The effect of punch speed on frictional contact mechanics of finite-thickness graded layer resting on the rigid foundati
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(2020) 42:343
TECHNICAL PAPER
The effect of punch speed on frictional contact mechanics of finite‑thickness graded layer resting on the rigid foundation Mehmet N. Balci1 Received: 21 January 2020 / Accepted: 11 May 2020 © The Brazilian Society of Mechanical Sciences and Engineering 2020
Abstract The present article investigates frictional contact mechanics between a moving punch possessing sharp ends and a finitethickness functionally graded layer resting on the rigid foundation. The rigid punch has either flat or semi-circular profiles, and it moves over the functionally graded layer at a steady subsonic speed. The tangential load developed by the moving punch is proportional to the normal applied load since Coulomb’s friction law is adopted. Variations of shear modulus and mass density through the thickness of the layer are expressed by exponential functions, whereas the variation of the Poisson’s ratio is neglected. Governing partial differential equations are derived considering two-dimensional theory of elastodynamics, and these equations are solved analytically utilizing Galilean and Fourier transformations. Equations are reduced to a singular integral equation of the second kind. Singular integral equation is solved, and results of analytical approach are compared with those obtained by means of the finite element method in elastostatic case. A very good agreement is achieved between analytical and computational results. Parametric analyses are performed to observe the influences of punch speed, material inhomogeneity and coefficient of friction upon contact stresses of a finite-thickness graded layer resting on the rigid foundation. Stresses observed for relatively thin softening layers are much sensitive to the variation in punch speed. Keywords Contact mechanics · Frictional moving punch · Finite-thickness graded layer · Rigid foundation · Singular integral equation · Finite element analysis
1 Introduction In materials science, functionally graded materials (FGMs) are characterized as heterogeneous composite materials synthesized by two or more kinds of material particles with volume fractions varying in the structure and composition over the volume. FGM concept was first proposed in 1984 by a group of Japanese scientists to deal with the harsh conditions of thermal shock in the space shuttle [1]. It was reported in many articles that FGMs have superior properties than other conventional materials in point of reducing mismatching stresses, increasing bonding strength, improving surface properties and providing against thermal and chemical environments [2]. Contact mechanics problems of FGMs have Technical Editor: João Marciano Laredo dos Reis. * Mehmet N. Balci [email protected] 1
Department of Mechanical Engineering, Hacettepe University, 06800 Ankara, Turkey
attracted many scientists since these materials have a great potential in the utilization of load transfer components in brake disks, cylinder linings, gears, gas turbines and other components in automotive, electronics and aer
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