Abstract
The effects of grain boundary configuration and creep conditions on the fractal dimension of the grain boundary fracture (D f) were investigated using commercial cobalt-based heat resistant alloys, namely, HS-21 and L-605 alloys. Creep-rupture experiments were carried out under the initial creep stresses of 19.6–176 MPa in the temperature range from 1089–1422 K in air. The value of D f was larger in specimens with serrated grain boundaries than in those with straight grain boundaries in the HS-21 alloy under the same creep condition, and the difference in the value of D f between these specimens was large in the scale range of the analysis which was less than about one grain boundary length. However, there was almost no difference in the value of D f between the specimens with serrated grain boundaries and those with straight grain boundaries in the L-605 alloy, because there was no obvious difference in the microstructure between these specimens. The value of D f increased with decreasing creep stress in the scale range of the fractal analysis larger than about one grain boundary length in both HS-21 and L-605 alloys, while the stress dependence of D f was larger in the HS-21 alloy. The stress dependence of D f was explained by the stress dependence on the number of grain boundary microcracks linked to the fracture surface. The value of D f estimated in the scale range smaller than about one grain boundary length showed essentially no stress dependence in both L-605 and HS-21 alloys.
Similar content being viewed by others
References
B. B. Mandelbrot, “The Fractal Geometry of Nature,” translated by H. Hironaka (Nikkei Science, Tokyo, 1985), p. 25.
B. B. Mandelbrot, D. E. Passoja and A. J. Paullay, Nature, 308 (1984) 721.
K. Banerji and E. E. Underwood, in Proc. 6th Conf. on Fracture, New Delhi, India, 1984, Advances in Fracture Research, eds S. R. Valluri, D. M. R. Taplin, P. Rama Rao, J. F. Knott, R. Dubey, (Pergamon Press, London, 1984), 1612 p. 1371.
E. E. Underwood and K. Banerji, Mater. Sci. Eng. 80 (1986), 1.
E. Hornbogen, Z, Metallkd. 78 (1987), 622.
Idem. Int. Mater. Rev. 34 (1989) 277.
R. H. Dauskardt, F. Haubensak and R. O. Ritchie, Acta Metall. 38 (1990) 142.
M. Tanaka and H. Iizuka, Z. Metallkd. 82 (1991) 442.
M. Tanaka, J. Mater. Sci. 27 (1992) 4717.
Idem. Ibid. 28 (1993) 5753.
Idem. Z. Metallkd. 84 (1993) 697.
H. Takayasu, “Fractals in the Physical Sciences,” (Manchester University Press, Manchester, 1990), p. 6.
S. Ishimura and S. Ishimura, “Fractal Mathematics,” (Tokyo Tosho Co., Tokyo, 1990), p. 246.
C. S. Pande, L. E. Richards, N. Louat, B. D. Dempsey and A. J. Schwoeble, Acta Metall. 35 (1987) 1633.
K. Banerji, Metall. Trans. A, 19A (1988) 961.
M. Tanaka, O. Miyagawa, T. Sakaki and D. Fujishiro, J. Iron Steel Inst. Japan 65 (1979) 939.
M. Tanaka, H. Iizuka and F. Ashihara, J. Mater. Sci. 24 (1989) 1623.
M. Tanaka, H. Iizuka and M. Tagami, ibid. 24 (1989) 2428.
M. Tanaka, O. Miyagawa, T. Sakaki, H. Iizuka and D. Fujishiro, Ibid. 23 (1988) 621.
M. Tanaka, H. Iizuka and F. Ashihara, Ibid. 27 (1992) 2636.
R. Ohtani and S. Nakayama, J. Mater. Sci. Japan 32 (1983) 635.
A. M. Gokhale, W. J. Drury and S. Mishra, in ASTM STP1203, American Society for Testing and Materials, Philadelphia, (1993), p. 3.
W. J. Drury and A. M. Gokhale, ibid.in, p. 58.
M. F. Ashby, Acta Metall. 20 (1972) 887.
M. F. Ashby, R. Raj and R. C. Gifkins, Scripta Metall. 4 (1970) 737.
R. Raj and M. F. Ashby, Metall. Trans. 2 (1971) 1113.
F. W. Crossman and M. F. Ashby, Acta Metall, 23 (1975) 425.
F. Garofalo, “Fundamentals of Creep and Creep Rupture in Metals,” translated by M. Adachi, (Maruzen Book Co. Ltd., Tokyo, 1968). p. 124.
T. G. Langdon and R. B. Vastava, in ASTM STP 765, American Society for Testing and Materials, Philadelphia, (1982), p. 435.
M. Tanaka, H. Iizuka and F. Ashihara, J. Mater. Sci. 23 (1988) 3827.
M. Tanaka and H. Iizuka Trans. ASME, J. Mater. Sci. Technol. 112 (1990), 353.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Tanaka, M. Fractal dimension of the grain boundary fracture in creep-fracture of cobalt-based heat resistant alloys. JOURNAL OF MATERIALS SCIENCE 31, 3513–3521 (1996). https://doi.org/10.1007/BF00360757
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/BF00360757