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Fractal fracture of single crystal silicon

Published online by Cambridge University Press:  31 January 2011

Y.L. Tsai  and
J.J. Mecholsky Jr.
Y.L. Tsai
Affiliation:
Department of Materials Science and Engineering, The University of Florida, Gainesville, Florida 32611
J.J. Mecholsky Jr.
Affiliation:
Department of Materials Science and Engineering, The University of Florida, Gainesville, Florida 32611
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Abstract

The quantitative description of surfaces that are created during the fracture process is one of the fundamental issues in materials science. In this study, single crystal silicon was selected as a model material in which to study the correlation of fracture surface features as characterized by their fractal dimension for two different orientations of fracture with the fracture toughness of the material as measured using the strength-indentation and fracture surface analysis techniques. The fracture toughness on the {110} fracture plane of single crystal silicon was determined to be 1.19 MPa m1/2 for the {100} tensile surface and 1.05 MPa m1/2 for the {110} tensile surface using the indentation-strength three-point bending method. The fracture surface features of these two orientations are correspondingly different. Within our limitations of measurements (1–100 μm), the fractal dimension appeared different in different regions of the fracture surface. It has a higher value in the branching region and a lower value in the pre-branching and post-branching regions. The fractal dimensions are about the same in the pre-branching regions and post-branching region for these two orientations (D = 1.01 ± 0.01), i.e., nearly Euclidean (smooth); but the fractal dimensions are higher in the branching region for these two orientations. The fractal dimension is 1.10 ±0.4 for the {100} tensile surface and is 1.04 ±0.3 for the {110} tensile surface. If we select the highest dimension on a surface to represent the dimensionality of the surface, then a material with a higher fracture toughness has a higher fractal dimension in the branching region.

Type
Articles
Information
Journal of Materials Research , Volume 6 , Issue 6 , June 1991 , pp. 1248 - 1263
Copyright
Copyright © Materials Research Society 1991

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References

1.Mecholsky, J. J., Freiman, S. W., and Rice, R. W., J. Mater. Sci. 11, 1310–1319 (1976).CrossRefGoogle Scholar
2.Mecholsky, J. J., Mackin, T. J., and Passoja, D. E., Adv. Ceram. 22, (1988).Google Scholar
3.Mackin, T. J. and Mecholsky, J. J., “A Fractal Analysis of Brittle Fracture,” Technical Report No. TR87–007, ARL (1987).Google Scholar
4.Underwood, E. E. and Banerji, K., Mater. Sci. Eng. 80, 1–14 (1986).CrossRefGoogle Scholar
5.Gilman, J. J., J. Appl. Phys. 31 (12), 2208–2218 (1960).CrossRefGoogle Scholar
6.Freiman, S. W., Mulville, R., and Mast, P. W., J. Mater. Sci. 8 (11), 1527 (1973).CrossRefGoogle Scholar
7.Anstis, G. R., Chantikul, P., Lawn, B. R., and Marshall, D. B., J. Am. Ceram. Soc. 64 (9), 533–538 (1981).CrossRefGoogle Scholar
8.Chantikul, P., Anstis, G. R., Lawn, B. R., and Marshall, D. B., J. Am. Ceram. Soc. 64 (9), 539–543 (1981).CrossRefGoogle Scholar
9.Ravi-Chandar, K. and Knauss, W. G., Int. J. Fract. 26, 65–80 (1984).CrossRefGoogle Scholar
10.Mecholsky, J. J., Freiman, S. W., and Rice, R. W., “Fractographic Analysis of Ceramics,” in ASTM STP 645, pp. 363–379 (1978).Google Scholar
11.Shand, E. B., J. Am. Ceram. Soc. 42 (10), 474–477 (1959).CrossRefGoogle Scholar
12.Kittel, C., Introduction to Solid State Physics, 5th ed. (J. Wiley & Son, Inc., New York, 1976).Google Scholar
13.Mandelbrot, B. B., The Fractal Geometry of Nature (W. H. Freeman, New York, 1982).Google Scholar
14.Rice, R. W., Fractography of Ceramic and Metal Failures, ASTM STP 827, edited by Mecholsky, J. J. and Powell, S. R., 5–103 (1984).CrossRefGoogle Scholar
15.Chen, C. P. and Leipold, Martin H., J. Am. Ceram. Soc. 59 (4), 469–472 (1980).Google Scholar
16.Mackin, T. J., “Fractals and Fracture,” Ph.D. Thesis, The Pennsylvania State University (1990).Google Scholar
17.Mecholsky, J. J., Adv. Ceram., Vol. 4, Nucleation and Crystallization in Glasses (Am. Ceram. Soc, 1982), pp. 261–276.Google Scholar
18.Mecholsky, J. J. and Freiman, S. W., Fracture Mechanics Applied to Brittle Materials, ASTM STP 678, edited by S. W., Freiman, 136–150 (1979).CrossRefGoogle Scholar
19.Kirchner, H. P. and Kirchner, J. W., J. Am. Ceram. Soc. 62 (3–4) (1979).CrossRefGoogle Scholar
20.Marshall, D. B., J. Am. Ceram. Soc. 66 (2), 127–131 (1983).CrossRefGoogle Scholar
21.Hagan, J. T., J. Mater. Sci. 14 (12), 2975–2980 (1979).CrossRefGoogle Scholar
22.Lawn, B. R. and Swain, M. V., J. Mater. Sci. 10 (1), 113–122 (1975).CrossRefGoogle Scholar
23.Lawn, B. R., Evans, A. G., and Marshall, D. B., J. Am. Ceram. Soc. 63 (9–10), 574–581 (1980).CrossRefGoogle Scholar
24.Lawn, B. R. and Evans, A. G., J. Mater. Sci. 12 (11), 2195–2199 (1977).CrossRefGoogle Scholar
25.Marshall, D. B. and Lawn, B. R., J. Mater. Sci. 14 (8), 2001–2012 (1979).CrossRefGoogle Scholar
26.Cook, R. F. and Lawn, B. R., J. Am. Ceram. Soc. 66 (11), C–200 (1983).CrossRefGoogle Scholar
27.Armentrout, S., class notes “Fractals,” spring semester 1987, The Pennsylvania State University, Dept. of Mathematics.Google Scholar
28.Mitchell, Morgan W. and Bonnell, Dawn A., J. Mater. Sci. 10, 2244–2254 (1990).Google Scholar
29.Kirchner, H. P. and Conway, J. C., Jr., J. Am. Ceram. Soc. 70 (8), 565–569 (1987).CrossRefGoogle Scholar
30.Lawn, B. R. and Wilshaw, Rodney, J. Mater. Sci. 10, 1049–1081 (1975).CrossRefGoogle Scholar
31.Lawn, B. R. and Fuller, E. R., J. Mater. Sci. 10, 2016–2024 (1975).CrossRefGoogle Scholar
32.Langford, S. C., Zhenyi, Ma, and Dickinson, J. T., J. Mater. Sci. 4, 1272–1279 (1989).Google Scholar
33.Passoja, D. E., “Fundamental Relationships between Energy and Geometry in Fracture,” Adv. in Ceramics 22: Fractography of Glasses and Ceramics (The American Ceramic Society, 1988).Google Scholar