Trilayer materials consisting of a functional outer layer on a substrate containing one intermediate layer are widely used in data-processing devices, biomedical components, and mechanical elements. The recent analytical frequency response functions (FRFs) derived by the authors' group for the contact of multilayer materials lead to the novel deterministic modeling of frictionless and frictional contact involving a trilayer material system designed with various thickness and elastic property combinations. Displacements and stresses for point contacts are calculated effectively by employing the discrete-convolution and fast Fourier transform (FFT) method based on the influence coefficients obtained from the analytical FRFs. The maximum von Mises stress and its location, which are critical information for understanding the material contact status, are thoroughly investigated for a wide range of trilayer materials. The results provide an informative guideline for the design of bilayer coatings without contact failure.
Issue Section:
Contact Mechanics
References
1.
Lawn
, B. R.
, Deng
, Y.
, Miranda
, P.
, Pajares
, A.
, Chai
, H.
, and Kim
, D. K.
, 2002
, “Overview: Damage in Brittle Layer Structures From Concentrated Loads
,” J. Mater. Res.
, 17
(12
), pp. 3019
–3036
.2.
Katta
, R. R.
, Nunez
, E. E.
, Polycarpou
, A. A.
, and Lee
, S.-C.
, 2009
, “Plane Strain Sliding Contact of Multilayer Magnetic Storage Thin-Films Using the Finite Element Method
,” Microsyst. Technol.
, 15
(7
), pp. 1097
–1110
.3.
Lee
, S.-C.
, Hong
, S.-Y.
, Kim
, N.-Y.
, Ferber
, J.
, Che
, X.
, and Strom
, B. D.
, 2009
, “Stress Induced Permanent Magnetic Signal Degradation of Perpendicular Magnetic Recording System
,” ASME J. Tribol.
, 131
(1
), p. 011904.4.
Miranda
, P.
, Pajares
, A.
, Guiberteau
, F.
, Deng
, Y.
, Zhao
, H.
, and Lawn
, B. R.
, 2003
, “Designing Damage-Resistant Brittle-Coating Structures—II: Trilayers
,” Acta Mater.
, 51
(14
), pp. 4357
–4365
.5.
Chai
, H.
, and Lawn
, B.
, 1999
, “Fracture Modes in Brittle Coatings With Large Interlayer Modulus Mismatch
,” J. Mater. Res.
, 14
(9
), pp. 3805
–3817
.6.
Chai
, H.
, and Lawn
, B. R.
, 2004
, “Fracture Mode Transitions in Brittle Coatings on Compliant Substrates as a Function of Thickness
,” J. Mater. Res.
, 19
(6
), pp. 1752
–1761
.7.
Chai
, H.
, and Lawn
, B. R.
, 2002
, “Cracking in Brittle Laminates From Concentrated Loads
,” Acta Mater.
, 50
(10
), pp. 2613
–2625
.8.
Chen
, W. T.
, 1971
, “Computation of Stresses and Displacements in a Layered Elastic Medium
,” Int. J. Eng. Sci.
, 9
(9
), pp. 775
–800
.9.
Chen
, W. T.
, and Engel
, P.
, 1972
, “Impact and Contact Stress Analysis in Multilayer Media
,” Int. J. Solids Struct.
, 8
(11
), pp. 1257
–1281
.10.
O'Süllivian
, T. C.
, and King
, R. B.
, 1988
, “Sliding Contact Stress-Field Due to a Spherical Indenter on a Layered Elastic Half-Space
,” ASME J. Tribol.
, 110
(2
), pp. 235
–240
.11.
Kuo
, C. H.
, and Keer
, L. M.
, 1992
, “Contact Stress-Analysis of a Layered Transversely Isotropic Half-Space
,” ASME J. Tribol.
, 114
(2
), pp. 253
–262
.12.
Nogi
, T.
, and Kato
, T.
, 1997
, “Influence of a Hard Surface Layer on the Limit of Elastic Contact—1: Analysis Using a Real Surface Model
,” ASME J. Tribol.
, 119
(3
), pp. 493
–500
.13.
Liu
, S. B.
, and Wang
, Q.
, 2002
, “Studying Contact Stress Fields Caused by Surface Tractions With a Discrete Convolution and Fast Fourier Transform Algorithm
,” ASME J. Tribol.
, 124
(1
), pp. 36
–45
.14.
Cai
, S.
, and Bhushan
, B.
, 2005
, “A Numerical Three-Dimensional Contact Model for Rough, Multilayered Elastic/Plastic Solid Surfaces
,” Wear
, 259
, pp. 1408
–1423
.15.
Plumet
, S.
, and Dubourg
, M. C.
, 1998
, “A 3-D Model for a Multilayered Body Loaded Normally and Tangentially Against a Rigid Body: Application to Specific Coatings
,” ASME J. Tribol.
, 120
(4
), pp. 668
–676
.16.
Leroy
, J. M.
, Floquet
, A.
, and Villechaise
, B.
, 1989
, “Thermomechanical Behavior of Multilayered Media: Theory
,” ASME J. Tribol.
, 111
(3
), pp. 538
–545
.17.
Yu
, C.
, Wang
, Z.
, and Wang
, Q. J.
, 2014
, “Analytical Frequency Response Functions for Contact of Multilayered Materials
,” Mech. Mater.
, 76
, pp. 102
–120
.18.
Yu
, C.
, Wang
, Z.
, Sun
, F.
, Lu
, S.
, Keer
, L. M.
, and Wang
, Q. J.
, 2013
, “A Deterministic Semi-Analytical Model for the Contact of a Wafer and a Rough Bi-Layer Pad in CMP
,” ECS J. Solid State Sci. Technol.
, 2
(9
), pp. P368
–P374
.19.
Wang
, Z.
, Yu
, C.
, and Wang
, Q.
, 2015
, “Model for Elastohydrodynamic Lubrication of Multilayered Materials
,” ASME J. Tribol.
, 137
(1
), p. 011501.20.
Wang
, Z.
, Yu
, C.
, and Wang
, Q. J.
, 2015
, “An Efficient Method for Solving Three-Dimensional Fretting Contact Problems Involving Multilayered or Functionally Graded Materials
,” Int. J. Solids Struct.
, 66
, pp. 46
–61
.21.
Jiang
, Y. Y.
, and Sehitoglu
, H.
, 1996
, “Rolling Contact Stress Analysis With the Application of a New Plasticity Model
,” Wear
, 191
(1–2
), pp. 35
–44
.22.
Luo
, J. F.
, Liu
, Y. J.
, and Berger
, E. J.
, 2000
, “Interfacial Stress Analysis for Multi-Coating Systems Using an Advanced Boundary Element Method
,” Comput. Mech.
, 24
(6
), pp. 448
–455
.23.
Komvopoulos
, K.
, 1988
, “Finite-Element Analysis of a Layered Elastic Solid in Normal Contact With a Rigid Surface
,” ASME J. Tribol.
, 110
(3
), pp. 477
–485
.24.
Komvopoulos
, K.
, and Choi
, D. H.
, 1992
, “Elastic Finite-Element Analysis of Multiasperity Contacts
,” ASME J. Tribol.
, 114
(4
), pp. 823
–831
.25.
Djabella
, H.
, and Arnell
, R. D.
, 1994
, “Finite-Element Analysis of Elastic Stresses in Multilayered Systems
,” Thin Solid Films
, 245
(1–2
), pp. 27
–33
.26.
Gorishnyy
, T. Z.
, Olson
, L. G.
, Oden
, M.
, Aouadi
, S. M.
, and Rohde
, S. L.
, 2003
, “Optimization of Wear-Resistant Coating Architectures Using Finite Element Analysis
,” J. Vac. Sci. Technol. A
, 21
(1
), pp. 332
–339
.27.
Chen
, J.
, and Bull
, S. J.
, 2009
, “Finite Element Analysis of Contact Induced Adhesion Failure in Multilayer Coatings With Weak Interfaces
,” Thin Solid Films
, 517
(13
), pp. 3704
–3711
.28.
Kot
, M.
, Rakowski
, W.
, Lackner
, J. M.
, and Major
, L.
, 2013
, “Analysis of Spherical Indentations of Coating-Substrate Systems: Experiments and Finite Element Modeling
,” Mater. Des.
, 43
, pp. 99
–111
.29.
Chen
, W. W.
, Zhou
, K.
, Keer
, L. M.
, and Wang
, Q. J.
, 2010
, “Modeling Elasto-Plastic Indentation on Layered Materials Using the Equivalent Inclusion Method
,” Int. J. Solids Struct.
, 47
(20
), pp. 2841
–2854
.30.
Bagault
, C.
, Nelias
, D.
, Baietto
, M. C.
, and Ovaert
, T. C.
, 2013
, “Contact Analyses for Anisotropic Half-Space Coated With an Anisotropic Layer: Effect of the Anisotropy on the Pressure Distribution and Contact Area
,” Int. J. Solids Struct.
, 50
(5
), pp. 743
–754
.31.
Zhou
, K.
, Keer
, L. M.
, and Wang
, Q. J.
, 2011
, “Analysis of Hard Coatings on a Substrate Containing Inhomogeneities
,” J. Mech. Mater. Struct.
, 6
(1–4
), pp. 627
–639
.32.
Sun
, Y.
, Bloyce
, A.
, and Bell
, T.
, 1995
, “Finite Element Analysis of Plastic Deformation of Various TiN Coating Substrate Systems Under Normal Contact With a Rigid Sphere
,” Thin Solid Films
, 271
(1–2
), pp. 122
–131
.33.
Diao
, D. F.
, 1999
, “Finite Element Analysis on Local Yield Map and Critical Maximum Contact Pressure for Yielding in Hard Coating With an Interlayer Under Sliding Contact
,” Tribol. Int.
, 32
(1
), pp. 25
–32
.34.
Djabella
, H.
, and Arnell
, R. D.
, 1993
, “Finite-Element Analysis of the Contact Stresses in Elastic Coating Substrate Under Normal and Tangential Load
,” Thin Solid Films
, 223
(1
), pp. 87
–97
.35.
Komvopoulos
, K.
, 1989
, “Elastic-Plastic Finite-Element Analysis of Indented Layered Media
,” ASME J. Tribol.
, 111
(3
), pp. 430
–439
.36.
Zhang
, P. Y.
, Diao
, D. F.
, and Wang
, Z. J.
, 2012
, “Three-Dimensional Local Yield Maps of Hard Coating Under Sliding Contact
,” ASME J. Tribol.
, 134
(2
), p. 021301
.37.
Johnson
, K. L.
, 1987
, Contact Mechanics
, Cambridge University Press
, Cambridge, UK
.38.
Yu
, C.
, 2014
, “Contact and Tribology of Surfaces With Engineered Topography and Multilayer Coatings
,” Ph.D. thesis
, Northwestern University
, Evanston, IL
.39.
Liu
, S. B.
, Wang
, Q.
, and Liu
, G.
, 2000
, “A Versatile Method of Discrete Convolution and FFT (DC-FFT) for Contact Analyses
,” Wear
, 243
(1–2
), pp. 101
–111
.40.
Polonsky
, I. A.
, and Keer
, L. M.
, 1999
, “A Numerical Method for Solving Rough Contact Problems Based on the Multi-Level Multi-Summation and Conjugate Gradient Techniques
,” Wear
, 231
(2
), pp. 206
–219
.41.
Song
, W.
, Li
, L.
, Ovcharenko
, A.
, Jia
, D.
, Etsion
, I.
, and Talke
, F. E.
, 2012
, “Plastic Yield Inception of an Indented Coated Flat and Comparison With a Flattened Coated Sphere
,” Tribol. Int.
, 53
, pp. 61
–67
.42.
Goltsberg
, R.
, Etsion
, I.
, and Davidi
, G.
, 2011
, “The Onset of Plastic Yielding in a Coated Sphere Compressed by a Rigid Flat
,” Wear
, 271
(11
), pp. 2968
–2977
.Copyright © 2016 by ASME
You do not currently have access to this content.
