PSI - Issue 61

Orhun Bulut et al. / Procedia Structural Integrity 61 (2024) 3–11

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O. Bulut et al. / Structural Integrity Procedia 00 (2024) 000–000

Fig. 2. Distribution of the phase field parameter with θ = 75°. Crack initiation (left), after complete failure (right)

For various orientations of the soft grain, crack initiation consistently occurred at the interface between the two grains as shown in Fig. 2. Cracks then propagate through the soft and hard grains simultaneously but the rate of crack growth in the hard grain is observed to outpace the soft grain crack growth rate. Crack paths are also influenced by the misorientation angle slightly. Although the phase field fracture model is isotropic, all simulations end up with a slanted crack path due to the inherent anisotropy of the crystal plasticity model. An alternative approach is detailed in Maloth and Ghosh (2023), where a phase field model with anisotropic fracture toughness is applied.

3.2. Crack nucleation and growth in a randomized polycrystal

A polycrystal RVE, shown in Fig. 3, is subjected to a static loading until failure to study crack growth in a more representative example of realistic grain structure. The model consists of 30 randomly oriented HCP grains in a 1 × 1 × 0 . 03 mm sheet generated using open source polycrystal generation software NEPER. Similar to the previous example, the model is restricted on one end to prevent rigid body motion and pulled from the other end with a constant strain rate of 10 − 3 . The mesh consists of 40368 hexahedral elements (C3D8T) with 3 elements in thickness. It should be noted that the structure is not related to a real microstructure but rather generated to assess the capability of the model in a polycrystal setting. The fracture toughness of the phase field model, G c , is taken as 10 N / mm, and the length scale is chosen as two times the minimum element size.

Fig. 3. Polycrystal RVE model (left). Distribution of phase field parameter at crack initiation (middle) and complete fracture (right)

In Fig. 3, the countours of the phase field parameter show crack initiation and propagation in the polycrystal. The interactions between misoriented grains act as stress and strain concentrators, accelerating crack nucleation in those regions. In the example shown, the crack initiated at a grain boundary and propagated inside the adjacent grains in the normal direction to the loading. The model is able to simulate the changes in the crack propagation direction due to the anisotropic nature of the crystal plasticity framework. It should be noted that both the initiation and propagation solely depend on the orientations of the grains and are found to vary in any other random orientation set.