Research Papers

A Semi-Infinite Strip Pressed Against an Elastic Half-Plane With Frictional Slip

[+] Author and Article Information
George G. Adams

Department of Mechanical Engineering,
Northeastern University,
Boston, MA 02115
e-mail: adams@coe.neu.edu

Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received January 3, 2018; final manuscript received February 23, 2018; published online March 20, 2018. Assoc. Editor: Shaoxing Qu.

J. Appl. Mech 85(6), 061001 (Mar 20, 2018) (7 pages) Paper No: JAM-18-1006; doi: 10.1115/1.4039456 History: Received January 03, 2018; Revised February 23, 2018

The subject of this investigation is the plane strain elasticity problem of a finite width semi-infinite strip with its end pressed against a half-plane of the same material with friction. From the existing integral equation solution for a perfect bond, it is shown that the length of the zone of frictional slip and the value of the slip displacement can both be inferred. It is further shown how this method allows a finite element stress analysis of a structure, obtained with the simple assumption of a perfect bond, to be used instead of the more complicated finite element structural analysis with frictional slip. Nonetheless, the results of this simpler finite element analysis can be used to infer the length of the frictional slip zone and the magnitude of the slip displacement. It is expected that this method will be valuable in the analysis of the mechanics of fretting. Damage due to fretting fatigue is initiated due to frictional slip near the edges of the interface between two connected materials. The stress analysis of structures, which includes these frictional slip zones, is considerably more complicated than it is for a perfect bond, often making it impractical to include in a comprehensive finite element model of the complete structure. Thus, the methodology used in this paper should allow the size of the frictional slip zones and the frictional slip displacements to be inferred directly from the stress analysis for a perfect bond.

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Grahic Jump Location
Fig. 3

Wedge analysis in the vicinity of the right corner of the punch half-plane interface

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Fig. 2

Decomposition of the problem depicted in Fig. 1 into the sum of: (a) the perfect bond problem and (b) the residual problem

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Fig. 1

A semi-infinite elastic strip in frictional contact with an elastic half-plane and acted upon by a compressive normal force (P) per unit depth

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Fig. 4

Variation of the order of the singularity (λ) with the friction coefficient (f). Frictional slip will not occur for f > 0.543 and as a consequence the order of the singularity becomes a constant, i.e., λ = 0.4555.

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Fig. 5

Normal and shear stress acting on the perfectly bonded interface between the semi-infinite strip and half-plane. Solid lines are from the integral equation solution whereas the dashed lines are from FEA.

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Fig. 7

Dimensionless slip zone length (r0/h = (h − a)/h) versus friction coefficient (f)

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Fig. 6

Bounded portions of normal and shear stress from the FEA solution of Fig. 1 configuration along the θ = 45 deg line of Fig. 3. The values of Q1* ≅ 0.420 and Q2* ≅ 0.255 represent the dimensionless generalized stress intensity factors for the normal and shear stresses, respectively.

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Fig. 8

Dimensionless slip displacement (ur(0,0)μ/P) versus coefficient of friction (f)



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