Phase Transformation Functions
The Microstructure based phase transformation model uses information deriving from, for example, grain size and chemical composition. Kirkaldy and Venugopalan (Ref. 11) expressed a set of phase transformation functions that were used to model the decomposition of austenite into ferrite, pearlite, and bainite. Based on this methodology, Li, Niebuhr, Meekisho, and Atteridge (Ref. 12) presented a similar set of phase transformation functions for the decomposition of austenite. In addition, Åkerström and Oldenburg (Ref. 13) modified the set of phase transformation functions by Kirkaldy and Venugopalan, to better capture the behavior of boron steels in press hardening applications. The general form for the phase transformations is
Overall, the following values for m, a, and Cr are
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m = 2 for the decomposition of austenite into bainite, and m = 3 otherwise.
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a = 2/5 for all phase transformations according to Li, Niebuhr, Meekisho, and Atteridge, and a = 2/3 otherwise.
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The retardation coefficient is Cr = 0, except where explicitly defined below.
The upper temperature limit Tu for the three phase transformations are
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Tu = Ae3 for the decomposition of austenite into ferrite.
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Tu = Ae1 for the decomposition of austenite into pearlite.
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Tu = Bs for the decomposition of austenite into bainite.
Austenite to Ferrite (Kirkaldy–Venugopalan)
The chemical dependence function was modified by Åkerström and Oldenburg to account for boron. In their formulation, the function is
Austenite to Pearlite (Kirkaldy–Venugopalan)
The chemical dependence function was modified by Åkerström and Oldenburg to account for boron. In their formulation, the function is
Austenite to Bainite (Kirkaldy–Venugopalan)
Austenite to Ferrite (Li–Niebuhr–Meekisho–Atteridge)
Austenite to Pearlite (Li–Niebuhr–Meekisho–Atteridge)
Austenite to Bainite (Li–Niebuhr–Meekisho–Atteridge)