Conversion of the hot torsion test results into flow curve with multiple regimes of hardening

The method of Fields and Backofen has been commonly used to reduce the data obtained by hot torsion test into flow curves. The method, however, is most suitable for materials with monotonic strain hardening behaviour. Other methods such as Stüwe’s method, tubular specimens, differential testing and the inverse method, each suffer from similar drawbacks. It is shown in the current work that for materials with multiple regimes of hardening any method based on an assumption of constant hardening indices introduces some errors into the flow curve obtained from the hot torsion test. Therefore such methods do not enable accurate prediction of onset of recrystallisation where slow softening occurs. A new method to convert results from the hot torsion test into flow curves by taking into account the variation of constitutive parameters during deformation is presented. The method represents the torque twist data by a parametric linear least square model in which Euler and hyperbolic coefficients are used as the parameters. A closed form relationship obtained from the mathematical representation of the data is employed next for flow stress determination. Two different solution strategies, the method of normal equations and singular value decomposition, were used for parametric modelling of the data with hyperbolic basis functions. The performance of both methods is compared. Experimental data obtained by FHTTM, a flexible hot torsion test machine developed at IROST, for a C–Mn austenitic steel was used to demonstrate the method. The results were compared with those obtained using constant strain and strain rate hardening characteristics.

A heuristic model selection scheme for representing hot flow data using the hot torsion test results

The problem of "model selection" for expressing a wide range of constitutive behaviour adequately using hot torsion test data was considered here using a heuristic approach. A model library including several nested parametric linear and non-linear models was considered and applied to a set of hot torsion test data for API-X 70 micro-alloyed steel with a range of strain rates and temperatures. A cost function comprising the modelled hot strength data and that of the measured data were utilized in a heuristic model selection scheme to identify the optimum models. It was shown that a non-linear rational model including ten parameters is an optimum model that can accurately express the multiple regimes of hardening and softening for the entire range of the experiment. The parameters for the optimum model were estimated and used for determining variations of hot strength of the samples with deformation.

Background paper : "Aid effectiveness and selectivity : integrating multiple objectives into aid allocation"

Research on development aid has largely focused on the effectiveness of these transfers in promoting growth or on their allocation among developing countries. Rarely if ever did these research areas intersect, in that studies seeking to explain observed or prescribe optimal inter-country aid allocations did not take into account effectiveness issues and vice versa. Collier and Dollar (C-D, 2002), in a move broadly consistent with the IDA’s long-standing approach to its country allocation system, changed this state of affairs with their “aid selectivity” approach to inter-country aid allocation. C-D, building on the empirical work of Burnside and Dollar (B-D, 1997, 2000), which concluded that the effectiveness of aid in promoting growth depended on the policy regimes of recipient countries, derived “poverty efficient” inter-recipient aid allocations. According to the prescriptive C-D selectivity approach, optimal aid allocation favours countries with high levels of poverty, low per capita incomes and sound policy regimes. Such allocations are considered poverty efficient by maximising the number of people pulled out of poverty. Countries with unsound policies regimes receive less aid in the C-D selectivity approach as these regimes lessen aid’s impact on growth and thus poverty reduction.