# About the memory of transformation-induced plasticity in 35NCD16 carbon steel subjected to various thermomechanical histories

Jose Jimenez, Lakhdar Taleb

► To cite this version:

Jose Jimenez, Lakhdar Taleb. About the memory of transformation-induced plasticity in 35NCD16 carbon steel subjected to various thermomechanical histories. ICRS 11 - The 11th International Conference on Residual Stresses, Mar 2022, Nancy, France. hal-04638528

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https://hal.science/hal-04638528v1

Submitted on 8 Jul 2024

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<figure><img src="image_1.png" /></figure>

Distributed under a Creative Commons Attribution 4.0 International License
# ABOUT THE MEMORY OF TRANSFORMATION-INDUCED PLASTICITY IN 35NCD16 CARBON STEEL SUBJECTED
## TO VARIOUS THERMOMECHANICAL HISTORIES

J. JIMENEZ—L. TALEB

Materials Physics Group (GPM), Mixed Research Unit for the French National Centre for Scientific Research (UMR CNRS) UMR CNRS 6634,
National Institute of Applied Sciences (INSA) of Rouen, 76800 St Etienne du Rouvray, France; jose.jimenez_reyes@insa-rouen.fr

## (1) Experimental procedure

**Transformation Induced Plasticity:** also known as TRIP, refers to an anomalous plastic strain observed when metallurgical transformation occurs under external stress much lower than the yield limit.

**Free dilatometry:** also known as FD, an FD test consists of subjecting a test specimen to a thermal cycle, which leads to the transformation of the ferritic phase into the austenitic phase during heating, followed by the transformation of the austenitic phase into the ferritic phase during cooling.

**Formula of evaluation of TRIP:**

$$ \epsilon^{tp} = \epsilon^{total} - \epsilon^{thm} - \epsilon^{e} $$

- $\epsilon^{tp}$ : TRIP strain.

- $\epsilon^{total}$ : measured deformation during TRIP test.

- $\epsilon^{thm}$ : measured deformation during FD test.

- $\epsilon^{e}$ : measured elastic deformation.

<figure><img src="image_2.png" /><figcaption>Complete thermomechanical cycle</figcaption></figure>

By subtracting the measured
deformation during the FD
test and the measured elastic
deformation, we obtain the
measured deformation during
the TRIP test.

<figure><img src="image_3.png" /><figcaption>TRIP strain cycle</figcaption></figure>

<figure><img src="image_4.png" /></figure>

## (2) Tests performed and obtained results

<figure><img src="image_5.png" /><figcaption>Dimensions (in mm) of 35NCD16 test specimen</figcaption></figure>

<figure><img src="image_6.png" /></figure>

Specimens undergo heat treatment leading to austenization to obtain the same initial mechanical and metallurgical state. This heat treatment consists of heating to 1050°C, holding for one hour, followed by slow cooling in the furnace, all under vacuum.

<table><caption>Thermo-mechanical histories applied during our tests</caption><thead><tr><th colspan="6">Memory after light thermomechanical history composed of one TRIP test</th></tr></thead><tbody><tr><td>VS</td><td>FD</td><td>T<sup>ref</sup><sub>σy/4</sub></td><td>FD</td><td>T<sub>σy/4</sub></td><td></td></tr><tr><td>VS</td><td>FD</td><td>T<sup>ref</sup><sub>σy/2</sub></td><td>FD</td><td>T<sub>σy/2</sub></td><td></td></tr><tr><td>VS</td><td>FD</td><td>T<sup>ref</sup><sub>3σy/4</sub></td><td>FD</td><td>T<sub>3σy/4</sub></td><td></td></tr><tr><th colspan="6">Memory after medium thermomechanical history composed of 3 TRIP tests</th></tr><tr><td>VS</td><td>FD</td><td>T<sup>ref</sup><sub>σy/4</sub></td><td>FD</td><td>T<sub>σy/2</sub></td><td>FD</td></tr><tr><td>VS</td><td>FD</td><td>T<sup>ref</sup><sub>σy/2</sub></td><td>FD</td><td>T<sub>3σy/4</sub></td><td>FD</td></tr><tr><td>VS</td><td>FD</td><td>T<sup>ref</sup><sub>3σy/4</sub></td><td>FD</td><td>T<sub>σy/4</sub></td><td>FD</td></tr><tr><th colspan="6">Memory after medium thermomechanical history composed of 2 TRIP tests</th></tr><tr><td>VS</td><td>FD</td><td>T<sup>ref</sup><sub>σy/4</sub></td><td>FD</td><td>T<sub>3σy/4</sub></td><td>FD</td></tr><tr><td>VS</td><td>FD</td><td>T<sup>ref</sup><sub>σy/2</sub></td><td>FD</td><td>T<sub>σy/4</sub></td><td>FD</td></tr><tr><td>VS</td><td>FD</td><td>T<sup>ref</sup><sub>3σy/4</sub></td><td>FD</td><td>T<sub>σy/2</sub></td><td>FD</td></tr><tr><th colspan="6">Memory after severe thermomechanical history in classical elastoplasticity</th></tr><tr><td>VS</td><td>FD</td><td>T<sup>ref</sup><sub>σy/4</sub></td><td>FD</td><td>Elastoplastic cycle</td><td>FD</td></tr><tr><td>VS</td><td>FD</td><td>T<sup>ref</sup><sub>σy/2</sub></td><td>FD</td><td>Elastoplastic cycle</td><td>FD</td></tr><tr><td>VS</td><td>FD</td><td>T<sup>ref</sup><sub>3σy/4</sub></td><td>FD</td><td>Elastoplastic cycle</td><td>FD</td></tr></tbody></table>

- $T_{\sigma y/4}^{ref}$ : refers to the reference TRIP test used for comparative purposes throughout the experiment.

- VS : Virgen specimen

**Comments and Observations:**

Elastoplastic cycles during our tests consist of performing a thermomechanical characterization at about 300°C just before the onset of the martensitic transformation, namely, during cooling. This means that when the temperature reaches 300°C, a high stress loading-unloading cycle, where both directions are considered, (tension and torsion) is applied quickly (with a duration of about 2s) while still maintaining the applied load below the yield limit of the specimen.

The elastoplastic cycles differ from the rest of the TRIP cycles in the duration of the application of the stress. As seen on the loading vs time plot on the first series of tests, the loading is applied at the Ms (Austenite → Martensite transformation) point until the end of the temperature cycle. However, for the tension and torsion cycles at the end of the series of tests, these are only applied for a brief moment (2 seconds when it reaches the Ms point). The amount of stress applied during the elastoplastic cycles is also higher than the others.

The TRIP response in comparison to reference TRIP test shows that the results for the post elastoplastic cycle shows the most significant difference compared to the others, which is a direct result of the high stress applied. However, for the rest of the cases, these results show that the specimen becomes reusable, even if necessary to check for oxidation after a certain number tests, allowing this to be a lower cost TRIP test compared to the classical procedure (One test = One specimen).

<figure><img src="image_7.png" /><figcaption>Comparison between reference TRIP strain vs Temperature starting and ending
with $T_{3\sigma y/4}$</figcaption></figure>

<figure><img src="image_8.png" /><figcaption>Comparison between reference TRIP strain vs Temperature starting and ending
with $T_{3\sigma y/4}$</figcaption></figure>

<figure><img src="image_9.png" /></figure>

## (3) TRIP parameter *k* and TRIP evolution versus volume proportion (Z) of the martensite phase

Kinetics of TRIP expression:

$$ (\epsilon^{tp}(Z)/(\epsilon^{tp}(Z = 1))) $$

- Z : Volume proportion of the martensite phase.

$$ Z = \frac{\epsilon^{thm} - \alpha_A \cdot (T - T^\alpha) - \Delta\epsilon_{MA}^{T^\alpha}}{(\alpha_M - \alpha_A) \cdot (T - T^\alpha) - \Delta\epsilon_{MA}^{T^\alpha}} $$

- $\alpha_A$ : dilatation coefficient of austenitic phase

- $\alpha_M$ : dilatation coefficient of martensitic phase

- $\alpha$ : dilatation coefficient of the mixture

- $T^\alpha$ : reference temperature of alpha phase

- $\Delta\epsilon_{MA}^{T^\alpha}$ : Compactness variation (also known as deformation of transformation) between the martensitic and the austenitic phases at room temperature. (For our case, this varies between 0.63% and 0.88% at room temperature at the beginning of the transformation)

<figure><img src="image_10.png" /><figcaption>TRIP Evolution versus Volume Proportion (Z) of the Martensite Phase</figcaption></figure>

Experimental results performed with 75% of the austenitic phase yield stress during the transformation. Leblond and Desalos' models obtained via prediction.

<figure><img src="image_11.png" /><figcaption>Final TRIP vs. Reference TRIP</figcaption></figure>

In the first case, only the reference TRIP results are considered. In the second case, for each stress level, the average value is considered.

TRIP parameter (*k*) allows us to analyze the TRIP rate of a test specimen as a function of the volume fraction of the product phase and the applied stress to it.

$$ k = \frac{\epsilon^{tp}}{z(2-z)\sigma}; \text{ if } z = 1, k = \frac{\epsilon_f^{tp}}{\sigma} \text{ Desalos' model} $$

$$ k = \frac{2\Delta\epsilon_{12}}{\sigma_y} \text{ Leblond's model} $$

$$ \Delta\epsilon_{12} = \Delta\epsilon_{MA}^{T^\alpha} $$

**Comments and Observations:**

The TRIP parameter (*k*) can be defined as a function of the transformation progress. It can be estimated experimentally using tests where applied stress does not generate classical plasticity or creep, which is why in most cases this is determined using test results that do not surpass half of the test specimen's yield stress. In Desalos' model, because of his conditions, *k* is constant. Because of this, it may be determined after a TRIP test as the ratio between the final TRIP and the applied stress.

In the experimental results vs Leblond and Desalos models via prediction, it is noticeable how much faster TRIP evolution is at the beginning of the transformation on our experimental results.

Final TRIP vs reference TRIP comparison shows how when there the elastoplastic histories applied to our test specimens are limited to Free Dilatometric tests and Transformation Induced Plasticity tests, there is only a small effect noticeable.

Future works envision studying the modelling of the effect of internal stress on TRIP. This can be analyzed by reapplying the tests and changing the moment of application of the stress to a bit before the Ms point, and leaving the applied stress for different time frames between the Ms point and the end of the test. These should provide significantly different results to the ones obtained so far following the previous methodology, and allow us to find certain correlations between the exact moments of application and release of stress on the specimens.