Hostname: page-component-848d4c4894-8kt4b Total loading time: 0 Render date: 2024-07-08T00:53:33.476Z Has data issue: false hasContentIssue false
  • English
  • Français

On the fractal nature of crack branching in MgF2

Published online by Cambridge University Press:  31 January 2011

J. J. Mecholsky Jr ,
Richard Linhart ,
Brian D. Kwitkin  and
Roy W. Rice
J. J. Mecholsky Jr
Affiliation:
University of Florida, Gainesville, Florida 32611
Richard Linhart
Affiliation:
University of Florida, Gainesville, Florida 32611
Brian D. Kwitkin
Affiliation:
University of Florida, Gainesville, Florida 32611
Roy W. Rice
Affiliation:
5411 Hopark Drive, Alexandria, Virginia 22310–1109
Get access

Abstract

Nineteen disks of IR window grade, hot pressed magnesium fluoride (˜0% porosity, grain size ˜1 μm) previously loaded in ring-on-ring flexure tests were used to analyze the crack branching patterns. Fractal geometry was used to determine the crack branching fractal dimension which was named the crack branching coefficient or CBC. The failure stress was proportional to the CBC and the number of pieces generated during the fracture. Thus, the number of pieces was proportional to the crack branching coefficient. The crack branching coefficient is distinct from the fractal dimension obtained from the onset of mist and hackle on the fracture surface. The fractal dimension of the fracture surface is, in most cases for brittle materials, a constant and related to the crack tip stress field. The crack branching fractal dimension is a function of the stress at fracture and the far-field stress distribution, or in other words, related to both the type and magnitude of loading. The findings in this work have strong implications for many commercial processes such as comminution, attrition, grinding, and basic studies in crack branching.

Type
Articles
Information
Journal of Materials Research , Volume 13 , Issue 11 , November 1998 , pp. 3153 - 3159
Copyright
Copyright © Materials Research Society 1998

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

1.Bar-on, I., in Engineered Materials Handbook (Ceramics and Glasses) (ASM INTERNATIONAL, The Materials Information Society, 1991), pp. 645–651.Google Scholar
2.Irwin, G. R., ASME Paper No. 62-MET-15, 1–13 (1962).Google Scholar
3.Griffith, A. A., Philos. Trans. R. Soc. London A 221, 163–197 (1921).Google Scholar
4.Langford, S. C and Dickinson, J. T., in ACS Symposium Series: Spectroscopic Characterization of Minerals and Their Surfaces, edited by Coyne, L. M.et al. (1990), Vol. 415, pp. 224–244.Google Scholar
5.Ravi-Chandar, K. and Knauss, W. G., Int. J. Fracture 28, 65–80 (1984).CrossRefGoogle Scholar
6.Cuneo, J, Master's Thesis, University of Florida (1996).Google Scholar
7.Preston, F. W., J. Soc. Glass Technol. 10, 234–269 (1926).Google Scholar
8.Rice, R. W., in Fractography of Ceramic and Metal Failures, ASTM STP 827, edited by Mecholsky, J. J. Jr, and Powell, S. R. Jr, (American Soc. for Testing and Materials, Philadelphia, PA, 1984), pp. 1–100.Google Scholar
9.Rice, R. W., in Surfaces and Interfaces of Glass and Ceramics, edited by Frechette, V., LaCourse, W., and Burdick, V. (Plenum Press, New York, 1974), pp. 439–472.CrossRefGoogle Scholar
10.Mecholsky, J. J. Jr, Mackin, T. J., and Passoja, D. E., in Adv. in Ceramics 22: Fractography of Ceramics and Glasses, edited by Varner, and Frechette, V. (The American Ceramic Soc., Westerville, OH, 1988).Google Scholar
11.Mecholsky, J. J Jr and Freiman, S. W., J. Am. Ceram. Soc. 74 (12), 3136–3138 (1991).CrossRefGoogle Scholar
12.Rossmanith, H. P., University of Maryland Report [NSF Grant #DAR-77–05171] (1980).Google Scholar
13.Frechette, V. D., Fractography of Glass and Ceramics (The American Ceramic Society, Westerville, OH, 1990).Google Scholar
14.Rice, R. W., in Adv. in Ceramics 22, in Fractography of Glasses and Ceramics, edited by Varner, and Frechette, V. (The American Ceramic Society, Inc., Westerville, OH, 1988), pp. 3–56.Google Scholar
15.Beauchamp, E. K., Sandia National Lab. Research Report SC-RR-70–766, Albuquerque, NM(1971).Google Scholar
16.Freiman, S. W., Mecholsky, J. J. Jr, and Becher, P. F., in Ceram. Trans. 17, op Cit., 55–78 (1991).Google Scholar
17.Randall, P. N., in ASTM STP 410 (1967), pp. 88–126.Google Scholar
18.Mecholsky, J. J. Jr, in Ceram. Trans., edited by Frechette, V. and Varner, (The American Ceram. Society, Westerville, OH, 1991), Vol. 17.Google Scholar
19.ASTM Annual Book of Standards, E616, p. 674, The American Society for Testing and Materials, 1916 Race St., Philadelphia, PA 19103 (1984).Google Scholar
20.Kirchner, H. P and Conway, J. C. Jr, in Fractography of Glass and Ceramics, Advances in Ceramics, Vol. 22 (The American Ceramics Society, Westerville, OH, 1988), pp. 187–213.Google Scholar
21.Newman, J. C and Raju, I. S., NASA TP 1578 (1979).Google Scholar
22.Broek, D., Elementary Engineering Fracture Mechanics (Sijthoff and Nordhoff, The Netherlands, 1978).Google Scholar
23.Tsai, Y. L and Mecholsky, J. J., Int. J. Fracture 57, 167–182 (1992).CrossRefGoogle Scholar
24.Mandelbrot, B. B., The Fractal Geometry of Nature (W. H. Freeman Co., New York, 1982).Google Scholar
25.Kertesz, J., in Disorder and Fracture, edited by Charmet, J. C., Roux, S., and Guyon, E. (Plenum Press, New York, 1990), pp. 51–62.CrossRefGoogle Scholar
26.Hecker, N., Grier, D. G., and Sander, L. M., in Fractal Aspects of Disordered Systems, edited by Weltz, D. A., Sander, L. M., and Mandelbrot, B.B. (Mater. Res. Soc. Symp. Proc. EA-17, Pittsburgh, PA, 1988), pp. 17–19.Google Scholar
27.Wu, X. L., Troin, S.M., Herbolzheimer, E., and Safran, S. A., in Fractal Aspects of Disordered Systems, edited by Weitz, D. A., Sander, L. M., and Mandelbrot, B. B.. (Mater. Res. Soc. Symp. Proc. EA-17, Pittsburgh, PA, 1988), pp. 71–73.Google Scholar
28.Herrmann, H. J. and de Arcangelis, L., in Fractal Aspects of Disordered Systems, edited by Weitz, D. A., Sander, L. M., and Mandelbrot, B. B.. (Mater. Res. Soc. Symp. Proc. EA-17, Pittsburgh, PA, 1988), pp. 149–163.Google Scholar
29.Heping, Xie, Int. J. Fracture 41 (4) 267–274 (1989).CrossRefGoogle Scholar
30.Arrault, J. and Pouligny, B., J. Physics I (France) 6, 431–441 (1996).CrossRefGoogle Scholar
31.Sakai, T., Ramulu, M., Ghoshand, A., and Bradt, R. C., in Ceram. Trans. 17 (1991).Google Scholar
32.Mecholsky, J. J. and Plaia, J. R., J. Non. Cryst. Solids 146, 249–255 (1992).CrossRefGoogle Scholar
33.Mandelbrot, B. B., Passoja, D. E., and Paullay, J., Nature (London) 308, 721–722 (1984).Google Scholar
34.Fahmy, Y., Russ, J. C., and Koch, C. C., J. Mater. Sci. 6, 1856–1861 (1991).Google Scholar
35.Mecholsky, J. J. and Mackin, T. J., J. Mater. Sci. Lett. 7, 1145–1147 (1988).CrossRefGoogle Scholar
36.Thompson, J. Y., Mecholsky, J. J., and Anusavice, K. J., JACerS 78, 3045–3049 (1995).Google Scholar
37.Tsai, Y. L. and Mecholsky, J. J. Jr, J. Mater. Res. 6, 1248–1263 (1991).CrossRefGoogle Scholar
38.Poon, C. Y., Sayles, R. S., and Jones, T. A., J. Phys. D: Appl. Phys. 25, 1269–1275 (1992).CrossRefGoogle Scholar
39.Bouchaud, E., Lapasset, G., Planès, J., and Navéos, S., Phys. Rev. B. 48, 2917 (1993).CrossRefGoogle Scholar
40.Conway, J. C. and Kirchner, H. P., J. Am. Ceram. Soc. 69 (8), 603–607 (1986).CrossRefGoogle Scholar
41.Chandresekar, S. and Chaudhri, M., ACerS Bull. 76 (4), 249 (1997).Google Scholar
42.Hassan, M. K. and Rodgers, G. J., Phys. Rev. Lett. A 208, 95–98 (1995).CrossRefGoogle Scholar