Reliability of Measured Fractal Dimension and Roughness Exponent as Materials Dimensionless Parameters for Fracture Surfaces

Abstract

Abstract: The effects of accuracy of measured fractal dimension D and roughness exponent H are investigated in this paper with a view to examine the reliability of D and H as materials dimensionless parameters of fracture surfaces. D and H are different from general physical quantity, because they are dimensionless quantities and often appear as exponents in a theoretical function or formula. In many cases, the error of the physical quantity related to D or H may far exceed 10%, if D or H has error around 10%. The required accuracy of fractal dimension and roughness exponent should be higher, but it depends on the specific material, the associated physical quantity and the scale of measurement.

Key words: Frectal dimension, Roughness exponent, Reliability, Fracture

Shenggang WANG, Hanlong LI, Chiwei LUNG. Reliability of Measured Fractal Dimension and Roughness Exponent as Materials Dimensionless Parameters for Fracture Surfaces[J]. J Mater Sci Technol, 2003, 19(05): 499-502.

References

[1] D.E.Passoja and D.J.Amborski: J. Micros. Sci., 1978, 6, 143．
[2] M.Coster and J.L.Chermant: Int. Met. Rev., 1983, 4, 228．
[3] Y.Zhang, F.Kong, Y.B.Wang, L.J.Qian,,W.Y.Chu, J.M.Xiao: Acta Metall. Sinica, 1993, 29, A395．
[4] Z.Q.Mu, S.Q.Li and C.W.Lung: Mater. Sci. Progress, 1990, 4, 247． (in Chinese)
[5] M.Tanaka: J. Mater. Sci., 1996． 31, 749．
[6] B.B.Mandelbrot, D.E.Passoja and A.J.Paullay: Nature, 1985,308, 721．
[7] K.K.Ray and G.Mandal: Acta Mater., 1992, 40, 463．
[8] C.W.Lung and Z.Q.Mu: Phys. Rev. B, 1988, 38, 11781．
[9] C.W.Lung: in Fractal in Physics, eds. L.Pietronero and E.Tosatti (Elsevier, New York,1986) , 189．
[10] C.W.Lung, J.Jiang, E.K.Tian and C.H.Zhang: Phys. Rev. E, 1999, 60, 5121．
[11] M.Matsushita, S.Ouhi and K.Honda: J. Phys. Society of Japan, 1991, 60, 2109．
[12] Q.Y.Long, Li Suqing and C.W.Lung: J. Phys. D: Appl. Phys., 1991, 24, 602．
[13] E.Bouchaud, G.Lapasset and J.Planes: Europhys. Lett,, 1990,13, 73．
[14] M.W.Mitchell and D.A.Bonnell: J. Mater. Res., 1990, 5, 2244．
[15] K.J.Malφy,A.Hansen and E.L.Hinrichsen: Phys. Rev. Lett.,1992,68,213．
[16] T.Engφy,K.J.Malφy, A. Hansen and S.Roux: Phys. Rev. Lett.,1994,73,834．
[17] M.Sahimi and S. Arbabi: Phys. Rev. B,1993,47,713．
[18] H.Takayasu: Phys. Rev. Lett.,1985,54,1099．
[19] S.Arabai and M.Sahimi: Phys. Rev. B,1990,41,772．
[20] G.George Batrouni and A.Hansen: Phys. Rev. Lett., 1998,80,325．
[21] V. Yu.Milman,R.Blumenfeld,N.A.Stelmashenko and R.C.Ball: Phys. Rev. Lett.,1993,71,204．
[22] J. Schmittbuhl,S.Roux,J. P. Vilotte and K.JMalφy: Phys. Rev. Lett.,1995,74,1787．
[23] B.K.Kalia, A.Nakano, A.Omeltchemko,K.Tsuruta and P.Vashishta, Phys. Rev. Lett.,1997,78,2144．
[24] C.W.Lung and Z.Q.Mu: J.Mater. Sci. Technol., 1996,12,479．
[25] M.Tanaka: J.Mater. Sci. Lett., 1996,15,1184．
[26] A.B.Mosolov: Europhys. Lett.,1993,24,673．
[27] Ph. Gollion and G.Grenet: Surface and Interface Analysis,1996,24,282．
[28] E.Bouchaud and S.Naveos: J. Phys. I France,1995,5,547．
[29] P.Daguier,E. Bouchaud and G.Lapasset: Eurouphys. Lett., 1995,31,367．v