PSI - Issue 39

Daniele Amato et al. / Procedia Structural Integrity 39 (2022) 582–598 Author name / Structural Integrity Procedia 00 (2019) 000–000 assumed and superposed: Solution (1) is the finite element solution for the problem of interest; solution (2) is an auxiliary solution. The domain of integration is a cylinder that encloses a portion of a crack front, as illustrated in Figure 6. For more information about the M -integral formulation and its implementation in FRANC3D, the reader is referred to [33] and [32], respectively. 589 8

Figure 6 Integration domain for M -integral calculation.

4. Deflection Angle calculation and Crack Growth process Typically, a mission consists of a very complex loads sequence, which must be modelled as several, sometimes hundreds, different loading steps. In fact, thermal and mechanical loads may have completely different dynamics during the mission cycle and, to accurately model the temperature evolution and the stress history, a very fine discretization may be needed. This results in a series of loading steps characterized by their own load combination and temperature, which reflects in different crack driving forces and propagation parameters for each single mission’s step. A unique mission’s deflection angle and propagation parameter need to be defined to obtain the cyclic crack propagation. The approach used in this study to cope with deflection angle calculation and the crack growth parameter are explained underneath in this section. The mission cycle is divided up into thirteen static steps (Figure 7), each of which results in a combination of all three fracture modes. The results in terms of stress for each loading step are read by FRANC3D as the extremal value of a zero-max cycle. Therefore, the crack driving force ( , , ) can be determined at any location of the crack front for every static step.

Figure 7 Load sequence of specimen 0_1_40_3 discretized in static steps.