Counting the number of the squares which crosses, or touches the profile, denoting by N, fractal geometry claims the following relation:

N (d) ∞ d ^-D (4)

Introducing positive proportional constant μ, eq. (4) can be expressed by

N (d) = μ・d^-D (5)

Taking logarithms of the terms on both sides of eq. (5),

log N (d) = - D・log d + log μ (6)

is derived. Continuously changing the size of the squares, the number of squares covering the profile can be counted. These data are plotted on the log N〜log d plane for each specimen. If the relation between both the values becomes linear, then the profile has fractal characteristics and the slope of that straight line is its fractal dimension D.

　

Fig. 14 log N〜log d plot for L=150 mm, t=10 s

　

A typical evaluated results are given in Fig. 14 for the specimen with the spraying distance L=150 mm, blasting time t=10 s. It can be easily observed that the plot is a straight line and the eroded surface has a fractal characteristics. Summarizing the evaluated fractal dimensions for the specimens, the relationship between fractal dimension and the blasting time is given in Fig.15. The fractal dimension increases initially and gets to the maximum around t=4〜5 s. After that they decrease. The maximum fractal dimension is 1.045, which is lower than it for the grit blasted surface of the steal substrate [13].

　

Fig. 15 Change of fractai dimension with time

　

5. Conclusions

　

Using the Alumina coatings deposited by plasma spraying technique on the stem substrates with changing the spraying distance 75〜200 mm, the erosion experiments were done by the grit blasting method. The related properties, hardness and fracture toughness were also evaluated. The following conclusions were obtained;

(1) Both the fracture toughness and hardness decrease with increase of the spraying distance.

(2) The wear weight rate becomes larger with increase of the spraying distance.

(3) The surface roughness and fractal dimension were evaluated for the eroded surfaces and depends on the spraying distance. Judging from these results, the bonding strength between lamella decrease with increase of the spraying clistanee.

　

6. References

　

[1] Wiederhorn, S. M. and Lawn, B. R., J. Am. Ceram Soc., Vol.60 (1997), p. 458

[2] Evans, A. G. Gulden, M. E. and Rosenblaff, M., Proc. Royal Soc. London, Ser. A, Vol. 361 (1978), p. 343

[3] Wada, S., Erosion of Ceramic materials (Edt. Ritter, J), Trans Techno. Pub., (1992), p. 57

[4] Akimune, Y., Akiba, T., Okamoto, Y. and Hirosaki, N., J. Ceram. Soc. Japan, Vol. 102(1994), p. 653

[5] Amada,S. and Ichimura, K., J. Ceram. Soc. Japan , Vol. 105(19970, p. 105

[6] Nieoll, A. R., Coatings for the High Temperature Applications( Edt. Lang, E. ), Applied Sci. Publ. (1983), p. 269

[7] Sonoike, K., 14th Thermal Spraying and Lining Research Committee (196), p. 1

[8] Arata, Y., Ohmori, A. and Li, C., JWRI Trans., Vol 15 (1986), p. 167

[9] Mandelbrot, B. B., The Fractal Geometry of Nature, Freeman (1982)

[10] Amada, S. and Yamada,H., J. Surface and Coatings Technol., Vol. 78 (1996), p. 50

[11] Ishimura,S., Fractal Mathematics, Tosho Publ. (1990)

[13] Amada, S. and Hirose, T., J. Surface and Coatings Technol., Vol. 102 (1998), p. 132

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