An Elastic Phase Field Model for Thermal Oxidation of Metals: Application to Zirconia


A multi-phase field model was developed for non-selective oxidation of metals which captures both the oxidation kinetics and stress generation. Phase field formulation involved a non-conserved phase field variable as the marker for the metallic substrate, oxide scale, and a fluid phase containing oxygen, and a conserved phase field variable representing the concentration of oxygen. The evolution equations of the phase field variables were coupled to the mechanical equilibrium equations to investigate the evolution of stress generation in both the oxide scale and the underlying metal. The governing equations were solved in a finite element framework. This phase field model predicts the oxygen composition depth and stress profiles in the oxide layer and at the metal-oxide interface. The model was proven successful in predicting the observed evolution of oxide thickness and growth stresses for Zircaloy-4 oxidized at 900 °C. The results of phase field simulations showed that the generation of stresses upon oxidation tends to slow down the oxidation kinetics, and this substantially improved the model predictability of experimental data.


Materials Science and Engineering

Research Center/Lab(s)

Center for High Performance Computing Research

Keywords and Phrases

Finite element method; Mathematical models; Oxygen; Phase interfaces; Scale (deposits); Stresses; Zirconia; Zirconium; Evolution equations; Governing equations; Growth stress; Mechanical equilibrium; Metal oxide interface; Metallic substrate; Phase field models; Phase-field simulation; Oxidation; Zirconium

International Standard Serial Number (ISSN)


Document Type

Article - Journal

Document Version


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© 2014 Elsevier, All rights reserved.

Publication Date

01 Jun 2014