PSI - Issue 25

R. Baptista / Procedia Structural Integrity 25 (2020) 186–194 Author name / Structural Integrity Procedia 00 (2019) 000–000

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�� �√�� � � �� � � � (10) This parameter shows that the contribution effect of T-Stress in regard to both SIF, is higher when B increases. Significant values of B may have an important effect over brittle fracture under mixed mode conditions, Smith et al. (2001), by affecting crack propagation direction and material fracture toughness, Miao et al. (2017). 2.5. FCG algorithm The FCG algorithm used in this paper is based on the previously developed automatic crack propagation algorithm by, Baptista et al. (2019). It is a modular algorithm based on three simple steps, similar to the methodology developed by Dirik et al. (2018). Firstly, initial conditions are set by a Matlab script. These conditions include the initial crack parameters (shape, length and orientation), load path and specimen geometry. Using this information, a second module, running on Python language, is used to create the FEA model. The present algorithm used the contour integral technique to extract SIF and T-Stress, requiring constant part remeshing, Dhondt (2014). On a third step ABAQUS solves the FEA problem, calculating the required fracture mechanics parameters, SIF and non-singular term T . These values are imported back to Matlab, where the algorithm decides if crack propagation occurs. If the crack propagates, then the algorithm must predict a new crack propagation direction, using the MTS or MSS criterion and the corresponding crack increment ∆ , based on the Paris law, Paris et al. (1963). ∆ � ∆ � ��∆� �� � � (11) In this paper two propagating crack were defined for all models. Therefore, one must consider a constant elapsed number of cycles ∆ . The corresponding crack increment is calculated for each crack, and the first module can update the model information in order for the cycle to be repeated. Propagation will continue using this algorithm, until a previously defined condition is met. Current FCG simulations were performed with an elapsed number of cycles, generating a crack increment of around 0.5 mm. This value was defined after an initial convergence study, and is similar to the one obtained by Shi et al. (2010), Breitbarth et al. (2018) or Ayatollahi et al. (2015). The material, Al 7075-T6, was considered to be linear elastic, with Paris constants C = 2.28*10 -10 and m = 3.1 (m/cycle, MPam 1/2 ), Misak et al. (2014). Different load path conditions were applied to the cruciform specimen. Load path influence can be observed in Fig. 2. On these four different cases, the applied loading was proportional, with in-phase loads applied to both axes. Fig. 2 a) and b) show crack propagation for an initially horizontal crack. When biaxial load ratio � � , the crack propagates horizontally as mode II SIF is zero and T-Stress is also equal to zero, Smith et al. (2001). If � ��� , Fig. 2 b), the horizontal crack will eventually be deflected. This behavior is similar to the experimental results obtained by Misak et al. (2014) for small cruciform specimens, or by Lee et al. (2011) for larger specimens. When analyzing the resulting T-Stress value on the crack front, one can see that initially they are positive, becoming negative once the crack has deflected. This behavior is in line with the work of Breitbarth et al. (2018). By applying different values and analyzing crack propagation trajectories, these authors conclude that positive T-Stress will lead to unstable crack propagation, facilitating crack kinking, while negative T-Stress leads to stable crack propagation. Fig. 2 c) and d) show crack propagation behavior for an inclined crack, with α = 30º. Again, if � � , mode II is absent, and therefore the crack will propagate according to the initial crack direction. An analysis of the T-Stress value showed that initially they are zero, but eventually become negative. If � ��� , the crack is immediately deflected, propagating along a perpendicular direction to the highest stress (mode I). This behavior has been experimentally verified by Misak et al. (2013). Once again T-Stress values were positive in the beginning of the simulation, but quickly became negative, stabilizing crack propagation direction. 3. Results and Discussion 3.1. Load path influence