численного исследования были реализованы в конечно-элементном пакете ANSYS. Подробно описаны два алгоритма формирования твердотельных и конечно-элементных моделей нерегулярных решеток Гибсона-Эшби с малой и с большой пористостью. В качестве примера для поликарбонатных пен осуществлены численные расчеты в широком диапазоне пористости. Проведено сравнение значений эффективных упругих модулей для регулярных и нерегулярных решеток и для аналитической модели Гибсона-Эшби. Результаты вычислительных экспериментов показали, что модель Гибсона-Эшби достаточно хорошо описывает поведение высокопористых материалов (с пористостью более 75 %), но при меньших значениях пористости дает менее удовлетворительное предсказание. Отмечено, что при большом числе ячеек статистически регулярные и нерегулярные решетки дают близкие результаты для эффективных модулей. Однако для отдельных структур нерегулярных решеток, особенно при сильно различающихся ячейках в отдельных направлениях, эффективные модули могут иметь существенно отличающиеся значения, а эффективная гомогенная среда может иметь ярко выраженные анизотропные свойства. Эти эффекты обусловлены геометрической анизотропией и концентрацией напряжений в длинных соединительных балках и на стыках балок различных размеров в сильно нерегулярных решетках Гибсона-Эшби. Приведены примеры подобных решеток, и дан анализ разброса значений относительных модулей, характеризующий анизотропию таких структур.

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Dynamic stability of a straight pipe conveying pulsatile flow under thermal loads

Статья научная

Pipes conveying fluid are considered as a fundamental dynamical problem in the field of fluid-structure interaction. They are widely used in the petroleum industry, in nuclear engineering, aviation and aerospace, in nanostructures. This article investigates the effect of temperature load on the dynamic stability of a straight pipe conveying pulsatile flow. The fluid velocity is a harmonic function of time. The Galerkin method is applied for the solution of the differential equation of the transverse vibrations of the pipe. The differential equation is reduced to a first-order differential equation system. The system of differential equations is transformed and rewritten in a matrix form. The harmonic function of the fluid velocity allows the Floquet theory to be applied in order to investigate the dynamic stability of the system. The static scheme of the investigated pipe is a beam with restricted horizontal and vertical displacements at both of its ends. A numerical solution for a straight pipe conveying fluid with specified geometric and physical characteristics has been carried out. The temperature load and the constant fluid rate are considered as parameters of the problem. The results show that the temperature load affects the vibrational characteristics of the pipe, as well as its critical velocity.

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Статья научная

Turbofan jet engines are among the most complex and responsible constructions in the world. The creation of modern globally competitive engines is impossible without the use of digital twin technologies: a set of computational models that fully describe the behaviour of the structure under any operating conditions. Today, composite materials are widely used in many industries. In aircraft engines, their use is very promising for fan blades and fan case to reduce the overall weight of the engine and inertial loads. The dovetail joint of the fan blade works in compound stress conditions. To assess the strength of this element, it is necessary to consider a three-dimensional formulation of the problem, which requires significant computational resources. The use of composite materials is complicated by the complexity of preparing mesh models. A correct choice of the material strength criterion is another important factor that must be taken into account during the analysis of the mechanical behaviour of the thick-walled composite structures. The chosen criterion largely determines the reliability and weight efficiency of the composite structure. This paper considers the possibility of replacing the three-dimensional statement of the problem with a two-dimensional one when choosing rational reinforcing schemes for the dovetail joint of a CFRP fan blade at the initial stages using Daniel strength criterion.

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Evaluation of the dynamics of elastic plate and liquid section dynamic absorber

Статья научная

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

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Memory dependent response in an infinitely long thermoelastic solid circular cylinder

Статья научная

Memory-dependent derivatives (MDD) have physical meaning, and compared to fractional derivatives, they are more suitable and convenient for temporal remodeling. In this study, the temperature and stress distributions in an infinitely extended generalized thermally elastic solid circular cylinder have been investigated by utilizing the concept of a memory-dependent heat conduction model. The homogeneous, isotropic, infinitely long solid circular cylinder is considered to have a lateral surface that is free of traction and is subjected to a known surrounding temperature. In the domain of the integral Laplace transform, the problem is worked out, and its complex inversion is performed numerically using the Fourier series expansion method. The material properties of copper metal are chosen for the purpose of numerical computation, and the thermoelastic impact of time delay on temperature distribution, displacement distribution, and thermal stresses are represented graphically. Also, time delay's effect on temperature history, displacement history, and thermal heat transfer stress history are shown, respectively. This study could also benefit mathematicians and researchers involved in the development of thermoelasticity, as it accounts for the memory-related derivatives that are useful in explaining the behaviour of a variety of physical processes. The thermal fluctuations captured by various factors with memory-dependent responses are used in engineering applications to realistically design machines or structures.

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Статья научная

Composite materials reinforced with synthetic fibres have been used in aviation and space technology for more than half a century. Fibre-reinforced composites with high specific strength and corrosion resistance are an attractive alternative to traditional structural materials, including steels, aluminium and titanium alloys. At the same time, composites based on carbon and glass fibres are inherently brittle structural materials with high strength sensitivity to stress concentrations due to the design features of the structures or defects that occur in operation. One way to solve this problem is hybridisation which makes it possible to increase the nonlinearity of the composite stress-strain diagram and reduce sensitivity to notches. Hybrid composites combine several types of reinforcing filler with different fracture strains and exhibit a pronounced pseudo-ductile plateau in tension. Such material behaviour ensures the redistribution of stresses near the concentrator and potentially reduce notch sensitivity. When designing hybrids, it is necessary to take into account the influence of different factors including the ratio between the components and their lay-up, using various technological methods, and the specific strength of the finished material. This paper presents the results of an experimental study on the strength of hybrid composites based on glass and carbon fabrics in the open hole tests. It was found that hybrids with an extended hardening area after the pseudo-yield plateau are were more notch sensitive. A low elongation component layers rotation on angles up to 10°, as well as the use of thin polymer veils, also reduce the sensitivity of the composite strength to the presence of the defects.

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Numerical and experimental study on CFRP structure optimization for coefficient of thermal expansion

Статья научная

This paper explores the optimization macrostructure to reach a stable low coefficient of thermal expansion αx of a composite with carbon fibers. To limit the search area, a necessary condition for the existence of αx local minima is proposed, expressed in terms of the radii of hyperspheres in the design space of the angular orientation of the layers transformed by the PСA algorithm. The analysis of the structure variants characterized by low αx shows different sustainability to lamina properties variability. Multi-criteria optimization was carried out. The objective functions are expectation E(αx) and variance Var(αx). The analysis of Pareto fronts and probability density functions make it possible to estimate the reachability of the calculated αx under given conditions of lamina properties variability. The reduction variance opportunity of αx distribution by modifying the polymer matrix with MWCNTs under conditions of reinforcing fibers disorientation and lamina properties variability is investigated. The microstructure modification of the polymer composite material allows to reduce the Var(αx) by 91.61 % with a volume ratio of MWCNTs up to 1 %. Requirement thermomechanical properties are reached by determining the orientation of anisotropic layers. Based on the obtained optimal structures, specimens of CFRP with 0, 1 and 2 vol.% MWCNTs were made. Scanning electron microscopy using FE-SEM Hitachi S-5500 was performed to check the uniformity of distribution and compatibility of the epoxy matrix and MWCNTs. The measurement of αx is determined using a TAInstrumentsQ400 thermomechanical analyzer. Measured αx of specimens is in the range from 6.2·10-8 to 1.98·10-7 1/K. The structure optimization approach proposed in this paper makes it possible to obtain a set of solutions with a consistently low αx in the range up to 1·10-7 1/K. The transformation of the design space of the layers’ orientation angles and the limitation of the search area allowed to reduce the range of solutions under consideration by 83.9 %.

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Статья научная

The intelligent design of lightweight, protective systems requires the use of numerical simulations widely to weed unsuccessful tests and minimise the number of expensive experiments. At the same time, it is necessary to have verified numerical models of all materials that are used in a protective structure to obtain adequate numerical simulation results. In this research, the impact performance of the ceramic-faced mosaic panel against the impactor with a complicated structure was studied using numerical simulations in thу commercially available package LS-DYNA. Backing types being considered were Aluminium AA 5083 and Dyneema® HB80 UD composite. A new mesoscale model of 99.5% alumina based on the bonded particle method was calibrated and verified through the comparison with the known experimental data. Further, designs with different configurations of mosaic ceramic layers having hex tiles were studied and compared. The results indicated that even small lateral gaps between ceramic tiles decreased the overall panel performance regardless of both the impact site and a backing type. At the same time, the presence of gaps reduces damages of the ceramic layer and can change the impactor trajectory that can be used in multi-layered structures with distant layers. Thus, it is necessary to find a balance between survivability and mass efficiency for each protective structure.

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On stress-affected kinetics of intermetallic compound growth in the presence of electromigration

Статья научная

This paper is concerned with the analytical modeling of an intermetallic compound formation in a eutectic tin solder joint on copper interconnects subjected to an electrical current. We propose a model that couples mechanical stresses, chemical reaction, diffusion, temperature, and electromigration. The kinetics of the chemical reaction fronts of the intermetallic phase formation is investigated based on the notion of the chemical affinity tensor within the small strain approximation. It allows incorporating the influence of stresses and strains on the chemical reaction rate and the normal component of the reaction front velocity in a rational manner. Electromigration is introduced into the model as an additional summand in the total flux of the diffusive constituents, which, in turn, also affects the reaction front velocity. In the considered model, the mechanical stresses arise due to the internal strains produced by the chemical transformation and by the thermal expansion. We formulate a model problem for planar reaction fronts. Within this model, the influence of stresses and electromigration on the reaction front kinetics is studied analytically. Based on the Mean-Time-To-Failure (MTTF) criteria, we calculate the critical thickness of the solder joint and estimate the amount of the accumulated vacancies. We introduce a dimensionless parameter, which characterizes the accumulation of vacancies due to electromigration enhanced diffusion. Finally, we discuss the coupling between the accumulated vacancies and Kirkendall void nucleation.

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Plane-strain extrusion of a green type porous plastic material through a wedge-shaped die

Статья научная

This paper presents the solutions for the plane-strain extrusion of porous material. We consider the problem of a stationary plastic flow through a wedge shaped die. We neglect friction between the die and the deformed material since it is rather a negative effect and should be avoided in manufacturing. The elliptic Green type yield condition and its piecewise-linear approximation are adopted for this problem. In the last case, we obtain analytical solution that links extrusion pressure and area reduction to the initial and final density of the porous material. For elliptic Green yield condition the problem reduced to nonlinear ODE that integrated numerically. The results are compared with known solution for Gurson model. The extrusion pressure predicted by the piecewise-linear model is lower than what obtained by the elliptic Green model. In turn, the pressure predicted by elliptic Green model is lower than the pressure obtained in the frame of Gurson model. At low values of area reduction, all three models predict approximately the same extrusion pressure. With a small initial porosity of the material, the Gurson model gives results that are close to the elliptic Green model, and with a large initial porosity, to the piecewise-linear Green model.

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Статья научная

The paper considers a complex experimental and theoretical approach to studying high-speed deformation of structural materials including a system of basic dynamic experiments aimed at determining the strength and deformation properties of materials under various types of stresses, a program for direct parametric identification of models of deformation and fracture, as well as a system of special verification experiments in the natural and numerical realizations, which makes it possible to assess the adequacy of the model obtained and its performance in conditions other than those in which it was received. To obtain a set of mechanical strength and deformation properties of materials under compression, tension or shear, a series of basic experiments was carried out on an installation that implements the Kolsky method using sets of split Hopkinson bar of various configurations. According to the results of these experiments, together with the data of static deformation, the parameters of the Johnson-Cook model of plasticity with various versions of the model factor responsible for the influence of the strain rate were identified. To test the adequacy of the model (verification), special test experiments have been developed that are simple enough, on the one hand, and allow an unambiguous interpretation of the results and numerical reproduction without simplifications, whilst, on the other hand, the stress state in these types of tests, as well as the history of changes in the loading parameters, differs from that in basic experiments. The chain of obtaining an adequate (verified) model of deformation and fracture used in software complexes for calculating the stress-strain state and the strength of critical structures under shock loading conditions is considered in the example of steel 3.

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Stability of chemical reaction fronts in the vicinity of a blocking state

Статья научная

In the current work we consider a chemical reaction localized on the sharp interface between a solid and a diffusive constituent. The driving force for the reaction front propagation is a normal component of the chemical affinity tensor. The configuration of the deformed state where the driving force is zero corresponds to the reaction blocking state. The paper is aimed at studying this configuration. The utilized approach to analyze the stability of the equilibrium interphase between two deformable domains involves a linearized analysis of the kinetic equation for the perturbed interface. Previously this method was applied for an interface stability analysis in the case of phase transformations. The advantage of this method is that it also shows how the loss of stability occurs. An analytical solution for the perturbed kinetic equation is only possible for some simple configurations. Numerical procedures were applied in order to solve these types of problems. As an example, we used the numerical procedure, and the problem of the chemical reaction front propagation in a hollow cylinder is solved. For the unstable configuration we analyzed a stress state in the vicinity of the reaction blocking.

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Статья научная

Assessment of the residual strength of composite structural elements that can be subjected to low-velocity impact during operation is still a vital engineering problem. Its solution requires not only the understanding of the basic mechanisms of energy dissipation in composites but, the study of factors affecting the impact resistance of the material. The thickness is one of the main parameters that affects the mechanical behaviour of the composite at low-velocity impacts and, as a consequence, its residual strength. This paper presents the experimental study of the material thickness and impact energy influence on the residual flexural strength of woven glass fibre-reinforced plastic specimens. At the first stage of the study, low-velocity impact tests with different impact energies on GFRP plate specimens with the thickness of 2 mm, 4 mm, and 6 mm were carried out. At the second stage, the beam specimens were cut out from the plate specimens with impact damages, and three-point bending tests were carried out. The dependencies of the residual flexural strength were obtained at various impact energies for all specimen thicknesses. The sensitivity of the Flexure-After-Impact test protocol to the delamination and fibre damages in the composite specimens were assessed.

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Статья научная

The work deals with development of a new approach for forecasting a high-cycle fatigue life-time of bolted connection of hydro turbines runner. Operation of hydro turbines on normal operation condition does not lead to high stresses rates in bolted connection. However the high cycle fatigue failures have been occurred. High rates stresses occur in bolted connection in transient (start/stop) regimes of hydro turbines operation. The frequency of transient regimes occurrence depends from many factors and defined in this paper as a random function of time. Long-time bolted connection operation lead to natural degradation of material (aging). The degradation process is also a random process of time. So, this work pays attention to developing stochastic mathematical model of damage accumulation that take into account stochastic nature of degradation process and frequency of transient regimes occurrence. Application of the developed models is shown on real engineering example. Degradation of properties has been modeled as a process of the reduction of fatigue (endurance) limit in time. Kinetics of damage accumulation is introduced in the context of the effective stress concept. Mathematical expectation, correlation function and the continuum damage parameter variance have been obtained as functions of time. Analysis of the influence of natural aging process on statistical parameters of damage accumulation as well as on the life-time has been carried out. The stress-strain state of bolted connection is determined by finite element method.

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