Phase Field Failure Modeling: Brittle‐Ductile Dual‐Phase Microstructures under Compressive Loading

Brazed joints of nickel‐based alloys with large gaps between the joining partners can show multiphase microstructures of brittle and ductile constituents. These microstructures show a complex failure behavior that includes microcracks evolving concurrently alongside plastic deformation. A promising approach to model this failure process on the microscale is the combination of phase field damage and crystal elastic‐plastic constitutive laws. In the case of external compressive loading, the driving force for damage and the load transmission in areas of damaged material need to be formulated thoughtfully regarding the asymmetric material behavior in tension and compression. Two approaches to account for asymmetric damage from the literature are compared for the case of microcrack‐controlled failure of polycrystalline microstructures with a brittle and a ductile phase. The investigated approaches differ strongly regarding the resulting microcrack pattern, the predicted compression at failure and the capability to depict mixed mode failure. An enhancement for one of the existing approaches is proposed based on the incorporation of intrinsic friction in the process zones of the microcracks. The incorporation of intrinsic friction can increase the predicted macroscopic compression at failure by a factor of 2–3. With the proposed, enhancement the two existing approaches can be identified as the limit cases of zero and infinite intrinsic friction in the process zones of the microcracks. To match the elongations at failure observed in experiments, the microstructure has to be modeled in three dimensions, as 2D simulations underestimate the material's ductility. Additionally, the amount of energy dissipated due to the new crack surface and small plastic deformation in the brittle phase showed a strong impact on the ductility of the whole microstructure. Overall, a 3D dual‐phase microstructure with intrinsic friction and a moderate amount of fracture toughness in the brittle phase due to microyielding shows good agreement in the comparison with experiments. Consequently, if the advantages of a high‐strength brittle phase and a well deformable ductile phase are combined, the brittle phase should show a minimum amount of fracture toughness, in the studied material system, at least 8 MPa.