PSI - Issue 38

Adrian Loghin et al. / Procedia Structural Integrity 38 (2022) 331–341 A. Loghin et al. / Structural Integrity Procedia 00 (2021) 000–000

334

4

Fig. 2: Comparison of di ff erent solvers (Ansys, Abaqus, CalculiX) for the same nominal configuration, fatigue crack growth life assessment.

and da / dN [mm / cycle]. An initial edge crack of 2.16 mm is introduced in the model. The plane of the crack is normal to the loading direction and located at 6.07 mm from the center of the hole (see Figure 1). An elasticity modulus of 7.17e4 MPa and a Poisson ratio of 0.33 define the linear elastic constitutive model. The fatigue crack propagation formulation uses maximum tangential stress criteria to define crack growth direction and displacement correlation technique to compute stress intensity factors for all three fracture modes. The 3D fatigue crack growth simulation is performed automatically for the nominal configuration presented above. Figure 2 shows a crack path comparison between experimental measurement and numerical procedure along with computed loading cycles using three di ff erent solvers: ANSYS (2021), ABAQUS (2021) and CalculiX (2021). Based on this comparison it can be concluded that the numerical uncertainty related to the solver is minimal and, the pre dicted crack path is successfully validated against experimental measurement. Both the geometric representation and associated mesh for the last considered step in the fatigue crack growth simulation are presented in Figure 3. As it can be easily observed in Figure 3, the crack surface has a uniform growth across thickness direction and mixed mode conditions develop when crack front reaches the hole location. Once the hole is passed, loading conditions at the crack front become mode I dominant again. A collected crack path digital measurement along the free model boundary (Figure 3, d)) is representative for a comparison against experimental measurements shown in Figure 2. An interaction between crack size and stress concentration factors at the hole is captured in Figure 4. As the crack front advances and reaches locations under the hole, the value of K Imax diminishes due to a load shedding e ff ect. As expected, the stress concentration factors ( K t ) at the two hole side locations show an opposite e ff ect: significant increase as the crack approaches locations under left side or right side of the hole. For the initial crack length it can be noticed that the two K t values are close to a value of 3 (as expected) and for a long crack that passed the hole location, the K t values approach 0 indicating no loading bearing at the hole location. The load shedding e ff ect provides an explanation to the shape of crack length vs. cycles presented in Figure 4 d). Two variability sources are considered for a sensitivity study: o ff -nominal geometry and intrinsic fatigue crack growth scatter. For geometric variability, the vertical position Y 1 of the initial crack relative to the hole was incremen tally modified and, for each o ff -nominal geometry a crack propagation simulation was performed using the modeling procedure described in the chapter above. Using 25 equally incremented discrete values of Y 1 from a minimum value of 5.25 mm and a maximum value of 6.75 mm, the surrogate model training data was collected from 3D FE crack propagation simulations using SimModeler as shown in Figure 5. For each deterministic simulation, the initial and final crack sizes of each run were set at a 0 = 2 . 16 mm and a f = 25 mm. About 220 increments were carried out for the entire crack growth analysis from the initial to the final crack size. The applied loads were the same as in nominal model described in Section 2.1 above. Each of these runs generated numerical data of the mode I and II stress 2.2. Surrogate Modeling - Calibration and Verification