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Research Papers: Contact Mechanics

Novel Model for Partial-Slip Contact Involving a Material With Inhomogeneity

[+] Author and Article Information
Zhanjiang Wang

e-mail: wangzhanjiang001@gmail.com

Xiaoqing Jin, Qian Wang

State Key Laboratory of Mechanical Transmission,
Chongqing University,
Chongqing 400030, China;
Department of Mechanical Engineering,
Northwestern University,
Evanston, IL 60208

Leon M. Keer

Department of Mechanical Engineering,
Northwestern University,
Evanston, IL 60208

1Corresponding author.

Contributed by the Tribology Division of ASME for publication in the JOURNAL OF TRIBOLOGY. Manuscript received October 26, 2012; final manuscript received April 27, 2013; published online June 24, 2013. Assoc. Editor: James R. Barber.

J. Tribol 135(4), 041401 (Jun 24, 2013) (15 pages) Paper No: TRIB-12-1189; doi: 10.1115/1.4024548 History: Received October 26, 2012; Revised April 27, 2013

Contacts involving partial slip are commonly found at the interfaces formed by mechanical components. However, most theoretical investigations of partial slip are limited to homogeneous materials. This work proposes a novel and fast method for partial-slip contact involving a material with an inhomogeneity based on the equivalent inclusion method, where the inhomogeneity is replaced by an inclusion with properly chosen eigenstrains. The stress and displacement fields due to eigenstrains are formulated based on the half-space inclusion solutions recently derived by the authors and solved with a three-dimensional fast Fourier transform algorithm. The effectiveness and accuracy of the proposed method is demonstrated by comparing its solutions with those from the finite element method. The partial slip contact between an elastic ball and an elastic half space containing a cuboidal inhomogeneity is further investigated. A number of in-depth parametric studies are performed for the cuboidal inhomogeneity with different sizes and at different locations. The results reveal that the contact behavior of the inhomogeneous material is more strongly influenced by the inhomogeneity when it is closer to the contact center and when its size is larger.

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Figures

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Fig. 1

Partial slip contact model, shown with an elastic sphere interacting with a half space containing a cuboidal inhomogeneity

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Fig. 2

Flow chart for the numerical calculation

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Fig. 3

Surface displacements along target lines y = 0 and y = 0.5, parallel to the x-axis, caused by cuboidal inclusion with uniform eigenstrains

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Fig. 4

Benchmarking the current model with the FEM, 128 × 128 × 64 cuboidal elements were used for the former and run for about 100 min, while for the latter, 56 × 56 × 44 elements took about 15 h of computation. (a) Dimensionless stresses along the z-axis, (b) dimensionless surface displacements along the x-axis

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Fig. 5

Calculated eigenstrains in the y = 0 plane: (a) ɛ11*, (b) ɛ22*, (c) ɛ33*, (d) 2ɛ13*

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Fig. 6

Contour plots of dimensionless von Mises stresses in the y = 0 plane caused by (a) pressure, (b) eigenstrains, and (c) considering the effects of pressure and eigenstrains

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Fig. 7

Dimensionless shear traction qx/ph along the x-axis for different E2 (the inhomogeneity depth h = a and the lengths in all directions are kept to be a, while parameter d varies from −a to a). (a) E2 = 2E1, (b) E2 = 0.5E1.

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Fig. 8

Streamlines of surface shear vectors on the material with an inhomogeneity of different E2 (the center of the inhomogeneity is located at (0, 0, a) and the lengths in all directions are kept to be a, while the tangential force, Fx, varies from 0 to 0.9μfW). (a) E2 = 2E1, (b) E2 = 0.5E1.

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Fig. 9

Dimensionless surface displacements ux/a and u˜x/a and slip sx/a along the x-axis for the material with an inhomogeneity of different E2 (the center of the inhomogeneity is located at (0, 0, a), the lengths in all directions are kept to be a, and the tangential force is Fx = 0.9μfW). (a) E2 = 2E1, (b) E2 = 0.5E1.

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Fig. 10

Contour plots of dimensionless von Mises stresses in the y = 0 plane for the material with an inhomogeneity of different E2 (the center of the inhomogeneity is located at (0, 0, a), the lengths in all directions are kept to be a, and the tangential force is Fx = 0.9μfW). (a) E2 = 2E1, (b) E2 = 0.5E1.

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Fig. 11

Dimensionless shear traction qx/ph along the x-axis for the material with an inhomogeneity of different E2 (the depth of the inhomogeneity, h, changed from 0.5 a to 2 a and the lengths in all directions are kept to be a). (a) E2 = 2E1, (b) E2 = 0.5E1.

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Fig. 12

Distributions of stick and slip regions for the material with an inhomogeneity of different E2 (the center of the inhomogeneity is located at (0, 0, 0.5 a) and the lengths in all directions are kept to be a, while the tangential force, Fx, varies from 0 to 0.9μfW). (a) E2 = 2E1, (b) E2 = 0.5E1.

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Fig. 13

Contour plots of dimensionless von Mises stresses in the y = 0 plane for the material with an inhomogeneity of different E2 (the center of inhomogeneity is located at (0, 0, 0.5 a), the lengths in all directions are kept to be a, and the tangential force is Fx = 0.9μfW). (a) E2 = 2E1, (b) E2 = 0.5E1.

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Fig. 14

Dimensionless pressure p/ph along the x-axis for the material with an inhomogeneity of different E2 (the center of inhomogeneity is located at (0, 0, a) and the length c varies from 0.5 a to 2 a). (a) E2 = 2E1, (b) E2 = 0.5E1.

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Fig. 15

Dimensionless shear traction qx/ph along the x-axis for the material with an inhomogeneity of different E2 (the center of inhomogeneity is located at (0, 0, a) and the length c varies from 0.5 a to 2 a). (a) E2 = 2E1, (b) E2 = 0.5E1.

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Fig. 16

Dimensionless shear traction qx/ph along the x-axis for the material with a layer of different E2 (the layer thickness is kept to be a, and three types of layers, defined by the center plane of the layer overlapping with the plane of z = 0.5 a, z = 1.5 a, and x = 0, respectively, are analyzed for various value of the tangential force, Fx). (a) E2 = 2E1, (b) E2 = 0.5E1.

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Fig. 17

Contour plots of dimensionless von Mises stresses in the y = 0 plane for different E2 (the layer thickness is kept to be a, and three types of layers, defined by the center plane of the layer overlapping with the plane of z = 0.5 a, z = 1.5 a, and x = 0, respectively, are analyzed for a fixed tangential force Fx = 0.9μfW). (a) E2 = 2E1, (b) E2 = 0.5E1.

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Fig. 18

Surface displacements caused by cuboidal inclusion with uniform eigenstrains

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