applied fracture mechanics

Foundations of Measurement Fractal Theory for the Fracture Mechanics 55where r is equal to the rugged crack length on a microscopic scale, as a function ofextension of the little boxes l 0 h 0by:2 20 0r l h(64)where l 0and h0are the microscopic sizes of the crack length in horizontal and verticaldirections, respectively. Substituting (64) in (63), one has:substituting (61) in (65), one has:v2 20 0L N l h(65)L02 2L l0 h0(66)l0Since that in the fracture process, the scales in orthogonal directions are the same physicalnature, one can choose v h l 0 / L0 , and one can writes from (62) that: 0 0 H H0L0Nh l l (67)being necessarily Nh Nv, one has:L 0H 0L0 l l l 0 0 0 H(68)rewriting the equation (66), one has:h0L L01 l 0 2(69)writing h0from (68), as:L0h0 H0l 0 H 1.(70)Eliminating in (69) the dependence of h0, by substituting (70) in (69), one has:H 0L0LL01 l 0l 0 2 2 H1(71)