PSI - Issue 39

Daniele Amato et al. / Procedia Structural Integrity 39 (2022) 582–598 Author name / Structural Integrity Procedia 00 (2019) 000–000

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This formula is implemented in FRANC3D for the ESIF range calculation. It is a general formulation, similar to other formulas in literatures e.g., Richard et al. [34]. It gives the user the possibility to calibrate the formula for his own requirements by inserting the values for and . Analogously to the Richard formulation, these numerical simulations were performed by setting those calibration parameters to = 1.155 and = 1 . The crack propagation process can start once the mission’s deflection angle and the increment is computed for each node along the crack front. The size of the increment per cycle is obtained by substituting Δ ( ∗ ) into the propagation law, reported in Eq. (7). = �� 1 1 − − � Δ � �1− Δ Δ ℎ � �1− � (7) The propagation law of Eq. (7) was proposed by FORMAN and METTU though it is better known as NASGRO equation. This crack growth model describes accurately all the crack propagation regimes by using the empirical material dependent constants , , and . For further information on the meaning of all the variable involved in Eq. (7), the reader is referred to [35]; for more details on its implementation in FRANC3D, cfr. [27]. All the material parameters involved in the numerical simulations are reported in Table 1; note that all the variables are homogeneous to [ ] and [ ] . Table 1 FORMAN/METTU parameters for the tested material 34CrNiMo6 with a survival probability = 50% . , + − 50% 9.38 ∙ 10 −7 1.89 2.39 0.43 1.14 145 3.89 0.05 1.9 0.3 At this stage, the crack front nodes can be extended by the quantity Δ a node , i towards the local propagation direction, as shown in Figure 8. The increment per propagation step is in a given proportion to a user defined crack growth increment Δ a user . This proportion is related to the ratio between the local ESIF range and the mean ESIF range along the front, as in Eq. (8). Δ a node , i = Δ a user � Δ , , Δ , � ( 8 )

Figure 8 Propagation of the -th node in a generic step .