|
The present model starts with an assumption that grain/ interphase boundary sliding (GBS)
that is dominant during optimal superplastic flow is slower than the accommodation processes
of dislocation emission from sliding boundaries, highly localized diffusion in the boundary
regions and/ or grain rotation that are present as a concomitant of the GBS process.
When boundary sliding develops to a mesoscopic scale (of the order of a grain diameter or more),
by the alignment of contiguous boundaries, plane interface formation / mesoscopic boundary
sliding is observed. Significant and simultaneous sliding along different plane interfaces and
their interconnection can lead to large scale deformation and superplasticity. The accommodation
steps, being faster than GBS, do not enter the strain rate equation. Mathematical development
of these ideas using transition state theory results in a transcendental strain rate equation
for steady state optimal superplastic flow, which when solved numerically helps one to describe
the phenomenon quantitatively in terms of two constants, the activation energy for the rate
controlling process, ΔF0 and the threshold stress needed to be overcome for the commencement
of mesoscopic boundary sliding, σ0.The analysis also explains quantitatively texture
randomization as a function of superplastic strain.
It is also pointed out, without going into details, that recently the problem has been reduced to FOUR "universal" constants, viz. the mean strain associated with a unit boundary sliding event γ0, specific grain boundary energy γB, which is assumed to be isotropic, N the average number of boundaries that align to form a plane interface during mesoscopic boundary sliding and "a" a grain-size- and shape- dependent constant that obeys the condition 0 < a < 0.5, in terms of which one can account for superplasticity in any material. In combination with the regression equations popularized by Frost and Ashby to predict the shear modulus of any material at any temperature, these four constants allow one to predict the steady state strain rate of any structurally superplastic material accurately, including those whose superplastic response is not considered for the analysis. The details of the last mentioned result, which are unpublished, will be presented elsewhere. |
full paper (pdf, 1696 Kb)