A Model for the Growth of Hydrogen Attack Cavities in Carbon Steels
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METALLURGICAL TRANSACTIONS A
must be avoided in practice, the regime of major practical importance is the incubation stage; specifically, the duration of the "incubation time" as a function of the environmental and metallurgical variables is the HA parameter of prime concern. Hence, we are interested in the mechanisms and kinetics of the nucleation and growth of grain boundary cavities. This paper deals with growth mechanisms; the problem of nucleation is discussed elsewhere. 13 A number of models have been proposed for bubble growth during HA. The most notable are models by Shewmon, 1~Sagues 6 and Shih. 8 Shewmon 1~suggested that bubble growth at high temperatures and low hydrogen pressures occurred by grain boundary vacancy diffusion and that at low temperature and high hydrogen pressures it is limited by the rate of methane production at the bubble surface. Sagues et a l 6 carried out the first numerical simulation of HA using kinetic formulation of Grabke and Martin '4 for methane production. The growth of bubbles was modeled using a combination of diffusion and power-law creep. This study concluded that bubble growth during the rapid attack stage occurred by power-law creep of the surrounding matrix. Shih8 carried out a similar, but more detailed study, and found that bubble growth occurred initially by grain boundary vacancy diffusion and by power-law creep during later stages of HA. A major deficiency of the models is their improper treatment of methane pressure which is, of course, the driving force for bubble growth. In particular, the models had assumed an equality between equilibrium methane fugacity and pressure. It is shown elsewhere '5 that this assumption breaks down at high fugacities and will lead to serious errors in estimation of bubble growth rates. A simulation study carried out by us ~6recently using an approximate equation-of-state for methane showed that the rate of HA during the initial stages is not limited by the rate of methane production even at low temperatures; rather bubbles grow by grain boundary vacancy diffusion with the pressure of the methane in bubbles nearly equal to the equilibrium value. Further, the estimated equilibrium methane pressures are considerably lower than fugacities for high values of fugacities ( ~ 1000 MPa) making bubble i
ISSN 0360-2133/81 / 1211-2071500.75/0 9 1981 AMERICAN SOCIETY FOR METALS AND VOLUME12A, DECEMBER 1981--2071 THE METALLURGICAL SOCIETY OF AIME
growth by power law creep less effective. The possibility of carbon diffusion as a rate limiting step for H A was also considered in a full kinetic simulation of the diffusion, methane production and cavity growth kinetics of HA. ~5 It was found that carbon diffusion is not a limiting process during the initial stage of HA. This was mainly a consequence of rapid diffusivity of carbon even at low temperatures 30,
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T = 658 K RUN 7
( ~ 5 7 3 K), Further, microstructural evidence showing formation of H A cavities on grain boundary carbides 7-H also suggests that the carbon diffusion may not be
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