THE MODELING OF GROWTH STRESSES DURING HIGH-TEMPERATURE OXIDATION

The development of stresses in the scale during the high-temperature o xidation of metals can have important consequences for the long-term p rotection of components in service, particularly if this leads to scal e failure, allowing access of the environment to the metal surface. Su ch stresses may result from externally applied deformation of the scal e/substrate system, from thermal effects due to differential thermal c ontraction/expansion between the scale and the metal, from geometrical effects or from the intrinsic scale-growth process itself. In this pa per, a review is presented of some of the models that have been publis hed to account for scale-growth stresses and thermal stresses, with em phasis on quantitative estimation of such stresses and the resulting s trains in the scale, in the metal and in the metal/scale interface. Al though most models of intrinsic scale-growth stresses are based on the volume change as metal is converted to oxide in a confined location w ithin the scale or at the scale/metal interface, there is little conse nsus on how these stresses develop. Several quantitative, but incompat ible, models have been proposed for outward-growing scales in which ox ide is assumed to form in the scale grain boundaries or at the base of these boundaries following inward transport of oxidant, although othe r qualitative models have stressed the importance of pores or cracks a s paths for such species. Most models for the development of growth st resses use elastic analysis and neglect plasticity and creep effects, which may not be justified for a slow-growing scale. A qualitative mod el 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 intrinsi c misfit interfacial dislocations into the metal to annihilate vacanci es 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 dur ing the oxidation of silicon. Reasonable quantitative models are now a vailable to describe the development of geometrically induced stresses and thermal stresses. The latter are generally based on elastic analy sis, which is justified for the high strain rates induced on rapid coo ling or heating cycles.