[Paper Review] A discrete dislocation dynamics study of precipitate bypass mechanisms in nickel-based superalloys

Sabyasachi Chatterjee, Yang Li+1 more|arXiv (Cornell University)|Apr 12, 2021

High Temperature Alloys and Creep72 references71 citations

TL;DR

This study uses discrete dislocation dynamics (DDD) simulations to investigate dislocation bypass mechanisms in Ni-based superalloys, introducing a novel winding number-based method to compute generalized stacking fault forces. It demonstrates that a hybrid shearing-looping mechanism operates over a wide range of precipitate volume fractions and radii, significantly influencing strength, and shows that lattice misfit increases bypass stress, with high misfit leading to pinning-dominated bypass similar to high-temperature creep.

ABSTRACT

Order strengthening in nickel-based superalloys is associated with the extra stress required for dislocations to bypass the $\gamma'$ precipitates distributed in the $\gamma$ matrix. A rich variety of bypass mechanism has been identified, with various shearing and Orowan looping processes giving way to climb bypass as the operating conditions change from the low/intermediate temperatures and high stress regime, to the high temperature and low stress regime. When anti phase boundary (APB) shearing and Orowan looping mechanisms operate, the bypass mechanism changes from shearing to looping with increased particle size and within a broad coexistence size window. Another possibility, supported by indirect experimental evidence, is that a third "hybrid" transition mechanism may operate. In this paper we use discrete dislocation dynamics (DDD) simulations to study dislocation bypass mechanisms in Ni-based superalloys. We develop a new method to compute generalized stacking fault forces in DDD simulations. We use this method to study the mechanisms of bypass of a square lattice of spherical $\gamma'$ precipitates by $a/2\langle110 angle\{111\}$ edge dislocations, as a function of the precipitates volume fraction and size. We show that the hybrid mechanism is possible and it operates as a transition mechanism between the shearing and looping regimes over a large range of precipitates volume fraction and radii. We also consider the effects of a $\gamma/\gamma'$ lattice misfit on the bypass mechanisms, which we approximate by an additional precipitate stress computed according to Eshelby's inclusion theory. We show that in the shearing and hybrid looping-shearing regimes, a lattice misfit generally results in an increased bypass stress. For sufficiently high lattice misfit, the bypass stress is controlled by the pinning of the trailing dislocation on the exit side of the precipitates.

Motivation & Objective

• To investigate the mechanisms by which dislocations bypass γ′ precipitates in Ni-based superalloys under varying microstructural and loading conditions.
• To develop and apply a novel DDD method for computing generalized stacking fault forces using the winding number concept from complex analysis.
• To determine the conditions under which a hybrid shearing-looping bypass mechanism operates, and to quantify its contribution to material strength.
• To examine the influence of γ/γ′ lattice misfit on bypass stress, using Eshelby’s inclusion theory to model misfit-induced stresses.
• To propose a simple model for the strength contribution of the hybrid bypass mechanism based on simulation results.

Proposed method

• A discrete dislocation dynamics (DDD) framework is employed to simulate the bypass of a/2⟨110⟩{111} edge dislocations by a square lattice of spherical γ′ precipitates.
• A new method is developed to compute generalized stacking fault forces using the winding number of a closed curve about a point, enabling accurate representation of stacking fault energy landscapes.
• The stacking fault energy (SFE) surfaces for both γ and γ′ phases are fitted using wave vector components and experimental/atomistic data, ensuring accurate SFE description.
• Lattice misfit is modeled via Eshelby’s inclusion theory, calculating an additional stress field from eigenstrains to simulate the effect of γ/γ′ mismatch.
• Critical bypass configurations are identified by tracking dislocation motion and stress drops during simulations, with bypass stress defined as the peak stress before a drop due to bypassing.
• A simple analytical model is proposed for the strength contribution of the hybrid mechanism based on simulation data and geometric constraints.

Experimental results

Research questions

• RQ1 Does a hybrid dislocation bypass mechanism exist between pure shearing and Orowan looping in Ni-based superalloys under varying precipitate size and volume fraction?
• RQ2 How does the newly developed winding number-based method for generalized stacking fault forces improve the accuracy of DDD simulations in capturing bypass mechanisms?
• RQ3 What is the quantitative contribution of the hybrid mechanism to the overall bypass stress across different precipitate sizes and volume fractions?
• RQ4 How does γ/γ′ lattice misfit affect the bypass stress, and does it alter the dominant bypass mechanism or critical configuration?
• RQ5 Can a simple analytical model be derived to predict the strength contribution of the hybrid bypass mechanism based on simulation data?

Key findings

• The hybrid shearing-looping mechanism is not only possible but operates as a dominant transition mechanism across a wide range of precipitate volume fractions and radii, challenging the classical two-regime model.
• For dislocation pairs, the bypass stress exceeds that predicted by the BKS model due to repulsive interactions from the leading dislocation's loop, which hinders closure of the trailing loop.
• The bypass stress increases with lattice misfit, and for sufficiently high misfit, the critical configuration shifts to one dominated by pinning of the trailing dislocation on the exit side of the precipitate.
• The simulation results show that the hybrid mechanism contributes significantly to strength, particularly in the transition regime between shearing and looping.
• The proposed simple model for the hybrid mechanism's strength is validated by simulation data and provides a predictive framework for microstructure design.
• The study confirms that lattice misfit can dramatically alter the bypass mechanism, shifting from shearing/looping to pinning-dominated behavior at high misfit, consistent with high-temperature creep observations.