For the title problem, the punch is assumed to be pressed vertically into the horizontal upper surface of the half space, then slide horizontally sideways. A range of such configurations is identified that permit Shtaerman’s solution for the contact pressure for a rigid frictionless punch to be modified so that it applies to a deformable punch and also yields the contact stresses when the punch slides in the presence of friction. Closed-form expressions are obtained for the peak edge-of-contact stresses. These edge-of-contact stresses can fluctuate significantly with even modest amounts of sliding.

References

References
1.
Sinclair
,
G. B.
,
Cormier
,
N. G.
,
Griffin
,
J. H.
, and
Meda
,
G.
,
2002
, “
Contact Stresses in Dovetail Attachments: Finite Element Modeling
,”
ASME J. Eng. Gas Turbines Power
,
124
(
1
), pp.
182
189
.
2.
Hertz
,
H.
,
1882
, “
Uber Die Berührung Fester Elastische Körper
,”
J. Reine Angew. Math.
,
92
(1), pp.
156
171
.
3.
Shtaerman
,
I. Y.
,
1949
,
Contact Problems of the Theory of Elasticity
,
Gostekhizdat Publishing
,
Moscow, Russia
.
4.
McEwen
,
E.
,
1949
, “
XLI. Stresses in Elastic Cylinders in Contact Along a Generatrix, Including the Effects of Tangential Friction
,”
Philos. Mag.
,
40
(
303
), pp.
454
459
.
5.
Poritsky
,
H.
,
1950
, “
Stresses and Deflections of Cylindrical Bodies in Contact With Application to Contact of Gears and Locomotive Wheels
,”
ASME J. Appl. Mech.
,
17
(3), pp.
191
201
.
6.
Smith
,
J. O.
, and
Liu
,
C. K.
,
1953
, “
Stresses Due to Tangential and Normal Loads on an Elastic Solid With Application to Some Contact Stress Problems
,”
ASME J. Appl. Mech.
,
20
(2), pp.
157
166
.
7.
Ciavarella
,
M.
,
Hills
,
D. A.
, and
Monno
,
G.
,
1998
, “
The Influence of Rounded Edges on Indentation by a Flat Punch
,”
Proc. Inst. Mech. Eng.
,
212
(4), pp.
319
328
.
8.
McVeigh
,
P. A.
,
Harish
,
G.
,
Farris
,
T. N.
, and
Szolwinski
,
M. P.
,
1999
, “
Modeling Interfacial Conditions in Nominally Flat Contacts for Application to Fretting Fatigue of Turbine Engine Components
,”
Int. J. Fatigue
,
21
(
Suppl. 1
), pp.
S157
S165
.
9.
Flamant
,
A.
,
1892
, “
Sur La Répartition Des Pressions Dans D’un Solide Rectangulaire Chargé Transversalement
,”
C. R. Acad. Sci. Paris
,
114
, pp.
1465
1468
.
10.
Johnson
,
K. L.
,
1989
,
Contact Mechanics
,
Cambridge University Press
,
Cambridge, UK
.
11.
Persson
,
A.
,
1964
, “
On the Stress Distribution of Cylindrical Elastic Bodies in Contact
,” Ph.D. dissertation, Chalmers Tekniska Hogskola, Göteborg, Sweden.
12.
Shtaerman
,
I. Y.
,
1939
, “
On Hertz’s Theory of Local Deformation in Compressed Elastic Bodies
,”
C. R. (Dokl.) Acad. Sci. URSS
,
25
(5), pp.
359
361
.
13.
Sadowsky
,
M. A.
,
1928
, “
Two-Dimensional Problems of Elasticity Theory
,”
Z. Angew. Math. Mech.
,
8
(
2
), pp.
107
121
.
14.
Boussinesq
,
J.
,
1892
, “
Des Pertubations Locales Que Produit Au-Dessons D’elle Une Forte Charge
,”
C. R. Acad. Sci. Paris
,
114
, pp.
1510
1516
.
15.
Avallone
,
E. A.
,
Baumeister
,
T.
, and
Sadegh
,
A. M.
, eds.,
2007
,
Marks’ Standard Handbook for Mechanical Engineers
,
11th ed.
,
McGraw-Hill
,
New York
.
16.
Michell
,
J. H.
,
1901
, “
The Inversion of Plane Stress
,”
Proc. London Math. Soc.
,
s1-34
(1), pp.
134
142
.
17.
Sinclair
,
G. B.
,
2016
, “Contact Stresses Induced by a Rigid Flat Punch Sliding With Friction Across an Incompressible Elastic Half Space,” Louisiana State University, Baton Rouge, LA, Report No. ME-MS3-16.
18.
Sinclair
,
G. B.
,
2016
, “Asymptotic Analysis of the Edge-of-Contact Stresses Attending Conforming Contact in the Presence of Friction of an Elastic Punch With an Elastic Half-Plane,” Louisiana State University, Baton Rouge, LA, Report No. ME-MS2-16.
You do not currently have access to this content.