PSI - Issue 52

Valery Shlyannikov et al. / Procedia Structural Integrity 52 (2024) 214–223 V.Shlyannikov,A.Sulamanidze,D.Kosov/ Structural Integrity Procedia 00 (2023) 000 – 000

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the experimental OOP and IP cycling, that is, between 400°C and 650°C. The crack tip behaviour of the SENT specimen is represented with temperature v ariations in the Young’s modulus as a function of the cycling time points and differences between the IP and OOP states. Notably, incorporating the role of the loading history through different time points with combinations of loading/unloading and heating/cooling stages leads to a variation in the stress levels ahead of the crack tip. Recall that for the IP cycle, time points 10 s, 20 s, and 30 s correspond to loading/heating (Fig.4a), while for the OOP cycle, these refer to loading/cooling periods (Fig.4b) in TMF triangular waveforms.

Fig. 5. Effective stress distributions ahead of the crack tip for (a) IP and (b) OOP TMF cycle as a function of the loading time.

It can be seen in Fig. 5 that the maximum effective von Mises stress σ eqv values occurred at time point t = 30 s, which corresponds to different temperatures (T = 650°C for IP and T = 400°C for OPP cycles). Accordingly, the stress values for these combinations of cycle time and temperature are used in further calculations of the stress intensity factors under thermo-mechanical IP and OOP loading. For conventional conditions of isothermal loading for pure fatigue and fatigue-creep interaction, the maximum values of stresses in the loading cycle were used to calculate the elastic SIF. 3.2. Stress intensity factors determination Several methods are known in the literature for determining the fracture resistance parameters to crack growth under cyclic loading at elevated temperatures. To this end Palmert et al. (2019) introduced effective stress intensity factor range, Ewest et al. (2016) proposed a modified compliance method for fatigue crack propagation, Fischer et al. (2015, 2016) accounted for crack closure effect and crack opening stress equation in order to interpreting the results of the crack-propagation rate under in-phase (IP) and out-of-phase (OOP) thermo-mechanical loading. In this study, we used the following numerical method for determining the elastic SIF, which is based on the analysis of stress distributions at the crack tip. Let us consider the structure of the numerical (FEM) crack tip stress fields to be of the following form ( ) ( ) 1 , , FEM FEM FEM ij ij r K r r      = , (1) where r,θ are the polar coordinates,  is the power of stress singularity, K 1 is denoted stress intensity factor. The angular distributions of the dimensionless stress components ( ) , FEM ij r   are normalized according to Equation (2) 1 2

3 2

  

  

1

FEM

FEM FEM

ij ij S S

,

(2)

=

=



,max

eqv

max

FEM

where eqv  is the dimensionless effective stress and S ij denotes the deviatoric stress. Solving Equation (1) with respect to the stress intensity factor, we obtain ,max