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Research Papers

# Sliding Contact Between a Cylindrical Punch and a Graded Half-Plane With an Arbitrary Gradient Direction

[+] Author and Article Information
Chen Peijian

School of Mechanics and Civil Engineering,
State Key Laboratory for Geomechanics
and Deep Underground Engineering,
China University of Mining and Technology,
Xuzhou, Jiangsu 221116, China

Chen Shaohua

LNM, Institute of Mechanics,
Chinese Academy of Sciences,
Beijing 100190, China
e-mail: shchen@LNM.imech.ac.cn;
chenshaohua72@hotmail.com

Peng Juan

School of Sciences,
China University of Mining and Technology,
Xuzhou, Jiangsu 221116, China

1Corresponding author.

Manuscript received January 21, 2015; final manuscript received February 9, 2015; published online February 26, 2015. Editor: Yonggang Huang.

J. Appl. Mech 82(4), 041008 (Apr 01, 2015) (9 pages) Paper No: JAM-15-1035; doi: 10.1115/1.4029781 History: Received January 21, 2015; Revised February 09, 2015; Online February 26, 2015

## Abstract

Contact behavior of a rigid cylindrical punch sliding on an elastically graded half-plane with shear modulus gradient variation in an arbitrary direction is investigated. The governing partial differential equations and the boundary conditions are achieved with the help of Fourier integral transformation. As a result, the present problem is reduced to a singular integral equation of the second kind, which can be solved numerically. Furthermore, the presently general model can be well degraded to special cases of a lateral gradient half-plane and a homogeneous one. Normal stress in the contact region is predicted with different material parameters, which is usually used to estimate the possibility of surface crack initiation. The moment that is needed to ensure stable sliding of the cylindrical punch on the contact surface is further predicted. The result in the present paper should be helpful for the design of novel graded materials with surfaces of strong abrasion resistance.

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## References

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## Figures

Fig. 1

The Hertzian contact model of a rigid cylindrical punch sliding on a graded half-plane with an arbitrarily gradient orientation. (a) External loads induce an asymmetric contact width with respect to the coordinate system; (b) shifting the normal load to the centerliner of contact punch x=c induces a variation of the moment needed by the rigid punch for stable sliding.

Fig. 2

Distribution of the normal traction σyy(x,0)/(P/(a+b)) in the contact model of a homogeneous half-plane with μf=0, where FEM results achieved by Dag et al. are given for comparison

Fig. 3

Distribution of the normal traction σyy(x,0)/(P/(a+b)) in the contact model of a laterally graded half-plane with δ(a+b)=1.0 and μf=0, where FEM results achieved by Dag et al. are given for comparison

Fig. 4

Distribution of the normal traction σyy(x,0)/(P/(a+b)) and in-plane stress σxx(x,0)/(P/(a+b)) in the contact model of a graded half-plane with a gradient variation angle θ=0.3π and different surface friction coefficient μf. (a) and (b) For δ(a+b)=1.0; (c) and (d) for δ(a+b)=-1.0.

Fig. 5

Distribution of the interface stresses inside the contact region in the contact model of a graded half-plane with θ=0.3π, μf=0.3, and different values of δ(a+b). (a) For the normal traction σyy(x,0)/(P/(a+b)); (b) for the in-plane stress σxx(x,0)/(P/(a+b)).

Fig. 6

Distribution of the normal traction σyy(x,0)/(P/(a+b)) and in-plane stress σxx(x,0)/(P/(a+b)) in the contact model of a graded half-plane with μf=0.3 and different gradient variation angles θ. (a) and (b) For δ(a+b)=-0.5; (c) and (d) for δ(a+b)=0.5.

Fig. 7

Variations of the nondimensional moment M/[P(a+b)/2] versus the friction coefficient μf for some selected δ(a+b) with ν = 0.3, δ(b-a) = 0, and θ = 0.3π

Fig. 8

The moment M/[P(a+b)/2] as a function of the parameter δ(a+b) for μf = 0.3 and different gradient variation angles θ

Fig. 9

The moment M/[P(a+b)/2] as a function of the gradient variation angle parameter θ for μf = 0.3 and different δ(a+b)

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