The poor rolling/sliding wear performance of transformation toughened ceramics (TTC) such as partially stabilized zirconia (PSZ) is believed to be a result of the volume expansion accompanying phase transformation of precipitates located immediately beneath the contacting surface. The expanding precipitates induce a surface uplift leading to surface waviness and altered rolling/sliding conditions. The very same precipitates, on the other hand enhance the toughness of the ceramic by preventing the growth of surface cracks. In order to find a compromise solution, an optimization problem is formulated for an idealized model consisting of an edge crack normal to the contacting surface and a periodic distribution of transformable grains in the layer immediately beneath this surface. The objective is to maximize the crack tip shielding by varying the volume fraction and size of the layer without exceeding a prescribed allowable surface uplift. It is shown that the maximum volume fraction of t-ZrO2 is attained at a certain depth below the surface but that its magnitude is considerably smaller than that pertaining in peak-aged PSZ.

1.
Andreasen
J. H.
, and
Karihaloo
B. L.
,
1994
, “
Surface Cracks in Transformation Toughening Ceramics
,”
International Journal of Solids and Structures
, Vol.
31
, pp.
51
64
.
2.
Braza
J. F.
,
Cheng
H. S.
, and
Fine
M. E.
,
1987
, “
Wear of Partially Stabilized Zirconia: Sliding vs. Rolling Contact
,”
Scripta Metallurgica
, Vol.
21
, pp.
1705
1710
.
3.
Braza
J. F.
,
Cheng
H. S.
,
Fine
M. E.
, and
Gangopadhyay
A. K.
,
Keer
L. M.
, and
Worden
R. E.
,
1989
, “
Mechanical Failure Mechanisms in Ceramic Sliding and Rolling Contacts
,”
Tribology Transactions
, Vol.
32
, pp.
1
8
.
4.
Budiansky
B.
,
Hutchinson
J. W.
, and
Lambropoulos
J. C.
,
1983
, “
Continuum Theory of Dilatant Transformation Toughening in Ceramics
,”
International Journal of Solids and Structures
, Vol.
19
, pp.
337
355
.
5.
Chiu
C.-H.
, and
Gao
H.
,
1993
, “
Stress Singularities along a Cycloid Rough Surface
,”
International Journal of Solids and Structures
, Vol.
30
, pp.
2983
3012
.
6.
Gao
H.
,
1991
, “
Stress Concentration at Slightly Undulating Surfaces
,”
Journal of Mechanics and Physics of Solids
, Vol.
39
, pp.
443
458
.
7.
Garvie
R. C.
,
Hannink
R. H. J.
, and
Pascoe
R. T.
,
1975
, “
Ceramic Steel?
,”
Nature
, Vol.
258
, pp.
703
704
.
8.
Greenwood
J. A.
,
1984
, “
A Unified Theory of Surface Roughness
,”
Proceedings of the Royal Society of London
, Series A
393
, pp.
133
157
.
9.
Greenwood
J. A.
, and
Tripp
J. H.
,
1967
, “
The Elastic Contact of Rough Spheres
,”
ASME Journal of Applied Mechanics
, Vol.
34
, pp.
153
159
.
10.
Hannink
R. H. J.
,
1988
, “
Significance of Microstructure in Transformation Toughening Zirconia Ceramics
,”
Materials Forum
, Vol.
11
, pp.
43
60
.
11.
Hannink, R. H. J., Murray, M. J., and Marmack, M., 1983, “Magnesia-Partially Stabilized Zirconias (Mg-PSZ) as Wear Resistant Materials,” Wear of Materials, K. C. Ludema ed., ASME, N.Y., p. 181.
12.
Hannink, R. H. J., Murray, M. J., and Scott, H. G., 1985, “Friction and Wear of Partially Stabilized Zirconia: Basic Science and Practical Applications,” Engineering Applications of Ceramic Materials, M. M. Schwartz, ed., American Society for Metals, Ohio, USA.
13.
Johnson, K. L., 1985, Contact Mechanics, Cambridge University Press, Cambridge, UK.
14.
Marshall
D. B.
, and
Swain
M. V.
,
1988
, “
Crack Resistance Curves in Magnesia-Partially-Stabilized Zirconia
,”
Journal of American Ceramic Society
, Vol.
71
, pp.
399
407
.
15.
McMeeking
R. M.
, and
Evans
A. G.
,
1982
, “
Mechanics of Transformation-Toughening in Brittle Materials
,”
Journal of American Ceramic Society
, Vol.
65
, pp.
242
246
.
16.
Muskhelishvili, N. I., 1963, Some Basic Problems of the Mathematical Theory of Elasticity, P. Noordhoff Ltd., Groningen, The Netherlands.
17.
Osyczka, A., 1984, Multicriterion Optimization in Engineering with FORTRAN Programs, Wiley, New York.
18.
Rainforth, W. M., Stevens, R., and Nutting, J., 1989, “Observations on the Sliding Wear Behaviour of Transformation Toughened Ceramics,” Proceedings of the First European Ceramic Society Conference, Vol. 3, pp. 3.533–3.537.
19.
Rose
L. R. F.
,
1987
, “
The Mechanics of Transformation Toughening
,”
Proceedings of the Royal Society of London
, Series A
412
, pp.
169
197
.
20.
Rose
L. R. F.
, and
Swain
M. V.
,
1986
, “
Two R-Curves for Partially Stabilized Zirconia
,”
Journal of American Ceramic Society
, Vol.
69
, pp.
203
207
.
21.
Scott, H. G., 1985, “Friction and Wear of Zirconia at Very Low Sliding Speeds,” Wear of Materials, K. C. Ludema, ed., ASME, N.Y., pp. 8–12.
22.
Seabra
J.
, and
Berthe
D.
,
1987
, “
Influence of Surface Waviness and Roughness on the Normal Pressure Distribution in the Hertzian Contact
,”
ASME JOURNAL OF TRIBOLOGY
, Vol.
109
, pp.
462
470
.
23.
Stump
D. M.
, and
Budiansky
B.
,
1989
, “
Finite Cracks in Transformation-Toughened Ceramics
,”
Acta Metallurgica
, Vol.
37
, pp.
3297
3304
.
24.
Thomsen, N. B., Stump, D. M., and Keer, L. M., 1995, “Surface Uplift due to Sub-Surface Phase Transformation,” International Journal of Mechanical Sciences (in press).
25.
Vanderplaats, G. N., 1987, ADS-A Fortran Program for Automated Design Synthesis, Ver 2.00, Engineering Design Optimization, Inc., Santa Barbara, CA, USA.
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