PSI - Issue 37

R. Baptista et al. / Procedia Structural Integrity 37 (2022) 57–64 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

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2.2. Automatic fatigue crack growth algorithm A previously developed FCG algorithm was used to automate crack propagation. Many FEA programs require constant part remeshing as crack length increases, in order to calculate and extract SIF values. The approach used in this paper consists in three different modules, with the goal of automating this procedure. In the first step Matlab scripting is used to setup the initial crack shape and location, and material properties. The initial conditions are translated to Python in order to create the model geometry, mesh, loads and boundary conditions. Materials properties are also applied to the model and the cracked region is created as a mesh modification. Crack faces are introduced by a special seam, and along the crack front a special spider-web mesh is introduced. Quadratic elements are used throughout the model, and singular collapsed elements are placed around the crack front, simulating the resulting crack stress field singularity. On the third step, the algorithm solves the FEA problem using Abaqus, and the necessary SIF are extracted using the contour integral method. These values are returned to Matlab, where crack propagation direction is calculated using the MTS or MSS criterion. In this paper a fixed 0.5 mm crack increment was used to update the model and repeat this cycle until a predefined crack length. Although not analyzed in this paper, eq. (4) or eq. (6) might be used to predict FCG life and propagation curves using a Paris law type equation. Similar approaches have been used by Ayatollahi et al. (2015), Huang et al. (2019) or Lesiuk et al. (2020), to simulate FCG on CTS specimens, showing good agreement between numerical and experimental work. 2.3. Specimens geometry Two specimen geometries were considered for FCG simulations. Fig. 2 a) shows the CTS specimen used, according to Lesiuk et al. (2020) specifications. Boundary conditions were applied as supports on the bottom specimen’s holes, while three different loads are applied to the top specimen’s holes. Mode I is simulated using α=0º, and pure mode II is obtained for α=90º. Fig. 2 b) shows the geometry, loads and boundary conditions for the FPB specimen. One popular way to apply different loading conditions to the FPB specimen, is to change one of the rollers support position. When L 2 =L 3 , pure mode II conditions are obtained, reducing L 2 value mode I proportion increases, reaching pure mode I for L 2 =0, Huang et al. (2019). Bottom rollers were considered as fixed supports, while loads applied to top rollers are proportional L 2 and L 1 . Both specimens notch width was considered as 2 mm and initial crack length and specimen width ratio (a/W) was 0.5. Material thickness was 19 mm for both specimens, but FEA simulations considered only plane strain 2D models. Fatigue loading was applied with a stress ratio R of 0.1, and a maximum load of 10 kN on the CTS specimen and 5 kN on the FPB specimen. High strength steel fracture toughness and Paris Law material properties were previously determined by Baptista et al. (2018).

F 2

F 1

α

(b)

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Fig. 2. (a) CTS; (b) FPB specimen ’s boundary and loading conditions.

3. Results and Discussion Crack propagation, with different load α angles, on CTS specimen was simulated using an automatic FCG algorithm. Using both the MTS and MSS crack propagation criteria, crack paths were obtained for loading conditions between pure mode I, mixed mode and pure mode II. When α=0º, pure mode I loading conditions are applied to the