applied fracture mechanics

Fractal Fracture Mechanics Applied to Materials Engineering 97of the material. The greater the material energy consumption in the fracture, straining itplastically, the longer will be its geometric path and more rugged will be the crack.Figure 14. Generalized J-R curves for different materials, modelled using the self-affine fractalgeometry, in function of the scale factor l0 L0of the crack length [43].In the self-similar limit l0 L0 H 0, equation (97) is applicable and the energetic andgeometric components are put in evidence in the equation below,H1 l0J0(2 eop)(2 H) L0 energeticgeometric(102)From equation (102), an expression can be derived which results in a constant valueassociated to each material,H 1H1 J0L0 (2 e0 p)(2 H) l0( const ) material(103)macroscopicmicroscopicIt is possible to conclude that the macroscopic and microscopic terms on the left and righthandsides of equation (103) are both equal to a constant, suggesting the existence of afracture fractal property valid for the beginning of crack growth, and justifiedexperimentally and theoretically. These constant values were calculated for each point ineach J-R curve for the tested materials. The average value for each material is listed in thelast column of Table 2 and Table 3. Observe that this new property is uniquely determinedby the process of crack growth, depending on the exponent H , the specific surface energy2e pand the minimum crack length l 0.