A model for the oxide growth stress and its effect on the creep of metals
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I.
II.
INTRODUCTION
IT is known
that a stress exists within the oxide scale on a metal surface, ]'2 and that the process of oxidation can cause deformation of unstressed metal. 3-8 Oxidation also can alter the deformation of stressed metal. 9'l~ The causes of these effects are not definitely known, but a major factor is thought to be the stress in the oxide scale. 3-8 The origin of this stress is uncertain, but many explanations are based upon the volumetric difference between the metal and its oxide, as expressed by the Pilling-Bedworth Ratio.lZ The problem of the stress in the oxide scale has been the subject of a number of excellent reviews.13-19 Oxidation stresses are of importance to a number of different fields. The maintenance of a protective oxide scale requires an adherent scale. Stresses within the scale may cause it to crack, blister, or decohere Oxidation accelerates high temperature creep, fatigue, and crack growth in metals. 2~ Stress in the scale may contribute to this by changing the stresses in the metal or by causing the scale to crack. Oxide stresses can affect the deformation of structural components, 3'z7 and should be considered when designing components of thin cross-sectional area to operate at high temperature in oxidizing environments. Previous mathematical models for the oxide growth stress may be grouped into elastic and inelastic models, depending on how the metal or oxide deforms. The elastic models 28'29'3~ calculate the average stress in the oxide scale from experimental deflection measurements by assuming that the metal deforms elastically. When the metal primarily deforms by creep, which occurs for high temperature oxidation, this elastic assumption is clearly inadequate. The inelastic models 3'4'3~ allow the metal to deform by creep. Their major drawbacks to these models are that they are uniaxial and neglect the biaxial state of stress in the scale, they assume that the stress is uniform across the scale thickness, and they ignore the deformation of the scale. The model presented in this paper is a three-dimensional inelastic analysis incorporating elastic and creep deformation of the metal and the growing oxide scale. This stress distribution in the metal and oxide is calculated, and a specific mechanism for the generation of a stress within the oxide scale is mathematically modeled. H.L. BERNSTEIN is Assistant Professor, Department of Mechanical Engineering, University of Houston, 4800 Calhoun Road, Houston, TX 77004. Manuscript submitted July 15, 1985. METALLURGICALTRANSACTIONS A
THE M O D E L
A. Origin of the Oxide Stress The exact origin of the oxide growth stress is not known. Reasons proposed for this stress are (1) the volumetric difference between the oxide and the metal, (2) concentration gradient of ions in the scale, 32 (3) vacancy injection into the metal, 33 and (4) the formation of new oxide in the grain boundaries of the already existing oxide scale. 4'34 The source of oxide stress modeled in this paper is the volumetric difference between the oxide and the
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