A direct analysis method for problems in repeated elastic-plastic rolling/sliding contact is presented. The method is shown to be an efficient technique for the determination of the steady-state solution under proportional or nonproportional cyclic loading and can provide such results as residual stress, residual strain, and cyclic strain range. Furthermore, the method is valid for both elastic and plastic shakedown. A two-dimensional rolling/sliding contact problem is considered with emphasis on the calculation of cyclic plastic strains. Several numerical techniques are employed to simplify and reduce the computational effort. These techniques consist of an operator split, the modified incremental projection method, middle-loading state, and decomposition into residual steady-state and cyclic parts. The resulting scheme is highly efficient and is ideally suited for parameter studies. To demonstrate the practical application of the approach, a two-dimensional contact problem, assuming a case-hardened material, is solved.

1.
Bhargava
V.
,
Hahn
G. T.
, and
Rubin
C. A.
,
1987
, “
Elastic-Plastic Analysis of Hardened Layers in Rims Subjected to Repeated Rolling Contacts
,”
Metall. Trans.
, Vol.
18A
, pp.
827
833
.
2.
Bower
A. F.
, and
Johnson
K. L.
,
1989
, “
The Influence of Strain Hardening on Cumulative Plastic Deformation in Rolling and Sliding Line Contact
,”
J. Mech. Phys. Solids
, Vol.
37
, No.
4
, pp.
471
493
.
3.
Dang Van
K.
, and
Maitournam
M. H.
,
1993
, “
Steady-State Flow in Classical Elastoplasticity: Applications to Repeated Rolling and Sliding Contact
,”
J. Mech. Phys. Solids.
Vol.
41
, No.
11
, pp.
1691
1710
.
4.
Dumas
G.
, and
Baronet
C. N.
,
1971
, “
Elastoplastic Indentation of a Half-Space by an Infinitely Long Rigid Circular Cylinder
,”
Int. J. Mech. Sci.
, Vol.
13
, pp.
519
530
.
5.
Johnson, K. L., 1987, “Plastic Flow, Residual Stress and Shakedown in Rolling Contact,” Proc. Symp. on Contact Mechanics and Wear of Rail/Wheel Systems II, Kingston, R. I. July 1986, University of Waterloo Press, pp. 83–97.
6.
Prager
W.
,
1955
, “
The Theory of Plasticity: a Survey of Recent Achievement
,”
Proc. Inst. Mech. Engrs.
, Vol.
169
, pp.
41
57
.
7.
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 JOURNAL OF APPLIED MECHANICS
, Vol.
20
, pp.
157
166
.
8.
Yu
M. M.-H.
,
Moran
B.
, and
Keer
L. M.
,
1993
, “
A Direct Analysis of Two-Dimensional Elastic-Plastic Rolling Contact
,”
ASME JOURNAL OF TRIBOLOGY
, Vol.
115
, pp.
227
236
.
9.
Yu, M. M.-H., Moran, B., and Keer, L. M., 1994, “A Direct Analysis of Three-Dimensional Elastic-Plastic Rolling Contact,” ASME JOURNAL OF TRIBOLOGY, 94-Trib-31.
10.
Zarka, J., and Casier, J., 1979, “Cyclic Loading on an Elastoplastic Structure, Practical Rule,” Mechanics Today, Vol. 6, Nemet-Nasser, S., ed., Pergamen Press.
11.
Zarka
J.
,
1980
, “
Direct Analysis of Elastic-Plastic Structures with ‘Overlay’ Materials During Cyclic Loading
,”
International Journal for Numerical Methods in Engineering
, Vol.
15
, pp.
225
235
.
This content is only available via PDF.
You do not currently have access to this content.