Contact problem of a layer–substrate system comprising of an elastic layer and an elastic substrate perfectly bonded to each other with surface effects based on Gurtin–Murdoch (GM) model indented by a long rigid cylinder is solved. The requisite Green's function relating surface displacement to surface load is obtained semi-analytically through the combination of the Airy stress function and Fourier transforms under the plane-strain condition. The contact solution is analyzed to study the influence of layer thickness, modulus mismatch between the layer and substrate, and surface parameters on contact size and contact pressure during indentation of a layer–substrate system. A map is presented which indicates whether during indentation by a rigid cylinder, a layer–substrate system is required or a homogeneous system based on layer properties is enough for a given shear modulus mismatch ratio and layer thickness. The map and the related analysis clearly indicate that whenever the contact size or layer thickness approaches intrinsic length scale based on the ratio of surface parameter and bulk elastic properties, surface effects should be considered.
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A Study of the Contact of an Elastic Layer–Substrate System Indented by a Long Rigid Cylinder Incorporating
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June 2016
Research-Article
A Study of the Contact of an Elastic Layer–Substrate System Indented by a Long Rigid Cylinder Incorporating
Surface Effects
Thamarai Selvan Vasu,
Thamarai Selvan Vasu
Department of Mechanical Engineering,
Indian Institute of Technology Bombay,
Powai,
Mumbai 400076, India
e-mail: thamaraivasu@iitb.ac.in
Indian Institute of Technology Bombay,
Powai,
Mumbai 400076, India
e-mail: thamaraivasu@iitb.ac.in
Search for other works by this author on:
Tanmay K. Bhandakkar
Tanmay K. Bhandakkar
Assistant Professor
Department of Mechanical Engineering,
Indian Institute of Technology Bombay,
Powai,
Mumbai 400076, India
e-mail: tbhanda2@iitb.ac.in
Department of Mechanical Engineering,
Indian Institute of Technology Bombay,
Powai,
Mumbai 400076, India
e-mail: tbhanda2@iitb.ac.in
Search for other works by this author on:
Thamarai Selvan Vasu
Department of Mechanical Engineering,
Indian Institute of Technology Bombay,
Powai,
Mumbai 400076, India
e-mail: thamaraivasu@iitb.ac.in
Indian Institute of Technology Bombay,
Powai,
Mumbai 400076, India
e-mail: thamaraivasu@iitb.ac.in
Tanmay K. Bhandakkar
Assistant Professor
Department of Mechanical Engineering,
Indian Institute of Technology Bombay,
Powai,
Mumbai 400076, India
e-mail: tbhanda2@iitb.ac.in
Department of Mechanical Engineering,
Indian Institute of Technology Bombay,
Powai,
Mumbai 400076, India
e-mail: tbhanda2@iitb.ac.in
1Corresponding author.
Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received January 14, 2016; final manuscript received March 13, 2016; published online April 6, 2016. Assoc. Editor: Shaoxing Qu.
J. Appl. Mech. Jun 2016, 83(6): 061009 (10 pages)
Published Online: April 6, 2016
Article history
Received:
January 14, 2016
Revised:
March 13, 2016
Citation
Vasu, T. S., and Bhandakkar, T. K. (April 6, 2016). "A Study of the Contact of an Elastic Layer–Substrate System Indented by a Long Rigid Cylinder Incorporating
Surface Effects." ASME. J. Appl. Mech. June 2016; 83(6): 061009. https://doi.org/10.1115/1.4033079
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