Abstract
The double differentiation method overestimates the critical stress associated with the initiation of dynamic transformation (DT) because significant amounts of the dynamic phase must be present in order for its effect on the work hardening rate to be detectable. In this work, an alternative method (referred to here as the free energy method) is presented based on the thermodynamic condition that the driving force is equal to the total energy obstacle during the exact moment of transformation. The driving force is defined as the difference between the DT critical stress (measured in the single-phase austenite region) and the yield stress of the fresh ferrite that takes its place. On the other hand, the energy obstacle consists of the free energy difference between austenite and ferrite, and the work of shear accommodation and dilatation associated with the phase transformation. Here, the DT critical stresses in a C-Mn steel were calculated using the free energy method at temperatures ranging from 870 °C to 1070 °C. The results show that the calculated critical stress using the present approach appears to be more accurate than the values measured by the double differentiation method.
Highlights
The application of the double differentiation method [1] on a stress-strain curve obtained from steel deformed at elevated temperatures has been proven to provide information regarding the initiation of various dynamic metallurgical softening phenomena such as twinning, recrystallization and recovery [2,3]
The inflection points in the plot of strain hardening rate versus stress (θ-σ) provide the initiation points of each dynamic softening mechanism
Hot compression tests were performed on a 100 kN
Summary
The application of the double differentiation method [1] on a stress-strain curve obtained from steel deformed at elevated temperatures has been proven to provide information regarding the initiation of various dynamic metallurgical softening phenomena such as twinning, recrystallization and recovery [2,3]. It has been proven by the present authors that this approach can identify the onset of dynamic transformation (DT) of austenite to ferrite during hot compression and rolling [4,5,6]. These points are clearly identified by the condition: δθ δσ
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