The effects of segregation on the kinetics of irrtergranular cavity growth under creep conditions
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I.
INTRODUCTION
THE purpose
of this paper is to investigate the possible effects of segregation on the kinetics of intergranular cavity growth under creep conditions. Both grain boundary segregation and segregation to the cavity surface will be considered. We will not consider the important effects of segregation on cavity nucleation as this is being done by Yoo and Trinkaus 1 in another paper in this series. Throughout this discussion we will assume the existence of grain boundary cavities having diameters in the range 0.2 bt m to 20 btm. We wish to review the physical mechanisms which control cavity growth under different circumstances and to speculate on the effects of solute segregation by considering how solutes may influence grain boundary and surface energy (T~B, Ts), grain boundary, surface and lattice diffusivity (Des, Ds, DL), and the creep strength of the matrix.
II.
MECHANISMS OF INTERGRANULAR CAVITY GROWTH
There are two limiting kinds of cavity growth that occur under creep conditions. They have been called unconstrained and constrained cavity growth, respectively. In the case of unconstrained cavity growth, cavities are present on all of the grain boundaries in the solid and are free to grow
to the point of complete failure. In the case of constrained cavity growth, cavities are present only on isolated boundaries. Here cavity growth on the cavitated boundary can proceed only if the surrounding matrix creeps, as the relative grain displacements associated with cavitation have to be accommodated by corresponding displacements in the matrix. Thus, in this case cavity growth may be limited entirely by creep flow of the matrix. Constrained cavity growth usually occurs under ordinary creep conditions. Typically, cavitation is quite inhomogeneous with only a few of the transverse boundaries being heavily cavitated. Under these circumstances cavity growth can be controlled by creep flow of the surrounding matrix. This may explain the success of the Monkman-Grant relation, in which the creep fracture time, tI, correlates strongly with the minimum creep rate, kin, through kmtI ~ constant. Although unconstrained cavity growth does not usually occur under ordinary creep conditions, it does occur in a number of important technological situations. Under irradiation conditions helium bubbles are often found to be uniformly distributed on the grain boundaries. Similarly, gas bubbles such as H20 and CO2 can be produced on grain boundaries in some metals through chemical interactions with the environment. Also, grain boundary porosity is inherent in some metals. In all of these cases cavity growth would occur in an unconstrained manner.
A. Mechanisms of Unconstrained Cavity Growth W.D. NIX, Professor and Associate Chairman, and K.S. YU and J. S. WANG, Graduate Research Assistants, are all with the Department of Materials Science and Engineering, Stanford University, Stanford, CA 94305. This paper is based on a presentation made at the symposium "The Role of Trace Elements and Interfaces in Creep Failure" held
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