Analytical and numerical methods of solution of three-dimensional problem of elasticity for functionally graded coated half-space

Kulchytsky-Zhyhailo, Roman; Bajkowski, Adam S.

doi:10.1016/j.ijmecsci.2011.10.001

Cited by 22 publications

(6 citation statements)

References 36 publications

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“…, 4-unknown functions of the parameters of integral transforms, which we determine to satisfy boundary conditions in Equations ( 5)- (9), written in transform space. Given that a similar conversion was described in [17], we give only several remarks.…”

Section: Methods Of the Solutionmentioning

confidence: 99%

Tensile Stresses in the Coating with Interlayer under Normal and Tangential Loading

et al. 2022

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In this paper, we obtained the analytic solution of the three-dimensional problem of elasticity concerning non-homogeneous half-space, in which the surface is under normal and tangential loading applied in a circular area. Half-space is composed of the homogeneous body, as well as coatings containing two homogeneous layers: interlayer and top layer. The analysis was carried out in cases where the Young’s modulus of the intermediate layer differed from the Young’s modulus of the substrate and the top layer. We have concentrated on first principal stress analysis. The obtained results can serve as an indication for the design of the composition of coatings in the context of tensile stress.

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Section: Methods Of the Solutionmentioning

confidence: 99%

Tensile Stresses in the Coating with Interlayer under Normal and Tangential Loading

et al. 2022

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“…Besides the thermal resistance, the TBCs can protect them from wear and significantly increase the service life of the friction pair elements. In order to get these features, the hard coatings are applied on the relatively soft substrates [ 2 ]. Metals and alloys are frequently used as a foundation of the coated elements to maintain structural rigidity and strength.…”

Section: Introductionmentioning

confidence: 99%

“…The main issue encountered is concerned with modeling continuously varying gradient of material structure. To overcome this problem, most FGM models use the multi-layered approximation approach [ 2 , 19 , 20 , 22 , 23 , 30 ]. This method relies on a model of graded material heterogeneity by a package of homogeneous layers, which leads to a stepwise change in coating properties along the gradient direction.…”

Section: Introductionmentioning

confidence: 99%

Use of Functionally Graded Material to Decrease Maximum Temperature of a Coating–Substrate System

2023

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A mathematical model for determining the temperature distribution in the system consisting of a coating deposited on the surface of substrate was proposed. The foundation material is homogeneous, while the coating is made of a functionally gradient material (FGM) with thermal conductivity increasing exponentially along the thickness. Heating processes of the outer surface of the coating were considered with a constant and linearly decreasing in time intensity of the heat flux. Such thermal loads are common in thermal problems of friction, particularly regarding frictional heating during braking. An exact (in quadrature) solution of the corresponding boundary-value problems of parabolic heat conduction was obtained. Asymptotic solutions to these problems were also found for small and large values of the Fourier number. Calculations were performed for a coating made of two-component FGM ZrO2—Ti-6Al-4V, applied on a cast iron substrate. In order to explain the effect of FGM on temperature, corresponding analysis was carried out for the coating made of a homogeneous (ZrO2) material.

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“…Other forms of elastic moduli variation were also considered: Altenbach and Eremeyev [11] analysed eigen-vibrations of a functionally graded material with a power law variation that corresponds to a graded distribution of the porosity in the material. Tangential loading of a power-law inhomogeneous layer bonded to a homogeneous half-space was considered by Kulchytsky-Zhyhailo and Bajkowskiy [12]. Awojobi [13] considered a hyperbolic variation of the elastic modulus, which modelled smooth transition of the sub-soil into a rigid bed.…”

Section: Introductionmentioning

confidence: 99%

Characterization of the Functionally Graded Shear Modulus of a Half-Space

et al. 2020

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In this article, a method is proposed for determining parameters of the exponentialy varying shear modulus of a functionally graded half-space. The method is based on the analytical solution of the problem of pure shear of an elastic functionally graded half-space by a strip punch. The half-space has the depth-wise exponential variation of its shear modulus, whose parameters are to be determined. The problem is reduced to an integral equation that is then solved by asymptotic methods. The analytical relations for contact stress under the punch, displacement of the free surface outside the contact area and other characteristics of the problem are studied with respect to the shear modulus parameters. The parameters of the functionally graded half-space shear modulus are determined (a) from the coincidence of theoretical and experimental values of contact stresses under the punch and from the coincidence of forces acting on the punch, or (b) from the coincidence of theoretical and experimental values of displacement of the free surface of the half-space outside the contact and coincidence of forces acting on the punch, or (c) from other conditions. The transcendental equations for determination of the shear modulus parameters in cases (a) and (b) are given. By adjusting the parameters of the shear modulus variation, the regions of “approximate-homogeneous” state in the functionally graded half-space are developed.

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Analytical and numerical methods of solution of three-dimensional problem of elasticity for functionally graded coated half-space

Cited by 22 publications

References 36 publications

Tensile Stresses in the Coating with Interlayer under Normal and Tangential Loading

Tensile Stresses in the Coating with Interlayer under Normal and Tangential Loading

Use of Functionally Graded Material to Decrease Maximum Temperature of a Coating–Substrate System

Characterization of the Functionally Graded Shear Modulus of a Half-Space

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