applied fracture mechanics

150 Applied Fracture Mechanics6 Will-be-set-by-IN-TECH2.4. Crack propagation statisticsTo describe crack statistics after the crack initiation stage is over it is necessary to make certainassumptions. The simplest assumptions of this kind are: the existing cracks do not heal andnew cracks are not created. In other words, the number of cracks in any material volumeremains constant in time. Based on a practically correct assumption that the defect distributionis initially scarce, the coalescence of cracks and changes in the general stress field are possibleonly when cracks have already reached relatively large sizes. However, this may happen onlyduring the last stage of crack growth the duration of which is insignificant for calculation offatigue life. Therefore, it can be assumed that over almost all life span of fatigue cracks theirorientations do not change. This leads to the equation for the density of crack distributionf (N, x, y, z, l) as a function of crack radius l after N loading cycles in a small parallelepipeddxdydz with the center at the point with coordinates (x, y, z)which being solved for f (N, x, y, z, l) givesf (N, x, y, z, l)dl = f (0, x, y, z, l 0 )dl 0 , (6)f (N, x, y, z, l)dl = f (0, x, y, z, l 0 ) dl 0dl , (7)where l 0 and dl 0 /dl as functions of N and l can be obtain from the solution of (4) in the forml 0 = {l 2−n2 + N( n 2 − 1)g 0[ max k 10] n } 22−n ,−∞