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

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methodology is the introduction of a damage threshold Borden et al. (2016). An alternative to this is to control the coupling through the choice of degradation function, opting in favor of a higher order function over the more common quadratic function. Thus the degradation function is defined as g ( ϕ ) = (3 − k )(1 − ϕ ) 2 + (1 − (3 − k ))(1 − ϕ ) 3 (13) where k is taken as 0.02 in all simulations. The model is implemented in Abaqus software through user-subroutines (UMAT and HETVAL). A similarity between the heat transfer equation and the phase field strong form is exploited to facilitate the use of coupled temp displacement elements with temperature behaving as a stand in for the phase field parameter as demonstrated in Navidtehrani et al. (2021). The performance of crystal plasticity coupled with the phase field fracture model is addressed through two exam ples. The first one is the modeling of crack initiation and growth between 2 misoriented HCP grains following the example in Maloth and Ghosh (2023). A Soft grain (favorably oriented for slip) is located within a frame of hard grains with identical orientations with their c-axis aligned with the loading axis as shown in Figure 1. The model is 100 µ m by 100 µ m with a 3 µ m thickness. In the current study, the misorientation angle is changed between 30°-90°to study the susceptibility to crack initiation. The model is restricted from the bottom surface to prevent rigid body motion and a displacement boundary condition is applied to the other end at a constant strain rate of 10 − 3 . The finite element model has a total of 102420 temperature-displacement coupled tetrahedral elements (C3D4T). The mesh density is increased near the grain boundary and inside the soft grain. For the phase field model, G c , is taken as 10 N / mm, and the length scale is chosen as at least twice the minimum element size. Simulations are performed with the implicit solver of Abaqus using the staggered solution scheme for the evolution of the phase field and the displacement field (see Navidtehrani et al. (2021)). 3. Results and Discussions 3.1. Crack nucleation and growth in a hard-soft grain interaction

Fig. 1. Hard-Soft grain interaction model (left). Stress vs. strain for various soft grain orientations (right).

In Fig. 1, stress-strain curves for various orientations of the soft grain are visualized. With increasing misorienta tion, the overall fracture toughness of the RVE reduces. Around 65°this phenomenon seems to saturate with no further significant loss in toughness. Increasing the θ angle, makes the grain more favorable for slip on basal and prismatic < a > slip systems which are known to have less slip resistance compared to the pyramidal < c + a > system. Additionally, the yield stress of the RVE continuously increases as we lower the misorientation angle.