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 5 as input for the FE analyses. The FE software reads the Matlab ® output and performs all the simulations in order to calculate the elastic strain energies. The result of this iterative and automated procedure is a set of crack path that represents the crack shapes during the propagation, all presenting the same area increment. 877

(a)

(b) Fig. 4. (a) Initial crack shape. (b) Crack shapes for the crack growth evaluation, considering the same increment of area ∆ A .

4. Finite element models

The ANSYS Mechanical APDL ® software was used to simulate the cracked specimens, using a script that recon structs the cracks in order to iteratively calculate the elastic strain energy of all crack configurations. The geometry is divided into two volumes (Fig. 6): one containing the crack and one without the crack. The uncracked volume does not change during the analyses, instead the cracked volume is updated according to the crack propagation. Within the cracked volume, a control volume for the crack front is made. The control volume is meshed with 20-nodes quadratic elements. Also the uncracked volume is meshed with quadratic elements, but more roughly. Fig. 6a shows the mesh of the penny shape cracked infinite body and Fig. 6b shows a detail of the mapped mesh around the crack front and the cracked volume. The same mesh strategy was considered for the other examples. A mesh sensitivity analysis has been carried out to ensure the results accuracy. However, it is important to highlight that the stress intensity factors computation is sensitive to the mesh regularity; on the opposite, the elastic strain energy calculation is less sensitive, allowing to use a rough mesh. Regarding the specimen with surface crack, the bending moment was obtained applying an equivalent linearly variable pressure along the side of the FE model (Fig. 3a), keeping in mind that solid elements do not have the rotational degrees of freedom.

5. Results

In the following, the three analysed cases are presented.

5.1. Penny shape cracked infinite body

The first analysed case is the infinite body with a penny shape crack, subjected to a tensile displacement. Fig. 7 shows the crack path propagation compared to a literature result obtained by Hachi et al. (2010) considering a stress intensity factor approach. In agreement with the literature, an initial circular crack, in the infinite body, keeps its