In this example, a fully austenitic base structure is cooled from 900°C to room temperature, across a range of constant cooling rates. Rates from 0.001 K/s to 1000 K/s are used, in ten increments per decade.

Phase transformation data and metallurgical phase material properties for general steels can be exported from JMatPro® (Ref. 1), and imported into COMSOL Multiphysics. Every phase transformation model in the Metal Processing Module is of the general form:

where the rate term As → d describes the rate at which a destination phase forms at the expense of a source phase. Each built-in phase transformation model in the Metal Processing Module is of this form, and the difference between models lies in the functional form for the rate term. When phase transformations are imported, applicable phase transformation models in the Metal Processing Module are automatically configured, that is, their respective rate terms are configured using the imported data. For diffusive phase transformations, this means that the Lebond–Devaux, the Johnson–Mehl–Avrami–Kolmogorov, and the Kirkaldy–Venugopalan, simplified phase transformation models are configured (using TTT data), and for the displacive martensitic phase transformation, the Koistinen–Marburger phase transformation model is configured. For the diffusive phase transformations, the imported data is additionally processed into a temperature-dependent interpolation function (rate term) A that makes no a-priori assumption as to an underlying phase transformation model structure. It has the form

where ρ is the phase fraction averaged density of the steel, evaluated at the initial phase composition and the volume reference temperature, and ρth is the phase fraction averaged density of the steel, evaluated at the current phase composition and the current temperature.

A common way to characterize, or illustrate, the phase transformation behavior of steels is through a CCT diagram, in which each curve corresponds to the time required to reach a certain phase fraction of a certain phase, at different cooling rates. Figure 1 shows the CCT diagram resulting from the imported phase transformation data. The red curve corresponds to 1% of ferrite having formed, and so on. The blue curve corresponds in this case effectively to the cessation of all phase transformations, as it represents the 1% line of (available) austenite.

The different metallurgical phases are of different, and temperature-dependent, densities. This is shown in Figure 2. Notably, the density curve for austenite is higher than other phases, suggesting that as the steel phase transforms during cooling, there is should be a density decrease, which should manifest itself as a thermal expansion. In the figure, the evolving effective density of the steel is shown. At the highest cooling rate (1000 K/s), the austenite decomposes fully into martensite, and the figure shows how the effective density transitions from the density of pure austenite, to that of pure martensite (the black curve). The effective density curves corresponding to lower cooling rates, where the resulting phase composition is a mixture of destination phases, all originate as pure austenite, but subsequently display various kinks corresponding to different phase transformations taking place. From the effective density, a thermal strain measure can be defined. Figure 3 shows, for a selection of cooling rates, the resulting (axial) thermal strain based on the evolving effective density of the steel. Note here, that since the computation started at an elevated temperature of 900°C, while the volume reference temperature of the phases was set to room temperature, this will appear as an initial strain (an offset).

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In the New window, click  Model Wizard.