Study of damage mechanisms of superalloys via a combined Phase-Field method

In this work, a combined phase-field method is proposed for the numerical evaluation of the damage mechanisms developing in superalloys. Specifically, a strategy combining the Phase-Field Cohesive Zone Model (PF-CZM) for quasi-brittle fracture with a phase-field resolution strategy of the multicomponent non-conserved Allen-Cahn equations used for representing the material microstructure is adopted. Both phase-field models are combined to address: (i) the material’s anisotropic behavior induced by the presence of grains which present different microstructure orientations, as well as (ii) the detection of interfaces between grains and the integration of the multiple effects that these have on the resulting mechanical performance of the superalloys. The paper features a novel secant formulation of the PF-CZM in a significantly more straightforward implementable form combined with an original strategy for the integration of the phase-field fracture model and the Allen–Cahn phase-field method for microstructure representation. The novel procedure features the transferring of the grain geometry, in-plane grain orientation, diffuse grain-boundary regions, and the corresponding spatial material-property fields from the Allen–Cahn representation to the fracture calculation. A set of numerical simulations are conducted to assess the performance of the proposed model. These include a unit square domain numerical benchmark as well as two study cases of real image-based superalloy microstructures of 271 and 520 grains respectively. The computations demonstrate the aptness of the model in addressing the challenges of the computer evaluation of failure mechanisms in superalloy microstructures containing a large number of grains. The model is able of reproducing both intergranular and transgranular crack propagation, as well as highly complex crack patterns involving multiple intersecting and merging cracks. It is also able to evaluate the effects of key aspects such as grain orientation angles, material strength and other relevant properties have on the resulting damage mechanisms in superalloy microstructures, demonstrating the effectiveness and generality of the proposed method.