Fracture toughness and crack morphology in indentation fracture of brittle materials

Foundations of Measurement Fractal Theory for the Fracture Mechanics

“…The geometric sequence, S is given by: (12) represented in Euclidean space, is a fractal when the measure of its geometric extension, given by the series,…”

Fractal Fracture Mechanics Applied to Materials Engineering

“…Substituting equation (13) in equation (22), one has the relationship between stresses on the rough and projected surfaces, …”

“…Also, the different geometric details contained in the fracture surface tell the history of the crack growth and the difficulties encountered during the fracture process [11]. For this reason, it is reasonable to consider in an explicit manner the fractal properties of fracture surfaces, and many scientists have worked on the characterization of the topography of the fracture surface using the fractal dimension [12,13]. At certain point, it became necessary to include the topology of the fracture surface into the equations of the Classical Fracture Mechanics theory [6,8,14].…”

“…The objective of this chapter is to include the fractal theory into the elastic and plastic energy released rates 0 G and 0 J , in a different way compared to other authors [8,13,14,17,18,19].…”

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

“…. The experimental results show that a general conclusion cannot easily be drawn [9]: some studies report a positive variation of fracture toughness along with the fractal dimension [6,[10][11][12][13], and others a negative one [14][15][16][17]. To other researchers, there is either no correlation [18][19][20] or the fractal dimension of the fractured surfaces is a universal constant [21].…”