## 4 Discussion  
Figure 6 shows the preferential propagation path for the three analyzed configurations and for Paris exponents \(m=2\), \(3\), and \(4\). For embedded cracks, the preferential path exhibits values of the aspect ratio higher than \(1\), they being close to \(1\) up to a depth \(a/t=0.4\), and slightly increases with the relative crack depth for \(a/t>0.4\). For surface and corner cracks such a preferential path presents  
Figure 5: Aspect ratio evolution with relative crack depth (propagation path) for corner cracks: (**a**) \(m=2\); (**b**) \(m=3\); (**c**) \(m=4\).  
aspect ratios lower than 1, which diminish along with the relative crack depth. The Paris coefficient \(m\) raises the preferential plot \(a/b\)-\(a/t\) for embedded cracks when \(a/t>0.4\) and lowers it for surface and corner flaws (this trend being valid for the whole range of \(a/t\)).  
The embedded defects in infinite solids under fatigue tend towards an iso-\(K\) state [27], but the free surface (front, back, and lateral side) of the plate ensures that the iso-\(K\) state is not reached for the preferential crack path.  
In the matter of the preferential cracking path, Figure 7 plots the dimensionless SIF \(K/(\sigma(\pi a)^{1/2})\) at three points of the crack front: points A and B (one of them always exhibiting the maximum SIF along the crack front) and an intermediate point. The latter corresponds to the half-length between the points A and B for the case of the embedded cracks (Figure 7a) and is associated with the minimum SIF over the crack front for the surface cracks (Figure 7b) and for the corner-type cracks (Figure 7c). The maximum dimensionless SIF over the crack front is higher in the case of corner cracks, intermediate for surface flaws, and lower for embedded defects. The exponent \(m\) of the Paris law makes the SIF decrease for the embedded case, whereas for the case of surface and corner cracks, it makes the SIF increase.  
The _embedded cracks_ exhibit approximately the same SIF over the crack front, up to \(a/t\sim\)0.4, from which the SIF diminishes continuously along the crack front (from a maximum value in A to a minimum in B). For _surface cracks_, the maximum SIF is achieved at point B (where the crack intersects the surface) and the minimum SIF at an intermediate point in such a manner that the SIF diminishes along the crack front when the point shifts away from the surface and increases along such a front when the point approaches the center. In the case of _corner cracks_, the shallower ones (with small depth) present the maximum SIF at point A (with close values in A and B) and the deeper ones exhibit that maximum SIF at point B. The minimum SIF for these cracks is achieved in an intermediate point over the crack front.  
The crack growth rate for the preferential crack path (Figure 8) is higher for the corner configuration than for the surface crack, and higher for the latter than for the embedded defect (in the same conditions). The dimensionless number of cycles \(n\) increases with the exponent \(m\) of the Paris law. The most dangerous situations are those for plates under tension with corner cracks inside because they exhibit quicker propagation rates and higher maximum SIFs.  
Figure 6: Preferential propagation paths. (The arrows indicate the direction in which the curves are moved with the increase of the Paris \(m\) exponent).  
Figure 7: Dimensionless SIFs for the preferential cracking paths given at the A, B, and intermediate points located on the front of a crack of the following types: (**a**) embedded; (**b**) surface; (**c**) corner. (The arrows indicate the direction in which the curves are moved with the increase of the Paris \(m\) exponent).