THE MODELING OF GROWTH STRESSES DURING HIGH-TEMPERATURE OXIDATION

The development of stresses in the scale during the high-temperature oxidation of metals can have important consequences for the long-term protection of components in service, particularly if this leads to scale failure, allowing access of the environment to the metal surface. Such stresses may result from externally applied deformation of the scale/substrate system, from thermal effects due to differential thermal contraction/expansion between the scale and the metal, from geometrical effects or from the intrinsic scale-growth process itself. In this paper, a review is presented of some of the models that have been published to account for scale-growth stresses and thermal stresses, with emphasis on quantitative estimation of such stresses and the resulting strains in the scale, in the metal and in the metal/scale interface. Although most models of intrinsic scale-growth stresses are based on the volume change as metal is converted to oxide in a confined location within the scale or at the scale/metal interface, there is little consensus on how these stresses develop. Several quantitative, but incompatible, models have been proposed for outward-growing scales in which oxide is assumed to form in the scale grain boundaries or at the base of these boundaries following inward transport of oxidant, although other qualitative models have stressed the importance of pores or cracks as paths for such species. Most models for the development of growth stresses use elastic analysis and neglect plasticity and creep effects, which may not be justified for a slow-growing scale. A qualitative model has been suggested that can account for the presence of a stress in such a scale without invoking formation of oxide within a constrained location. Rather, it results from climb of a fraction of the intrinsic misfit interfacial dislocations into the metal to annihilate vacancies at the scale/metal interface, followed by adjustment of the spacing of the remaining dislocations to maintain epitaxy. The importance of relaxation has been demonstrated in the model of stress generation during the oxidation of silicon. Reasonable quantitative models are now available to describe the development of geometrically induced stresses and thermal stresses. The latter are generally based on elastic analysis, which is justified for the high strain rates induced on rapid cooling or heating cycles.