An extension of the Hertz theory for 2D coated components

Liu, Shanliangzi; Peyronnel, A.; Wang, Q.J.; Keer, Leon M.

doi:10.1007/s11249-005-3611-z

Cited by 41 publications

(31 citation statements)

References 21 publications

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“…modulation (bilayer) periods of 31, 62, 125, 250 and 500 nm (totally 32,16,8,4, and 2 bilayers, respectively) and Ti:TiN modulation ratio of 1:1, as well as 2. bilayer period of 125 nm (8 bilayers) and modulation ratio of 1:2 and 1:4. Before mounting the mirror-polished austenitic steel samples (DIN 1.4301) on the substrate holder in 100 mm distance and pumping down the equipment [26] to 1 × 10 −5 mbar start pressure, all substrates were ultrasonically cleaned in acetone and ethanol.…”

Section: Methodsmentioning

confidence: 99%

“…1a). This method allows us to calculate deformation and stress fields (stress concentrations) [29][30][31] including plastic deformation of substrates which is impossible by applying only extended Hertz theory for coating-substrate systems [32,33]. In our models the mesh was densified close to the contact zone to the indenter, where significant stress concentration was expected (Fig.…”

Section: Simulationmentioning

confidence: 99%

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Microscale interpretation of tribological phenomena in Ti/TiN soft-hard multilayer coatings on soft austenite steel substrates

Lackner¹,

Major²,

Kot³

2011

Bulletin of the Polish Academy of Sciences: Technical Sciences

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Abstract. The mechanical and tribological behavior of physical vapor deposited coatings on soft substrate materials gains increasing interest due to economical and environmental aspects -e.g. substitution of steels by light-weight metals or polymers in transport vehicles. Nevertheless, such soft materials require surface protection against wear in tribological contacts. Single layer hard coatings deposited at room temperature are brittle with a relatively poor adhesion. Therefore, they should be better substituted by tough multilayer coatings of soft-hard material combinations. However, the mechanics of such multilayer coatings with several 10 nm thick bilayer periods is difficult and yet not well described. The presented work tries to fill the gap of knowledge by focusing both on mechanical investigations of hardness, adhesion, and wear and on microscopic elucidation of deformation mechanisms. In the paper 1 µm thick Ti/TiN multilayer stacks were deposited by magnetron sputtering on soft austenitic steel substrates at room temperature to prevent distortion of functional components in future applications. High hardness was found for 8 and 16 bilayer films with modulation ratio Ti:TiN = 1:2 and 1:4. This was attributed (with use of transmission electron microscopy) to stopping the crack propagation in thin Ti layers of the multilayer systems by shear deformation combined with different fracture mechanisms in comparison with that for the TiN single layers (edge cracks at the border of the contact area and ring cracks outside, respectively).

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Section: Methodsmentioning

confidence: 99%

Section: Simulationmentioning

confidence: 99%

Microscale interpretation of tribological phenomena in Ti/TiN soft-hard multilayer coatings on soft austenite steel substrates

Lackner¹,

Major²,

Kot³

2011

Bulletin of the Polish Academy of Sciences: Technical Sciences

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“…In this work there are 513 equally-spaced points For the coated elastic contact problem, an explicit Green's function is not available for the normal displacement in the space domain. Its frequency response function, however, is available in the frequency domain [22]. Previous studies have derived the 2D frequency response function of the Green function for a single body of line contact as [22]: …”

Section: Model Parametersmentioning

confidence: 99%

“…Its frequency response function, however, is available in the frequency domain [22]. Previous studies have derived the 2D frequency response function of the Green function for a single body of line contact as [22]: …”

Section: Model Parametersmentioning

confidence: 99%

Tribological behavior of coated spur gear pairs with tooth surface roughness

Liu

Zhu

et al. 2018

Friction

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Abstract:Coating is an effective way to reduce friction and wear and to improve the contact-fatigue lives of gear components, which further guarantees a longer service life and better reliability of industrial machinery. The fact that the influence coefficient linking the tractions and stress components could not be expressed explicitly increases the difficulty of coated solids contact analysis. The complicated tribological behavior between tooth surfaces influenced by lubrication and surface roughness further adds difficulty to the coated gear pair contact problems. A numerical elastohydrodynamic lubricated (EHL) contact model of a coated gear pair is proposed by considering the coupled effects of gear kinematics, coating properties, lubrication, and surface roughness. The frequency response function and the discrete convolute, fast Fourier transformation (DC-FFT) method are combined to calculate the surface deformation and the subsurface stress fields at each meshing position along the line of action (LOA). The Ree-Eyring fluid is assumed to incorporate the non-Newtonian effect, which is represented in the generalized Reynolds equation. Influences of the ratio between the Young's modulus of the coating and the substrate on the contact performance, such as pressure, film thickness, tooth friction coefficient, and subsurface stress field, are studied. The effect of the root mean square (RMS) value of the tooth surface roughness is studied by introducing the roughness data, deterministically measured by an optical profiler.

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“…Chudoba 등 [12] 은 박막 코팅의 탄성 범위 내에서 구형 압입자를 사용하여 탄성계수를 결정할 수 있는 가능성을 제시하 였고 Liu 등 [13] 은 하중-깊이 곡선을 이용하여 탄성계수와 포아송 의 비를 결정할 수 있는 방법과 절차에 관하여 연구하였다. 하지만 나노인덴테이션 시험에서는 데이터의 신뢰성 확보를 위해 최대 압입 깊이를 재료 두께의 1 [14] . …”

Section: Fig 1 Schematic Diagram Of Contact Model Between a Cantileverunclassified

Evaluation of Elastic Properties for Nanoscale Coating Layers Using Ultrasonic Atomic Force Microscopy

Kwak¹,

Cho²,

Park

2015

Journal of the Korean Society of Manufacturing Technology Engin

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ARTICLE INFO ABSTRACTArticle history:Ultrasonic atomic force microscopy (Ultrasonic-AFM) has been used to investigate the elastic property of the ultra-thin coating layer in a thin-film system. The modified Hertzian theory was applied to predict the contact resonance frequency through accurate theoretical analysis of the dynamic characteristics of the cantilever. We coat 200 nm thick Aluminum and Titanium thin films on the substrate using the DC Magnetron sputtering method. The amplitude and phase of the contact resonance frequency of a vibrating cantilever varies in response to the local stiffness constant. Ultrasonic-AFM images were obtained using the variations in the elastic property of the materials. The morphology of the surface was clearly observed in the Ultrasonic-AFM images, but was barely visible in the topography. This research demonstrates that Ultrasonic-AFM is a promising technique for visualizing the distribution of local stiffness in the nano-scale thin coatings.

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An extension of the Hertz theory for 2D coated components

Cited by 41 publications

References 21 publications

Microscale interpretation of tribological phenomena in Ti/TiN soft-hard multilayer coatings on soft austenite steel substrates

Microscale interpretation of tribological phenomena in Ti/TiN soft-hard multilayer coatings on soft austenite steel substrates

Tribological behavior of coated spur gear pairs with tooth surface roughness

Evaluation of Elastic Properties for Nanoscale Coating Layers Using Ultrasonic Atomic Force Microscopy

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