PSI - Issue 66

Guido Dhondt et al. / Procedia Structural Integrity 66 (2024) 102–107 Author name / Structural Integrity Procedia 00 (2025) 000–000

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is pretty well established, based, e.g. on the mixed-mode K-factors at the crack tip. In reality, however, the loading frequently consists of a set of loading steps, each with its own mixture of K-factors and temperature. For instance, a flight of an aircraft engine usually leads to a mixture of multi-axial loadings in time combined with a phase shifted temperature curve. The crack propagation speed for the mission is frequently obtained by performing a rain flow analysis and evaluating all cycles separately, finally adding all contributions. The deflection angle for each loading step, however, can clearly not just be summed. So the question arises how to find the mission deflection angle based on the mixed-mode K-distributions of each step. In this article, several criteria are analyzed. One could argue that the mission angle is the mean of the deflection angle in each step separately as in BEASY(2011). Alternatively, one can assume that the mission inherits its deflection angle from a step which is somehow dominant, Rodella et al. (2021). In FRANC3D (2021), however, the crack propagation direction seems to be defined by a dominant cycle. In this article, these criteria are applied to some well-defined tension-torsion and static-cyclic cruciform tests. A comparison of the numerical prediction with the experimental data leads to the selection of the (so far) best criterion. 2. Mission deflection angle criteria In the following, missions are considered, i.e. sequences of data points characterized by K-factors K I , K II and K III obtained by linear elastic calculations and a temperature T. No contact is modeled between the crack faces, therefore K I can be negative. It will be assumed that a procedure has been established to calculate an equivalent K-factor and the crack deflection angle in each such data point, such as in Rodella et al. (2021).

Figure 1: K-factors along the mission

Figure 2: Crack propagation rate

A typical mission is illustrated in Figure 1, in which K stands for the equivalent K-factor. In order to proceed, the equivalent K-factor is modified into a crack propagation rate (da/dN)* (Figure 2) satisfying: � � ∗ � � � ����� � �� , �� 0 �� �� , �� � 0 � � ∗ � � � � ����� �� �� , �� 0 � , �� � 0 where f th is a factor taking the threshold K th into account, R=K min /K max and (da/dN) Paris is the crack propagation due to the Paris equation only (in the form (da/dN) Paris =C( Δ K) m ). The idea of this transformation is to take the temperature effect into account. Indeed, a high K-factor at low temperature may be less damaging than a lower K-factor at high temperature. Notice that all positive data points below threshold in Figure 1 are mapped to zero in Figure 2. For simplicity the threshold value in Figure 1 is drawn as constant, although in reality it is a (sometimes highly) nonlinear function of temperature. Now, (da/dN)* is used to determine the dominant step (maximum da/dN*) and the dominant cycle (coupling the step smax with maximum da/dN* with the step smin with minimum da/dN*). The following mission deflection angle criteria are analyzed: