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.
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References
I. Bar-on, in Engineered Materials Handbook (Ceramics and Glasses) (ASM INTERNATIONAL, The Materials Information Society, 1991), pp. 645–651.
G.R. Irwin, ASME Paper No. 62-MET-15, 1–13 (1962).
A. A. Griffith, Philos. Trans. R. Soc. London A221, 163–197 (1921).
S.C. Langford and J. T. Dickinson, in ACS Symposium Series: Spectroscopic Characterization of Minerals and Their Surfaces, edited by L.M. Coyne et al. (1990), Vol. 415, pp. 224–244.
K. Ravi-Chandar and W.G. Knauss, Int. J. Fracture 28, 65–80 (1984).
J. Cuneo, Master’s Thesis, University of Florida (1996).
F.W. Preston, J. Soc. Glass Technol. 10, 234–269 (1926).
R.W. Rice, in Fractography of Ceramic and Metal Failures, ASTM STP 827, edited by J. J. Mecholsky, Jr. and S. R. Powell, Jr. (American Soc. for Testing and Materials, Philadelphia, PA, 1984), pp. 1–100.
R.W. Rice, in Surfaces and Interfaces of Glass and Ceramics, edited by V. Frechette, W. LaCourse, and V. Burdick (Plenum Press, New York, 1974), pp. 439–472.
J. J. Mecholsky, Jr., T. J. Mackin, and D. E. Passoja, in Adv. in Ceramics 22: Fractography of Ceramics and Glasses, edited by Varner and V. Frechette (The American Ceramic Soc., Westerville, OH, 1988).
J. J. Mecholsky, Jr. and S. W. Freiman, J. Am. Ceram. Soc. 74 (12), 3136–3138 (1991).
H.P. Rossmanith, University of Maryland Report [NSF Grant #DAR-77-05171] (1980).
V.D. Frechette, Fractography of Glass and Ceramics (The American Ceramic Society, Westerville, OH, 1990).
R.W. Rice, in Adv. in Ceramics 22, in Fractography of Glasses and Ceramics, edited by Varner and V. Frechette (The American Ceramic Society, Inc., Westerville, OH, 1988), pp. 3–56.
E.K. Beauchamp, Sandia National Lab. Research Report SC-RR-70-766, Albuquerque, NM (1971).
S.W. Freiman, J. J. Mecholsky, Jr., and P.F. Becher, in Ceram. Trans. 17, op Cit., 55–78 (1991).
P.N. Randall, in ASTM STP 410 (1967), pp. 88–126.
J. J. Mecholsky, Jr., in Ceram. Trans., edited by V. Frechette and Varner (The American Ceram. Society, Westerville, OH, 1991), Vol. 17.
ASTM Annual Book of Standards, E616, p. 674, The American Society for Testing and Materials, 1916 Race St., Philadelphia, PA 19103 (1984).
H.P. Kirchner and J. C. Conway, Jr., in Fractography of Glass and Ceramics, Advances in Ceramics, Vol. 22 (The American Ceramics Society, Westerville, OH, 1988), pp. 187–213.
J.C. Newman and I.S. Raju, NASA TP 1578 (1979).
D. Broek, Elementary Engineering Fracture Mechanics (Sijthoff and Nordhoff, The Netherlands, 1978).
Y.L. Tsai and J. J. Mecholsky, Int. J. Fracture 57, 167–182 (1992).
B.B. Mandelbrot, The Fractal Geometry of Nature (W. H. Freeman Co., New York, 1982).
J. Kertesz, in Disorder and Fracture, edited by J. C. Charmet, S. Roux, and E. Guyon (Plenum Press, New York, 1990), pp. 51–62.
N. Hecker, D. G. Grier, and L. M. Sander, in Fractal Aspects of Disordered Systems, edited by D.A. Weltz, L. M. Sander, and B. B. Mandelbrot (Mater. Res. Soc. Symp. Proc. EA-17, Pittsburgh, PA, 1988), pp. 17–19.
X. L. Wu, S. M. Troin, E. Herbolzheimer, and S. A. Safran, in Fractal Aspects of Disordered Systems, edited by D.A. Weitz, L.M. Sander, and B. B. Mandelbrot (Mater. Res. Soc. Symp. Proc. EA-17, Pittsburgh, PA, 1988), pp. 71–73.
H. J. Herrmann and L. de Arcangelis, in Fractal Aspects of Disordered Systems, edited by D. A. Weitz, L. M. Sander, and B. B. Mandelbrot (Mater. Res. Soc. Symp. Proc. EA-17, Pittsburgh, PA, 1988), pp. 149–163.
Xie Heping, Int. J. Fracture 41 (4) 267–274 (1989).
J. Arrault and B. Pouligny, J. Physics I (France) 6, 431–441 (1996).
T. Sakai, M. Ramulu, A. Ghoshand, and R. C. Bradt, in Ceram. Trans. 17 (1991).
J. J. Mecholsky and J. R. Plaia, J. Non. Cryst. Solids 146, 249–255 (1992).
B. B. Mandelbrot, D. E. Passoja, and J. Paullay, Nature (London) 308, 721–722 (1984).
Y. Fahmy, J.C. Russ, and C. C. Koch, J. Mater. Sci. 6, 1856–1861 (1991).
J. J. Mecholsky and T. J. Mackin, J. Mater. Sci. Lett. 7, 1145–1147 (1988).
J. Y. Thompson, J. J. Mecholsky, and K. J. Anusavice, JACerS 78, 3045–3049 (1995).
Y.L. Tsai and J. J. Mecholsky, Jr., J. Mater. Res. 6, 1248–1263 (1991).
C.Y. Poon, R. S. Sayles, and T. A. Jones, J. Phys. D: Appl. Phys. 25, 1269–1275 (1992).
E. Bouchaud, G. Lapasset, J. Planès, and S. Navéos, Phys. Rev. B. 48, 2917 (1993).
J. C. Conway and H. P. Kirchner, J. Am. Ceram. Soc. 69 (8), 603–607 (1986).
S. Chandresekar and M. Chaudhri, ACerS Bull. 76 (4), 249 (1997).
M.K. Hassan and G. J. Rodgers, Phys. Rev. Lett. A 208, 95–98 (1995).
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Mecholsky, J.J., Linhart, R., Kwitkin, B.D. et al. On the fractal nature of crack branching in MgF2. Journal of Materials Research 13, 3153–3159 (1998). https://doi.org/10.1557/JMR.1998.0429
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DOI: https://doi.org/10.1557/JMR.1998.0429