applied fracture mechanics

Fractal Fracture Mechanics Applied to Materials Engineering 75andUUUU2Lt l l l2tL l l l L L2Lt2tLrr(24)(25)Using equation (11), the surface energy of the projected length L0is given byUU2tL 0 0 02tL 0 0 0(26)where 0 r. The surface energy equation (25) can be rewritten in terms of the projectedlength L0of a self-affine fractal crack2 2H2H 0l 0U02rtL01 l L 0 0 (27)To see the influence of crack roughness on the surface energy, one may consider postulatesIII and IV, thusU02 2H22r L 0 0 0U 1H l 2 l L 0 0 (28)5. Stable or quasi-static fracture mechanics to the rough pathIn this section, a review of the conceptual changes introduced by Irwin (1957) in Griffith'stheory (1920) is presented considering an irregular fracture surface, taking into account thepostulates previously proposed. The purpose of this section is to use the mathematicalformalism of Linear Elastic Fracture Mechanics for stable growth of smooth cracks,generalizing it to the case of an irregular rough crack.5.1. The Griffith energy balance in terms of fractal geometryAccording to Griffith´s energy balance, one haswhilst 0dUT d Ui ULF U (29)FUL U (30)