> For the complete documentation index, see [llms.txt](https://dante-solutions-inc.gitbook.io/dante-6.3-help-documentation/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://dante-solutions-inc.gitbook.io/dante-6.3-help-documentation/readme/material-models-for-steels/rate-dependent-austenitizing-model.md).
# Rate Dependent Austenitizing Model
Rate dependent austenitizing model is used to calculate the rate of phase transformation from the initial phase to austenite. The material data is defined using the following keywords in the \*DQT file. Please reference [**Steel Material Phase Transformation Data File**](/dante-6.3-help-documentation/readme/material-database/steel-alloy-data/steel-material-phase-transformation-data-file.md).
* \***STEEL\_HKIN\_FAUST**\*: Ferrite to Austenite transformation
* \***STEEL\_HKIN\_PAUST**: Pearlite to Austenite transformation
* \***STEEL\_HKIN\_UBAUST**: Upper Bainite to Austenite transformation
* \***STEEL\_HKIN\_LBAUST**: Lower Bainite to Austenite transformation
* \***STEEL\_HKIN\_MAUST**: Martensite to Austenite transformation
* \***STEEL\_HKIN\_TMAUST**: Tempered Martensite to Austenite transformation
The equation to define the austenitizing phase transformation is below. The same equation is used for the transformation to austenite from different phases.
$$\frac{dA}{dt} = v\_1 \cdot \frac{1}{\exp(v\_2 + v\_3 \cdot \ln\left(\frac{v\_4 - T}{v\_5}\right))} \cdot A^{v\_6} \cdot (1 - A)^{v\_7} \cdot P$$
Where *A* is volume fraction of austenite, *t* is time, *P* is volume fraction of initial phase, *T* is temperature, and *v1*, *v2*, *v3*, *v4*, *v5*, *v6*, *and v7* are constants.
The rate based austenitizing model is critical for high heating rate and short soaking time heat treatment processes, such as laser heating and induction heating.
Using pearlite to austenite transformation as an example, the model parameters are explained.
```
** Pearlite-->Austenite
*STEEL_HKIN_PAUST
** Line 1: Kinetics (9 values)
730.0, 1400.0, 0.0250, 9.0575, 15.965, 1025.0, 150.0, 0.150, 0.90
```
There are 9 model parameters, and they are explained below.
* Parameter 1: Low temperature bound for austenitizing transformation
* Parameter 2: High temperature bound for austenitizing transformation
* Parameters 3-9: Variable values for *v1*, *v2*, *v3*, *v4*, *v5*, *v6*, *and v7* in the austenitizing equation
An example of heating rate effect on the austenitizing temperature and rate is shown in the figure below. The X-axis is the material temperature, and the Y-axis is the strain of the material including thermal expansion and volume shrinkage caused by austenitizing. With higher heating rate, the transformation starting and finishing temperatures (AC1, AC3) to austenite are increased.
A continuous heating transformation (CHT) diagram is plotted using DANTE utility tool [**CHT Generator**](https://github.com/DANTE-Solutions/DANTE-6.3-Docs/blob/main/docs/utility-tools/cht-generator/README.md) for reference.
After transformation to austenite, the inherited carbides from the initial phases will start to dissolve in austenite. The carbide dissolution model is described below.
$$\frac{d\text{Carbide}}{dt} = V\_0 \cdot (\text{Carbide})^{\alpha} \cdot V\_{\max}$$
where *Carbide* is weight fraction of iron carbide, or actual volume fraction of alloy precipitate (alloy carbide), *t* is time, *V**0* and *α* are coefficients, *Vmax* is the maximum amount of carbide can be dissolved. The equation is used to calculate the carbide decomposing rate for a given temperature, and the rate at different temperature are interpolated.
An example of carbide decomposing data is given below, and the data is defined in the **\*PHA** file. Please reference [**Steel Material Precipitation Hardening Data File**](/dante-6.3-help-documentation/readme/material-database/steel-alloy-data/steel-material-precipitation-hardening-data-file.md).
```
****Temperature for Carbide Decomposing in Austenite
** Three (3) data lines are required
** 1st line: temperature
** 2nd line: FE3C decomposing in aust
** 3rd line: PPTA decomposing in aust
*STEEL_AUST_CBDDCP
800.0
0.000, 1.00, 1.00
0.000, 1.50, 1.00
*STEEL_AUST_CBDDCP
840.0
0.010, 1.00, 1.00
0.005, 1.50, 1.00
*STEEL_AUST_CBDDCP
860.0
0.020, 1.00, 1.00
0.010, 1.50, 1.00
*STEEL_AUST_CBDDCP
900.0
0.030, 1.00, 1.00
0.015, 1.50, 1.00
**
```
An example of carbide decomposing behavior is shown in the figure below using DANTE utility tool [**Mat Simulator**](https://github.com/DANTE-Solutions/DANTE-6.3-Docs/blob/main/docs/utility-tools/mat-simulator/README.md). With larger initial carbide size and lower temperature, the decomposing rate is slower. This model is useful for high heating rate and shorter soaking time process, such as induction heating or laser heating.
With different carbon amount dissolved in austenite, the material hardenability and martensite transformation (Ms and rate) are different. Below is a series dilatometry strain curves from the same material with different austenitizing conditions.
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