In this paper, residual stresses due to indentation and rolling of a rigid cylinder on a finite plate at a very high rolling load with a relative peak pressure of 22 are examined by two-dimensional plane strain finite element analyses using abaqus for the first time. In the finite element analyses, the roller is modeled as rigid and has frictionless contact with the finite plate. The geometry of the finite plate and its boundary conditions are assigned to correspond to those of fillet rolling of crankshafts with the constraint in the rolling direction. Finite element analyses with different meshes for single indentation on an elastic flat plate under plane strain conditions are first carried out, and the results are benchmarked with those of the elastic Hertzian solutions to establish the requirement of the finite element meshes for acceptable numerical results. The results show that the accuracy of computational results is limited by the discretization of the finite element analysis by a plot of the contact width as a function of the load. For accurate peak pressure, a total of at least eight linear elements are needed. Finite element analyses with different meshes for single indentation on an elastic–plastic flat plate under plane strain conditions are then carried out. The plate material is modeled as an elastic–plastic power-law strain hardening material with a nonlinear kinematic hardening rule for loading and unloading. The computational results are compared to establish the requirement of the finite element meshes for acceptable numerical results within 4 mm distance to the rolling surface for the crankshaft fatigue analyses. The computational results for rolling at the relative peak pressure of 22 show that the symmetric Hertzian or modified Hertzian pressure distribution should not be used to represent the contact pressure distribution for rolling simulation, while the computational results for rolling at the relative peak pressure of 5 show that the symmetric Hertzian or modified Hertzian pressure distribution may be used to represent the contact pressure distribution for rolling simulation. The computational results for the rolling case also show a significantly higher longitudinal compressive residual stress and a lower out-of-plane compressive residual stress along the contact surface when compared to those for the single indentation case. The results suggest that the effects of rolling must be accounted for when two-dimensional finite element analyses of crankshaft sections are used to investigate the residual stresses due to fillet rolling of the crankshafts under the prescribed roller loads. Due to the boundary conditions of the finite plate, the compressive residual stresses are larger when compared to those when the boundary conditions of the finite plate are fully relaxed.

References

References
1.
Love
,
R. J.
, and
Waistall
,
D. N.
,
1954
, “
The Improvement in the Bending Fatigue Strength of Production Crankshafts by Cold Rolling
,” M.I.R.A. Report No. 1954/1, pp.
1
8
.
2.
Chien
,
W. Y.
,
Pan
,
J.
,
Close
,
D.
, and
Ho
,
S.
,
2005
, “
Fatigue Analysis of Crankshaft Sections Under Bending With Consideration of Residual Stresses
,”
Int. J. Fatigue
,
27
(
1
), pp.
1
19
.10.1016/j.ijfatigue.2004.06.009
3.
Spiteri
,
P.
,
Ho
,
S.
, and
Lee
,
Y. L.
,
2007
, “
Assessment of Bending Fatigue Limit for Crankshaft Sections With Inclusion of Residual Stresses
,”
Int. J. Fatigue
,
29
(
2
), pp.
318
329
.10.1016/j.ijfatigue.2006.03.009
4.
Ho
,
S.
,
Lee
,
Y.-L.
,
Kang
,
H.-T.
, and
Wang
,
C. J.
,
2009
, “
Optimization of a Crankshaft Rolling Process for Durability
,”
Int. J. Fatigue
,
31
(
5
), pp.
799
808
.10.1016/j.ijfatigue.2008.11.011
5.
Choi
,
K. S.
, and
Pan
,
J.
,
2009
, “
Simulations of Stress Distributions in Crankshaft Sections Under Fillet Rolling and Bending Fatigue Tests
,”
Int. J. Fatigue
,
31
(
3
), pp.
544
557
.10.1016/j.ijfatigue.2008.03.035
6.
Choi
,
K. S.
, and
Pan
,
J.
,
2009
, “
A Generalized Anisotropic Hardening Rule Based on the Mroz Multi-Yield-Surface Model for Pressure Insensitive and Sensitive Materials
,”
Int. J. Plast.
,
25
(
7
), pp.
1325
1358
.10.1016/j.ijplas.2008.09.005
7.
Dumas
,
G.
, and
Baronet
,
C. N.
,
1971
, “
Elastoplastic Indentation of a Half-Space by an Infinitely Long Rigid Circular Cylinder
,”
Int. J. Mech. Sci.
,
13
(
6
), pp.
519
530
.10.1016/0020-7403(71)90039-7
8.
Hardy
,
C.
,
Baronet
,
C. N.
, and
Tordion
,
G. V.
,
1971
, “
The Elasto-Plastic Indentation of a Half-Space by a Rigid Sphere
,”
Int. J. Numer. Methods Eng.
,
3
(
4
), pp.
451
462
.10.1002/nme.1620030402
9.
Lee
,
C. H.
,
Masaki
,
S.
, and
Kobayashi
,
S.
,
1972
, “
Analysis of Ball Indentation
,”
Int. J. Mech. Sci.
,
14
(
7
), pp.
417
426
.10.1016/0020-7403(72)90099-9
10.
Kral
,
E. R.
,
Komvopoulos
,
K.
, and
Bogy
,
D. B.
,
1993
, “
Elastic-Plastic Finite Element Analysis of Repeated Indentation of Half-Space by a Rigid Sphere
,”
ASME J. Appl. Mech.
,
60
(
4
), pp.
829
841
.10.1115/1.2900991
11.
Sinclair
,
G. B.
,
Follansbee
,
P. S.
, and
Johnson
,
K. L.
,
1985
, “
Quasi-Static Normal Indentation of an Elasto-Plastic Half-Space by a Rigid Sphere-II. Results
,”
Int. J. Solids Struct.
,
21
(
8
), pp.
865
888
.10.1016/0020-7683(85)90039-3
12.
Merwin
,
J. E.
, and
Johnson
,
K. L.
,
1963
, “
An Analysis of Plastic Deformation in Rolling Contact
,”
Proc. Inst. Mech. Eng.
,
177
(1), pp.
676
690
.10.1243/PIME_PROC_1963_177_052_02
13.
Bhargava
,
V.
,
Hahn
,
G. T.
, and
Rubin
,
C. A.
,
1985
, “
An Elastic-Plastic Finite Element Model of Rolling Contact Part 1: Analysis of Single Contacts
,”
ASME J. Appl. Mech.
,
52
(
1
), pp.
67
74
.10.1115/1.3169028
14.
Bhargava
,
V.
,
Hahn
,
G. T.
, and
Rubin
,
C. A.
,
1985
, “
An Elastic-Plastic Finite Element Model of Rolling Contact Part 2: Analysis of Repeated Contacts
,”
ASME J. Appl. Mech.
,
52
(
1
), pp.
75
82
.10.1115/1.3169030
15.
Bhargava
,
V.
,
Hahn
,
G. T.
, and
Rubin
,
C. A.
,
1988
, “
Analysis of Rolling Contact With Kinematic Hardening for Rail Steel Properties
,”
Wear
,
122
(
3
), pp.
267
283
.10.1016/0043-1648(88)90014-2
16.
Kulkarni
,
S. M.
,
Hahn
,
G. T.
,
Rubin
,
C. A.
, and
Bhargava
,
V.
,
1990
, “
Elastoplastic Finite Element Analysis of Three-Dimensional, Pure Rolling Contact at the Shakedown Limit
,”
ASME J. Appl. Mech.
,
57
(1), pp.
57
65
.10.1115/1.2888324
17.
Kulkarni
,
S. M.
,
Hahn
,
G. T.
,
Rubin
,
C. A.
, and
Bhargava
,
V.
,
1991
, “
Elasto-Plastic Finite Element Analysis of Three-Dimensional Pure Rolling Contact Above the Shakedown Limit
,”
ASME J. Appl. Mech.
,
58
(
2
), pp.
347
353
.10.1115/1.2897192
18.
Kulkarni
,
S.
,
Hahn
,
G. T.
,
Rubin
,
C. A.
, and
Bhargava
,
V.
,
1991
, “
Elasto-Plastic Finite Element Analysis of Repeated Three-Dimensional, Elliptical Rolling Contact With Rail Wheel Properties
,”
ASME J. Tribol.
,
113
(
3
), pp.
434
441
.10.1115/1.2920643
19.
Jiang
,
Y.
,
Xu
,
B.
, and
Sehitoglu
,
H.
,
2002
, “
Three-Dimensional Elastic-Plastic Stress Analysis of Rolling Contact
,”
ASME J. Tribol.
,
124
(
4
), pp.
699
708
.10.1115/1.1491978
20.
Hearle
,
A. D.
, and
Johnson
,
K. L.
,
1987
, “
Cumulative Plastic Flow in Rolling and Sliding Line Contact
,”
ASME J. Appl. Mech.
,
54
(
1
), pp.
1
7
.10.1115/1.3172958
21.
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
,
37
(
4
), pp.
471
493
.10.1016/0022-5096(89)90025-2
22.
McDowell
,
D. L.
, and
Moyar
,
G. J.
,
1991
, “
Effects of Non-Linear Kinematic Hardening on Plastic Deformation and Residual Stresses in Rolling Line Contact
,”
Wear
,
144
(
1–2
), pp.
19
37
.10.1016/0043-1648(91)90004-E
23.
Jiang
,
Y.
, and
Sehitoglu
,
H.
,
1994
, “
An Analytical Approach to Elastic-Plastic Stress Analysis of Rolling Contact
,”
ASME J. Tribol.
,
116
(
3
), pp.
577
587
.10.1115/1.2928885
24.
Jiang
,
Y.
, and
Sehitoglu
,
H.
,
1996
, “
Rolling Contact Stress Analysis With the Application of a New Plasticity Model
,”
Wear
,
191
(
1–2
), pp.
35
44
.10.1016/0043-1648(95)06663-2
25.
Yu
,
M.
,
Moran
,
B.
, and
Keer
,
L. M.
,
1993
, “
A Direct Analysis of Two-Dimensional Elastic-Plastic Rolling Contact
,”
ASME J. Tribol.
,
115
(
2
), pp.
227
236
.10.1115/1.2920996
26.
Yu
,
M. M. H.
,
Moran
,
B.
, and
Keer
,
L. M.
,
1995
, “
A Direct Analysis of Three-Dimensional Elastic-Plastic Rolling Contact
,”
ASME J. Tribol.
,
117
(
2
), pp.
234
243
.10.1115/1.2831236
27.
Bijak-Zochowski
,
M.
, and
Marek
,
P.
,
1997
, “
Residual Stress in Some Elasto-Plastic Problems of Rolling Contact With Friction
,”
Int. J. Mech. Sci.
,
39
(
1
), pp.
15
32
.10.1016/0020-7403(96)00018-5
28.
Park
,
H.-S.
, and
Dang
,
X.
,
2015
, “
Multiobjective Optimization of the Heating Process for Forging Automotive Crankshaft
,”
ASME J. Manuf. Sci. Eng.
,
137
(
3
), p.
031011
.10.1115/1.4029805
29.
Chaise
,
T.
, and
Nelias
,
D.
,
2011
, “
Contact Pressure and Residual Strain in 3D Elasto-Plastic Rolling Contact for a Circular or Elliptical Point Contact
,”
ASME J. Tribol.
,
133
(
4
), p.
041402
.10.1115/1.4004878
30.
Nelson
,
A. W.
,
Malik
,
A. S.
,
Wendel
,
J. C.
, and
Zipf
,
M. E.
,
2014
, “
Probabilistic Force Prediction in Cold Sheet Rolling by Bayesian Inference
,”
ASME J. Manuf. Sci. Eng.
,
136
(
4
), p.
041006
.10.1115/1.4027434
31.
Sun
,
Q.
,
Chen
,
J.
, and
Pan
,
H.
,
2015
, “
Prediction of Edge Crack in Cold Rolling of Silicon Steel Strip Based on an Extended Gurson–Tvergaard–Needleman Damage Model
,”
ASME J. Manuf. Sci. Eng.
,
137
(
2
), p.
021003
.10.1115/1.4028827
32.
ABAQUS Version 6.10 User Manual, 2010, SIMULIA, Providence, RI.
33.
Choi
,
K. S.
,
Pan
,
J.
, and
Ho
,
S.
,
2004
, “
Fatigue Failures of Rollers in Crankshaft Fillet Rolling
,” SAE Technical Paper No. 2004-01-1498.
34.
Choi
,
K. S.
,
Pan
,
J.
, and
Ho
,
S.
,
2005
, “
Effects of Roller Geometry on Contact Pressure and Residual Stress in Crankshaft Fillet Rolling
,” SAE Technical Paper No. 2005-01-1908.
35.
Johnson
,
K. L.
,
1987
,
Contact Mechanics
,
Cambridge University Press
,
Cambridge, UK
.
36.
McEwen
,
E.
,
1949
, “
Stress in Elastic Cylinders in Contact Along a Generatrix
,”
Philos. Mag.
,
40
, pp.
454
459
.10.1098/rspa.1999.0423
37.
Mesarovic
,
S. Dj.
, and
Fleck
,
N. A.
,
1999
, “
Spherical Indentation of Elastic-Plastic Solids
,”
Proc. R. Soc. London, Ser. A
,
455
(1987), pp.
2707
2728
.10.1098/rspa.1999.0423
You do not currently have access to this content.