Density measurements as an assessment of creep damage and cavity growth
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exp ( - Q g b / R T )
where - Ap is the density change, P is the original density, 9 is the strain, t is the time, d is the linear intercept grain size, o is the applied stress, G is the shear modulus, QgbiS the activation energy for grain boundary diffusion, R is the gas constant, T is the absolute temperature, and B and q are constants with q ~ 2 to 3. This expression is consistent with the theory of unconstrained grain boundary diffusion growth of cavities provided there is also concomitant strain-dependent nucleation. The expression does not support the power-law growth of cavities, growth by surface diffusion, or constrained grain boundary diffusion growth.
1. I N T R O D U C T I O N
IT is frequently observed that cavities are nucleated and grow at the grain boundaries during the high temperature deformation of metals and alloys, and the interlinkage of these cavities generally leads to an intergranular type of fracture. Several detailed investigations of cavitation have been reported using a number of different alloy systems and various experimental techniques. A determination of the change in specimen density with strain provides a simple nondestructive method of measuring the extent of cavitation, and thus gives an indication of the amount of creep damage. However, since nucleation is often a continuous process during creep, 1-3 an inherent limitation of this technique is that it is unable to differentiate between the nucleation and growth processes. The first detailed measurements of changes in specimen density during creep were obtained by Boettner and Robertson 4 on Cu, and it was subsequently demonstrated by Woodford 5 that these data may be represented by an empirical equation involving time, stress, and an activation energy. To date, no further attempt has been made to develop this approach. The present work was undertaken with three objectives: 1) To determine whether the empirical relationship suggested by Woodford 5 is generally applicable to the large number of density measurements now available for Cu covering a wide range of experimental conditions; 2) To determine whether the same relationship also applies to density measurements on other mateDAVID A. MILLER, formerly Research Associate, University of Southern California, is now Research Officer, Central Electricity Generating Board, South West Region, Bedminster Down, Bristol BS13 8AN, England. TERENCE G. LANGDON is Professor, Departments of Materials Science and Mechanical Engineering, University of Southern California, Los Angeles, CA 90007. Manuscript submitted October 10, 1979.
rials, and, in particular, to check the observation of Greenwood 6 that the mechanism of cavitation appears to be relatively insensitive to crystallographic structure; and 3) To use the results of this analysis to provide information on the mechanism of cavity growth. 2. ANALYSIS F O R Cu Using the results of Boettner and Robertson, 4 Woodford 5 showed that all of the experimental datum points were in reasonable agreement with an empirical relationship given by
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