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Research Papers

Plane Contact and Adhesion of Two Elastic Solids With an Interface Groove

[+] Author and Article Information
Fan Jin

Institute of Systems Engineering,
China Academy of Engineering Physics,
Mianyang 621900, Sichuan, China
e-mail: jinfan2046@163.com

Xu Guo

State Key Laboratory of Structural
Analysis for Industrial Equipment,
Department of Engineering Mechanics,
Dalian University of Technology,
Dalian 116023, China

Qiang Wan

Institute of Systems Engineering,
China Academy of Engineering Physics,
Mianyang 621900, Sichuan, China

1Corresponding author.

Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received September 16, 2017; final manuscript received January 12, 2018; published online February 2, 2018. Assoc. Editor: Kyung-Suk Kim.

J. Appl. Mech 85(4), 041002 (Feb 02, 2018) (10 pages) Paper No: JAM-17-1516; doi: 10.1115/1.4039040 History: Received September 16, 2017; Revised January 12, 2018

A systematic study is performed on the plane contact and adhesion of two elastic solids with an interface groove. The nonadhesion and Johnson–Kendall–Roberts (JKR) adhesion solutions for a typical groove shape are obtained in closed form by solving singular integral equations and using energy release rate approaches. It is found that the JKR adhesion solution depends solely on a dimensionless parameter α and the groove is predicted to be unstably flattened with no applied load when α0.535. Furthermore, the corresponding Maugis–Dugdale adhesion model has been revisited with three possible equilibrium states. By introducing the classical Tabor parameter μ, a complete transition between the nonadhesion and the JKR adhesion contact models is captured, which can be recovered as two limiting cases of the Maugis–Dugdale model. Depending on two nondimensional parameters α and μ, where α2 represents the ratio of the surface energy in the groove to the elastic strain energy when the grooved surface is flattened, different transition processes among three equilibrium states are characterized by one or more jumps between partial and full contact. Larger values of α and μ tend to induce more energy loss due to adhesion hysteresis. Combination values of α and μ are also suggested to design self-healing interface grooves due to adhesion.

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Figures

Grahic Jump Location
Fig. 1

Schematics of adhesive contact between an elastic flat surface and an elastic surface with a single interface groove subjected to a remotely applied normal traction p¯ (positive when compressive, negative when tensile)

Grahic Jump Location
Fig. 2

Nonadhesive contact behaviors of the interface groove. (a) The groove half-width versus the applied compressive traction. (b) The groove shapes at some typical loading stages. (c) The contact pressure distributions at some typical loading stages.

Grahic Jump Location
Fig. 3

The normalized groove half-width versus the normalized applied normal traction in the JKR adhesion model for different values of α

Grahic Jump Location
Fig. 4

Schematics of the cohesive zone within the interfacial groove. Adhesive traction in the Maugis–Dugdale model is assumed to be constant σ0 acting over a cohesive zone with separation less than hc.

Grahic Jump Location
Fig. 5

Maugis–Dugdale adhesive contact behaviors of the interface groove for α=0.3 and μ=0.6. (a) The groove half-width versus the applied normal traction. The nonadhesion and JKR adhesion curves are also included for comparison. (b) The groove shapes at some typical loading stages. Curves A and E correspond to initial shape and full contact cases, respectively.

Grahic Jump Location
Fig. 6

The groove half-width versus the applied normal traction in the Maugis–Dugdale model with α=0.4 for (a) μ=0.01, (b) μ=0.7, (c) μ=1.2, and (d) μ=4. The corresponding nonadhesion and JKR adhesion curves are also included for comparison.

Grahic Jump Location
Fig. 7

The groove half-width versus the applied normal traction in the Maugis–Dugdale model with α=1 for (a) μ=0.01, (b) μ=0.4, (c) μ=1.2, and (d) μ=4. The corresponding nonadhesion and JKR adhesion curves are also included for comparison.

Grahic Jump Location
Fig. 8

Maugis–Dugdale and JKR adhesion regions of α and μ for self-healing interface grooves

Grahic Jump Location
Fig. 9

Critical compressive traction to achieve full contact as a function of the Tabor parameter for different values of α. The subplot (b) is an enlarged part of plot (a) where the behavior for α=0.4 can be seen in more detail.

Grahic Jump Location
Fig. 10

The critical load for gap initiation as a function of the Tabor parameter for different values of α

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