PSI - Issue 38

Adrian Loghin et al. / Procedia Structural Integrity 38 (2022) 331–341

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A. Loghin et al. / Structural Integrity Procedia 00 (2021) 000–000

Fig. 5: Surrogate model training data set: 25 three-dimensional FEA based fatigue crack growth assessments.

out-of-plane crack growth analysis in SimModeler, it was found that the K IImax values are not needed to calibrate the surrogate model. The automated crack growth results showed nearly uniform crack growth across the front i.e. the initial straight through crack remained as straight-through throughout the entire propagation simulation. For this reason, a single parameter characterizing the crack tip driving force was deemed su ffi cient for the surrogate model. This parameter was taken to be K Imax since R = 0 ( K Imax = ∆ K I ) at model boundary to be consistent with [ a X , a Y ] definition. In addition, the path solutions shown in Figure 5 indicated all crack paths remained to be parallel with no overlaps for the majority of the solutions. This allowed us to use the following three RBF based surrogate model components: 1. K I ( Y 1 , a X , a Y ): mode I SIF as a function of Y 1 , a X and a Y – planar crack tip position (at model boundary) during propagation simulation. 2. a X ( Y 1 , a ): as a function of Y 1 and the instantaneous crack length a . 3. a Y ( Y 1 , a ): as a function of Y 1 and a . To verify the surrogate model performance, a new set of test data was generated by running ten additional automated crack propagation simulations at randomly selected initial crack Y 1 -positions within the calibration Y 1 range. Figure 6 shows the correlation plots between the surrogate model and the FE results of K Imax and a X for both calibration and test data. Because of the underlying RBF interpolation models that were used, the surrogate models are expected to predict the calibration points shown by blue circles perfectly; this is what is observed in the plots. However, the surrogate models also exhibit very good performance with the test data shown in red. The performance of the third surrogate model for a Y was very similar to a X and hence its correlation plot is omitted here for brevity. With the verified surrogate model components in place, a crack propagation routine was developed to incrementally grow the crack from the initial size to the final size. With the predefined initial crack size, the crack location defined by Y 1 and the nominal fatigue crack growth rate parameters C and n , the routine follows these steps: 1. Compute the mode I SIF value for the given crack size using the surrogate model for K I ( Y 0 , a X , a Y ) at maximum load. Consider R = K Imin / K Imax = 0, ∆ K I = K Imax − K Imin = K Imax identical to the deterministic solution. 2. Grow the crack size by the incremental amount da and estimate the corresponding incremental number of cycles dN using the Paris law relationship da / dN = C ( ∆ K I ) n . 3. For the new crack length a , estimate the new crack tip position using the surrogate models a X ( Y 1 , a ) and a Y ( Y 1 , a ). 4. Repeat the loop until the final crack length is reached.