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) Fig. 3. Surface cracked plate: (a) geometry and applied bending simulated as variable pressure along the thickness; (b) Details of the considered symmetries.

crack shapes for the propagation that have di ff erent combinations of the semi-axes a i and b i (Fig. 4). In this way, it is possible to consider crack shapes having the same area increment but di ff erent aspect ratios. The second hypothesis regards the elastic strain energy that is calculated for equilibrium configurations. At the equilibrium, the potential energy Π is equal to 0 and it implies that the elastic strain energy U is equal to the work done by the external forces W eq. (1). Π i j = i , j U i j − W i j = 0 (1) where: Π i j is the potential energy, U i j is the elastic strain energy, W i j is the work done by the external forces, i is the index of the initial crack and j is the index of the crack shape considered for the propagation. Under equilibrium conditions, the propagation is driven by the minimization of the elastic strain energy U i j . Thus, considering di ff erent shapes for the crack growth and calculating the elastic strain energy for all of them, the minimum value corresponds to the new crack configuration. The crack path evaluation analyses were carried out through an automated procedure that links a Matlab ® script to an ANSYS Mechanical APDL ® parametric model. Fig. 5 shows the workflow. The Matlab ® script initializes all the variables useful for the calculation. Only for the first calculation step, the Matlab ® script needs the initial crack semi-axes and the area increment as input. From the second step, an iterative routine allows to acquire the elastic strain energy values U i j from an input file deriving from the FE analyses, looking for the minimum value of the elastic strain energy. The minimum value of the elastic strain energy corresponds to an elliptical crack configuration characterised by semi-axes a i and b i , that are the new initial semi-axes for the following step of the analysis. An external Matlab ® function calculates a set of crack shapes (in terms of semi-axes), starting from the initial ones, imposing a fixed increment of area ∆ A . The new initial crack and all the di ff erent configurations are saved as Matlab ® output and used