applied fracture mechanics

60Applied Fracture MechanicsFigure 23. Schematization of a rugged surface which is inclined with respect to its projection.The ruggedness must depend on infinitesimally of the projected length and its relativeorientation to it. In this case, the surface roughness by the usual definition adds an errorequal to the angle secant , or L L 0ML 1 LL// .L 0 ML //L 0McosHowever, by the definition proposed herein, when only one inclines a smooth surface againstdL dL dLoMto the horizontal, one has: L L0Mand L0M L0and again, 1 .dL dL dLo oM oWithin this philosophy will be considered as rugged any surface that presents in andLinfinitesimal portion a variation of their contour such that 1dL , therefore has to be:o(84)dL1dL . (85)o4.3.3. Preliminary considerations on the proposed modelConsidering a fractal model for the fracture surface given by the equation:2 2H2H ol oLLo1 ,l oL o (86)it is possible to describe its ruggedness in order to include it in the mathematical formalismCFM to obtain a Fractal Fracture Mechanics (FFM). This derivative of equation (86) defines afractal surface ruggedness, which for the case of a self-affine crack which grows with,H l , is given by:0 0