Finite element solutions are presented for the subsurface stress and deformation fields in a layered elastic-plastic half-space subjected to repeated frictionless indentation by a rigid sphere. A perfectly adhering layer is modeled using two different thicknesses and elastic modulus and yield stress two and four times greater than those of the substrate. The significance of strain hardening during plastic deformation is investigated by assuming elastic-perfectly plastic and isotropically strain-hardening constitutive laws for both the layer and substrate materials. At least three load-unload cycles are applied to a peak load of 300 times the load necessary to initiate yielding in a homogeneous half-space with substrate properties. The effects of the layer thickness and material properties of the layer and substrate on the loaded and residual stresses are interpreted, and the consequences for subsurface crack initiation are discussed. The maximum principal and interfacial shear stresses are given as a function of a nondimensional strain parameter. The effect of subsequent load cycles on the loaded, residual, and maximum tensile and interfacial shear stresses and the protection provided by the harder and stiffer layer are analyzed. Reyielding during unloading and the possibility of elastic shakedown are discussed, and the accumulation of plastic strain in the yielding regions is tracked through subsequent load cycles.

1.
Burmister
D. M.
,
1945
a, “
The General Theory of Stresses and Displacements in Layered Systems
,”
J. Appl. Phys.
, Vol.
16
, pp.
89
94
.
2.
Burmister
D. M.
,
1945
b, “
The General Theory of Stresses and Displacements in Layered Systems
,”
J. Appl. Phys.
, Vol.
16
, pp.
126
127
.
3.
Chen
W. T.
,
1971
, “
Computation of Stresses and Displacements in a Layered Elastic Medium
,”
Int. J. Engng. Sci.
, Vol.
9
, pp.
775
800
.
4.
Gupta
P. K.
,
Walowit
J. A.
, and
Finkin
E. F.
,
1973
, “
Stress Distributions in Plane Strain Layered Elastic Solids Subjected to Arbitrary Boundary Loading
,”
ASME Journal of Lubrication Technology
, Vol.
95
, pp.
427
433
.
5.
Johnson, K. L., 1985, Contact Mechanics, Cambridge University Press, Cambridge, U.K., pp. 286–292.
6.
Kennedy
F. E.
, and
Ling
F. F.
,
1974
, “
Elasto-Plastic Indentation of a Layered Medium
,”
ASME Journal of Engineering Materials and Technology
, Vol.
96
, pp.
97
103
.
7.
King
R. B.
, and
O’Sullivan
T. C.
,
1987
, “
Sliding Contact Stresses in a Two-Dimensional Layered Elastic Half-Space
,”
Int. J. Solids Structures
, Vol.
23
, No.
5
, pp.
581
597
.
8.
Komvopoulos
K.
,
Saka
N.
, and
Suh
N. P.
,
1987
, “
The Role of Hard Layers in Lubricated and Dry Sliding
,”
ASME Journal of Tribology
, Vol.
109
, pp.
223
231
.
9.
Komvopoulos
K.
,
1988
, “
Finite Element Analysis of a Layered Elastic Solid in Normal Contact With a Rigid Surface
,”
ASME Journal of Tribology
, Vol.
110
, pp.
477
485
.
10.
Komvopoulos
K.
,
1989
, “
Elastic-Plastic Finite Element Analysis of Indented Layered Media
,”
ASME Journal of Tribology
, Vol.
111
, pp.
430
439
.
11.
Kral
E. R.
,
Komvopoulos
K.
, and
Bogy
D. B.
,
1993
, “
Elastic-Plastic Finite Element Analysis of Repeated Indentation of a Half-Space by a Rigid Sphere
,”
ASME JOURNAL OF APPLIED MECHANICS
, Vol.
60
, pp.
829
841
.
12.
Kral
E. R.
,
Komvopoulos
K.
, and
Bogy
D. B.
,
1995
, “
Finite Element Analysis of Repeated Indentation of an Elastic-Plastic Layered Medium by a Rigid Sphere, Part I: Surface Results
,”
ASME JOURNAL OF APPLIED MECHANICS
, Vol.
62
, pp.
20
28
.
13.
Merwin
J. E.
, and
Johnson
K. L.
,
1963
, “
An Analysis of Plastic Deformation in Rolling Contact
,”
Proc. Instn. Mech. Engrs.
, Vol.
177
, No.
25
, pp.
676
690
.
14.
Montmitonnet
P.
,
Edlinger
M. L.
, and
Felder
E.
,
1993
, “
Finite Element Analysis of Elastoplastic Indentation: Part II—Application to Hard Coatings
,”
ASME Journal of Tribology
, Vol.
115
, pp.
15
19
.
15.
O’Sullivan
T. C.
, and
King
R. B.
,
1988
, “
Sliding Contact Stress Field Due to a Spherical Indenter on a Layered Elastic Half-Space
,”
ASME Journal of Tribology
, Vol.
110
, pp.
235
240
.
16.
Tangena
A. G.
, and
Hurkx
G. A. M.
,
1985
, “
Calculations of Mechanical Stresses in Electrical Contact Situations
,”
IEEE Trans. on Components, Hybrids, and Manuf. Tech.
, Vol.
CHMT-8
, No.
1
, pp.
13
20
.
17.
Tian
H.
, and
Saka
N.
,
1991
, “
Finite Element Analysis of an Elastic-Plastic Two-Layer Half-Space: Normal Contact
,”
Wear
, Vol.
148
, pp.
47
68
.
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