A creep-damage phase-field model: Predicting topological inversion in Ni-based single crystal superalloys

Highlights: • A Rabotnov-Kachanov type continuum damage model implemented in a multi-phase field formulation. • The model predicted the complete microstructural evolution, including topological inversion, during creep. • Explained microstructural degradation as an important damaging mechanism in the Ni-based SX superalloys. • The study revealed the role of γ′ volume fraction in topological inversion. • The onset of topological inversion occurred at the transition from the secondary to the tertiary creep stage. The lifetime of Ni-based single crystal superalloys is connected to the integrity of the strengthening phase, γ′. Hence, fundamentally understanding and predicting how the mechanical behavior of the γ′ phase softens with the evolution of damage is essential to improve their lifetime predictions. During high-temperature creep, the γ′ phase coalesces, coarsens, and is finally topologically inverted, viz. surrounds the γ phase and acts as the matrix. The topological inversion comes along with an increase in the plastic strain rate known as the tertiary creep. X-ray tomography experiment has recently revealed that the tertiary creep initiates before the expected increase in the volume fraction of pores. Thus, the initiation of the tertiary creep stage might also be due to the destabilization of the γ/γ′ interfacial dislocation network leading to the massive shearing of γ rafts concomitantly resulting in topological inversion. Therefore, to account for microstructural degradation as damage, we proposed a 'macroscopic damage-coupled crystal-plasticity' informed elasticity formulation in phase-field. The predictions from this 'creep-damage phase-field model' agree with the experimental observations; are strikingly similar to the SEM images, and gives a complete microstructural evolution, including topological inversion, leading to further insights about the role of γ′ volume fraction in topological inversion.