applied fracture mechanics

40Applied Fracture Mechanicsanalysis of quantities such as average grain size, roughness, etc. From geometrical viewpoint this description of the irregular fracture surface, was based, until recently, thefoundations of Euclidean geometry. However, this procedure made this description a tasktoo complicated. With the advent of fractal geometry, it became possible to approach theproblem analytically, and in more authentic way.Figure 12. Fracture surfaces of different parts mades with the same material, a) Lot A9 b) Lot A1 [56 1999].Inside the fractography, fractal description of rugged surfaces, has emerged as a powerfultool able to describe the fracture patterns found in brittle and ductile materials. With thisnew characterization has become possible to complement the vision of the fracturephenomenon, summarizing the main geometric information left on the fracture surface injust a number, " D ", called fractal dimension. Therefore, assuming that there is a closerelationship between the physical phenomena and fractal pattern generated as a fracturesurface, for example, the physical properties of these objects have implications on theirgeometrical properties. Thinking about it, one can take advantage of the geometricdescription of fractals to extract information about the phenomenology that generated it,thereby obtaining a greater understanding of the fracture process and its physicalproperties. But before modeling any irregular (or rough) fracture surface, using fractalgeometry, will be shown some of the difficulties existing and care should be taken in thismathematical description.4.2. Fractal models of a rugged fracture surfaceA fracture surface is a record of information left by the fracture process. But the ClassicalFracture Mechanics (CFM) was developed idealizing a regular fracture surface as beingsmooth and flat. Thus the mathematical foundations of CFM consider an energy equivalencebetween the rough (actual) and projected (idealized) fracture surfaces [57]. Besides themathematical complexity, part of this foundation is associated with the difficulties of anaccurate measure of the actual area of fracture. In fact, the geometry of the crack surfaces isusually rough and can not be described in a mathematically simple by Euclidean geometry