applied fracture mechanics

Fractal Fracture Mechanics Applied to Materials Engineering 734.2. A self-affine fractal model for a crack - LEFMTo take the roughness into account, it will be inserted in the CFM equations a self-affinefractal model developed in a previous chapter of this book.4.2.1. The relationship between strain energies for rugged UL and projected UL0 cracks interms of fractal geometryThe crack length of the self-affine fractal can be expressed asH 0L 0L L01 l 0l 0 2 2 H1(13)where H0is the vertically projected crack length and the unloading fractal area of theelastic energy can be expressed as a function of the apparent length,And results thatA20mL0 0 (14)22 2H2rH 0l 0UL0 2 m * t 1 2H L0dL02 E' 0l 0L (15) 0 Therefore, the elastic energy released by the introduction of a crack length L0is2 2H2H 0l 0where 0 r1 l 0L 0 2 20L0UL0 m*t(16)2 E'Observe that equation (12) is recovered from equation (16) applying the limits H0 l0 L0and H 1.0 with r 0and E' E'0.To understand the effect of crack roughness on the change of elastic strain energy, one mayconsider postulates III and IV, thus0m* LH lULoUL 1 2 E' l 0L 02 22 2H2 r 0 0 0(17)It can be noticed that for H 1 , which corresponds to a smoother surface, the relationshipbetween the strain energy and the projected length L 0is more linear. While for H 0 ,