applied fracture mechanics

52Applied Fracture Mechanicsenergy balance, from which the crack comes to exist, because below this size, there is nosense speak of crack length. Therefore, the scale that must be considered is given by:where a is given by relation (40).min aL0, (57)Therefore, the statistical self-similarity or self-affinity of a fracture surface, or a crack islimited by a cutoff lower scale min, determined by the minimum critical size, l 0 a , and acutoff upper scale max, given by the macroscopic crack length, L0.In two dimensions, the problem of existence of a minimum scale size (possibly given by theMishnaevky minimum size), leads to abstraction of a microsurface with minimum area,whose shape will be investigated further, in Appendices, in terms of the number of stressconcentrators nearest existing within a material.4.3. Model of self-affine fracture surface or profilesIn this section one intend to present the development of fractal models of self-similarsurfaces. From a rough fracture surface can be extracted numerous profiles also rough onthe crack propagation direction. However, in this section is considered only one profile,which is representative of the entire fracture surface (Figure 18). The plane strain conditionadmits this assumption. Because, although the fracture toughness varies along the thicknessof the material to a plastic zone reduced in relation to material thickness, it can beconsidered a property. This means that it is possible to obtain a statistically rough profile,equivalent to other possible profiles, which can be obtained within the thickness rangeconsidered by plane strain conditions.Figure 18. Statistically equivalent profiles along the thickness of the materialIn order also equivalent to this, it is also possible to obtain an average projected crack lengthas a result of an average of the crack size along the thickness of the material thickness withinthe range considered by plane strain, for the purpose of calculations in CFM, it is considered