Review of fractal analysis of fracture surfaces in various materials using three-dimensional images reconstructed by stereo matching method

Abstract

The fractal analysis of fracture surfaces using the three-dimensional images reconstructed by the computer-aided stereo matching method was reviewed in various materials. The fractal dimension of the fracture surface was estimated on 15 kinds of fracture surfaces such as fatigue fracture surfaces, creep fracture surfaces and impact fracture surfaces of metallic materials or ceramics, with fracture surface patterns including dimples, striations or grain-boundary facets. The fractal dimension of the fracture surface was compared to that of the fracture surface profile or the fracture surface contour on the reconstructed fracture surface images. The results of the fractal analysis seemed to indicate that the reconstructed material fracture surface images are generally not completely isotropic. When estimated in the length scale range that is associated with the size ranges of the principal fracture surface patterns on 10 kinds of fracture surfaces, the results of the three-dimensional fractal analysis were well correlated to those of the two-dimensional fractal analysis of the actual fracture surface profile of metallic materials or the indentation crack of ceramics. It was confirmed that the computer-aided stereo matching method can reproduce the principal fracture surface topography to give important information for investigation of material fracture, except subsurface cracks and overlaps of the fracture surface. For detailed geometrical analysis of material fracture surfaces, it is suitable to conduct the fractal analysis in correlation with the size range of the principal fracture surface patterns.

Keywords

Fractal dimension fracture surfaces fracture surface topography stereo matching method metallic materials ceramics

Get full access to this article

View all access options for this article.

References

Almqvist

, Fractal analysis of scanning probe microscopy images, Surface Sci.355 (1996), 221–228.

Dauskardt

R.H.

Haubensak

and Ritchie

R.O.

, On the interpretation of the fractal character of fracture surfaces, Acta Metall.38(2) (1990), 143–159.

Drury

W.J.

and Gokhale

A.M.

, Statistical analysis of profilometric sampling for roughness parameters, in: Fractography of Modern Engineering Materials: Composites and Metals, Second Volume, ASTM STP 1203 Masters

J.E.

and Gilbertson

L.N.

(eds), American Society for Testing and Materials, Philadelphia, PA, 1993, pp. 58–70.

Gokhale

A.M.

Drury

W.J.

and Mishra

, Recent developments in quantitative fractography, in: Fractography of Modern Engineering Materials: Composites and Metals, Second Volume, ASTM STP 1203 Masters

J.E.

and Gilbertson

L.N.

(eds), American Society for Testing and Materials, Philadelphia, PA, 1993, pp. 3–22.

Ikeshoji

and Shioya

, Brittle–ductile transition and scale dependence: Fractal dimension of fracture surface of materials, Fractals7(2) (1999), 159–168.

Kobayashi

and Shockey

D.A.

, A fractographic investigation of thermal embrittlement in cast duplex stainless steel, Metall. Trans.18A(11) (1987), 1941–1949.

Komai

and Kikuchi

, Three-dimensional image analysis of fatigue fracture surface, J. Soc. Mater. Sci. Jpn34(6) (1985), 648–652.

X.W.

Tian

J.F.

Kang

and Wang

Z.G.

, Quantitative analysis of fracture surface by roughness and fractal method, Scripta Metall. Mater.33(5) (1995), 803–809.

Mandelbrot

B.B.

, translated by H. Hironaka, in: The Fractal Geometry of Nature, Nikkei Science, Tokyo, 1985, p. 25.

10.

Mandelbrot

B.B.

, translated by H. Hironaka, in: The Fractal Geometry of Nature, Nikkei Science, Tokyo, 1985, p. 116.

11.

Mandelbrot

B.B.

Passoja

D.E.

and Paullay

A.J.

, Fractal character of fracture surfaces of metals, Nature308 (1984), 721–722.

12.

Matsuoka

Sumiyoshi

and Ishikawa

, Fractal character of scanning tunneling microscopic images of brittle fracture surfaces on chromium, Trans. JSME56(10) (1990), 2091–2097.

13.

Mecholsky

J.J.

Passoja

D.E.

and Feinberg-Ringel

K.S.

, Quantitative analysis of brittle fracture surfaces using fractal geometry, J. Am. Ceram. Soc.72(1) (1989), 60–65.

14.

Pande

C.S.

Richards

L.E.

Louat

Dempsey

B.D.

and Schwoeble

A.J.

, Fractal characterization of fracture surfaces, Acta Metall.35(7) (1987), 1633–1637.

15.

Stampfl

and Kolednik

, The separation of the fracture energy in metallic materials, Int. J. Fracture101 (2000), 321–344.

16.

Stampfl

Scherer

Gruber Berchthaler

and Kolednik

, Determination of the fracture toughness by automatic image processing, Int. J. Fracture78 (1996), 35–44.

17.

Takayasu

, Fractals in the Physical Sciences, Manchester University Press, Manchester and New York, 1990, p. 11.

18.

Takayasu

, Fractals in the Physical Sciences, Manchester University Press, Manchester and New York, 1990, p. 20.

19.

Tanaka

, Effects of Microstructures and creep conditions on the fractal dimension of grain boundary fracture in high-temperature creep of heat-resistant alloys, Z. Metallkd.84(10) (1993), 697–701.

20.

Tanaka

, Fractal dimension of the grain boundary fracture in creep-fracture of cobalt-based heat resistant alloys, J. Mater. Sci.31(13) (1996), 3513–3521.

21.

Tanaka

, Relationship between fracture toughness and crack morphology of brittle materials, J. Soc. Mater. Sci. Jpn47(2) (1998), 169–176.

22.

Tanaka

and Kato

, Fractal analysis of fracture surfaces and simulation of fracture process using fractal dimension maps in stainless steels fatigued by repeated bending, ISIJ Int.52(9) (2012), 1683–1692.

23.

Tanaka

Kayama

and Kato

, Relations between microstructures, fracture mechanism and fatigue properties in structural materials, J. Mater. Sci. Lett.18(2) (1999), 107–110.

24.

Tanaka

Kimura

Chouanine

Kato

and Taguchi

, Fractal analysis of the three-dimensional fracture surfaces in materials by the box-counting method, J. Mater. Sci. Lett.22(18) (2003), 1279–1281.

25.

Tanaka

Kimura

Chouanine

Taguchi

and Kato

, Quantitative analysis of three-dimensional fatigue fracture surface reconstructed by stereo matching method, ISIJ Int.43(9) (2003), 1453–1460.

26.

Tanaka

Kimura

Kayama

Kato

and Taguchi

, Fractal Analysis of three-dimensional fracture surfaces in metals and ceramics, ISIJ Int.44(7) (2004), 1250–1257.

27.

Tanaka

Kimura

Kayama

Taguchi

and Kato

, Geometrical analysis and pattern recognition using mapping technologies of three-dimensional fracture surfaces in materials, J. Mater. Sci.40(23) (2005), 6291–6299.

28.

Tanaka

Kimura

Taguchi

and Kato

, Fracture surface topography and fracture mechanism in austenitic SUS316 steel plates fatigued by repeated bending, J. Mater. Sci.41(10) (2006), 2885–2893.

29.

Tanaka

Ono

Sakashita

and Kato

, Fractal dimension of grain-boundary fracture for characterization of high-temperature fracture in heat-resistant alloys, ISIJ Int.49(8) (2009), 1229–1238.

30.

Tanaka

Tagami

Kato

Akiyama

Oyama

and Ono

, Quantitative evaluation of the impact fracture surfaces of SS400 steel by the three-dimensional geometrical analysis, ISIJ Int.47(1) (2007), 178–186.

31.

Ueno

Kishimoto

Kino

and Ishii

, Topographical fractography and fracture simulation with scanning laser microscope, Trans. JSME63(11) (1997), 2393–2399.

32.

Underwood

E.E.

and Banerji

, Fractals in fractography, Mater. Sci. Eng.80 (1986), 1–14.