# Multi-layer model for moving contact problems of functionally graded coatings with general variations in physical properties

2022-04-01
This paper presents a multi-layer model for moving contact problems of functionally graded coatings whose physical properties have general spatial variations. The coating is assumed to be composed of an arbitrary number of layers and perfectly bonded to an elastic substrate. Wave equations for the layers and the substrate are derived in accordance with the plane theory of elastodynamics. The equations are solved by the application of Galilean and Fourier transformations. Flat and triangular punch profiles are considered, and the formulation is reduced to a singular integral equation of the second kind in both cases. The integral equations are solved by means of Jacobi expansion and collocation techniques. Proposed procedures are verified through comparisons to the results available for a special case in the literature. Parametric analyses are carried out for functionally graded coatings possessing ceramic-rich, metal-rich, and linear profiles. The results presented demonstrate the influences of factors such as punch speed, coefficient of friction, material property variation profile, and contact-length-to-thickness ratio on contact stresses, punch stress intensity factors, and required contact force. It is shown that the multi-layer model is required to account for general property distributions in a functionally graded coating subject to moving contact.
PROCEEDINGS OF THE INSTITUTION OF MECHANICAL ENGINEERS PART L-JOURNAL OF MATERIALS-DESIGN AND APPLICATIONS

# Suggestions

 Consideration of spatial variation of the friction coefficient in contact mechanics analysis of laterally graded materials Dağ, Serkan (2016-01-01) This paper presents a new analytical approach for sliding contact analysis of laterally graded materials, which allows taking into account the spatial variation of the friction coefficient. The method is developed by considering a sliding frictional contact problem between a laterally graded elastic medium and a rigid flat punch. Governing partial differential equations entailing the displacement components are derived in accordance with the theory of plane elasticity. General solutions are determined and b...
 Stresses in multi-layer coatings in Hertzian contact with a moving circular punch Toktaş, Selim Ercihan; Dağ, Serkan (2022-07-01) © 2022 Elsevier LtdThis article presents analytical solution procedures for moving Hertzian contact problems involving multi-layer and functionally graded coatings. A frictional circular punch is assumed to slide down the surface of the coating with a specified velocity. Formulation is based on wave equations of plane elasticity, and reduced to a singular integral equation by Galilean and Fourier transformations. Developed procedures are verified through comparisons to the findings available in the literatu...
 Coupled thermoviscoplasticity of glassy polymers in the logarithmic strain space based on the free volume theory Miehe, Christian; Mendez Diez, Joel; Göktepe, Serdar; Schaenzel, Lisa Marie (Elsevier BV, 2011-06-15) The paper outlines a constitutive model for finite thermo-visco-plastic behavior of amorphous glassy polymers and considers details of its numerical implementation. In contrast to existing kinematical approaches to finite plasticity of glassy polymers, the formulation applies a plastic metric theory based on an additive split of Lagrangian Hencky-type strains into elastic and plastic parts. The analogy between the proposed formulation in the logarithmic strain space and the geometrically linear theory of pl...
 Hybrid finite element for analysis of functionally graded beams Sarıtaş, Afşin; Soydas, Ozan (2017-01-01) A hybrid finite element model is presented, where stiffness and mass distributions over a beam with functionally graded material (FGM) are accurately modeled for both elastic and inelastic material responses. Von Mises and Drucker-Prager plasticity models are implemented for metallic and ceramic parts of FGM, respectively. Three-dimensional stress-strain relations are solved by a general closest point projection algorithm, and then condensed to the dimensions of the beam element. Numerical examples and veri...
 Nonlinear Vibrations of a Functionally Graded Material Microbeam with Geometric Nonlinearity Uz, Canan; Ciğeroğlu, Ender (2017-02-02) In this paper, nonlinear vibration analysis of micro scale functionally graded material (FGM) beams with geometric nonlinearity due to large deflection is studied using modified couple stress theory (MCST). MCST is a nonlocal elasticity theory which includes a material length scale parameter since the size of an atomic microstructure becomes comparable to the length of the microbeam. Equations of motion of the micro scale FGM beam are obtained by using Hamilton's principle. Nonlinear free vibrations of the ...
Citation Formats
S. E. Toktaş and S. Dağ, “Multi-layer model for moving contact problems of functionally graded coatings with general variations in physical properties,” PROCEEDINGS OF THE INSTITUTION OF MECHANICAL ENGINEERS PART L-JOURNAL OF MATERIALS-DESIGN AND APPLICATIONS, pp. 0–0, 2022, Accessed: 00, 2022. [Online]. Available: https://hdl.handle.net/11511/97251.