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One problem with the previous formulae, is that the crack spacing has to be less than the plate thickness. Thus, for a given closed crack the fracture toughness will be maximum when the crack spacing is half the plate thickness. So, for a given crack spacing, the maximum fracture toughness will be the larger of the two values given by both equations. The implication is that an increase in notch size tends to decrease the fracture toughness regardless of the crack's orientation and whether the crack length is less than the plate thickness. In addition, a large notch diameter will not improve the fracture toughness of the long crack, but will only enhance the cracking of a large crack from a small notch. However, in the last two years, researchers have come up with new approach which do not have this problem, see below.

Here we will deal with the case of the long crack traversing a notch, as shown in Fig. 2. As in the original model of Irwin, we postulate that the defect (i.e., the crack) is present in the middle of a extit{load-free crack plane.} Four families of cracks are examined. In one family, the crack is perpendicular to the loading surface and is of a fixed length (a) the distance d (the nodal spacing) is kept constant while the loading surface is rotated such that the long axis of the notch is always perpendicular to the crack. In the second family, the length of the crack is kept fixed and nodal spacing d is decreased from its value in the first family. In the two remaining families, the condition nd ≤ d/2 is maintained and the nodal spacing is varied such that the long axis of the notch remains perpendicular to the crack. These four families of cracks correspond to different orientations of the crack with respect to the loading surface. The fracture toughness of the four families of cracks is plotted as a function of crack length and shown in Figure 3. d2c66b5586