> 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/hardness-model.md).

# Hardness Model

Hardness is calculated based on the volume fraction of individual phases calculated, and the defined hardness values of each individual phase. The hardness values of individual phases are defined for multiple carbon levels in the \*.HRD material data file. Interpolation between two neighbor carbon levels is used to calculate the hardness of a given carbon value. For carbon level outside the defined carbon range, the nearest carbon point is used instead of extrapolation. To understand further the hardness model in DANTE, the following items should be considered.

* A general mixture law is used.
* Iron carbide and alloy carbide contribute to hardness using mixture if their sizes are at their largest size (size class 11).
* If the sizes of iron carbide and alloy carbide is less than their largest size (< size class 11), their effect on the hardness is through the overall carbon content.
* The hardness of tempered martensite is calculated from the hardness of as-quenched martensite, hardness of tempered martensite (iron carbide size class 10), iron carbide size, amount of alloy carbide, and size of the alloy carbide.
* Iron carbide coarsening model is time and temperature dependent, which has the most direct control of the tempered martensite hardness.
* For high alloy steel with secondary (precipitation) hardening feature, the precipitation rate and amount of alloy carbide, coarsening rate, and its hardening effect of unit fraction should be defined in the material data file. These data are used in calculating the hardness of the tempered martensite.

The format of material hardness (\*.HRD) data file is below. ***STEEL\_HRD\_CBDC*** is used to define the hardness of iron carbide. ***STEEL\_HRD\_CBDA*** is used to define the hardness of alloy precipitate. The hardness value of individual phases for each carbon level is defined between the keyword pair ***STEEL\_HRDSET\_START*** and ***STEEL\_HRDSET\_END***. The hardness values of iron carbide (CBDC) and alloy precipitate (CBDA) are defined outside the definition of individual phase hardness values of a given carbon valves.

```
	*STEEL_HRDSET_START
	** 1st line: Carbon (Percentage)
	** 2nd line: HRC-AUST;FERR;PEAR;MART;TMART(SIZE10);CBDA(SIZ1);(SIZ10)
	** 3rd line: Bs--------Bm---------Bf(C) (Temperature UBAIN LBAIN definition)
	** 4th line: HRC-UBAINH; UBAINL; LBAINH; LBAINL  (UBAIN and LBAIN Hardness)
	** 5th line: Initial Hardness of Bainite
	*STEEL_HRD_PHASE
	 0.0
	**HRC-AUST; FERR; PEAR; MART; TMART(FE3C);CBDA(SIZ1);(SIZ10)
	   15.0,  13.0,  18.0,  35.0,    23.0,       8.5, 0.5
	** Bs--------Bm---------Bf(C) (Temperature range for UBAIN and LBAIN formation)
	   560.0,    450.0,    350.0
	** HRC-UBAINH--UBAINL--LBAINH--LBAINL  (UBAIN and LBAIN Hardness)
	        20.0,   23.5,   23.5,   32.0
	** Initial Hardness of Bainite
	   23.5
	*STEEL_HRDSET_END
```

Below is the description of the data line for keyword “\*STEEL\_HRD\_PHASE”

* 1st line: Carbon (Percentage)
* 2nd line: hardness (HRC) for Austenite, Ferrite, Pearlite, Tempered martensite with iron carbide of size class 10, Alloy carbide size 1 contribution and alloy carbide size 10 \*
* 3rd line: Bs--------Bm---------Bf(C) (Temperature separating upper bainite and lower bainite)\*
* 4th line: Hardness of upper bainite (2 values) and lower bainite (2 values) \*
* 5th line: Initial Hardness of Bainite\* Figure below shows an example of hardness plots in terms of carbon for individual phases.

<figure><img src="/files/EiiNh9XiaEGh5GszG4nV" alt=""><figcaption></figcaption></figure>

The hardness values of iron carbide (CBDC) and alloy carbide (CBDA) are considered in the overall hardness calculation. For carbides with the size less than the largest size class, the hardness of tempered martensite is calculated based on the factor of the carbide. For the carbide size at its largest size class, its contribution is calculated based on the mixture law using the direction carbide hardness. For all other phases other than tempered martensite, the total carbon (carbon + carbide) is used to calculate their contributions to the hardness.

The hardness of tempered martensite is calculated based on the as-quenched martensite hardness, fully tempered hardness (with iron carbide size class 10), and precipitation and hardening of alloy carbide.

Precipitation of alloy precipitation is defined by the keyword ***STEEL\_KIN\_TMPCIPA*** in the \*CQT file by keyword ***STEEL\_KIN\_TMPCIPA***. 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).

The coarsening of iron carbide is defined by the keyword ***STEEL\_TMCBD\_CCRSN***, and the coarsening of alloy carbide is defined by the Precipitation of alloy carbide is defined by the “STEEL\_TMCBD\_ACRSN” 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). One advantage of DANTE hardness model is that the hardness during tempering is both time and temperature dependent. Using DANTE material customization tool, [**Mat Simulator**](broken://pages/hHHem0japgBjV4KcKSpg), the hardness changes of AISI 4140 after oil quench to martensite are plotted for two different temperature temperatures: 300° C and 500° C.

<figure><img src="/files/MPtJN9JcmxSFzJoDEq8E" alt=""><figcaption></figcaption></figure>

<figure><img src="/files/3AidWXmJsw1x8PCseoIH" alt=""><figcaption></figcaption></figure>

**What will affect the accuracy of the predicted hardness?**

* With different surface treatments involved, such as carburizing or nitriding, the volume fraction of the retained austenite can vary significantly. The total predicted hardness has a linear relation to the volume fraction of the phases. Therefore, the predicted surface hardness can be different from the measurements if the retained austenite prediction on the surface is inaccurate. In DANTE , the retained austenite is a function of carbon and is handled by the austenite to martensite phase transformation kinetics.
* The hardness value of each individual phase will affect the predicted hardness. The hardness values are given in the \*.HRDB / \*.HRD file (hardness as a function of phase, carbon, and nitrogen; used for through hardening and carburization models). The users should provide reasonable or more accurate hardness data, if applicable, to accurately predict total hardness. Isolating a single phase during physical testing can be challenging and microstructural analysis, including X-ray diffraction techniques, are recommended to correlate the hardness and phase fraction measurements to the DANTE model.


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