Metallurgical Phase Transformations
Definitions
The material consists of a number of metallurgical phases. The fraction of each phase i is denoted ξi. There are in general N phases, where
The initial phase fraction must be defined for each phase, and the sum of initial phase fractions should be one. At the onset of an analysis, some phases may not be present, and have zero initial phase fraction.
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The phase fractions are defined in the material frame.
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Because of the employed weighting scheme for the effective mass density of the compound material, the phase fractions become algebraic fractions.
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See Compound Material Properties.
Each phase transformation describes how a source phase s transforms into a destination phase d. A phase transformation is formally defined by the rate at which the destination phase d forms at the expense of the source phase s. This can be expressed as
(3-1)
Note that this equation describes only a single contribution to the total rates at which the destination phase forms, and the source phase decomposes. With several simultaneous phase transformations, some phases may receive more than one contribution. As an example, consider the case of three phases and two phase transformations, where phase 1 transforms into phases 2 and 3. Using the terminology above, the total rate equations for the three phases can be expressed as
Note that these rate equations satisfy
In COMSOL Multiphysics, a weak contribution is generated for each phase i:
where the summation is done over every phase transformation for which phase j transforms into phase i.