Arch Appl Mech
Ali Nili · Saeed Adibnazari · Ardavan Karimzadeh
Stress ﬁeld in the thermoelastic rolling contact of graded
Received: 28 October 2017 / Accepted: 30 May 2018
© Springer-Verlag GmbH Germany, part of Springer Nature 2018
Abstract The thermoelastic rolling contact problem for an FGM-coated half plane under the plane strain
deformation is studied in this paper. A rigid roller rolls over the surface of coating with constant translational
velocity generating frictional heating in the slip zones of the contact patch. The material properties of the FGM
vary exponentially along the thickness direction. It is assumed that the contact area consists of a central stick
zone and two slip zones of the same sign. The transfer matrix method and Fourier integral transform technique
are used to achieve a system of two Cauchy singular integral equations. The coupling effect of tangential traction
is eliminated by adapting the conventional Goodman approximation. The associated governing equations
are discretized by applying the Gauss–Chebyshev integration method gaining a system of linear algebraic
equations. The effects of moving velocity, thermal conductivity and expansion coefﬁcients’ ratios on through
the thickness stress distribution are studied.
Keywords Thermoelastic rolling contact · Stress ﬁeld · Functionally graded coatings
Functionally graded material (FGM) may be characterized by the variation in composition and structure
gradually over volume, resulting in corresponding changes in the thermomechanical properties of the material.
The purpose of designing a compositionally graded material is to withstand thermomechanical loadings by
having a heat-resistant, anti-oxidation surface layer with a mechanically tough material on the inside .
In the contact mechanics of graded materials ﬁeld of study, Liu et al.  introduced a method to solve the
axisymmetric frictionless contact problem of functionally graded materials (FGMs), based on the fact that an
arbitrary curve can be approached by a series of continuous but piecewise linear curves. Comez and Erdol 
studied the frictional contact problem for a layer bonded to a homogeneous substrate according to the theory
of elasticity. Recently, Comez  considered frictional moving contact problem for a rigid cylindrical punch
and an elastic layer, with the punch subjected to concentrated normal and tangential force, and moving steadily
with a constant subsonic velocity on the boundary.
Guler et al.  investigated rolling contact problem of an FGM-coated homogeneous substrate for a
contact patch containing a central stick zone and two slip zones of the same sign. Alinia et al.  investigated
A. Nili (
) · S. Adibnazari
Aerospace Engineering Department, Sharif University of Technology, Tehran, Iran
Civil Aviation Technology College, Tehran, Iran