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Numerical analysis of fracture behavior of functionally graded materials using 3D-XFEM

Benhamena Ali, Fatima Benaoum, Foudil Khelil, Baltach Abdelghani, Chaouch Mohamed Ikhlef

Advances in Materials Science

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2023

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Vol. 23, nr 3(77)

33--46

EN

This paper presents the numerical evaluation of mixed stress intensity factors (SIFs) and non-singular terms of William's series (T-stress) of functionally graded materials (FGMs) using three-dimensional extended finite element method (3D-XFEM). Four-point bending specimen with crack perpendicular to material gradation have been used in this investigation in order to study the effect of some parameters (crack position, crack size, specimen thickness) on the failure of FGMs materials. The fracture parameters (KI KII, phase angle ψ and T-stress) obtained by the present simulation are compared with available experimental and numerical results. An excellent correlation was found of the 3D-XFEM simulations with those available in the literature. From the numerical results, a fitting procedure is performed in order to propose an analytical formulation and subsequently are validated against the 3D-XFEM results.

2

Thermomechanical responses of functionally graded cylinders

Eker Mehmet, Yarımpabuç Durmuş

Journal of Applied Mathematics and Computational Mechanics

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2021

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Vol. 20, nr 4

19--28

EN

In this study, thermal and mechanical stresses in hollow thick-walled functionally graded (FG) cylinders is presented under the convection boundary condition. The convective external condition and constant internal temperature in hollow cylinders are investigated. Inhomogeneous material properties produce irregular and two-point linear boundary value problems that are solved numerically by the pseudospectral Chebyshev method. The displacement and thermal stress distributions are examined for two different material couples under particular boundary conditions that are similar to their real engineering applications.Results have demonstrated that the pseudospectral Chebyshev method has low computation costs, high accuracy and ease of implementation and can be easily customized to such engineering problems.

3

Free vibration analysis of imperfect functionally graded sandwich plates: analytical and experimental investigation

Njim E.K., Bakhy S.H., Al-Waily M.

Archives of Materials Science and Engineering

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2021

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Vol. 111, nr 2

49--65

EN

Purpose: This paper develops a new analytical solution to conduct the free vibration analysis of porous functionally graded (FG) sandwich plates based on classical plate theory (CPT). The sandwich plate made of the FGM core consists of one porous metal that had not previously been taken into account in vibration analysis and two homogenous skins. Design/methodology/approach: The analytical formulations were generated based on the classical plate theory (CPT). According to the power law, the material properties of FG plates are expected to vary along the thickness direction of the constituents. Findings: The results show that the porosity parameter and the power gradient parameter significantly influence vibration characteristics. It is found that there is an acceptable error between the analytical and numerical solutions with a maximum discrepancy of 0.576 % at a slenderness ratio (a/h =100), while the maximum error percentage between the analytical and experimental results was found not exceeding 15%. Research limitations/implications: The accuracy of analytical solutions is verified by the adaptive finite elements method (FEM) with commercial ANSYS 2020 R2 software. Practical implications: Free vibration experiments on 3D-printed FGM plates bonded with two thin solid face sheets at the top and bottom surfaces were conducted. Originality/value: The novel sandwich plate consists of one porous polymer core and two homogenous skins which can be widely applied in various fields of aircraft structures, biomedical engineering, and defense technology. This paper presents an analytical and experimental study to investigate the free vibration problem of a functionally graded simply supported rectangular sandwich plate with porosities. The objective of the current work is to examine the effects of some key parameters, such as porous ratio, power-law index, and slenderness ratio, on the natural frequencies and damping characteristics.

4

Impact of vibro-compaction on microstructure and properties of aluminium matrix composite with SiC particles

Godzierz Marcin, Olszówka-Myalska Anita, Dudzińska Karolina, Urbiczek Mateusz

Inżynieria Materiałowa

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2019

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Vol. 40, nr 6

140--145

EN

In the paper, the effect of vibro-compaction in processing of sintered SiCp – aluminium matrix composite was presented. The composite with 15% vol. of SiCp, obtained with three stages: vibro-compaction with use of different amplitude (0.75 mm, 1.125 mm and 1.5 mm), cold pressing and pressure less sintering. The obtained composites were characterized by porosity measurements, microhardness, quantitative metallography analysis and dry sliding tests. It was proved that the application of chosen compaction method, for powder mixture consisting of powders with different density (Al and SiC), allows to obtain graded structure composite. An increase of SiC particles volume fraction as well as microhardness increase was observed towards the bottom of the sample. The most beneficial effect, in SiCp distribution and microhardness values, was noted for the sample were the amplitude of vibro-compaction was 1.5 mm. Moreover, the tribological examinations showed differences in friction coefficients and mass losses for opposite surfaces of composite samples, due to different SiCp volume fraction across the sample. The vibro-compacted material revealed lower porosity, higher mean value of friction coefficient and lower mass loss comparing to the reference composite.

PL

Głównym obszarem zastosowania kompozytów na osnowie aluminium zbrojonych cząstkami ceramicznymi są skojarzenia ślizgowe i cierne, takie jak grupa tłokowo-cylindrowa maszyn tłokowych i łożyska ślizgowe, a w przemyśle samochodowym klocki hamulcowe, sprzęgła, przekładnie pasowe czy bloki silnika. W wielu elementach nie są wymagane takie same właściwości tribologiczne materiału na całym przekroju lub nie jest technologicznie możliwe uzyskanie ekstremalnie wysokich parametrów użytkowych związanych z dużą zawartością cząstek w całej objętości. W takich przypadkach rozwiązaniem mogą być materiały charakteryzujące się gradientowym rozmieszczeniem cząstek ceramicznych i istnieje wiele koncepcji technologicznych pozwalających uzyskać ten typ mikrostruktury. W pracy przedstawiono możliwość uzyskania metodą metalurgii proszków struktury gradientowej w kompozycie Al–SiCp, dla udziału zbrojenia w mieszaninie wyjściowej 15% obj. Założono, że gradientowe zróżnicowane rozmieszczenie zbrojenia w osnowie powstanie dzięki różnicy gęstości komponentów (Al 2,7 g/cm3, SiC 3,21 g/cm3), podczas zgęszczania wibracyjnego, dzięki bardziej intensywnemu w porównaniu z proszkiem aluminium przemieszczaniu się cząstek SiC w dół formy.

5

Elastic and Viscoelastic Stresses of Nonlinear Rotating Functionally Graded Solid and Annular Disks with Gradually Varying Thickness

Allam M. N. M., Tantawy R., Yousof A., Zenkour A. M.

Archive of Mechanical Engineering

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2017

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Vol. LXIV, nr 4

423--440

EN

Analytical and numerical nonlinear solutions for rotating variable-thickness functionally graded solid and annular disks with viscoelastic orthotropic material properties are presented by using the method of successive approximations.Variable material properties such as Young’s moduli, density and thickness of the disk, are first introduced to obtain the governing equation. As a second step, the method of successive approximations is proposed to get the nonlinear solution of the problem. In the third step, the method of effective moduli is deduced to reduce the problem to the corresponding one of a homogeneous but anisotropic material. The results of viscoelastic stresses and radial displacement are obtained for annular and solid disks of different profiles and graphically illustrated. The calculated results are compared and the effects due to many parameters are discussed.

6

Calculation of Stress Intensity Factor for an Internal Circumferential Crack in a Rotating Functionally Graded Thick-Walled Hollow Circular Cylinder under Thermal Shock

Ghafoor E. M. R., Rokhi M. M.

Archive of Mechanical Engineering

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2017

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Vol. LXIV, nr 4

455--479

EN

In this article, the fracture behavior of functionally graded thick-walled cylinder under thermo-mechanical shock is investigated. For this purpose, classical coupled thermoelastic equations are used in calculations. First, these equations are discretized with extended finite element method (XFEM) in the space domain and then they are solved by the Newmark method in the time domain. The most general form of interaction integral is extracted for axially symmetric circumferential crack in a cylinder under thermal and mechanical loads in functionally graded materials and is used to calculate dynamic stress intensity factors (SIFs). The problem solution has been implemented in MATLAB software.

7

Characterization of the starting materials for functionally graded thermoelectric materials for pseudobinary system of Bi2Te3-Sb2Te3

Januszko K., Chetty R., Mashimo T., Wojciechowski K.T.

Mechanik

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2016

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R. 89, nr 5-6

522--523

EN

Samples of Bi-Sb-Te system were prepared by solid state synthesis from pure elements, microstructure and thermoelectric properties were characterized. From obtained powders segmented samples were construct-ed in order to confirm change of the thermoelectric properties with composition. Segmented element is expected to have better efficiency.

PL

Próbki otrzymane w wyniku syntezy z czystych pier-wiastków zostały scharakteryzowane pod względem mikrostruktury i właściwości termoelektrycznych. Z otrzymanych proszków skonstruowano element seg-mentowy i potwierdzono zmianę właściwości termoelektrycznych ze zmianą składu chemicznego. Przewiduje się podwyższoną sprawność takiego elementu.

8

Zastosowanie metody elementów brzegowych dla środowisk niejednorodnych na przykładzie badania zawilgocenia murów

Pańczyk M., Sikora J.

Zeszyty Naukowe. Elektryka / Politechnika Łódzka

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2015

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z. 126

117--124

PL

Artykuł prezentuje opis matematyczny implementacji środowisk niejednorodnych w metodzie elementów brzegowych. Wyniki obliczeń porównane są z realnymi pomiarami zawilgocenia zbudowanego w warunkach laboratoryjnych muru, wykonanymi z użyciem 26 elektrodowego tomografu impedancyjnego i klasycznej metody suszarkowo-wagowej.

EN

The boundary element method implementation used to find tomographic image of damped wall humidity distribution is presented. Damped wall represents nonhomogeneous media where humidity has a spatial distribution that varies with two coordinates. Real measurements were taken and function coefficients where found using boundary element method, verified again by finite element method.

9

Finite element formulation for the large-amplitude vibrations of FG beams

Javid M., Hemmatnezhad M.

Archive of Mechanical Engineering

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2014

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Vol. LXI, nr 3

469--482

EN

On the basis of Euler-Bernoulli beam theory, the large-amplitude free vibration analysis of functionally graded beams is investigated by means of a finite element formulation. The von Kármán type nonlinear strain-displacement relationship is employed where the ends of the beam are constrained to move axially. The material properties are assumed to be graded in the thickness direction according to the powerlaw and sigmoid distributions. The finite element method is employed to discretize the nonlinear governing equations, which are then solved by the direct numerical integration technique in order to obtain the nonlinear vibration frequencies of functionally graded beams with different boundary conditions. The influences of power-law index, vibration amplitude, beam geometrical parameters and end supports on the free vibration frequencies are studied. The present numerical results compare very well with the results available from the literature where possible.

PL

W oparciu o teorię Eulera-Bernouliego przeprowadzono analizę wielkoamplitudowych drgań belki gradientowej posługując się metodą elementów skończonych. Związek między odkształceniem i przemieszczeniem, typu von Kármána, zastosowano tam, gdzie końce belki są utwierdzone i mogą poruszać się osiowo. Zakłada się, że właściwości materiału zmieniają się w kierunku poprzecznym (grubości) zgodnie z funkcją potęgową lub sigmoidalną. Metoda elementów skończonych jest zastosowana w celu dyskretyzacji nieliniowych równań sterujących, z których po rozwiązywaniu metodą bezpośredniego całkowania numerycznego wyznacza się częstotliwości drgań nieliniowych belki gradientowej dla różnych warunków brzegowych. Badany jest wpływ wykładnika funkcji, amplitudy drgań, geometrycznych parametrów belki i podparcia końców na częstotliwości drgań swobodnych. Wyniki numeryczne, przedstawione w artykule, zgadzają się dobrze z wynikami podawanymi w dostępnej literaturze.