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Research Papers: Contact Mechanics

Maximum von Mises Stress and Its Location in Trilayer Materials in Contact

[+] Author and Article Information
Chengjiao Yu

Department of Mechanical Engineering,
Northwestern University,
Evanston, IL 60208
e-mail: cyu@u.northwestern.edu

Zhanjiang Wang

State Key Laboratory of Mechanical
Transmission,
Chongqing University,
Chongqing 400030, China
e-mail: wangzhanjiang001@gmail.com

Geng Liu

School of Mechanical Engineering,
Northwestern Polytechnical University,
Xi'an, Shaanxi 710072 China

Leon M. Keer

Department of Civil and Environmental
Engineering and Mechanical Engineering,
Northwestern University,
Evanston, IL 60208

Q. Jane Wang

Department of Mechanical Engineering,
Northwestern University,
Evanston, IL 60208;
State Key Laboratory of Mechanical
Transmission,
Chongqing University,
Chongqing 400030, China
e-mail: qwang@northwestern.edu

1Corresponding authors.

2Current affiliation: Baker Hughes.

Contributed by the Tribology Division of ASME for publication in the JOURNAL OF TRIBOLOGY. Manuscript received June 15, 2015; final manuscript received September 10, 2015; published online xx xx, xxxx. Assoc. Editor: James R. Barber.

J. Tribol 138(4), 041402 (Jul 08, 2016) (13 pages) Paper No: TRIB-15-1201; doi: 10.1115/1.4032888 History: Received June 15, 2015; Revised September 10, 2015

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.

FIGURES IN THIS ARTICLE
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Copyright © 2016 by ASME
Topics: Stress , Coatings , Friction
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Figures

Grahic Jump Location
Fig. 1

Schematics of the contact between a spherical rigid indenter and a trilayer material with two coatings and two interfaces

Grahic Jump Location
Fig. 2

Normalized contact radius (a) and peak contact pressure (b) for group 1 materials

Grahic Jump Location
Fig. 3

Diagram showing the location of the maximum von Mises stress in group 1 materials when μ = 0. The results for trilayer materials (in the shaded regions) are given by symbols, while the results for bilayer materials (along the two-dotted lines) and the homogenous material (intersection of the two-dotted lines) are shown by letters for clarity. Letters c, i, and sub indicate maximum stress location in the coating, interface, and substrate of the bilayer materials, respectively. Letter b is the maximum stress in the body of a homogenous material with all E's equal. The dashed circles mark three representative cases: trilayers with two stiff coatings(E1/Esub = 4 and E2/Esub = 2) on a compliant substrate, a stiff and a stiffer coating (E1/Esub = 4.25 and E2/Esub = 14.45) on a compliant substrate (the dental crown case), and two compliant coatings (E1/Esub = 0.25 and E2/Esub = 0.5) on a stiff substrate, in regions 1, 2, and 3, respectively. Region 1 includes two-shaded areas below the diagonal. Region 2 is above both dotted lines. Region 3 is above the diagonal and below the horizontal line.

Grahic Jump Location
Fig. 4

Contour plots of the normalized von Mises stress J2/P0 in the y = 0 plane for the contact problems of materials whose E2 = Esub and E1/Esub = 1/8, 1/4, 1/2, 1, 2, and 4 (corresponding to the thinner single layer cases along the horizontal line in Fig. 3)

Grahic Jump Location
Fig. 5

Contour plots of the normalized von Mises stress J2/P0 in the y = 0 plane for the contact problems of materials whose E1/Esub = E2/Esub = 1/8, 1/4, 1/2, 2, 4, and 8 (corresponding to thicker single layer cases along the diagonal in Fig. 3)

Grahic Jump Location
Fig. 6

Location of the maximum von Mises stress in group 1 materials when μ = 0.25 (a) and μ = 0.5 (b). The results for trilayer materials are given by symbols, while the results for bilayer materials and the homogenous material are shown by letters for clarity. Letters c and i indicate maximum stress location in the coating and interface of the bilayer materials, respectively. Letter b is for the maximum stress in the body of a homogenous material with all E's equal. Letter s shows the maximum stress at the surfaces of either bilayer material or homogenous material. The dashed circles mark three representative cases: trilayers with two stiff coatings(E1/Esub = 4 and E2/Esub = 2) on a compliant substrate, a stiff and a stiffer coating (E1/Esub = 4.25 and E2/Esub = 14.45) on a compliant substrate (the dental crown case), and two compliant coatings (E1/Esub = 0.25 and E2/Esub = 0.5) on a stiff substrate.

Grahic Jump Location
Fig. 7

Contour plots of normalized von Mises stress J2/P0 in the y = 0 plane for the contact of a spherical indenter and trilayer materials with friction coefficients of 0, 0.25, and 0.5. The trilayer materials are representatives of materials in each region marked by the circles in Figs. 3 and 6. The locations of the maximum stress are marked by the crosses, and the highest values indicated by the bars next to the contour plots.

Grahic Jump Location
Fig. 8

Normalized contact radius (a) and peak contact pressure (b) of group 2 materials

Grahic Jump Location
Fig. 9

Diagram showing the locations of the maximum von Mises stresses of group 2 materials when μ = 0. The results for trilayer materials are given by symbols, while the results for bilayer materials are shown by letters for clarity. Letters c, i, and sub indicate maximum stress location in the coating, interface, and substrate of the bilayer materials, respectively.

Grahic Jump Location
Fig. 10

Contour plots of the normalized von Mises stress J2/P0 in the y = 0 plane for the contact problems of materials with h1/h2 = 2, 3, 4, and 24 and E1 = 2E2 = 4Esub

Grahic Jump Location
Fig. 11

Locations of the maximum von Mises stresses in group 2 materials when μ = 0.25 (a) and μ = 0.5 (b). The results for trilayer materials are given by symbols, while the results for bilayer materials are shown by letters for clarity. Letters s, c, and i indicate maximum stress location in the surface, coating, and interface of the bilayer materials, respectively.

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