applied fracture mechanics

34Applied Fracture Mechanicsup the boundary count until to reach out to the border of the object under consideration.This is done initially by setting the counting origin from a fixed point on the object, asshown in Figure10. This method seems to be the most advantageous, as well as to establish acoordinate system, or a origin for calculating the fractal dimension, it also allows, in certaincases, to infer dynamic data from static scaling, as shown by Alves [47].Figure 10. Fragment of a crack on test specimen showing the variation of measurement of the cracklength L with the measuring scale, k k / L0 for a partition Lk variável , and k l0(fixed), withsectioning done for counting by one-dimensional Sand-Box scaling method.In the Sand-Box method (Figure10), the figure is recovered with boxes of different sizes Lk,no matter the form, which can be rectangular or spherical, however, fixed at a any point " O" on figure called origin, from which the boxes are enlarged. It is counted the number ofelementary structures, or seeds, which fit within each box. Plotting the graph oflog Nk logk minLkin the same manner as in the above method the fractal dimensionis obtained. Note that in this case the maximum partition is achieved whenN Lkk min L0 l0, where L L0is the projected crack length and min l0it isthe length of the lower measuring ruler practicable.3.2.3. The global and local box dimensionsTo define the box dimension, DB, is assumed that all the space containing the fractal isrecovered with a grid (set of -dimensional units juxtaposed in the same shape and size, )