applied fracture mechanics

Fractal Fracture Mechanics Applied to Materials Engineering 85where dL0is the incremental growth of the crack length. In the two-dimensional case,where the fracture surface is characterized by a crack with length L0and a unit thicknessbody, one has dV dxdy andd0 dx uJ0 W dy T. ds.dL 0dLV 0LC 0 (82)For a fixed boundary C , d dL0 d dx , and the J 0-integral for the plane projected crackpath can be written only in terms of the boundary,uJ0 Wdy T. ds.xVC(83)Figure 4. Boundary around to the rugged crack tip where is defined the J-Integral [43].Now, the J-R Eshelby-Rice integral theory is modified to include the fracture surfaceruggedness. Initially, equation (82) is rewritten, dx dL u dL J0W dy T. ds.dL dLV0L dL C 0 (84)From postulate IV, the new J-integral on the rugged crack path is given byd dx * uJ W dy * T.dsdL dLLVC (85)where the * symbol represents coordinates with respect to the rugged path. So, in ananalogous way to the J-integral for the projected crack path given by equation (85), sinced dL d dx * , one hasuJ Wdy * T. ds.x*VC(86)