PSI - Issue 47

Gianmarco Villani et al. / Procedia Structural Integrity 47 (2023) 873–881 G. Villani et al. / Structural Integrity Procedia 00 (2023) 000–000

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(a)

(b)

(c) Fig. 7. Penny shape cracked infinite body; (a) Crack path during the propagation: energetic approach; (b) Crack path during the propagation: SIF approach (Hachi et al. (2010)); (c) Stress distribution along the crack front.

5.2. Infinite body with elliptical crack

Similarly to the previous case, the infinite body contains a crack with an initial elliptical shape, subjected to a tensile displacement. As shown in Fig. 8, the initial elliptical crack starts to propagate increasing its dimension in the direction of the minor semi-axis. Then, when the minor semi-axis length reaches the major one (the elliptical crack turns into a circular crack), the crack continues the propagation maintaining the circular shape. Even in this case, the stress field justifies this behaviour (Fig. 8c): the stress state on the minor semi-axis is higher than the stress state on the major one; hence, the propagation starts increasing the dimension of the crack along the minor semi-axis, in agreement with the indication given by orthogonal stress intensity factor balance.

5.3. Surface cracked plate with bending load

Previous examples regard uniform nominal stress-fields. The novelty of this third example concerns the application of a variable stress field in the specimen width in order to simulate an applied bending load. Fig. 9 shows the crack path during the propagation compared to a literature reference (Lin and Smith (1999b)). The initial crack shape was circular, but similar considerations would result starting from a semi-elliptical surface crack. It can be noticed, see Fig. 9a, that initially the crack propagates increasing the length of the semi-axis along the surface and, only after a while, the semi-axis along the thickness starts to propagate. It can be justified looking at the stress state in Fig. 9c. Applying a bending moment, the highest stress value occurs on the surface. Consequently, the semi-axis on the surface shows the highest stress state, higher than the stress state at the through the thickness semi-axis. Then, the crack propagates along the surface initially, but during the propagation the stress distribution changes along the crack front increasing in correspondence of the depth semi-axis and starting to propagate through the thickness as well.