## No 4 (2014)

**Year:**2014**Articles:**11**URL:**https://ered.pstu.ru/index.php/mechanics/issue/view/27**DOI:**https://doi.org/10.15593/perm.mech/2014.4

Technologies and problems of composite materials mechanics for production of outlet guide vane for aircraft jet engine

#### Abstract

The goal of this work is an analysis of modern technologies and problem definitions of mechanics of composite materials for production of outlet guide vane for new domestic aviation propulsion PD-14, planned for installation on the short-range and mid-range jet aircraft MS-21. Outlet guide vanes (OGV), also called flow straightening vanes, are radially disposed behind the fan to straighten out the airflow to reduce losses in the outer contour of the engine. Considering a large number of vanes in the engine, the weight reduction can be very significant due to using polymer composite materials (PCM) instead of the metal in OGV. It is predicted that the weight reduction of each vane, at certain approach to design, can reach 40 %. The results of literature search of composite materials application in the details of fan for aircraft jet engines of world top manufacturers are presented in this paper. The analysis of advanced techniques for production of composite outlet guide vane, such as prepreg technology with autoclave molding, resin transfer molding (RTM), the use of thermoplastic binders and press-materials was carried out. It was noted that the formulation and solution of complex problems of engineering mechanics of composite materials are necessary for high-rate realization of mechanical properties in constructions and reducing the occurrence of defects. The possible problem definitions of deformable solid body mechanics, describing such processes as filtration, physical and chemical conversion, visco-elastic-plastic deformation in heterogeneous medium, typical for composite materials production cycle were considered. The influence of autoclave molding parameters on the mechanical properties of several types of carbon fiber reinforced plastics (CFRP) was analyzed. Using the equations of mechanics of laminated composite plates and shells we calculated effective elastic and strength properties of quasi-isotropic CFRP. A comparative estimate of the effectiveness of composite materials application in the design of OGV was obtained.

**PNRPU Mechanics Bulletin**. 2014;(4):5-44

Modelling hysteresis of energy dissipation at vibration of mechanical systems

#### Abstract

The paper discusses a phenomenological approach to describe the energy dissipation hysteresis at nonstationary vibrations of mechanical systems. The mechanical system is considered as a “black box” with the known relationships between external factors and the observed reactions. A mathematical model is constructed for which the identification of parameters is carried out using the experimental data for steady-state vibrations of a system. To describe the hysteresis the authors have suggested the differential approach, called kinematic one, according to which the force and kinematic parameters are associated by the special differential equation of the first order, the right part of which is selected from a class of functions that provides the asymptotic approximation of the solution to the curves of the limit hysteresis cycle. The limit cycle is formed by curves of direct and reverse processes (“loading-unloading” processes), which are based on experimental data for the maximum possible or permissible intervals of parameter changes during the steady vibrations. Coefficients in the right part are determined from experimental data for the limit hysteresis cycle. Approximation curves of the limit cycle are constructed using the methods of minimizing the discrepancy of analytical representations to the number of experimental points. The proposed approach allows (based on one differential equation) describing the trajectory of hysteresis with a random starting point within the area of the limit cycle. As an example, the problem of forced vibrations of the pendulum-type damper for damping low-frequency vibrations is considered. The authors have considered the dampers, which are used for damping low-frequency vibrations of conductors of overhead transmission lines. The algorithm for energy dissipation analysis is suggested, allowing optimizing the damper constructions at the design stage. The proposed approach has the generality and can be used in the modelling of nonlinear behavior of different structures, mechanisms and systems where it is necessary to take into account the energy dissipation hysteresis in conditions of nonstationary vibrations.

**PNRPU Mechanics Bulletin**. 2014;(4):45-67

Coupled model of fluid-saturated porous materials based on a combination of discrete and continuum approaches

#### Abstract

The numerical model of fluid-saturated porous brittle materials is proposed. The model is based on a hybrid approach combining the particle-based numerical method with finite difference method. In the framework of the model an enclosing porous solid is described with the discrete element method. An ensemble of discrete elements is used to model the processes of deformation of a porous solid and filtration of single-phase fluid in interconnected network of “micropores” (which are the pores, channels and other discontinuities enclosed in the volume of discrete elements). Relations between stress and strain of a discrete element, the change in volume of its pore space and fluid pore pressure in the “micropores” are proposed. Fluid mass transfer between the “micropores” and “macropores” (which are considered as the areas between spatially separated and non-interacting discrete elements) is calculated on the finer grid freezed in the laboratory system of coordinates. The developed coupled model was applied to study the mechanical response of samples of elastic-brittle material with water-saturated pore space under uniaxial compression. It is shown that the strength of fluid-saturated samples is determined by not only the strength properties of “dry” (unfilled) material and the fluid pore pressure, but largely by sample aspect ratio, rate of deformation and the characteristics of porosity of the material. Analysis of simulation results allowed authors to suggest a generalizing dependence of the uniaxial compressive strength of water-saturated permeable brittle material on the reduced diameter of filtration channels, which is the ratio of the characteristic diameter of the filtration channels to the square root of the sample strain rate. Presented results demonstrate the ability of the developed model to study nonstationary processes of deformation and fracture of fluid-saturated materials under dynamic loading.

**PNRPU Mechanics Bulletin**. 2014;(4):68-101

Influence of micro-arc oxidation modes on mechanical properties of aluminum alloy samples

#### Abstract

This paper presents the results of the experimental study influence of micro-arc oxidation (MAO) modes on the yield strength and temporary resistance of aluminum alloy samples marked 2024. The paper describes the research methodology, including the formation of hardened MAO layer on the surface of experimental samples and strength studies by means of experiments with tensile. The studies were conducted according to the theory of experiment planning for a fractional factorial experiment type 23-1. MDO process was carried out using an alkaline electrolyte that is why component concentration of electrolyte (potassium hydroxide - KOH and sodium silicate - Na2SiO3) and electrical parameters of the process, determined by capacity of technological plant, were selected as MAO process factors. Thickness and microhardness of MAO-layer on the cross-sections were determined as well as the yield strength and tensile strength. Regression equations were developed based on data that has been obtained and the conclusions about the degree of influence of modes of micro-arc oxidation on the mechanical properties of the samples were obtained. The results showed that the existence of MAO-layer had almost no effect on the tensile strength of the samples, but it promotes the yield strength increase, the value of which may be increased to 18% depending on the mode of processing. This work was conducted to study the prospects of using the technological method of surface modification - micro-arc oxidation method to improve not only durability but also the strength characteristics of aluminum alloy details.

**PNRPU Mechanics Bulletin**. 2014;(4):102-117

MODELLING OF MARTENSITIC TRANSFORMATIONS IN STEELS: KINEMATICS OF THE MESO-LEVEL

#### Abstract

The derivation of the kinematic relations for the martensitic transformations in steels is considered. Martensitic transformations are diffusion-less solid-state phase ones, occur at speeds close to the sonic speed and lead to changes in the type of the metal lattice. Therefore, when describing the kinematics of the martensitic transition, on the one hand, we are to take into account the basic physical phenomena such as restructuring lattice, accommodation of residual stresses caused by the restructuring; and on the other hand, - the existence of invariant (habitus) plane, making the transition possible at such high speeds. The derived kinematic relations are the part of a two-level mathematical model of solid-state phase transformations during thermomechanical processing of steels. The model is based on physical approaches of the theory of plasticity, allowing taking into account the physical mechanisms of deformation due to introduction of additional internal variables at the mesolevel. The derivation of the relations for the gradient of transformation deformation of mesolevel representative volume as a deformation with an invariant plane is presented. Analogues to the plastic deformation, the transformation deformation is given by a corresponding system of vectors, i.e. the vector normal to the invariant plane and the vector of the sliding direction (these vectors are not mutually perpendicular). These vectors are not known from crystallography, as their analogues in the theory of plastic shear on slip planes. They are calculated taking into account the magnitude of the changes in the lattice parameters at the phase transition and accommodative mechanisms. The results of calculation of transformation systems resulting due to accommodation of residual stresses by plastic shears and twinning on various possible systems in the martensite are given. After calculating transformation systems, gradients of deformation for the martensitic transition in steel and their geometric interpretation are made. The found eigenvalues of gradients give an insight into the volume change at the martensitic transformation. The results are compared with the available experimental and theoretical data.

**PNRPU Mechanics Bulletin**. 2014;(4):118-151

Optimal support of rigid-plastic singly and doubly connected polygonal plates

#### Abstract

In the model of an ideal rigid-plastic body the general solution of a problem of the limit behavior and dynamic bend is obtained for regular singly and doubly connected polygonal plates, hinge supported on immobile polygonal contour, located inside of the plate. The plate is under a short-term dynamic load of an explosive type with high intensity, uniformly distributed over the surface. It is shown that there are several mechanisms of limit and dynamic deformation of plates depending on the location of the support contour and on the availability of hole. In all schemes the plate deforms as a set of identical rigid areas in the form of a trapezium, separated by linear plastic hinges with normal bending moment equal to the limit value. For each of the mechanisms the governing equations are obtained and the conditions of their implementation are defined. The simple analytic expressions are obtained for the limit load and maximum final deflection of plates. The optimal location of support is determined. The optimal support is a support at which the plate has a maximum limit load. The study shows that the inner support is optimal if a plastic hinge is formed on it. We have defined the locations of the support contour at which the plate with a hole will be more durable than a plate without a hole. The solution of the problem extended to the case of plates with polygon contours, into which you can inscribe the circle. The study obtained that these plates have the same respective limit loads, time of deformation and the maximum final deflection which does not depend on the number of sides of the polygon contours and coincides with the same values for circular and annular plate. Numerical examples are given. The solution can be useful in engineering.

**PNRPU Mechanics Bulletin**. 2014;(4):152-177

Method of determining endurance limit stress of cylindrical specimens made of structural steels by residual stresses of “check test piece”

#### Abstract

We consider the criteria of the estimation of surface strengthening influence on the endurance limit stress increase of the solid and hollow cylindrical specimens with cuts under the bend for the symmetrical cycle of loading. We check the possibility of “check test piece” method using forecasting of the tested standard specimens endurance limit stress. The “check test piece” method allows preventing the destruction of standard specimens when the residual stresses are determined experimentally. In this case the endurance limit stress of the standard specimens can be calculated by the residual stresses of “check test piece” that is strengthened simultaneously with the standard specimens by the same technology. We assume the standard specimens and the “check test piece” having the equal isotropic initial strain, the shear strains are small and we do not take them into account for the initial strain determination. We explore the solid and hollow cylindrical specimens of different diameters made of steel 20 and steel 45. The circular cuts of the specimens were strengthened by the anticipatory surface plastic deformation technology using the air/hydraulic shot blasting. The obtained results make it possible to conclude that the compressive residual stresses, calculated for smooth cylindrical specimens by the initial strains of “check test piece”, do not differ much from those that have been determined experimentally (up to 7 %). We compute the increment of the endurance limit stress of the strengthened specimens with cuts by the developed procedure using the mean integral residual stresses criterion. The difference between the calculated increase of the endurance limit stress of cylindrical specimens with cuts under the bend for the symmetrical cycle of loading and the experimental data is not more then 11 %.

**PNRPU Mechanics Bulletin**. 2014;(4):178-196

ELASTIC INTERACTION OF GRAINS IN POLYCRYSTALLINE MATERIALS

#### Abstract

The method of solution of the problem of elastic interaction of grains in polycrystals based on field theory approach is proposed. The solution of boundary value problem for strains in grains decomposed into two parts - zero order solution, which coresponds to formal absence of intergranular interactions, and the part which responds for this interaction. The zero order solution takes into account the intragrain interaction of strains. Intergranular interaction is considered as perturbation to zero order solution or small parameter of the task. Representation of the exact solution in the form of infinite series of perturbation theory (in field theory terminology) transforms the integral equation of initial boundary values problem into infinite consequence of interconnected systems of integral equations for corrections of different orders to zero order solution. From mathematical point of view it is analogous to situation in the theory of many interacting particles in statistical physics (the chain of Bogolubov equations for multiparticles distribution functions) and quantum theory of interacting fields (chain of Dyson-Shwinger equations for field Green's functions). The neglection of inhomogenuity of strains within individual grain (but taking into account the difference of strains in different grains) reduces the infinite consequence of integral equations to infinite chain of interconnected linear algebraic equations systems which can be solved by contemporary numerical procedures. Coefficients of linear equations depend on shape and positional relationship of the grains, id est they are determined by microstructure of material. Interaction with nearer and more remote grains is taken into account. The numerical evaluations for influence of intergranular interaction on deformation fields in the closest neighbours approximation, adopted from quantum condensed matter theory, are obtained.

**PNRPU Mechanics Bulletin**. 2014;(4):197-220

Eksperimental'noe issledovanie vliyaniya vysokotemperaturnoy obrabotki tkanogo napolnitelya na prochnostnye svoystva uglerodnykh kompozitov

#### Abstract

Исследуется поведение углеродного композита (УКМ) в процессе механических испытаний на растяжение и сжатие. Образцы для испытаний изготавливались из углеродных заготовок с разных технологических этапов производства углерод-углеродного композита. В качестве армирующего компонента материала использовались два типа наполнителя, один из которых подвергался дополнительной высокотемпературной обработке. Механические испытания проводились на универсальной электромеханической системе Instron 5882 с использованием бесконтактного видеоэкстензометра AVE Instron для записи продольных деформаций в образце. В процессе испытаний проводилась непрерывная запись сигналов акустической эмиссии (АЭ) системой AMSY-6 с использованием высокочастотных преобразователей с рабочим диапазоном частот 450-1150 кГц. Во избежание записи шумов, возникающих от рабочих частей испытательной машины, проводилась фильтрация сигналов по низкочастотной компоненте. Также проводилась синхронизация системы записи сигналов АЭ с видеоэкстензометром и установкой для механических испытаний. По полученным результатам строились графики зависимостей нагрузки и параметров сигналов АЭ (пиковая амплитуда, энергетический параметр) от перемещений, а также распределения пиковых амплитуд от количества сигналов. На основании значений параметров выделялись основные механизмы разрушения композита. В зависимости от технологического этапа и типа используемого наполнителя у образцов выявлены различия в процессе накопления повреждений. Сделано предположение, что у материала на основе наполнителя, подвергаемого дополнительной высокотемпературной обработке, наблюдается худшая адгезия компонентов, чем у материала без дополнительной обработки наполнителя. Также выявлено, что изучение прочностных свойств и механизмов разрушения заготовок УКМ с начальных этапов изготовления позволяет спрогнозировать поведение готового материала, без прохождения дорогостоящего и длительного процесса производства.

**PNRPU Mechanics Bulletin**. 2014;(4):221-239

Strategy of damping vibration of structures with piezoelectric elements and external electrical circuits and their experimental illustration

#### Abstract

This paper presents basic concepts of smart-materials and strategies of vibration damping structures with piezoelectric elements and external circuits, based on the well-known works. Different variants of external passive electrical circuits consisting of resistors, inductance and capacitance, and the main circuit of active electric circuits with feedback and feed forward adaptive filtering are considered. The authors presented the results of experimental studies on damping vibrations of cantilever steel beam with different types of external passive electrical circuits and the locations of piezoelectric elements. Research results lead to the following conclusions: the use of resonant circuits for the damping of vibrations of the structure is more effective than the resistive circuits; vibration damping increases when piezoelectric elements are placed in the zones with the largest gradient forming; parallel connection to an external electrical circuit of additional piezoelectric elements allows achieving a greater degree of vibration damping and decrease of values related to optimal inductance and resistance; there are modes of vibration of structures, in which there are no sufficient in size electric potential at the surface of the piezoelectric elements, to be able to use the piezoelectric damping of the oscillation mode; optimal parameters of a shunt circuit for the corresponding vibration modes do not depend on the amplitude of the oscillations determined by levels of external influence. The paper presents the results of the experiment on damping vibrations at impact loading through the use of the active external electric circuit in case of feedback control.

**PNRPU Mechanics Bulletin**. 2014;(4):240-270

Characterization of low velocity local impact of sandwich panels

#### Abstract

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.

**PNRPU Mechanics Bulletin**. 2014;(4):271-282