Statistics of branched fracture surfaces

Roughness effects on the critical fracture toughness of materials under uniaxial stress

“…A diverse variety of studies on very different materials ͑i.e., aluminium alloys, steels, titanium 6211, rocks, intermetallics, glass, bakelite, porcelain, graphite, carbon surfaces, polymers, etc.͒, and with different techniques ͓i.e., scanning electron microscopy, scanning tunneling microscopy, mechanical profilometry, electrochemistry, electron micrograph imaging, sectioning methods, etc.͔ revealed that the corresponding static or roughness scaling exponent was found in the range HϷ0.6-1.0. [1][2][3] All these experimental results in connection with theoretical ideas based on directed polymer models supported enormously the idea that fracture surfaces are commonly described in terms of selfaffine scaling with the most common roughness exponent near the value HϷ0.75. 2 Nevertheless, exponents close to the value HϷ0.5 4 ͑minimal energy surface͒ were also reported in cases which can be considered very different.…”

“…5 The existence of a universality class with Hϳ0.8 seemed to prevail when dynamical effects ͑i.e., rapid crack propagation͒ play a significant role. 3,6,7 Moreover, recent studies on fatigue fracture surfaces of metallic alloys and stress corrosion fracture surfaces of silicate glass by Daguier et al, 5 revealed exponents close to HϷ0.5 at small length scales which cross over to the value HϷ0.78 at a length scale depends strongly on the material and the crack velocity. However, despite the achieved consensus up to now the universality of the roughness exponent still remains controversial and under continuous investigation.…”

“…The statistical description of fracture surfaces in terms of fractal theory has been a topic of intense research the past ten years [1][2][3] because of considerable fundamental and technological importance. A diverse variety of studies on very different materials ͑i.e., aluminium alloys, steels, titanium 6211, rocks, intermetallics, glass, bakelite, porcelain, graphite, carbon surfaces, polymers, etc.͒, and with different techniques ͓i.e., scanning electron microscopy, scanning tunneling microscopy, mechanical profilometry, electrochemistry, electron micrograph imaging, sectioning methods, etc.͔ revealed that the corresponding static or roughness scaling exponent was found in the range HϷ0.6-1.0.…”

Statistical artefacts in the determination of the fractal dimension by the slit island method

“…In spite of a few serious problems with the method [3,19,32,[34][35][36][37][38][39] a lot of papers have been published over the past 10 years concerning the relationship between mechanical properties and the fractal dimension calculated by the SIM. The most surprising result was an inversion relation between fractal dimension and toughness for the same material [6,14] that allows us to investigate if all the criticisms against the method were not due to some statistical errors.…”

“…As it was shown that real surfaces such as fractured surfaces in materials are fractal [3][4][5] i.e. self-similar (or self-affine) over a wide range of scales, extensive work was done to correlate the fractal dimension of the surfaces with mechanical properties such as impact energy [6], fracture toughness [7], fatigue crack propagation [8].…”