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Fractal dimension of metallic fracture surface

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Abstract

In this study, a complete method of determination of the fractal dimension for fracture surfaces of ferrous alloys has been proposed. This dimension is determined for the vertical profile obtained by the profile technique cross-section. The image of the profile, seen through the microscope coupled with a camera, is recorded in a computer, where numerical processing is performed. For calculation of the same fractal dimension, the fd3 program has been used, which is available through the Internet. The essential element of the method is optimisation concerning microscopic magnification (scale of a length), resolution of the recorded image and selection of the grey level threshold at binarization. The tests for the stability of discretization, which enable minimization of the error of the measurement, have also been carried out. These tests consist in checking the difference in fractal dimensions for the same profile obtained in two different methods of contouring as well as the difference between capacitive, informative and correlative dimensions. In both cases, too big difference suggests that the determined dimension is not reliable. This method allows determination of the fractal dimension with an absolute accuracy of 0.05 in non-dimensional units. The method has been employed in many studies. In this paper the following tests have been presented: a “fractal map” of the fracture surface was made, an influence of the mechanical notch radius in a compact specimen on the fractal dimension of the fracture surface, an influence of the distortion rate on the fractal dimension, an effect of fatigue crack propagation rate on the fractal dimension and influence of the stress-intensity factor on the fractal dimension of the fracture surface. The following materials were examined: Armco iron, P355N steel and 41Cr4 steel in different states after the heat treatment. The measurements have been made for the specimens of the compact type. There was considered an influence of location of the place of measurement on the fractal dimension being determined. The dimension was determined on the profiles lying longwise and crosswise the crack propagation direction. It has been found that the fractal dimension of the fracture surface does not depend on a place of measurement. This suggests, among other things, that a distinction between the places, which were created under conditions of the plane stress, and the places, which were created under conditions of the plane strain state, cannot be made with the help of the fractal dimension. When testing an influence of the radius of the mechanical tip notch on the fractal dimension of a fracture surface, this dimension was determined in the places located at different distances from the tip of the mechanical notch. With respect to the radii up to 1.0 mm, no significant differences in fractal dimensions have been found. The fractal dimensions of the fracture surface for all examined materials were practically the same and they ranged from 2.02 to 2.10. However in some ranges of da/dN rate the dimension was changing inversely proportional to da/dN. Obtained results confirm that fractal dimension do not depend on the investigated material.

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References

  • T Babadagli K Develi (2003) ArticleTitleFractal characteristics of rocks fractured under tension Theoret Appl Fract Mech 39 73–88 Occurrence Handle10.1016/S0167-8442(02)00139-8

    Article  Google Scholar 

  • AS Balankin GN Yanevich (1991) ArticleTitleErgodynamics of impact cratering and principles of simulation of an impact Soviet Tech Phys Lett 17 236–238

    Google Scholar 

  • AS Balankin (1992) ArticleTitleFractal mechanics of deformed media and the topology of fracture in solids Doklady Akademii Nauk 322 869–874 Occurrence Handle1172008

    MathSciNet  Google Scholar 

  • AS Balankin O Susarrey (1996) ArticleTitleStatistical topography of the set of admissible crack paths in a brittle solid Int J Fract 81 R27–R32 Occurrence Handle10.1007/BF00033183

    Article  Google Scholar 

  • AS Balankin (1997) ArticleTitlePhysics of fracture and mechanics of self-affine cracks Eng Fract Mech 57 IssueID2/3 135–203 Occurrence Handle10.1016/S0013-7944(97)00007-6

    Article  Google Scholar 

  • AS Balankin D Morales Gomez-Mancilla O Susarrey I Campos (2000) ArticleTitleFractal properties of fracture surfaces in steel 1045 Int J Fract 106 L21–L26 Occurrence Handle10.1023/A:1022670017422

    Article  Google Scholar 

  • AS Balankin O Susarrey G Urriolagoitia LH Hernandez (2002) ArticleTitleSelf-affine nature of the stress-strain behavior of an elastic fractal network Phys. Lett. A 297 376–386 Occurrence Handle1068.74531 Occurrence Handle10.1016/S0375-9601(02)00427-9 Occurrence Handle2002PhLA..297..376B

    Article  MATH  ADS  Google Scholar 

  • AS Balankin D Morales (2005) ArticleTitleAnomalous roughness of turbulent interfaces with system size dependent local roughness exponent Phys Lett A 339 23–32 Occurrence Handle10.1016/j.physleta.2005.02.064 Occurrence Handle2005PhLA..339...23B Occurrence Handle1137.80314

    Article  ADS  MATH  Google Scholar 

  • Bažant ZP (1995a) Scaling theories for quasibrittle fracture: recent advances and new directions. 2nd International Conference on Fracture Mechanics of Concrete and Concrete Surfaces, at ETH, Zürich, 515–534

  • ZP Bažant (1995b) ArticleTitleScaling of quasi-brittle fracture and fractal question J Eng Mater Technol 117 316–367

    Google Scholar 

  • ZP Bažant (1997a) ArticleTitleFracturing truss model: size effect in shear failure of reinforced concrete J Eng Mech ASCE 123 IssueID12 1276–1288

    Google Scholar 

  • ZP Bažant (1997b) ArticleTitleScaling of quasi-brittle fracture: Hypotheses of invasive and lacunar fractality, their critique and Wiebull connection Int J Fract 83 41–65 Occurrence Handle10.1023/A:1007335506684

    Article  Google Scholar 

  • ZP Bažant A Yavari (2005) ArticleTitleIs the cause of size effect on structural strength fractal or energeticá1statistical Eng Fract Mech 72 1–31 Occurrence Handle10.1016/j.engfracmech.2004.03.004

    Article  Google Scholar 

  • FM Borodich (1992) ArticleTitleFracture energy in a fractal cracks propagating in concrete or rock Doklady Rossiyskoy Akademii Nauk 325 IssueID6 1138–1141

    Google Scholar 

  • FM Borodich (1994) ArticleTitleFracture energy of brittle and fractal cracks Fractals Nat Appl Sci 41 61–68

    Google Scholar 

  • FM Borodich (1997) ArticleTitleSome fractal models of fracture J Mech Phys Solid 45 IssueID2 239–259 Occurrence Handle0969.74572 Occurrence Handle10.1016/S0022-5096(96)00080-4 Occurrence Handle1997JMPSo..45..239B

    Article  MATH  ADS  Google Scholar 

  • FM Borodich (1999) ArticleTitleFractals and fractal scaling in fracture mechanics Int J Fract 95 239–259 Occurrence Handle10.1023/A:1018660604078

    Article  Google Scholar 

  • FM Borodich DA Onishchenko (1999) ArticleTitleSimilarity and fractality in the modelling of roughness by a multilevel profile with hierarchical structure Int J Solid Struct 36 2585–2612 Occurrence Handle0939.74004 Occurrence Handle1686801 Occurrence Handle10.1016/S0020-7683(98)00116-4

    Article  MATH  MathSciNet  Google Scholar 

  • FM Borodich (2001) ArticleTitleSelf-similar models and size effect of multiple fracture Fractals 9 IssueID1 17–30 Occurrence Handle10.1142/S0218348X01000579

    Article  Google Scholar 

  • E Bouchaud G Lapasset J Planes (1990) ArticleTitleFractal dimension of fractured surfaces: a Universal Value? Europhys Lett 13 IssueID1 73–79 Occurrence Handle1990EL.....13...73B

    ADS  Google Scholar 

  • E Bouchaud (1994) ArticleTitleComplex microstructures analysis: fracture surfaces as an example Solid State Phenomena 35–36 353–368

    Google Scholar 

  • E Bouchaud (1997) ArticleTitleScaling properties of cracks J Phys: Condens Matter 9 4319–4344 Occurrence Handle10.1088/0953-8984/9/21/002 Occurrence Handle1997JPCM....9.4319B

    Article  ADS  Google Scholar 

  • E Bouchaud JP Bouchaud DS Fisher S Ramanathan JR Rice (2002) ArticleTitleCan crack front waves explain the roughness of cracks? J Mech Phys Solid 50 1703–1725 Occurrence Handle1041.74061 Occurrence Handle10.1016/S0022-5096(01)00137-5 Occurrence Handle2002JMPSo..50.1703B

    Article  MATH  ADS  Google Scholar 

  • SR Brown CH Scholz (1985) ArticleTitleBroad bandwidth study of the topography of natural rock surfaces J Geophys Res 90B 12575–12582 Occurrence Handle1985JGR....9012575B Occurrence Handle10.1029/JB090iB14p12575

    Article  ADS  Google Scholar 

  • A Carpinteri (1994) ArticleTitleScaling laws and renormalization groups for strength and toughness of disordered materials Int J Solid Struct 31 IssueID3 291–302 Occurrence Handle0807.73050 Occurrence Handle10.1016/0020-7683(94)90107-4

    Article  MATH  Google Scholar 

  • Carpinteri A, Chiaia B, Maradei F (1995) Experimental determination of the fractal dimension of disordered fracture surfaces In Advanced technology for design and fabrication of composite materials and structures, Kluwer, New York, pp 269–292

  • A Carpinteri B Chiaia P Cornetti (2002) ArticleTitleA scale-invariant cohesive crack model for quasibrittle materials Eng Fract Mech 69 207–217 Occurrence Handle10.1016/S0013-7944(01)00085-6

    Article  Google Scholar 

  • A Celli A Tucci L Esposito C Palmonari (2003) ArticleTitleFractal analysis of cracks in aluminazirconia composites J Euro Ceram Soc 23 469–479 Occurrence Handle10.1016/S0955-2219(02)00148-6

    Article  Google Scholar 

  • D Chapparda I Degasnea G Hurec E Legrandb M Audranb MF Baslea (2003) ArticleTitleImage analysis measurements of roughness by texture and fractal analysis correlate with contact profilometry Biomaterials 24 1399–1407 Occurrence Handle10.1016/S0142-9612(02)00524-0

    Article  Google Scholar 

  • GP Cherepanov AS Balankin VS Ivanova (1995) ArticleTitleFractal fracture mechanics—a review Eng Fract Mech 51 IssueID6 997–1033 Occurrence Handle10.1016/0013-7944(94)00323-A

    Article  Google Scholar 

  • BL Cox JS Wang (1993) ArticleTitleFractal surfaces: measurement and applications in the earth sciences Fractals 1 87–115 Occurrence Handle0878.58046 Occurrence Handle10.1142/S0218348X93000125

    Article  MATH  Google Scholar 

  • RH Dauskardt F Haubensak RO Ritchie (1990) ArticleTitleOn the interpretation of the fractal character of fractured surfaces Acta Metall Mater 38 143–159 Occurrence Handle10.1016/0956-7151(90)90043-G

    Article  Google Scholar 

  • F Dossou R Gauvin (1994) ArticleTitleThe correlation between the fractal dimension of fractured surfaces and mechanical properties of 6061/Al2O − 3/10–20% p Fractals 2 249–252 Occurrence Handle10.1142/S0218348X94000272

    Article  Google Scholar 

  • B Dubuc JF Quiniou C Roques-Carmes (1989) ArticleTitleEvaluating the fractal dimension of profiles Phys Rev A 39 1500–1512 Occurrence Handle983085 Occurrence Handle10.1103/PhysRevA.39.1500 Occurrence Handle1989PhRvA..39.1500D

    Article  MathSciNet  ADS  Google Scholar 

  • Falconer K (1990) Fractal geometry—mathematical foundations and applications. University of Bristol

  • K Falconer (1997) Techniques in fractal geometry John & Sons Chichester Occurrence Handle0869.28003

    MATH  Google Scholar 

  • J Feder (1988) Fractals Plenum Press New York Occurrence Handle0648.28006

    MATH  Google Scholar 

  • H Gao (1993) ArticleTitleSurface roughening and branching instabilities in dynamic fracture J Mecha Phys Solids 41 457–486 Occurrence Handle10.1016/0022-5096(93)90044-G Occurrence Handle1993JMPSo..41..457G

    Article  ADS  Google Scholar 

  • RV Gol‘dshteĭn AB Mosolov (1991) ArticleTitleCracks with a fractal surface Doklady Akademii Nauk 36 IssueID8 603–605 Occurrence Handle1152399

    MathSciNet  Google Scholar 

  • RV Gol‘dshteĭn AB Mosolov (1992) ArticleTitleFractal cracks J Appl Mat Mech 56 IssueID4 563–571 Occurrence Handle10.1016/0021-8928(92)90012-W

    Article  Google Scholar 

  • RV Gol‘dshteĭn AB Mosolov (1993) ArticleTitleMultifractal failure geometry and the scale effect Doklady Akademii Nauk 329 IssueID4 429–431

    Google Scholar 

  • AA Griffith (1920) ArticleTitleThe phenomenon of rupture and flow in solids Phil Trans Roy Soc London A221 163–198 Occurrence Handle1921RSPTA.221..163G

    ADS  Google Scholar 

  • A Hansen T Engoy KJ Måly (1994) ArticleTitleMeasuring Hurst exponents with the first return method Fractals 2 527–533 Occurrence Handle0937.60500 Occurrence Handle10.1142/S0218348X94000740

    Article  MATH  Google Scholar 

  • A Hansen F Plauraboue S Roux (1995) ArticleTitleShadows in a self-affine landscape Fractals 3 91–98 Occurrence Handle1066.68565 Occurrence Handle10.1142/S0218348X95000084

    Article  MATH  Google Scholar 

  • Y Hao Z Wang Y Kang (1994) ArticleTitleFractal analysis on the fatigue fracture surface along the crack propagation direction Steel Res 65 IssueID7 305–308

    Google Scholar 

  • K Hisatsune Y Takuma Y Tanaka K Udoh K Kawasaki (1998) ArticleTitleFractal dimension of grain boundary in CuAu alloys refined by platinum addition J Mater Sci 33 4783–4785 Occurrence Handle10.1023/A:1004409725726

    Article  Google Scholar 

  • A Imre T Pajkossy L Nyikos (1992) ArticleTitleElectrochemical determination of the fractal dimension of fractured surfaces Acta Metallica Material 40 1819–1826 Occurrence Handle10.1016/0956-7151(92)90168-E

    Article  Google Scholar 

  • VS Ivanova AS Balankin V Ermishkin Y Kovnerisryi P Tamayo (1993) ArticleTitleThe fractal geometry of amorphous structures and the synergetics of vitrifivation of metallic alloys Soviet Phys Doklady 37 222–224 Occurrence Handle1993DokPh..38..222I

    ADS  Google Scholar 

  • Ivanova VS, Balankin AS, Bunin IJ, Oksogoev AA (1994) Synergetics and fractals in materials science. Nauka, Moscow.

  • J Kappraff (1991) Connections: the geometric bridge between art and science McGraw-Hill New York Occurrence Handle0729.51001

    MATH  Google Scholar 

  • A Kedzia M Rybaczuk J Dymecki (1997) ArticleTitleFractal estimation of the senile brain atrophy Folia Neuropath 35 235–238

    Google Scholar 

  • Kedzia A, Rybaczuk M (1998) The Fractal analysis of the human cortex vessels. Folia Morphologica 57.

  • Krupa K, Stoppel P (1993) Programs for filtration of bitmap files and for fractal dimensions estimation. Raport IMMT nr PRE–14/93 (in polish), Wrocław University of Technology, Wrocław.

  • Kotowski P (1996) Fractal dimension of fracture surface. Preparation of the fracture surface XVI Sympozjum nt. Zmeczenie i Mechanika Pekania (in polish), Bydgoszcz.

  • Kotowski P, Rybaczuk M, Stoppel P (1996) Fracture toughness and fractal dimension. Method of fractal dimension estimation. XVII Sympozjum Mechaniki Eksperymentalnej Ciała Stałego (in polish), Warszawa.

  • Kotowski P (2003) Fractal characteristics of the fracture surface of chosen iron alloys. Doctor thesis (in polish), Wrocaw University of Technology, Wrocław.

  • Kuznetsov PV, Panin VE, Levin KV, Lipnitskii AG, VI, Schreiber J (2001) Fractal dimension and effects of correlation of the mesostructure of the surface of plastically deformed iron silicide polycrystals and austenitic corrosion-resistant steel. Mater Sci Heat Treatment 43:89–94

  • S Kyriacos S Buczkowski F Nekka L Cartilier (1994) ArticleTitleA modified box-counting method Fractals 2 321–324 Occurrence Handle0906.92001 Occurrence Handle10.1142/S0218348X94000417

    Article  MATH  Google Scholar 

  • J Lopez G Hansali Zahouani JC Le Bosse T Mathia (1995) ArticleTitle3-D fractal based characterization for engineered surface topography Int J Mech Tool Manufacture 35 211–217 Occurrence Handle10.1016/0890-6955(94)P2375-P

    Article  Google Scholar 

  • CW Lung SG Wang QY Long (2000) ArticleTitleElastic fracture in driven media Physica B 279 139–141 Occurrence Handle10.1016/S0921-4526(99)00703-6 Occurrence Handle2000PhyB..279..139L

    Article  ADS  Google Scholar 

  • A Majumdar CL Tien (1990) ArticleTitleFractal characterization and simulation of rough surfaces Wear 136 313–327 Occurrence Handle10.1016/0043-1648(90)90154-3

    Article  Google Scholar 

  • KJ Måloy A Hansen EL Hinrichsen S Eoux (1992) ArticleTitleExperimental measurements of the roughness of brittle cracks Phys Rev Lett 68 213–215 Occurrence Handle10.1103/PhysRevLett.68.213 Occurrence Handle1992PhRvL..68..213J

    Article  ADS  Google Scholar 

  • Mandelbrot BB (1982) The fractal geometry of nature. W. H. Freeman, San Francisco.

  • BB Mandelbrot DE Passoja AJ Paullay (1984) ArticleTitleFractal character of fractured surfaces of metals Nature 308 721–722 Occurrence Handle10.1038/308721a0 Occurrence Handle1984Natur.308..721M

    Article  ADS  Google Scholar 

  • P Meakin (1991) ArticleTitleModels for materials failure and deformation Science 252 226–234 Occurrence Handle10.1126/science.252.5003.226 Occurrence Handle1991Sci...252..226M

    Article  ADS  Google Scholar 

  • P Meakin (1993) ArticleTitleThe growth of rough surfaces and interfaces Phys Report 235 189–289 Occurrence Handle10.1016/0370-1573(93)90047-H Occurrence Handle1993PhR...235..189M

    Article  ADS  Google Scholar 

  • JG Moreira JK Silva SO Kamphorst (1994) ArticleTitleOn the fractal dimension of self-affine profiles J Phys A: Mathematics General 27 8079–8089 Occurrence Handle0835.28004 Occurrence Handle10.1088/0305-4470/27/24/018 Occurrence Handle1994JPhA...27.8079M

    Article  MATH  ADS  Google Scholar 

  • S Morel J Schmittbuhl E Bouchaud G Valentin (2000a) ArticleTitleScaling of crack surfaces and implications for fracture mechanics Phys Rev Lett 85 1678–1681 Occurrence Handle10.1103/PhysRevLett.85.1678 Occurrence Handle2000PhRvL..85.1678M

    Article  ADS  Google Scholar 

  • Morel S, Bouchaud E, Valentin G (2000b) Size effect in fracture: roughening of crack surfaces and asymptotic analysis. Phys Rev B 65.

  • S Morel E Bouchaud J Schmittbuhl G Valentin (2000) ArticleTitleR-curve behavior and roughness development of fracture surfaces Int J Fract 114 307–325 Occurrence Handle10.1023/A:1015727911242

    Article  Google Scholar 

  • O Morgenstern IM Sokolov A Blumen (1993) ArticleTitleStatistical model for surface fracture Europhys Lett 22 487–492 Occurrence Handle1993EL.....22..487M

    ADS  Google Scholar 

  • AB Mosolov (1991a) ArticleTitleCracks with fractal surfaces Dokl Akad Nauk SSSR 319 IssueID4 840–844

    Google Scholar 

  • AB Mosolov (1991b) ArticleTitleFractal J-integral in fracture Sov Tech Phys Lett 17 698–700

    Google Scholar 

  • AB Mosolov FM Borodich (1992) ArticleTitleFractal fracture of brittlebodies during compression Dokl Akad Nauk SSSR 37 IssueID5 263–265 Occurrence Handle1198581

    MathSciNet  Google Scholar 

  • AB Mosolov (1993) ArticleTitleMechanics of fractal cracks in brittle solids Europhys Lett 24 IssueID8 673–678 Occurrence Handle1993EL.....24..673M

    ADS  Google Scholar 

  • AA Neimark (1992) ArticleTitleA new approach to the determination of the surface fractal dimension of porous solids Physica A 191 258–262 Occurrence Handle10.1016/0378-4371(92)90536-Y Occurrence Handle1992PhyA..191..258N

    Article  ADS  Google Scholar 

  • PD Panagiotopoulos (1992) ArticleTitleFractal geometry in solids and structures Int J Solid Struct 29 2159–2175 Occurrence Handle0764.73012 Occurrence Handle1165419 Occurrence Handle10.1016/0020-7683(92)90063-Y

    Article  MATH  MathSciNet  Google Scholar 

  • PD Panagiotopoulos OK Panagouli ES Mistakidis (1993) ArticleTitleFractal geometry and fractal material behavior in solids and structures Arch Appl Mech 63 1–24 Occurrence Handle0767.73007 Occurrence Handle10.1007/BF00787906

    Article  MATH  Google Scholar 

  • C Pande S Smith LE Richards (1987) ArticleTitleFractal characteristics of fractured surfaces J Mater Sci Lett 6 295–297 Occurrence Handle10.1007/BF01729330

    Article  Google Scholar 

  • WL Power TE Tullis SR Brown GN Boitnott CH Scholz (1987) ArticleTitleRoughness of Natural Fault Surfaces Geophys Res Lett 14 29132

    Google Scholar 

  • WL Power TE Tullis (1991) ArticleTitleEuclidean and fractal models for description of rock surface roughness J Geophys Res 96 415–424 Occurrence Handle1991JGR....96..415P

    ADS  Google Scholar 

  • S Rough J Schmittbuhl JP Vilotte A Hansen (1993) ArticleTitleSome physical properties of self-affine rough surfaces Europhys Lett 23 277–282 Occurrence Handle1993EL.....23..277R

    ADS  Google Scholar 

  • Russ JC (1994) Fractal surfaces. NY Plenum Press.

  • J Schmittbuhl S Gentier S Roux (1993) ArticleTitleField measurements of the roughness of fault surfaces Geophys Res Lett 20 639–641 Occurrence Handle1993GeoRL..20..639S

    ADS  Google Scholar 

  • J Schmittbuhl S Roux Y Berthaud (1994) ArticleTitleDevelopment of roughness in crack propagation Europhys Lett 28 585–590 Occurrence Handle1994EL.....28..585S

    ADS  Google Scholar 

  • J Schmittbuhl F Schmitt C Scholz (1995) ArticleTitleScaling invariance of crack surfaces J Geophys Res 100 IssueIDB4 5953–5973 Occurrence Handle10.1029/94JB02885 Occurrence Handle1995JGR...100.5953S

    Article  ADS  Google Scholar 

  • J Schmittbuhl JP Vilotte (1995) ArticleTitleReliability of self-affine measurements Phys Rev E 51 131–147 Occurrence Handle10.1103/PhysRevE.51.131 Occurrence Handle1995PhRvE..51..131S

    Article  ADS  Google Scholar 

  • J Schmittbuhl A Delaplace KJ Måly H Perfettini JP Vilotte (2003) ArticleTitleSlow crack propagation and slip correlations Pure Appl Geophys 160 961–976 Occurrence Handle10.1007/PL00012575 Occurrence Handle2003PApGe.160..961S

    Article  ADS  Google Scholar 

  • Simonsen I, Hansen A (1998) Determination of the Hurst Exponent by use of Wavelet Transforms. Phys Rev E 58(3)

  • H Sumiyoshi S Matsuoka K Ishikawa M Nihei (1992) ArticleTitleFractal characteristic of scanning tunneling microscopic images of brittle fracture surfaces on molybdenum JSME Int J 35 449–445

    Google Scholar 

  • M Tanaka (1997) ArticleTitleThe creep-rupture properties and the initiation and growth of the grain-boundary cracks in the cobalt-base HS-21 alloy J Mat Sci 32 1781–1788 Occurrence Handle10.1023/A:1018536319231

    Article  Google Scholar 

  • M Tanaka A Kayama R Kato Y Ito (1999) ArticleTitleEstimation of the fractal dimension of fracture surface patterns by box-counting method Fractals 7 IssueID3 335–340 Occurrence Handle10.1142/S0218348X99000335

    Article  Google Scholar 

  • M Tanaka A Kayama (2001) ArticleTitleAutomated image processing for fractal analysis of fracture surface profiles in high-temperature materials J Mater Sci Lett 20 907–909 Occurrence Handle10.1023/A:1010924732086

    Article  Google Scholar 

  • M Tanaka R Kato A Kayama (2002) ArticleTitleSize distribution of surface cracks and crack pattern in austenitic SUS316 steel plates fatigued by cyclic bending J Mater Sci 37 3945–3951 Occurrence Handle10.1023/A:1019676027293

    Article  Google Scholar 

  • PS Theocaris PD Panagiotopoulos (1993) ArticleTitleThe fractal assumption in cracks: bilateral calculation methods Int J Numer Methods Eng 36 1597–1604 Occurrence Handle0772.73065 Occurrence Handle1215811 Occurrence Handle10.1002/nme.1620360911

    Article  MATH  MathSciNet  Google Scholar 

  • EE Underwood K Banerji (1983) ArticleTitleStatistical analysis of facets in a computer simulated surface Acta Stereol 2 IssueID1 75–80

    Google Scholar 

  • EE Underwood K Banerji (1986) ArticleTitleFractals in fractography Mater Sci Eng 80 1–14 Occurrence Handle10.1016/0025-5416(86)90297-1

    Article  Google Scholar 

  • Underwood EE, Banerji K (1992) Fractal analysis of fracture surface. Metals Handbook, vol. 12. Fractography, ASM, New York, 211–215

  • D Vandembroucq S Roux (1997) ArticleTitleConformal mapping on rough boundaries. 1. Applications to harmonic problems Phys Rev E 55 IssueID5B 6171–6185 Occurrence Handle1448400 Occurrence Handle10.1103/PhysRevE.55.6171 Occurrence Handle1997PhRvE..55.6171V

    Article  MathSciNet  ADS  Google Scholar 

  • SG Wang (2003) ArticleTitleThe dependence of the fractal dimension of crack on material for brittle fracture in two dimensions Phys Lett A 308 455–460 Occurrence Handle1010.74053 Occurrence Handle10.1016/S0375-9601(02)01774-7 Occurrence Handle2003PhLA..308..455W

    Article  MATH  ADS  Google Scholar 

  • J Weiss (2001) ArticleTitleSelf-affinity of fracture surfaces and implications on a possible size effect on fracture energy Int J Fract 109 365–381 Occurrence Handle10.1023/A:1011078531887

    Article  Google Scholar 

  • P Wong J Howard JS Lin (1986) ArticleTitleSurface roughening and the fractal nature of rocks Phys Rev Lett 57 637–640 Occurrence Handle10.1103/PhysRevLett.57.637 Occurrence Handle1986PhRvL..57..637W

    Article  ADS  Google Scholar 

  • H Xie (1989) ArticleTitleThe fractal effect of irregularity on crack branching on the fracture toughness of brittle materials Int J Fract 41 267–274 Occurrence Handle10.1007/BF00018858

    Article  Google Scholar 

  • H Xie DJ Sanderson (1995a) ArticleTitleFractal effect of crack propagation on dynamic stress intensity fractors and crack velocities Int J Fract 74 29–42 Occurrence Handle10.1007/BF00018573

    Article  Google Scholar 

  • H Xie DJ Sanderson (1995b) ArticleTitleFractal kinematics of crack propagation in geomaterials Eng Fract Mech 50 529–536 Occurrence Handle10.1016/0013-7944(94)00203-T

    Article  Google Scholar 

  • A Yavari KG Hockett S Sarkani (2000) ArticleTitleThe fourth mode of fracture in fractal fracture mechanics Int J Fract 101 IssueID4 365–384 Occurrence Handle10.1023/A:1007650510881

    Article  Google Scholar 

  • A Yavari S Sarkani ET Moyer (2002) ArticleTitleThe mechanics of self-similar and self-affine fractal cracks Int J Fract 114 IssueID1 1–27 Occurrence Handle10.1023/A:1014878112730

    Article  Google Scholar 

  • X Zhang MA Knackstedt DYC Chan L Peterson (1996) ArticleTitleOn the universality of fracture surface roughness Europhys Lett 34 121–126 Occurrence Handle10.1209/epl/i1996-00426-2 Occurrence Handle1996EL.....34..121Z

    Article  ADS  Google Scholar 

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  1. Institute of Materials Science and Applied Mechanics, Wrocław University of Technology, Smoluchowskiego Str. 25, 50-370, Wrocław, Poland

    Piotr Kotowski

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Kotowski, P. Fractal dimension of metallic fracture surface. Int J Fract 141, 269–286 (2006). https://doi.org/10.1007/s10704-006-8264-x

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