# Future Trends on Displacive Stress and Strain Induced Transformations in Steels

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## Abstract

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## 1. Introduction

## 2. Metastable Phases Formed by Stress and Strain Induced Transformations

_{B}) is always either body-centered cubic (bcc) or body centered tetragonal (bct) and it has morphology of plate or lath. Depending on the chemical composition of the steel, a bainitic microstructure can contain cementite, martensite, and/or retained austenite, apart from α

_{B}. Figure 1a,b show two micrographs showing the granular bainite and plate-like bainite microstructures that were formed in a medium carbon high silicon steel by a DIT at 520 °C and 400 °C, respectively [35].

_{B}has not been reported, to the authors’ knowledge, at room temperature, although it has been found in fully austenitized steels [35] and in multiphase steels [1,3,57] deformed at high temperatures.

## 3. Conditions of Stress/Strain Induced Transformations

#### 3.1. Stacking Fault Energy

^{−2}, (b) twinning occurs if SFE is in the range 18–45 mJ m

^{−2}and (c) dislocation glide happens if SFE >45 mJ m

^{−2}[62]. In addition, for SIT/DIT to happen, it is not only the SFE that must be below 18 mJ m

^{−2}, but also the transformation must be thermodynamically feasible. An austenitic structure is said to be highly stable if it is required that a very high stress/strain is applied so that the transformation is induced. Although the γ stability mainly depends on the SFE, the driving force for the transformation also has an effect [63].

#### 3.2. Critical Temperatures and Thermodynamics

#### 3.2.1. Spontaneous Martensite and Bainite Transformations

^{−1}[31]) and $\Delta {G}_{N}$ is the critical driving force for the nucleation (in J mol

^{−1}), which can be calculated by the expression derived by Bhadeshia as a function of the temperature [81,82].

#### 3.2.2. Stress-Induced Martensite and Bainite Transformations

_{B}SIT cannot take place are named ${M}_{s}^{{\alpha}^{\prime}}\left(\sigma \right)$, ${M}_{s}^{\epsilon}\left(\sigma \right)$ and ${B}_{s}\left(\sigma \right)$, respectively. If one considers the maximum stress for a SIT, ${\sigma}_{Y}$, one can define the critical temperatures for any α′, ε and α

_{B}SIT: ${M}_{s}^{{\alpha}^{\prime}}\left({\sigma}_{Y}\right)$, ${M}_{s}^{\epsilon}\left({\sigma}_{Y}\right)$, and ${B}_{s}\left({\sigma}_{Y}\right)$ [35,64]. For a given temperature, the critical stress that must be applied so that a α′, ε or a α

_{B}SIT starts is called ${\sigma}_{crit-{\alpha}^{\prime}-SIT}$, ${\sigma}_{crit-\epsilon -SIT}$ and ${\sigma}_{crit-{\alpha}_{B}-SIT}$, respectively. For the sake of clarity, in this review, the terms ${M}_{s}\left({\sigma}_{Y}\right)$ and ${M}_{s}\left(\sigma \right)$ are used to refer to the highest temperature at which a martensite SIT can happen under a stress ${\sigma}_{Y}$ or $\sigma $, respectively. Similarly, the critical stress for which a SIT of any type starts at a given temperature is referred to as ${\sigma}_{crit-SIT}$.

_{B}are assessed. Regarding the second phase, so far, it has been assumed that the stress does not affect the α

_{B}nucleation [31,83]. Therefore, to calculate ${\sigma}_{crit-{\alpha}^{\prime}-SIT}$ and ${\sigma}_{crit-{\alpha}_{B}-SIT}$ as a function of the temperature, as shown in Figure 2, one can use the balances in Equations (1)–(3). In this case, $\Delta {G}^{\gamma \to \alpha}$ is no longer equal to $\Delta {G}_{ch}^{\gamma \to \alpha}$, but equal to $\Delta {G}_{ch}^{\gamma \to \alpha}+\Delta {G}_{mech}$, where $\Delta {G}_{mech}$ is defined in Equation (4) [84]. Also, note that the critical temperatures ${M}_{s}^{{\alpha}^{\prime}}\left({\sigma}_{Y}\right)$ and ${B}_{s}\left({\sigma}_{Y}\right)$ coincide with the temperatures at which the ${\sigma}_{crit-{\alpha}^{\prime}-SIT}$ and ${\sigma}_{crit-{\alpha}_{B}-SIT}$ lines meet the austenite ${\sigma}_{Y}$ line in Figure 2 [64].

_{B}transformation, which usually lie in the ranges 0.20–0.45 [85,86,87,88,89] and 0.03–0.04, respectively [85,86,87,89].

_{B}transformations, where the transformation is promoted in a higher extent if the deformation mode is tension. However, if an hydrostatic deformation is applied, the transformation is not promoted, but impeded [84]. Note that an expression for other deformation modes that have been studied, such as torsion, were not derived by Patel and Cohen, although it would be possible to derive their expressions from Equation (4).

_{B}transformations are thermodynamically possible in the absence of stress or strain. This has been considered because the application of stress in those temperature ranges further stimulates the corresponding reaction and the transformation stops once the stress is removed. For instance, in the case of α′, if a steel is cooled down to a temperature T

_{1}in the range ${M}_{f}^{{\alpha}^{\prime}}$-${M}_{s}^{{\alpha}^{\prime}}$, see Figure 3, a certain volume fraction P

_{1}< 100% transforms to α′. However, if a stress below ${\sigma}_{Y}$ is applied to the structure, the driving force for the transformation increases (in absolute value) and so does the volume fraction of α′, reaching even 100% in some cases. It has been previously reported that austenitic structures subjected to stress are able to transform to α′ in a higher extent than the same structures in a stress-free state [49]. After that, if the load was removed, the volume fraction of austenite would not further go up. In the case of bainite, let us take austenite to the α

_{B}temperature range and hold the temperature for a long enough time so that the transformation is finished. Subsequently, an external stress is applied to the structure, which increases the driving force for the transformation and, thus, shifts the T

_{0}curve, line that shows the carbon content in austenite above which bainitic transformation becomes thermodynamically impossible [94]. This promotes that the transformation goes further and the volume fraction of α

_{B}further increases. If the stress is removed before the new T

_{0}carbon content is achieved, the transformation stops. Note that, although this behavior is ‘theoretically’ expected, so far, this type of experiment has not been carried out.

#### 3.2.3. Strain Induced Martensite and Bainite Transformations

_{B}DIT, they happen below the critical temperatures ${M}_{d}^{{\alpha}^{\prime}}$, ${M}_{d}^{\epsilon}$ and ${B}_{d}$, respectively, provided that the applied stress is higher than a critical stress ${\sigma}_{crit-{\alpha}^{\prime}-DIT}$, ${\sigma}_{crit-\epsilon -DIT}$, or ${\sigma}_{crit-{\alpha}_{B}-DIT}$, respectively, always higher than the austenite ${\sigma}_{Y}$, as previously mentioned and shown in Figure 2 [23,25]. Similarly to martensite SIT, from now on, when it is aimed to talk about a critical temperature for martensite DIT and it is not necessary to specify whether the product phase is α′ or ε, the general term ${M}_{d}$ is used. Also, the critical stress for a DIT at a given temperature is named ${\sigma}_{crit-DIT}$. Although the ε DIT has been reported in many studies [39,40,41], it has not been formulated how the application of stress and plastic strain affects the thermodynamic state of the system. Regarding α′ and α

_{B}, the dislocations introduced during the deformation affect the growth of both of them, altering the nucleation and growth energy balance in Equation (1) and the growth balance in Equation (3). For a plate/lath to grow, there is an additional driving force needed to overcome the dislocation density introduced by plastic deformation, ${\Delta G}_{disl}$. The new energy balances read now as shown in Equations (8) and (9) [70,97,98].

_{B}, although it is known that is promoted by the presence of a larger amount of defects or slip bands [99] generated during plastic deformation [31], it has not been reported how the nucleation condition found in Equation (2) is modified because of the increase of nucleation sites. Further information on the calculation of the ${M}_{d}^{{\alpha}^{\prime}}$ and ${B}_{d}$ critical temperatures or energies can be found in [35].

_{B}DIT can happen below the ${M}_{s}^{{\alpha}^{\prime}}\left({\sigma}_{Y}\right)$ and ${B}_{s}\left({\sigma}_{Y}\right)$ temperatures, respectively, as seen in Figure 2 because, even though the α′ and α

_{B}transformations are thermodynamically possible below those temperatures if plastic deformation is not applied, the application of plastic strain enables to further stimulate both transformations. Coming back to Figure 3 and assuming that austenite is cooled down to a temperature T

_{2}in the range ${M}_{s}^{{\alpha}^{\prime}}$-${M}_{s}^{{\alpha}^{\prime}}\left({\sigma}_{Y}\right)$, if neither stress nor strain are applied, the structure remains fully austenitic. However, if stress is increased up to σ

_{Y}, the α′ transformation is induced by stress until a fraction P

_{2}is reached. If the stress is further increased, α′ is be strain-induced and the fraction could increase up to P

_{3}. Note that, in this case, P

_{3}< 100%. Also, in the case of α

_{B}, it is possible that the modification of the thermodynamics due to the application of strain also modifies the kinetics, although only while the stress is applied. For instance, it has been previously reported that a α

_{B}DIT taking place while deforming a fully austenitized medium carbon steel at 520 °C and 400 °C got interrupted after the load was removed. Bainitic transformation did not start again until several tens of seconds later [35].

## 4. Resultant Microstructures of Stress and Strain Induced Transformations and Their Strain Hardening Capacity

_{B}SIT and DIT are described. These transformations can be obtained by different routes that are detailed next. The most common scenarios are shown in Figure 4. Note that the deformation temperatures could be reached in Figure 4b,c by heating, instead of cooling, depending on the chemical composition of the steel and on whether an initial fully austenitic or multiphase microstructure is aimed. In those cases, the microstructure may need a previous austenitization or a previous heat-treatment, respectively. The characteristics of the SIT/DIT taking place during the mentioned treatments would only be expected to vary significantly depending on the initial structure and not on how the initial structure was obtained.

#### 4.1. Stress or Strain Induced Martensite Transformations

#### 4.1.1. Continuous Cooling Treatments under Constant Stress

#### 4.1.2. Deformation at a Constant Temperature

_{B}, the amount of dislocations introduced during the transformation in the retained austenite mechanically stabilize it [122].

#### 4.2. Stress or Strain Induced Bainite Transformations

_{B}transformation has been assessed in isothermal treatments, as in Figure 4c. It has been found out that the application of an elastic uniaxial stress accelerates the α

_{B}transformation [30,31,32,33,34], provided that the stress is not very low (few MPa) [33], attributed to the increase of driving force (in absolute value). The kinetics of the transformation were also shown to be accelerated when plastic uniaxial deformation was applied during the isothermal holding [31,99,138,139,140] as a result of the increase in nucleation sites (defects) [31]. Regarding the α

_{B}volume fraction, although it would be expected to increase if the transformation happened under elastic stress due to the addition of the mechanical driving force, Shipway and Bhadeshia did not report changes for $\sigma $ < ${\sigma}_{Y}$ in a Fe-0.45C2.08Si-2.69Mn (wt %) steel [32]. If higher stresses are applied, the effect on the volume fraction of α

_{B}is not clear, though. Although previous results have shown that the introduction of dislocations prior to the transformation mechanically stabilizes the austenite against either α

_{B}or α′ transformation [97,98,141], theoretically, the addition of the mechanical driving force would shift the T

_{0}curve towards higher carbon content values. This would imply that the transformation would not stop until the austenite reached a higher carbon content, which may lead to a higher fraction of α

_{B}. Although this fact was not discussed by Freiwillig et al., they showed that, when deformation was applied during an isothermal holding, the final volume fraction of α

_{B}decreased with respect to the one obtained by the standard treatment if the steel carbon content was above 0.86 wt %, while it increased with respect to the one obtained by the standard treatment for a steel with carbon content of 0.43 wt % [138]. The application of stress has also been shown to lead to transformation plasticity strains, i.e., anisotropic portion of the transformation strains: the changes in length due to the α

_{B}transformation are not the same along all axes [32,33,34,142,143]. This transformation plasticity is due to variant selection effects driven by the same mechanisms that drive the α′ transformations during continuous cooling under constant stresses, i.e., variants which are preferentially promoted by the applied stress (those whose habit plane lies at about 45° with respect to the deformation direction) tend to form first and their fraction tends to be the highest [30,33,34,104,143,144,145]. Variant selection affects the microstructure, which becomes much more organized after transformation under stress, i.e., in each PAG, there are fewer sheaves which are bigger than the ones obtained by stress-free transformation. The reduction of sheaves affects the number of blocks of austenite that are present in the microstructure, i.e., microstructures show less blocky γ if they have been transformed under the effect of stress [145]. To the best knowledge of the authors, the effect of the stress on the thickness of the α

_{B}has not been assessed, although it would be expected that microstructures are refined because of the increase of driving force [146,147,148], ${\sigma}_{Y}$ (in the case ${\sigma}_{Y}$ is overcome) [146,147,148], and transformation kinetics [149]. It has been reported, though, that applying stress while a specimen is isothermally treated promoted the coalescence of α

_{B}plates [150]. Nevertheless, further research is needed.

_{B}SIT/DIT happening while straining a fully austenitic structure is not very common, only reported in [35,36] to the authors’ knowledge. In multiphase structures, the α

_{B}SIT/DIT at temperatures higher than room temperature have been reported in few studies [2,3,4,19,29], although their effect on the mechanical properties or the differences with respect to the SIT/DIT taking place in fully austenitic structures has not been discussed. Further research would be needed in order to know if the conclusions made with the α′ and ε transformations could be extrapolated to α

_{B}transformations, although some differences are expected, such as: (a) while the martensite transformation can be spontaneous, the bainitic transformation is thermally activated, which may inhibit the SIT/DIT in some extent; (b) while martensite transformation does not lead to any carbon partition, carbon is partitioned from α

_{B}after a plate/lath is fully grown, which is expected to increase the SFE [151,152] and the driving force for the transformation [149], inhibiting the SIT/DIT in a higher extent as the transformation progresses [153]; (c) bainitic ferrite may not be as hard as martensite because of their different carbon contents, hence, the α

_{B}TRIP effect may not lead to such a pronounced strengthening as the α′ TRIP.

## 5. Issues That Require Further Research

- -
- there is no agreement about the thermodynamic conditions that govern the formation of ε, neither athermally nor induced by stress or strain
- -
- it has been assumed that the nucleation of bainite is not affected by elastic stress, although it has not been experimentally proven
- -
- although it is known that the application of plastic deformation promotes the nucleation of α
_{B}, this fact has not been modeled thermodynamically yet - -
- the scale of the α′ and α
_{B}stress/strain-induced laths/plates formed during continuous cooling or during isothermal treatments, respectively, has not been previously reported - -
- the effect of a constant stress on continuous cooling bainitic microstructures has not been assessed in the literature so far
- -
- the effect on the volume fraction of strain induced α
_{B}formed during isothermal treatments under constant stresses needs to be clarified - -
- the effect of the matrix on the selection of variants of metastable phases formed by TRIP effect in multiphase microstructures is still unclear
- -
- the α
_{B}SIT/DIT during tensile/compression deformation from a fully austenitic microstructure has not been studied in the literature and, therefore, it would be necessary to study these transformations, as there are several reasons that suggest that their mechanisms could be different to the ones governing the formation of martensite in the same conditions.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 1.**(

**a**) Strain induced (granular) bainite formed at 520 °C in a medium carbon high silicon steel surrounded by a martensite matrix, reprinted from [35], Copyright (2021) with permission from Elsevier; (

**b**) strain induced (plate-like) bainite formed at 400 °C in the same medium carbon high silicon steel surrounded by a martensite matrix, after [35]; (

**c**) In-situ TEM micrograph taken during traction test showing the direct γ →α′ transformation observed while straining a 304 stainless steel at −32 °C, where the white arrows point the interface front and the straight white line is the invariant line; reprinted from [37], Copyright (2021) with permission from Elsevier; (

**d**) in-situ TEM micrograph taken during traction test showing a α′ embryo on a band of ε in a 304L steel deformed at −196 °C, reprinted from [38], Copyright (2021) with permission from Taylor & Francis.

**Figure 2.**Schematic representation showing the stress–temperature conditions that must be met so that different types of transformations are thermodynamically possible. SIT and DIT stand for stress and strain induced transformation, respectively. Adapted from [64]. Units are arbitrary.

**Figure 4.**Diagrams showing the possible scenarios to obtain stress induced martensite or bainitic ferrite, where (

**a**) represents a continuous cooling under a constant load; (

**b**) represents a treatment where a deformation is applied at a fixed temperature and (

**c**) represents a pure isothermal treatment under a constant load. The dashed lines show critical temperatures. Units are arbitrary.

**Figure 5.**(

**a**) Stress–strain curves and (

**b**) strain hardening rate–strain curves corresponding to three different steels with a fully austenitic structure before the test starts and with the same austenite ${\sigma}_{Y}$. Steel A is plastically deformed and no stress/strain induced transformation occurs and steels B and C undergo stress and strain transformations, respectively. Units are arbitrary.

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Eres-Castellanos, A.; Garcia-Mateo, C.; Caballero, F.G.
Future Trends on Displacive Stress and Strain Induced Transformations in Steels. *Metals* **2021**, *11*, 299.
https://doi.org/10.3390/met11020299

**AMA Style**

Eres-Castellanos A, Garcia-Mateo C, Caballero FG.
Future Trends on Displacive Stress and Strain Induced Transformations in Steels. *Metals*. 2021; 11(2):299.
https://doi.org/10.3390/met11020299

**Chicago/Turabian Style**

Eres-Castellanos, Adriana, Carlos Garcia-Mateo, and Francisca G. Caballero.
2021. "Future Trends on Displacive Stress and Strain Induced Transformations in Steels" *Metals* 11, no. 2: 299.
https://doi.org/10.3390/met11020299