A continuum approach to combined γ/γ′ evolution and dislocation plasticity in Nickel-based superalloys - Wu, Ronghai; Zaiser, Michael; Sandfeld, Stefan (International Journal of Plasticity, 2017)
In single crystal Nickel-based superalloys subject to creep loading, the gamma/gamma' phase microstructure co-evolves with the system of dislocations under load. Computational modeling thus requires multiphysics approaches capable of describing and simulating both phase and defect microstructures within a common conceptual framework. To do so, we formulate a coupled continuum model of the evolution of phase and dislocation microstructures. The simulated gamma/gamma' phase microstructure accounts for concentration as well as crystallographic order parameters. Dislocation microstructure evolution is described in terms of dislocation densities and associated stress-driven dislocation fluxes. The creep strain curve is obtained as a natural by-product of the microstructure evolution equations. We perform simulations of gamma/gamma' evolution for different dislocation densities and establish the driving forces for microstructure evolution by analyzing in detail the changes in different contributions to the elastic energy and chemical free energy density, as well as the evolution of stress concentrations that may trigger the transition from dislocation flow in the gamma channels towards shearing of the gamma' precipitates. Our investigation reveals the mechanisms controlling the process of directional coarsening (rafting) and demonstrates that the kinetics of rafting significantly depends on characteristics of the dislocation microstructure. In addition to rafting under constant load, we investigate the effect of changes in loading conditions and explore the possibility of improving creep properties by pre-rafting along a different loading path. (C) 2017 Elsevier Ltd. All rights reserved.
Keywords: Continuum dislocation dynamics; Microstructure; Creep; Superalloy; Phase-field

A dislocation dynamics-assisted phase field model for Nickel-based superalloys: The role of initial dislocation density and external stress during creep - Wu, Ronghai; Sandfeld, Stefan (Journal of Alloys and Compounds, 2017)
Keywords: Phase-field model; Superalloy; Dislocation dynamics; Microstructure; Creep

Insights from a minimal model of dislocation-assisted rafting in single crystal Nickel-based superalloys - Sandfeld, Stefan; Wu, Ronghai (Scripta Materialia, 2016)
Nickel-based superalloys play a major role in many technologically relevant high temperature applications. Understanding and predicting the evolution of the phase microstructure during high temperature creep together with the evolution of the dislocation microstructure is a challenge that up to date has not yet been fully accomplished. Our two-dimensional coupled phase-field/continuum dislocation dynamics model explains microstructural mechanisms which are important during the early stage of rafting in a single crystal system. It shows how γ/γ phases and dislocations interact giving rise to realistic creep behavior; no phenomenological fit parameters are required.
Keywords: Continuum dislocation dynamics; Microstructure; Phase-field model; Rafting; Superalloy

Some Steps towards Modelling of Dislocation Assisted Rafting: A Coupled 2D Phase Field - Continuum Dislocation Dynamics Approach - Wu, Ronghai; Sandfeld, Stefan (145th Annual Meeting and Exhibition, TMS 2016, 2016)
The interaction between edge dislocations and γ′ precipitates as in nickel-based super-alloys is studied by coupling a phase field model and a 2D continuum dislocation dynamic model. Various stresses, which serve as communicator between dislocations and precipitates, are calculated by an eigenstrain method for both the γ/γ′ misfit and the dislocations. Our simulations show how edge dislocations tend to move to and pile up at specific γ/γ′ interfaces. The growth of γ′ is inhibited at the interface where dislocations are piling up, due to the reduction of elastic energy. The potential of our coupled model for simultaneous microstructure patterning and mechanical property prediction is discussed.
Keywords: Continuum dislocation dynamics; Nickel-based superalloy; Phase field; Rafting