On the experimental validation of a mesoscopic grain boundary sliding-controlled flow model for structural superplasticity

Abstract

Different mechanisms have been suggested by many authors as controlling the rate of superplastic flow in different materials. From the viewpoint of computational effort and aesthetics, it is highly desirable to explain the phenomenon, independent of the material/system considered, on a common basis. With this aim, a mesoscopic grain boundary sliding-controlled deformation model was proposed sometime ago as being responsible for superplastic flow in materials of different kinds. In this paper, a rigorous numerical computational procedure for the experimental validation of the model, which takes into account all the physical requirements of the model, is presented. The soundness of the new procedure is established by analysing the experimental data pertaining to many systems belonging to different classes of materials, and matching the results of the analysis with the experimental findings.

Appendix A: Application to intermetallics, dispersion strengthened alloys and composites

(This section was completed in collaboration with M. Raviathul Basaria).

Table 5 presents the results obtained by the procedure outlined in the main paper. Systems 1–4 were studied in [14, 15], systems 5–9 in [16] and the rest in [17]. As before, the required material properties were extracted from [41, 42, 48]. For comparison, the values obtained earlier are also included in Table 5. The measure of prediction accuracy was defined, as before, as the larger value between $\left( {\dot{\varepsilon }_{\text{experimental}} /\dot{\varepsilon }_{\text{predicted}} } \right)$ and $\left( {\dot{\varepsilon }_{\text{predicted}} /\dot{\varepsilon }_{\text{experimental}} } \right)$ ratios (Tol).

Table 5 Details and the results of the intermetallic and other systems analysed

In this case also, in accordance with theory, the value of γ ₀ for a given system increases with increasing temperature. In the earlier numerical validation procedures, γ ₀ was assumed (as an approximation) to be independent of temperature and system. A few more points are also worthy of note: for systems 1–4 the accuracy of predictions has improved with the present algorithm. For systems 3 and 4 of similar composition, in each paper the grain size and temperature are different. In these cases the values of ΔF ₀ and γ ₀ at the common temperature of 1723 K are found to agree very well, which demonstrates the robustness of the present algorithm. For the rest of the systems, it is noted that in the earlier method [16, 17] ΔF ₀ value was calculated at each temperature for each datum point and then a mean value was obtained which gave rise to very accurate predictions. But that method did not use the method of least squares, as done here, which makes the statistics used here more formal/correct.

The correlation coefficient for the relation between γ ₀ and T for the Ti–Al systems (systems 7–9) is 0.9983; similarly for the aluminium-based systems 10–12, of similar composition, a correlation coefficient of 0.9159 is obtained. System 13 is omitted from this correlation although it is also an Al alloy because of its considerably different composition.

See Table 5.