A note on grain boundary diffusion controlled cavity growth during elevated temperature fatigue
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Helpful correspondence with Professor S. Saimoto of Queen's University is gratefully acknowledged. REFERENCES 1. L.G. Schulz: J. Appl. Phys., 1949, vol. 20, pp. 1030-33. 2. C.K. Chow and A.M. Duclos: unrestricted, unpublished Atomic Energy of Canada Limited Report WNRE-62, Canada, 1983. 3. A.J. Heckler, J. A. Elias, and A. P. Woods: Trans. TMS-AIME, 1967, vol. 239, pp. 1241-44. 4. E. Tenckhoff: J. Appl. Phys., 1970, vol. 41, pp. 3944-48. 5. A.J.C. Wilson: J. Sci. lnstrum., 1950, vol. 27, pp. 321-25. 6. R.A. Holt and J.E. Winegar: J. Appl. Phys., 1977, vol. 48, pp. 3557-59. 7. C. Feng: J. Appl. Phys., 1965, vol. 36, pp. 3432-35. 8. D. Wilson and D.W. Bainbridge: Metall. Trans., 1971, vol. 2, pp. 2925-29. 9. W.P. Chernock and P.A. Beck: J. Appl. Phys., 1952, vol. 23, pp. 341-45.
A Note on Grain Boundary Diffusion Controlled Cavity Growth during Elevated Temperature Fatigue N. Y. TANG and A. PLUMTREE In fatigue at elevated temperatures the fracture path frequently becomes intergranular, caused by the nucleation, growth, and coalescence of voids on grain boundaries. Several models have been proposed to explain this mechanism. Some authors~-4 suggested that cavity growth is grain boundary diffusion controlled. Skelton ~ modified the Hull and Rimmer 5 model for diffusional growth of cavities in creep to account for cavity growth during fatigue. Weertman 3 analyzed this problem in a similar manner. Both concluded that the critical radius of a cavity to grow was given by 4kTy
ac
~f~
[1]
where k is Boltzmann's constant, T is the absolute temperature, 3' is the surface tension, 0-0 is stress amplitude, and fl is the atomic volume. It must be pointed out that Eq. [1] is applicable only for a balanced sinusoidal wave with zero mean stress. The type of waveform, in fact, is expected to influence the value of the critical radius. An attempt has recently been made to clarify this effect and, in particular, its role in the growth behavior of fatigue cavities. The preliminary results are reported here. In Skelton's original treatment I it was implicitly assumed that the cyclic frequency was so low that at any given instant in time the flow of vacancies to a void was expressed by the static solution with the stress equal to the instantaneous value. J. Weertman 3 demonstrated that this assumption was valid at any arbitrary frequency. However, in more recent work, J.R. Weertman 6 showed that a transient period existed during which the cavity growth rate deviated considerably from that calculated according to Skelton's assumption. The duration of the transient stage was related to a characteristic time period r which was governed by the interparticle spacing and grain boundary diffusivity for a given temperature. 6 When cycling copper at zero mean stress this transient lasts about 0.1 ~-. Subsequently, a quasisteady state diffusional boundary traction is established. Our analysis will deal only with the growth behavior of a cavity during this steady-state period when the transient component for vacancy flow into the cavity due to
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