In wiresaw manufacturing processes, such as those in slicing silicon wafers for electronics fabrication, abrasive slurry is carried by high-speed wire (5 to 15 m/s), which exerts normal load to the surface via hydrodynamic effects and bow of taut wire. As a result, the abrasives carried by slurry are constrained to indent onto and roll over the surface of substrate. In this paper, the axisymmetric indentation problem in the free abrasive machining (FAM) is studied by modeling a rigid abrasive of different shapes pushing onto an elastic half space. Based on the harmonic property of dilatation, the closed-form solution of stress distribution inside the cutting material for three different indentation processes in common FAM process are presented: cylindrical and conical abrasives as well as uniform pressure distribution. Along the symmetrical axis, von-Mises stress is two times larger than that of local maximum shear stress for all three indentation conditions. The von-Mises stress is infinity at the contact point for sharp pointed indentation, a location of crack initiation and nucleation. For indentation by abrasive of flat surface, which also can be provided by the localized effects due to the hydrodynamic pressure acting on the surface, both the von-Mises and local maximum shear stress reach maximum underneath the contact zone.

1.
Kao, I., Bhagavat, M., and Prasad, V., 1998, “Integrated Modeling of Wiresaw in Wafer Slicing,” Proceedings, NSF Design and Manufacturing Grantees Conference, Monterrey, Mexico, January 5–8, NSF, Virginia, pp. 425–426.
2.
Li
J.
,
Kao
I.
, and
Prasad
V.
,
1998
, “
Modeling Stresses of Contacts in Wiresaw Slicing of Polycrystalline and Crystalline Ingots: Application to Silicon Wafer Production
,”
ASME JOURNAL OF ELECTRONIC PACKAGING
, Vol.
120
, No.
2
, pp.
123
128
.
3.
Kao, I., Prasad, V., Chiang, F. P., Bhagavat, M., Wei, S., Chandra, M., Costantini, M., Leyvraz, P., Talbott, J., and Gupta, K., “Modeling and Experiments on Wiresaw for Large Silicon Wafer Manufacturing,” Proceedings, 8th Int. Symp. on Silicon Mat. Sci. and Tech., San Diego, CA, The Electrochemical Society, New Jersey.
4.
Chandra, M., Leyvraz, P., Talbott, J, A., Gupta, K., Kao, I., and Prasad, V., 1998, “Challenges in Slicing Large Diameter Silicon Wafers Using Slurry Wiresaw,” Proceedings, IMECE’98, ASME, New York.
5.
Bhagavat, M., Yang, F., and Kao, I., 1998, “Elasto-Plastic Finite Element Analysis of Indentations in Free Abrasive Machining,” Proceedings, IMECE’98, ASME, New York.
6.
Harding
J. W.
, and
Sneddon
I. N.
,
1945
, “
The Elastic Stress Produced by the Indentation of the Plane Surface of a Semi-Infinite Elastic Solid by a Rigid Punch
,”
Proc. Cam. Phil. Soc.
, Vol.
41
, pp.
16
26
.
7.
Sneddon, I. N., 1966, Mixed Boundary Value Problems in Potential Theory, North-Holland, Amsterdan.
8.
Sneddon
I. N.
,
1948
, “
Boussinesq’s Problem for a Rigid Cone
,”
Proc. Cambridge Phil. Soc.
, Vol.
44
, pp.
492
507
.
9.
Kao, I., Prasad, V., Li, J., and Bhagavat, M., 1997, “Wafer Slicing and Wire Saw Manufacturing Technology,” Proceedings, NSF Grantees Conference, Seattle, Washington, January 7–11, 1997, NSF, Virginia, pp. 239–240.
10.
Kao, I., Prasad, V., Li, J., Bhagavat, M., Wei, S., Talbott, J., and Gupta, K., 1997, “Modern Wiresaw Technology for Large Crystals,” Proceedings, ACCGE/East-97, Sept. 28–Oct. 1, 1997, ACCGE.
11.
Kao, I., Wei, S., and Chiang, F.-P., 1998, “Vibration of Wiresaw Manufacturing Processes and Wafer Surface Measurement,” Proceedings, NSF Design and Manufacturing Grantees Conference, Monterrey, Mexico, January 5–8, 1998, NSF, Virginia, pp. 427–428.
12.
Buijs
M.
, and
Houten
K. K.
,
1993
, “
A Model for Lapping of Glass
,”
Journal of Materials Science
, Vol.
28
, pp.
3014
3020
.
13.
Srinivasan
S.
, and
Scattergood
R. O.
,
1987
, “
On Lateral Cracks in Glass
,”
Journal of Materials Science
, Vol.
22
, pp.
3463
3469
.
14.
Todhunter, I., and Pearson, K., 1893, History of the Theory of Elasticity, Vol. 2, Cambridge University Press, Cambridge, UK.
15.
Green, A. F., and Zerna, W., 1954, Theoretical Elasticity, Oxford, UK.
16.
Collins
W. D.
,
1962
, “
Some Axially Symmetric Stress Distributions in Elastic Solids Containing Penny-Shaped Cracks: i—Cracks in an Infinite Solid and Thick Plate
,”
Proc. Roy. Soc. London, Ser. A
, Vol.
A266
, pp.
359
386
.
17.
Mossakovski
V. I.
,
1954
, “
The Fundamental Mixed Problems of the Theory of Elasticity for a Half-Space With a Circular Line Separating the Boundary Conditions
,”
Prikl. Mat. Meh.
, Vol.
18
, pp.
187
196
.
18.
Ufliand
I. A. S.
,
1956
, “
The Contact Problem of the Theory of Elasticity for a Die, Circular in its Plane
,”
Prikl. Mat. Meh.
, Vol.
20
, pp.
578
587
.
19.
Keer
L. M.
,
1967
, “
Mixed Boundary-Value Problems for an Elastic Half-Space
,”
Proc. Cam. Phil. Soc.
, Vol.
63
, pp.
1379
1386
.
20.
Yu
H. Y.
,
Sandy
S. C.
, and
Rath
B. B.
,
1990
, “
The Effect of Substrate on the Elastic Properties of Films Determined by the Indentation Test—Axisymmetric Boussinesq Problem
,”
J. Mech. Phys. Solids
, Vol.
38
, pp.
745
764
.
21.
Bacci
A.
, and
Bennati
S.
,
1992
, “
A Contact Problem for an Elastic Layer Indented by a Circular Punch
,”
Mechanics of Structures and Machines
, Vol.
20
, pp.
195
214
.
22.
Timoshenko, S., and Goodieer, N., 1954, Theory of Elasticity, McGraw-Hill, New York.
23.
Titchmarsh, E, C., 1937, An Introduction to the Theory Fourier Integrals, Oxford, UK.
24.
Yang, F., and Kao, I., 1998, “Stress Analysis in the Wiresaw Cutting,” Technical Report, TR98-011, Dept. of Mech. Engr., SUNY at Stony Brook.
25.
Bhagavat, M., Prasad, V., and Kao, I., 1998, “Elasto-Hydrodynamic Interaction in the Free Abrasive Wafer Slicing Using a Wiresaw: Modeling and Finite Element Analysis,” technical report, TR98-012, Dept. of Mech. Engr., SUNY at Stony Brook, New York.
This content is only available via PDF.
You do not currently have access to this content.