A numerical study on the influence of grain boundary oxides on dwell fatigue crack growth of a nickel-based superalloy

Abstract

• A computational multi-physical modeling approach to oxide-assisted intergranular dwell crack growth of γ′ strengthened nickel-based superalloys is presented. The modeling framework explicitly couples mass transport of chemical species involved in oxide formation to the evolution of mechanical fields ahead of a crack tip. The viscoplastic response accounts for the influence of the γ′ dispersion. • Detailed Quantitative study of the interaction between the dynamic stress-assisted oxide formation ahead of the crack tip and the resulting near crack-tip stress fields was implemented. • A method for extracting crack growth rates based on failure of the oxide wedge ahead of a crack tip is presented • The predicted rates are shown to be in good agreement with available experimental data without any direct information or calibration of model parameters to crack growth rate data in advance. • Established model shows capability of reveal the effect of particle dispersion of nickel-based superalloy on the dwell fatigue crack growth rate. A theoretical treatment on the oxide-controlled dwell fatigue crack growth of a γ’ strengthened nickel-based superalloys is presented. In particular, this study investigates the influence of an externally applied load and variations in the γ’ dispersion on the grain boundary oxide growth kinetics. A dislocation-based viscoplastic constitutive description for high temperature deformation is used to simulate the stress state evolution in the vicinity of a crack at elevated temperature. The viscoplastic model explicitly accounts for multimodal γ’ particle size distributions. A multicomponent mass transport formulation is used to simulate the formation/evolution of an oxide wedge ahead of the crack tip, where stress-assisted vacancy diffusion is assumed to operate. The resulting set of constitutive and mass transport equations have been implemented within a finite element scheme. Comparison of predicted compositional fields across the matrix/oxide interface are compared with experiments and shown to be in good agreement. Simulations indicate that the presence of a fine γ’ size distribution has a strong influence on the predicted ow stress of the material and consequently on the relaxation in the vicinity of the crack-tip/oxide wedge. It is shown that a unimodal dispersion leads to reduced oxide growth rates (parabolic behavior) when compared to a bimodal one. Stability conditions for oxide formation are investigated and is associated with the prediction of compressive stresses within the oxide layer just ahead of the crack tip, which become progressively negative as the oxide wedge develops. However, mechanical equilibrium requirements induce tensile stresses at the tip of the oxide wedge, where failure of the oxide is predicted. The time taken to reach this critical stress for oxide failure has been calculated, from which dwell crack growth rates are computationally derived. The predicted rates are shown to be in good agreement with available experimental data.