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Research Papers

# Modeling of Oxygen Diffusion Along Grain Boundaries in a Nickel-Based Superalloy

[+] Author and Article Information
L. G. Zhao

Department of Mechanical and Design Engineering, University of Portsmouth, Anglesea Building, Anglesea Road, Portsmouth, Hampshire PO1 3DJ, UK

J. Eng. Mater. Technol 133(3), 031002 (Jun 24, 2011) (7 pages) doi:10.1115/1.4003777 History: Received August 10, 2010; Revised March 04, 2011; Published June 24, 2011; Online June 24, 2011

## Abstract

Finite element analyses of oxygen diffusion at the grain level have been carried out for a polycrystalline nickel-based superalloy, aiming to quantify the oxidation damage under surface oxidation conditions at high temperature. Grain microstructures were considered explicitly in the finite element model where the grain boundary was taken as the primary path for oxygen diffusion. The model has been used to simulate natural diffusion of oxygen at temperatures between $650∘C$ and $800∘C$, which are controlled by the parabolic oxidation rate and oxygen diffusivity. To study the effects of mechanical stress on oxygen diffusion, a sequentially coupled deformation-diffusion analysis was carried out for a generic specimen geometry under creep loading condition using a submodeling technique. The material constitutive behavior was described by a crystal plasticity model at the grain level and a unified viscoplasticity model at the global level, respectively. The stress-assisted oxygen diffusion was driven by the gradient of hydrostatic stress in terms of pressure factor. Heterogeneous deformation presented at the grain level imposes a great influence on oxygen diffusion at $750∘C$ and above, leading to further penetration of oxygen into the bulk material. Increased load level and temperature enhance oxygen concentration and penetration within the material. At $700∘C$ and below, mechanical loading seems to have negligible influence on the oxygen penetration because of the extremely low values of oxygen diffusivity and pressure factor. In the case of an existing surface microcrack, oxygen tends to accumulate around the crack tip due to the high stress level presented near the crack tip, leading to localized material embrittlement and promotion of rapid crack propagation.

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## Figures

Figure 1

(a) Finite element mesh for a generic two-dimensional global model (width W=7mm and height H=12.5mm), (b) the 150-grain submodel with random grain orientation, and (c) inverse pole figure for the 150 grains

Figure 2

Contour plots of oxygen concentration after 200 h oxidation at (a) 650∘ C and (b) 800∘ C

Figure 3

Oxygen concentration against the distance from the surface after 200 h oxidation at 650∘C, 700∘ C, 750∘ C, and 800∘ C, respectively

Figure 4

Contour plot of the hydrostatic stress for the submodel loaded for 200 h at a constant stress of 1100 MPa

Figure 5

Contour plot of the oxygen concentration for the submodel after 200 h oxidation at 750∘C: (a) under the 1100 MPa stress and (b) natural diffusion

Figure 8

Effect of stress level on the accumulation of oxygen concentration near the crack tip at 750∘C

Figure 9

Comparison of the evolution of oxygen concentration near the crack tip at 650∘C for the conditions with (700 MPa) and without stress (natural diffusion)

Figure 10

Comparison of the evolution of oxygen concentration near the crack tip at 700∘C for the conditions with (700 MPa) and without stress (natural diffusion)

Figure 6

Effects of loading level and exposure temperature on the penetration depth of oxygen where the penetration depth of oxygen (δ) is normalized against that for natural diffusion (δ0)

Figure 7

(a) Contour plot of the hydrostatic stress for the submodel with an intergranular surface crack loaded for 50 h at a constant stress of 700 MPa and (b) contour plot of oxygen concentration near the crack tip

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