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

Yevtushenko, A.A.; Topczewska, Katarzyna; Zamojski, Przemysław

doi:10.3390/ma16062265

Cited by 7 publications

(13 citation statements)

References 44 publications

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“…to the transformed solution in Equations ( 25)-( 31), and by carrying out the integration on the plane of the complex variable p, according to the methodology described in the articles [10,35], with account of the following relations [40]:…”

Section: Exact Solutionmentioning

confidence: 99%

“…Usage of the exact solutions (35) and (36) requires the numerical integration over a semi-limited interval, which requires the application of appropriate, sometimes complex, software. In this section, the asymptotic solutions (for small and large values of the Fourier number τ) will be developed, which are devoid of this problem.…”

Section: Some Special Cases Of Solutionmentioning

confidence: 99%

“…Many computational models have been recently developed to evaluate the thermal response of FGMs, which is crucial for predicting failure mechanisms and designing friction couples [24][25][26][27][28][29][30][31][32][33]. Comprehensive reviews of the literature on thermal and thermoelastic problems of friction for functionally graded materials are given in our previous articles [34][35][36]. In these studies, the authors obtained the solutions of the boundary-value problems of heat conduction for a coating (layer) made of FGM with a heated surface that was ideally thermally connected to the surface of a homogeneous substrate (half-space) [35].…”

Section: Introductionmentioning

confidence: 99%

“…Comprehensive reviews of the literature on thermal and thermoelastic problems of friction for functionally graded materials are given in our previous articles [34][35][36]. In these studies, the authors obtained the solutions of the boundary-value problems of heat conduction for a coating (layer) made of FGM with a heated surface that was ideally thermally connected to the surface of a homogeneous substrate (half-space) [35]. Then, the process of heat generation in a friction system consisting of a homogeneous semi-space sliding on the surface of the FGM strip applied to a homogeneous semi-space was investigated [36].…”

Section: Introductionmentioning

confidence: 99%

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Effect of Convective Cooling on the Temperature in a Friction System with Functionally Graded Strip

et al. 2023

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An exact solution of the boundary-value problem of heat conduction was obtained with consideration of heat generation due to friction and convective cooling for the strip/semi-space system. Analytical solutions to this problem are known for the case with both friction elements made of homogeneous materials or a composite layer with a micro-periodic structure. However, in this study, the strip is made of a two-component functionally gradient material (FGM). In addition, the exact, asymptotic solutions were also determined at small and large values of the Fourier number. By means of Duhamel’s theorem, it was shown that the developed solution for a constant friction power allows to obtain appropriate solutions with a changing time profile of this value during heating. Numerical analysis in dimensionless form was carried out for the FGM (ZrO2—Ti-6Al-4V) strip in combination with the cast iron semi-space. The influence of the convective cooling intensity (Biot number) on the temperature field in the considered friction system was investigated. The developed mathematical model allows for a quick estimation of the maximum temperature of systems, in which one of the elements (FGM strip) is heated on the friction surface and cooled by convection on the free surface.

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Section: Exact Solutionmentioning

confidence: 99%

Section: Some Special Cases Of Solutionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Effect of Convective Cooling on the Temperature in a Friction System with Functionally Graded Strip

et al. 2023

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“…However, modern friction elements can have far more complicated internal structure, such as functionally graded materials (FGMs), which have continuously changing properties throughout the volume of material [ 24 ]. Some analytical solutions to the heat conduction problems formulated for braking systems with functionally graded friction materials have already been obtained in [ 25 , 26 , 27 , 28 , 29 , 30 ]. However, these studies concerned simpler geometrical schemes, including a two FGM semi-spaces system [ 25 , 26 ]; functionally graded semi-infinite body coupled with homogeneous element [ 27 , 28 ]; and a one-element system consisting of a heating semi-space with deposited functionally graded coating, heated by the frictional heat flux on the friction surface [ 29 ].…”

Section: Introductionmentioning

confidence: 99%

Influence of Functionally Graded Protective Coating on the Temperature in a Braking System

2023

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A mathematical model of heat generation due to friction in a disc–pad braking system was developed with consideration of a thermal barrier coating (TBC) on the friction surface of the disc. The coating was made of functionally graded material (FGM). The three-element geometrical scheme of the system consisted of two homogeneous half-spaces (pad and disc) and a functionally graded coating (FGC) deposited on the friction surface of the disc. It was assumed that the frictional heat generated on the coating-pad contact surface was absorbed to the insides of friction elements along the normal to this surface. Thermal contact of friction between the coating and the pad as well as the heat contact between the coating and the substrate were perfect. On the basis of such assumptions, the thermal friction problem was formulated, and its exact solution was obtained for constant and linearly descending specific friction power over time. For the first case, the asymptotic solutions for small and large values of time were also found. A numerical analysis was performed on an example of the system containing a metal ceramic (FMC-11) pad, sliding on the surface of a FGC (ZrO2–Ti-6Al-4V) applied on a cast iron (ChNMKh) disc. It was established that the application of a TBC made of FGM on the surface of a disc could effectively reduce the level of temperature achieved during braking.

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Thermal Stress Analysis for Functionally Graded Plates with Modulus Gradation, Part II

Baytak,

Tosun,

Ipek

et al. 2024

Exp Mech

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Background The gradation of thermal expansion coefficient was analyzed in the earlier study. The analytical formulation derived here, which is quite different, should be validated to understand the thermal stress distribution in a laminated composite and functionally graded material. Besides this solution, a validated numerical model can also be used to optimize the material gradation of plates in terms of sustainability. Objective To validate the analytical formulation derived here, an experimental model is presented to understand the thermal stress concentration for functionally graded and laminated composite plates. A numerical model is also validated to extend to understand the effects of the number of layers, the thickness of a layer, the gradation function, the ratio of elastic moduli, and the coating. Methods The experimental problems in the production of the experimental models with layers of different elastic moduli are discussed here. In the experimental analysis, a three-dimensional photoelastic stress analysis of two- and four-layer composite plate was used to mechanically model the thermal expansion. The analytical solution for the thermal stress in a free plate was derived by the strain suppression method based on the principle of superposition. The numerical models were analyzed using finite element software. The step variation in the experiment was used as a reference point for a continuous or multi-layer (> 2) step variation of material coefficients in the models. Results The variation of stress concentration is shown for various cases of laminated and continuous gradations of elastic modulus. The four-layer experimental model provides the difference in thermal stress distribution as a result of a layered coating. The validated analytical and numerical models provide reasonable results. An empirical formula to optimize the material gradation in terms of elastic modulus is derived. Conclusions The experimental model can be used to analyze thermal stress in functionally graded materials. The gradations of the material in the plate or the coating of the plates can be optimized by the validated analytical and numerical models. The empirical formula can be used to determine the elastic modulus of the coating to minimize the stress concentration.

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

Cited by 7 publications

References 44 publications

Effect of Convective Cooling on the Temperature in a Friction System with Functionally Graded Strip

Effect of Convective Cooling on the Temperature in a Friction System with Functionally Graded Strip

Influence of Functionally Graded Protective Coating on the Temperature in a Braking System

Thermal Stress Analysis for Functionally Graded Plates with Modulus Gradation, Part II

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