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1

Piezoelectric effect on thermoelastic Lamb waves in functionally graded plates

Wang X., Ren X., Yu J., Zhou H., Zhang X., Leng J

Archives of Mechanics

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2023

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Vol. 75, nr 1-2

3--26

EN

Based on the Lord–Shulman thermoelectric elasticity theory, the piezoelectric effect on the thermoelastic Lamb wave propagation in the functionally graded material (FGM) plate is investigated. The coupled wave equations are solved by employing the Legendre polynomial series approach (LSPA), which poses the advantages of small scale of eigenvalues matrix and a convenient solution. It can directly obtain the complex wave number solutions without iteration. The obtained complex solutions, which represent the wave propagation and attenuation, are compared with those available data. Numerical examples show that the influence of gradient is profound. Results indicate that the piezoelectric effects on attenuation with the open and closed circuit condition are consistent for the S0 and S1 modes, but are inconsistent for the A0 and A1 modes. Although the piezoelectric effect is weak on the dispersion and attenuation of thermal waves, it is notable for their physical field distributions. In addition, the relaxation time is critical to electric displacements of a thermal wave mode, but is not essential for those of Lamb-like modes. The results can be used for the optimization of thermo-electric-elastic coupling structures.

2

Numerical study of the mechanical behaviour and damage of fgm bent pipes under internal pressure and combined bending moment

Houari Amin, Madani Kouider, Amroune Salah, Zouambi Leila, Elajrami Mohamed

Acta Mechanica et Automatica

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2023

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Vol. 17, no. 3

460--468

EN

The main objective of this work is the numerical prediction of the mechanical behaviour up to the damage of the bends of the functionally graded material (FGM) type ceramic/metal pipes. Firstly, the effective elastoplastic proper-ties of bent FGM pipes were determined using the homogenisation law by the Mori–Tanaka models for the elastic part and TTO (Tamura-Tomota-Ozawa) for the plastic part based on a rule of mixtures per function in the form of a power law. Our work also aims at the use of a meshing method (UMM) to predict the behaviour of the FGM by finite element in the mesh of the model. The analysis was performed using the UMM technique for different loading cases and volume fraction distribution. Two stages are necessary for the analysis of the damage: the first is the model of initiation of the damage established by the criterion of maximum deformation named MAXPE and the second is criterion of the energy of the rupture according to the theory Hillerborg used to determine damage evolution. Both stages involve a 3D finite element method analysis. However, for damage, the XFEM technique was used in our UMM method to predict crack initiation and propagation in FGM pipe bends. The results of the numerical analysis concerning the mechanical behavior showed, that if the nature of the bent pipes is in FGM, a good reduction of the various stresses compared to those where the nature of the pipe is metallic material. The results were presented in the form of a force–displacement curve. The validation of the proposed numerical methodology is highlighted by comparisons of current results with results from the literature, which showed good agreement. The analysis took into account the effect of the main parameters in a bent FGM pipe under internal pressure and bending moment on the variation of the force–strain curves.

3

Free vibration analysis of FGM stepped nanostructures using nonlocal dynamic stiffness model

Lien Tran Van, Duc Ngo Trong, Dinh Tran Binh, Dat Pham Tuan

Journal of Theoretical and Applied Mechanics

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2022

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Vol. 60 nr 2

279--292

EN

A nonlocal Dynamic Stiffness Model (DSM) for free vibration analysis of Functionally Graded Material (FGM) stepped nanostructures based on the Nonlocal Elastic Theory (NET) is proposed. An exact solution to the equation of motion of a nanobeam element according to the Timoshenko beam theory, NET, and taking into account position of the neutral axis is constructed. Nondimensional frequencies and mode shapes of complete FGM stepped nanostructures are easily obtained using the nonlocal DSM. Numerical results are presented to show significance of the material distribution profile, nonlocal effect, and boundary conditions on free vibration of nanostructures.

4

On thermo-mechanical bending response of porous functionally graded sandwich plates via a simple integral plate model

Mahmoud S. R., Ghandourah E., Algarni Ali, Balubaid Mohammed, Tounsi Abdelouahed, Bourada Fouad

Archives of Civil and Mechanical Engineering

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2022

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Vol. 22, no. 4

art. no. e186, 2022

EN

This work investigates the thermo-mechanical bending response of porous functionally graded sandwich plates which can be considered for military and civil use. Integral four-unknown shear deformation theory is proposed to present the kinematic of the structure. The differential equilibrium equations are determined via the principle of virtual work and solved with Navier’s procedure. The influence of porosity parameters is examined to explain the structural integrity of such structures that can be utilized in military and civil industries. In addition, a detailed parametric investigation is performed to highlight the impact of the “volume fraction variation”, “geometrical ratios” and “thermal load” on thermo-mechanical bending response of the porous functionally graded sandwich plates.

5

Axisymmetric thermoelastic analysis of long cylinder made of FGM reinforced by aluminum and silicone carbide using DQM

Saeedi S., Kholdi M., Loghman A., Ashrafi H., Arefi M.

Archives of Civil and Mechanical Engineering

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2022

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Vol. 22, no. 1

art. no. e48, 2022

EN

In this study, the thermoelastic stress analysis of a thick-walled cylinder made of functionally graded material (FGM) is investigated. The FGM is assumed a mixture of aluminum and silicone carbide in which the effective material properties are estimated through modified mixture law. Temperature distribution is obtained using the solution of one-dimensional heat transfer equation with the assumption of boundary condition. Solution procedure is developed based on the differential quadrature method. Effect of FGM characteristics such as percentages of ceramic particles at the outer side of cylinder's wall, and power of ceramic particles distribution, on the distribution of stress components, and temperature along the thickness are presented. In addition, stress distribution arising from the thermomechanical loading on structure, along the thickness are is investigated. Verification of the method, formulation and solution procedure is confirmed through comparison with available results in literature.

6

On the nonlocal interaction range for stability of nanobeams with nonlinear distribution of material properties

Jankowski Piotr

Acta Mechanica et Automatica

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2022

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Vol. 16, no. 2

151--161

EN

The present study analyses the range of nonlocal parameters’ interaction on the buckling behaviour of nanobeam. The intelligent nonhomogeneous nanobeam is modelled as a symmetric functionally graded (FG) core with porosity cause nonlinear distribution of material parameters. The orthotropic face-sheets are made of piezoelectric materials. These kinds of structures are widely used in nanoelectromechanical systems (NEMS). The nanostructure model satisfies the assumptions of Reddy third-order beam theory and higher-order nonlocal elasticity and strain gradient theory. This approach allows to predict appropriate mechanical response of the nanobeam regardless of thin or thick structure, in addition to including nano-sized effects as hardening and softening. The analysis provided in the present study focuses on differences in results for nanobeam stability obtained based on classical and nonlocal theories. The study includes the effect of diverse size-dependent parameters, nanobeams’ length-to-thickness ratio and distributions of porosity and material properties through the core thickness as well as external electro-mechanical loading. The results show a dependence of nonlocal interaction range on geometrical and material parameters of nanobeam. The investigation undertaken in the present study provides an interpretation for this phenomenon, and thus aids in increasing awareness of nanoscale structures’ mechanical behaviour.

7

Elastic solutions based on the Mori-Tanaka scheme for pressurized functionally graded cylinder

Eker Mehmet, Yarımpabuç Durmu, Yıldırım Ali, Çelebi Kerimcan

Journal of Applied Mathematics and Computational Mechanics

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2020

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Vol. 19, nr 4

57--68

EN

In this paper, an elastic analysis of a thick-walled functionally graded cylinder subjected to internal pressure is examined. Material properties for the isotropic material are estimated to obey the Mori-Tanaka homogenization scheme through the thickness. The resulting two-point irregular boundary value problem is solved by the pseudospectral Chebyshev method that converts the boundary value problem to the system of equations, which can be solved by any appropriate decomposition method. Benchmark solutions are used to validate the method. The effect of the arbitrarily chosen volume fraction index is demonstrated for stress and displacement distributions. The effective stresses for different inner radius and volume fraction index are also discussed.

8

Manufacturing of ZrO2-Ni graded composites via centrifugal casting in the magnetic field

Wachowski M., Kosturek R., Winkler H., Miazga A., Lada P., Kaszuwara W., Konopka K., Zygmuntowicz J.

Bulletin of the Polish Academy of Sciences. Technical Sciences

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2020

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Vol. 68, nr 3

539--545

EN

The paper presents the possibility of fabricating ceramic-metal composites by an innovative method of centrifugal slip casting in the magnetic field. It was examined whether the use of this method would allow obtaining a gradient concentration of metal particles in the ceramic matrix. In the applied technique, the horizontal rotation axis was used. The study investigated the effect of solid phase content on the properties and microstructure of the products. Water-based suspensions with 35, 40, 45 and 50 vol.% of solid-phase content were prepared with 10 vol.% additional of nickel powder. The viscosity of prepared slurries was considered. The gradient distribution of nickel particles in the zirconia matrix was observed on SEM. Vickers hardness of ZrO2-Ni composites has been measured. The research revealed that the physical properties depend on the volume fraction of solid content and increase as the volume of solid content increases.

9

Transient analysis of transversely functionally graded Timoshenko beam (TFGTB) in conjunction with finite element method

Khafaji Salwan Obaid Waheed, Al-Shujairi Mohammed A., Aubad Mohammed Jawad

Archive of Mechanical Engineering

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2020

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LXVII, nr 3

299--321

EN

In this work, transient and free vibration analyses are illustrated for a functionally graded Timoshenko beam (FGM) using finite element method. The governing equilibrium equations and boundary conditions (B-Cs) are derived according to the principle of Hamilton. The materials constituents of the FG beam that vary smoothly along the thickness of the beam (along beam thickness) are evaluated using the rule of mixture method. Power law index, slenderness ratio, modulus of elasticity ratio, and boundary conditions effect of the cantilever and simply supported beams on the dynamic response of the beam are studied. Moreover, the influence of mass distribution and continuous stiffness of the FGM beam are deeply investigated. Comparisons between the current free vibration results (fundamental frequency) and other available studies are performed to check the formulation of the current mathematical model. Good results have been obtained. A significant effect is noticed in the transient response of both simply supported and cantilever beams at the smaller values of the power index and the modulus elasticity ratio.

10

Stress and deformation analysis of clamped functionally graded rotating disks with variable thickness

Thawait Amit K., Sondhi Lakshman, Sanyal Shubhashis, Bhowmick Shubhankar

Mechanics and Mechanical Engineering

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2019

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Vol. 23, nr 1

202--211

EN

The present study reports the linear elastic analysis of variable thickness functionally graded rotating disks. Disk material is graded radially by varying the volume fraction ratios of the constituent components. Three types of distribution laws, namely power law, exponential law and Mori-Tanaka scheme are considered on a concave thickness profile rotating disk, and the resulting deformation and stresses are evaluated for clamped-free boundary condition. The investigation is carried out using element based grading of material properties on the discretized elements. The effect of grading on deformation and stresses is investigated for each type of material distribution law. Further, a comparison is made between different types of distributions. The results obtained show that in a rotating disk, the deformation and stress fields can be controlled by the distribution law and grading parameter n of the volume fraction ratio.

11

Efficient numerical modeling of functionally graded shell mechanical behavior

Koubaa Sana, Mars Jamel, Dammak Fakhreddine

Applied Computer Science

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2019

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Vol. 15, no 1

84--94

EN

Numerical analysis of the static bending and free vibration mechanical behavior of FGM are performed using the UMAT-USDFLD subroutines in ABAQUS software. Different combinations of geometries, mechanical loading and boundary conditions are adopted. The material properties according to the coordinates of the integration points are defined in the developed numerical model. The First Order Deformation Theory is used for thin and moderately thick FG shells analysis. The accuracy and the robustness of the numerical model are illustrated through the solution of several non trivial structure problems. The proposed numerical procedure is significantly efficient from the computational point of view.

12

Zagadnienie zakrzywionej anizotropowej oraz funkcjonalnie gradowanej powłoki poddanej działaniu pola temperatury

Szubartowski D.

Zeszyty Naukowe Politechniki Rzeszowskiej. Mechanika

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2018

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z. 90 [298], nr 2

237--244

PL

Praca dotyczy problematyki zakrzywionej powłoki wykonanej z anizotropowego materiału o funkcyjnej gradacji. W rachunku wykorzystano koncepcję tensora krzywizny Riemanna-Christoffela wzbogaconą o wpływ pola temperatury przez obecność tensora właściwości termicznych. W ramach wykonanych obliczeń różnica wektora poddanego koneksji afinicznej wzdłuż infinitezymalnego czworokąta wyraża się, zależnie od drogi przejścia, sumą zarówno efektu geometrycznego, reprezentowanego tensorem krzywizny Riemanna-Christoffela, jak również efektu termicznego wyrażonego przez symbol krzywizny termicznej.

EN

This work concerns the problem of a curvilinear shell made of anisotropic material with functional gradation. The calculus is based on the concept of the Riemann-Christoffel curvature tensor enhanced by the influence of temperature field through the presence of a thermal tensor. Calculations comprise estimation of the difference of a vector subjected to the affine connection along the infinitesimal quadrangle expressed, correspondingly to the shifting path, by a sum of both the geometric effect, represented by the Riemann-Christoffel curvature tensor, as well as certain symbol of the thermal curvature.

13

Dynamic behavior of sandwich FGM beams

Bouamama M., Refassi K., Elmeiche A., Megueni A.

Mechanics and Mechanical Engineering

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2018

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Vol. 22, nr 4

919--929

EN

This work is consisted to investigate the vibration behavior of FGM beams under different boundary conditions with diverse volume fraction. The main objective in this paper is to study the thickness in influence of the sandwich beams skin on the frequencies of the structures. The classical Euler-Bernoulli theory (CLBT) with assuming that the material properties of the FGM layer will evaluated continuously in the thickness direction according to the power law (P-FGM) is used to derived the equation of motion. The frequencies obtained are compared with the natural frequencies of a two-material and those of the base materials.

14

On axisymmetric heat conduction problem for multilayer graded coated half-space

Perkowski D. M., Kulchytsky-Zhyhailo R., Kołodziejczyk W.

Journal of Theoretical and Applied Mechanics

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2018

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Vol. 56 nr 1

147--156

EN

The technique of integral Hankel transform to find the solution of heat conduction in half-space coated by a multilayered package of homogenous laminae is applied. The half-space is heated by the given heat flux on the boundary surface. The temperature and heat flux distribution in the radial direction is analyzed for two types of coatings: 1) when the heat conductivity coefficient is described by a power or exponential function of the distance to the boundary surface; 2) multilayered coating has a periodic structure.

15

Fabrication of Al2O3-Ni graded composites by centrifugal casting in an ultracentrifuge

Zygmuntowicz J., Zielant D., Suchecki P., Konopka K., Kaszuwara W.

Composites Theory and Practice

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2018

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R. 18, nr 3

174--179

EN

The work explored the possibility of producing Al2O3-Ni gradient composites using non-absorbent molds in a high-speed centrifuge. As a result of the centrifugal force, the mass was compacted and the solvent was separated from the solid part. The influence of rotational speed and the change in the solid phase content in the slurry on the obtained microstructure of the composites was investigated. The produced composites were characterized on the basis of macroscopic observations of the obtained samples immediately after the casting process (green body) and after the sintering process. To determine the gradient of the metallic phase, the observations were made on cross sections of the samples. Densification of the sinters was determined by the Archimedes method. The obtained results showed that using an appropriate correlation of technological parameters, i.e. rotational speed and solid phase content in the slurry, enables the fabrication of Al2O3-Ni composites with a microstructure gradient by the centrifugal casting method using non-absorbent forms. It was found that with an increase in the solid phase content in the mass, a clear boundary is formed which separates the area containing only ceramic (Al2O3) and metallic (Ni) particles.

PL

W ramach pracy zbadano możliwość wytwarzania kompozytów gradientowych Al2O3-Ni z zastosowaniem form nienasiąkliwych. W tym celu zastosowano wirówkę wysokoobrotową. W wyniku działania siły odśrodkowej nastąpiło zagęszczenie masy poprzez odseparowanie rozpuszczalnika od części stałej. Zbadano wpływ prędkości obrotowej oraz zmianę zawartości fazy stałej w masie lejnej na uzyskaną mikrostrukturę kompozytów. Wytworzone kompozyty scharakteryzowano na podstawie obserwacji makroskopowych uzyskanych próbek bezpośrednio po procesie odlewania, jak również po procesie spiekania. Przeprowadzono obserwacje wzdłuż przekroju poprzecznego próbek w celu określenia gradientu rozmieszczenia fazy metalicznej. Zagęszczenie spieków oceniono poprzez pomiar gęstości metodą Archimedesa. Uzyskane rezultaty pokazały, że zastosowanie odpowiedniej kombinacji parametrów technologicznych, tj. szybkości obrotowej oraz zawartości fazy stałej w masie lejnej, umożliwia wytworzenie metodą odlewania odśrodkowego, przy użyciu form nienasiąkliwych, kompozytów Al2O3-Ni z gradientem mikrostruktury. Stwierdzono, że wraz ze wzrostem zawartości fazy stałej w masie lejnej powstaje wyraźna granica rozdzielająca obszar zawierający cząstki ceramiczne (Al2O3) oraz metaliczne (Ni).

16

The analysis of non-linear free vibration of FGM nano-beams based on the conformable fractional non-local model

Rahimi Z., Sumelka W., Shafiei S.

Bulletin of the Polish Academy of Sciences. Technical Sciences

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2018

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Vol. 66, nr 5

737--745

EN

Continuum models generalized by fractional calculus are used in different mechanical problems. In this paper, by using the conformable fractional derivative (CFD) definition, a general form of Eringen non-local theory as a fractional non-local model (FNM) is formulated. It is then used to study the non-linear free vibration of a functional graded material (FGM) nano-beam in the presence of von-Kármán non-linearity. A numerical solution is obtained via Galerkin and multiple scale methods and effects of the integer and non-integer (fractional) order of stress gradient (in the non-local stress-strain relation) on the ratio of the non-local non-linear natural frequency to classical non-linear natural frequency of simply-supported (S-S) and clamped-free (C-F) FGM nano-beams are presented.

17

Numerical creep analysis of FGM rotating disc with GDQ method

Zharfi H., Toussi H. E.

Journal of Theoretical and Applied Mechanics

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2017

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Vol. 55 nr 1

331--341

EN

Rotating discs are the vital part of many kinds of machineries. Usually, they are operating at relatively high angular velocity and temperature conditions. Accordingly, in practice, the creep analysis is an essential necessity in the study of rotating discs. In this paper, the time dependent creep analysis of a thin Functionally Graded Material (FGM) rotating disc investigated using the Generalized Differential Quadrature (GDQ) method. Creep is described with Sherby’s constitutive model. Secondary creep governing equations are derived and solved for a disc with two various boundary conditions and with linear distribution of SiC particles in pure Aluminum matrix. Since the creep rates are a function of stresses, time and temperature, there is not a closed form solution to these equations. Using a solution algorithm and the GDQ method, a solution procedure for these nonlinear equations is presented. Comparison of the results with other existing creep studies in literature reveals the robustness, precision and high efficiency beside rapid convergence of the present approach.

18

Influence of the transverse inhomogeneity on the nonlinear post-buckling path of compressed FG cylindrical panels

Lykhachova O., Kołakowski Z.

Engineering Transactions

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2017

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Vol. 65, iss. 4

563--577

EN

In this paper, nonlinear stability of axially compressed cylindrical panels simply supported according to two types of boundary conditions (with possible or limited circumferential displacements of unloaded sides) is presented. Panels made of functionally graded materials (FGMs) of two constituents (metallic and ceramic phases) are treated as multi-layered composite structures with transverse inhomogeneity. Volume fractions of ceramics and metal distribution throughout the layer thickness are described by a simple power law. The influence of the transverse inhomogeneity of FGM panels on unsymmetrical stable post-buckling paths is shown. Special attention is paid to effect of the imperfection sign on post-buckling paths of investigated FGM panels. Some validations of the finite element analysis are discussed for isotropic panels compressed according to two (force and kinematic) loading schemes.

19

Some aspects of dynamic coupled response of functionally graded thin-walled columns with square cross-sections under in-plane pulse compression

Kołakowski Z., Teter A.

Journal of Theoretical and Applied Mechanics

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2016

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Vol. 54 nr 2

449--462

EN

The present paper deals with a dynamic coupled response of functionally graded columns with a quadratic cross-section subjected to an in-plane pulse loading. An Al-TiC metal- -ceramic material is applied. It is assumed that functionally graded materials (FGMs) are subject to Hooke’s law. The thin-walled structures are simply supported at the ends. This study is devoted to the stability problem of rectangular dynamic pulse load. The effects of temperature, wave propagation and damping are neglected. In order to obtain the equations of motion of individual plates, the classic laminate plate theory (CLPT) has been modified in such a way that it additionally accounts for all components of inertial forces. A plate model is adopted for the structures. The problem of an interaction of the global mode with the local ones is concerned (i.e., a three-modes approach). Attention has been focused on some unexpected aspects related to dynamic interactive buckling of columns having two axes of the cross-section symmetry. In the present study, a new approach to the description of this phenomenon, based on Koiter’s theory, has been applied.

20

Wear resistance of piston sleeve made of layered material structure: MMC A356R, anti-abrasion layer and FGM interface

Hernik S.

Acta Mechanica et Automatica

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2016

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Vol. 10, no. 3

207--212

EN

The aim of this paper is the numerical analysis of the one of main part of car engine – piston sleeve. The first example is for piston sleeve made of metal matrix composite (MMC) A356R. The second improved material structure is layered. Both of them are comparison to the classical structure of piston sleeve made of Cr-Ni stainless steel. The layered material structure contains the anti-abrasion layer at the inner surface of piston sleeve, where the contact and friction is highest, FGM (functionally graded material) interface and the layer of virgin material on the outer surface made of A356R. The complex thermo-elastic model with Archard's condition as a wear law is proposed. The piston sleeve is modelling as a thin walled cylindrical axisymmetric shell. The coupled between the formulation of thermoelasticity of cylindrical axisymmetric shell and the Archard’s law with functionally changes of local hardness is proposed.