applied fracture mechanics

Fractal Fracture Mechanics Applied to Materials Engineering 81where dL / dL0is derived from equation (13),dLR0 R (59)dL02 2H2H 0l 01 (2 H)dL l 0 L 0 dL0H0 l02 1 l 0L 02 2H2 1Therefore, the crack growth resistance ( R -curve), which is defined for a flat projectedsurface, is given substituting equation (56) and equation (60) in equation (59),(60)2 2H20l0H 1 (2 H) l 0 L 0R0 2 r2 2H2H0 l02 1 l 0L 0(61)5.6. Final remarks about equivalent quantities of smooth, rugged and projectedfracture surfacesIt is important to emphasize that the energetic equivalence between the rugged surfacecrack path and its projection was considered such that the developed equations of theFracture Mechanics for the flat plane path are still valid in the absence of any roughness.However, if a flat and smooth fracture Llis considered with the same length of a projectedfracture L0, the energetic quantities and their derivatives have the following relationship,anddU dUU U G G(62)L L0Ll L0 l 0dLldL0dU dUU U R R ,(63)l0l0 l 0dLldL0which have produced conflicting conclusions in the literature [37, 38, 46]. Since the energylfor the smooth length L 0is smaller than the energy for the projected L 0or rough Llengths, one hasdL (64)U Ll U L G lG dL 0