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.

References

1.
Adams
,
G. G.
,
2016
, “
Frictional Slip of a Rigid Punch on an Elastic Half-Plane
,”
Proc. R. Soc. A
,
472
(
2191
), p. 20160352.
2.
Spence
,
D. A.
,
1973
, “
An Eigenvalue Problem for Elastic Contact With Finite Friction
,”
Proc. Cambridge Philos. Soc.
,
73
(
1
), pp.
249
268
.
3.
Muskhelishvili
,
N. I.
,
1953
,
Some Basic Problems of the Mathematical Theory of Elasticity
,
P. Noordhoff Ltd
.,
Groningen, The Netherlands
.
4.
Adams
,
G. G.
,
2014
, “
Adhesion and Pull-Off Force of an Elastic Indenter From an Elastic Half-Space
,”
Proc. R. Soc. A
,
470
(
2169
), p. 20140317.
5.
Adams
,
G. G.
, and
Bogy
,
D. B.
,
1976
, “
The Plane Solution for the Elastic Contact Problem of a Semi-Infinite Strip and Half-Plane
,”
ASME J. Appl. Mech.
,
43
(4), pp.
603
607
.
6.
Adams
,
G. G.
, and
Hills
,
D. A.
,
2014
, “
Analytical Representation of the Non-Square-Root Singular Stress Field at a Finite Angle Sharp Notch
,”
Int. J. Solids Struct.
,
51
(
25–26
), pp.
4485
4491
.
7.
Chen
,
D.-H.
,
1994
, “
A Crack Normal to and Terminating at a Bimaterial Interface
,”
Eng. Fract. Mech.
,
49
(4), pp.
517
532
.
8.
Adams
,
G. G.
,
2015
, “
Critical Value of the Generalized Stress Intensity Factor for a Crack Perpendicular to an Interface
,”
Proc. R. Soc. A
,
471
(
2183
), p. 20150571.
9.
Hills
,
D. A.
, and
Nowell
,
D.
,
1994
,
Mechanics of Fretting Fatigue
,
Kluwer Academic Publishers
, Dordrecht,
The Netherlands
.
10.
Nowell
,
D.
, and
Hills
,
D. A.
,
2006
, “
Recent Developments in the Understanding of Fretting Fatigue
,”
Eng. Fract. Mech.
,
73
(
2
), pp.
207
222
.
11.
Lee
,
J. H.
,
Gao
,
Y.
,
Bower
,
A. F.
,
Xu
,
H.
, and
Pharr
,
G. M.
,
2018
, “
Stiffness of Frictional Contact of Dissimilar Elastic Solids
,”
J. Mech. Phys. Solids
,
112
, pp.
318
333
.
12.
Hills
,
D. A.
, and
Dini
,
D.
,
2011
, “
Characteristics of the Process Zone at Sharp Notch Roots
,”
Int. J. Solids Struct.
,
48
(
14–15
), pp.
2177
2183
.
13.
Gdoutos
,
E. E.
, and
Theocaris
,
P. S.
,
1975
, “
Stress Concentrations at the Apex of a Plane Indenter Acting on an Elastic Half Plane
,”
ASME J. Appl. Mech.
,
42
(
3
), pp.
688
692
.
14.
Bogy
,
D. B.
,
1971
, “
Two Edge-Bonded Elastic Wedges of Different and Wedge Angles Under Surface Tractions
,”
ASME J. Appl. Mech.
,
38
(
2
), pp.
377
386
.
15.
Williams
,
M. L.
,
1952
, “
Stress Singularities Resulting From Various Boundary Conditions in Angular Corners of Plates in Extension
,”
ASME J. Appl. Mech.
,
19
(4), pp.
526
528
.http://resolver.caltech.edu/CaltechAUTHORS:20140730-111744170
16.
Comninou
,
M.
,
1977
, “
The Interface Crack
,”
ASME J. Appl. Mech.
,
44
(
4
), pp.
631
636
.
17.
Barber
,
J. R.
,
2002
,
Elasticity
,
Kluwer Academic Publishers
,
Dordrecht, The Netherlands
.
18.
Bogy
,
D. B.
,
1975
, “
Solution of the Plane End Problem for a Semi-Infinite Elastic Strip
,”
J. Appl. Math. Phys. (ZAMP)
,
26
(
6
), pp.
749
769
.
19.
Erdogan
,
F.
, and
Gupta
,
G. D.
,
1972
, “
On the Numerical Solution of Singular Integral Equations
,”
Q. Appl. Math.
,
29
(
4
), pp.
525
534
.
20.
Debnath
,
L.
, and
Bhatta
,
D.
,
2007
,
Integral Transforms and Their Applications
, 2nd ed.,
Chapman & Hall/CRC
,
Philadelphia, PA
.
21.
Bogy
,
D. B.
,
1968
, “
Edge-Bonded Dissimilar Orthogonal Elastic Wedges Under Normal and Shear Loading
,”
ASME J. Appl. Mech.
,
35
(
3
), pp.
460
466
.
22.
Tranter
,
C. J.
,
1948
, “
The Use of the Mellin Transform in Finding the Stress Distribution in an Infinite Wedge
,”
Q. J. Mech. Appl. Math.
,
1
(
1
), pp.
125
130
.
23.
Timoshenko
,
S. P.
, and
Goodier
,
J. N.
,
1970
,
Theory of Elasticity
, 3rd ed.,
McGraw-Hill
,
New York
.
24.
Wolfram, 2017, “
Mathematica® 10.0
,” Wolfram Inc., Champaign, IL, accessed Dec. 10, 2017, http://wolfram.com/mathematica/?source=wordcloud
You do not currently have access to this content.