13th International Conference on Fracture June 16–21, 2013, Beijing, China -8- 3.2. Dimensionless Compliance The evolution of the dimensionless compliance f during fatigue crack propagation is shown in Figs. 8 to 10, for different initial crack depths ((a/D)0={0.1, 0.3, 0.5}), initial crack aspect ratios (a/b)0=0.08 (quasi-straight front) and (a/b)0=1.00 (circular front), and different loading conditions (tension under free ends and bending). In cracked cylindrical bars, dimensionless compliance f depends on the loading conditions, on the relative crack depth a/D and on the crack aspect ratio a/b. During fatigue crack growth starting from different initial crack geometries, it is observed how the dimensionless compliance f increases with the relative crack depth a/D and how the influence of the crack aspect ratio a/b is lower as the crack grows, due to the marked geometrical convergence taking place for the deepest cracks, in which the compliance reaches the highest values. The dimensionless compliance f for initially quasi-straight cracks is approximately twice than that for initially circular crack, both being really small at the beginning (initial cracks) and increasing clearly and approaching between them under fatigue. The dimensionless compliance f in the cracked bars is higher under tensile loading (with free ends) than under bending moment, the ratio being as high as five for the deepest cracks of the present analysis (a/D=0.7). The f-a/D plots starting from an initially circular crack front (a/b)0=1 and from an initially quasi-straight crack front (a/b)0=0.08 are closer when (i) the applied load is bending instead of tension, (ii) the exponent m of the Paris law is higher, (iii) the initial crack depth (a/D)0 is lower. Furthermore, during fatigue crack growth, materials with higher values of the Paris parameter m produce slightly greater dimensionless compliance. 4. Conclusions According to the Paris-Erdogan law, in fatigue propagation the different initial crack geometries tend to a unique path on the a/b vs. a/D plot, this convergence (proximity between the curves representing the crack advance from different initial crack shapes) being faster for higher coefficients m of Paris and quicker for bending moment than for tensile loading. With quasi-circular initial geometries (i.e., (a/b)0=1), the crack aspect ratio a/b always diminishes with the crack growth, whereas when the initial crack is quasi-straight (i.e., (a/b)0=0.08), the aspect ratio a/b increases at the beginning and decreases at the end (with the exception of initially deep crack with (a/D)00.5). In fatigue crack propagation, relative crack depth a/D influences more on dimensionless compliance f than the aspect ratio a/b, because the crack fronts tend to converge as the cracks propagate from different initial geometries, the convergence being quicker for initially short cracks than initially long cracks. The f-a/D plots starting from an initially circular crack front (a/b)0=1 and from an initially quasi-straight crack front (a/b)0=0.08 are closer when the applied load is bending, the exponent m of the Paris law is higher or the initial crack depth (a/D)0 is lower. Materials with higher values of the Paris parameter m produce slightly greater dimensionless compliance during fatigue crack growth. The greater the m coefficient of the Paris law, the greater the convergence of the different initial crack conditions: geometry of the crack front (a/b) and dimensionless compliance f. The difference between the results for the different values of m is always bigger between m=2 and m=3 than between m=3 and m=4, which implies that, as this parameter increases, there is less dependence of results on it.
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