A model for diffusional cavity growth in superplasticity

Abstract

There is an enhancement in the diffusional growth of cavities in superplastic materials if the cavity size exceeds the grain size so that vacancies diffuse into the cavity along a number of grain boundary paths. A model for this process is developed, and it is shown that the rate of change of cavity radius with strain due to superplastic diffusion growth is given by dr/dε ~ -45Ω δD_g^b/d²kT (σ/ε) where r is the cavity radius, ε is the total strain, Ω is the atomic volume, δ is the grain boundary width, D^gb is the coefficient for grain boundary diffusion, d is the spatial grain size, k is Boltzmann's constant, T is the absolute temperature, σ is the applied stress and ε is the strain rate. Superplastic diffusion growth is therefore independent of the instantaneous cavity radius and inversely proportional to the square of the grain size; in practice, this process becomes important at the lower testing strain rates and when the specimen grain size is typically less than ~5 μm. It is demonstrated that the occurrence of superplastic diffusion growth is capable of providing an explanation for the experimental observations of large rounded cavities in several superplastic materials.