11. Microstructure Aspects of the Deformation Mechanisms in Metastable Austenitic Steels

Plastic deformation of metals is typically based on dislocation slip. Perfect dislocations in fcc austenite have the Burgers vectors \( \langle 110\rangle \) and glide on the close-packed planes \( \left\{ {111} \right\} \). In austenitic steels, the perfect dislocations tend to split into Shockley partial dislocations, which can be described by the following reaction:

In (11.1), \( a \) is the lattice parameter of the fcc structure and \( \frac{a}{2}\left[ {10\bar{1}} \right] \) the Burgers vector of the original perfect dislocation. The Burgers vectors of the Shockley partials are \( \frac{a}{6}\left[ {11\bar{2}} \right] \) and \( \frac{a}{6}\left[ {2\bar{1}\bar{1}} \right] \). This dissociation reaction is a consequence of the line energy reduction upon dissociation. As the line energies of dislocations are proportional to the square of their Burgers vectors [6], the sum of the line energies of the partials is lower than the line energy of the perfect dislocation. The equilibrium dissociation width x₀ is reciprocally proportional to the stacking fault energy (SFE) \( \gamma_{\text{SF}} \). For screw dislocations, the following relationship holds [6]:

In (11.2), G is the shear modulus, b_p the magnitude of the Burgers vector of the partial dislocations and \( \nu \) the Poisson ratio. The reciprocity of the equilibrium dissociation width and SFE means that the dissociation width is small for metals with a high SFE like Al (~200 mJ/m² [7]), where it is comparable with the length of the Burgers vector, and large for fcc materials with a low SFE, e.g. Ag (~25 mJ/m² [7]).

The occurrence of partial dislocations modifies the stacking order of the adjacent atomic planes \( \left\{ {111} \right\} \). In unfaulted fcc crystals, the stacking sequence of the close-packed planes \( \left\{ {111} \right\} \) along the respective perpendicular direction \( \langle 111\rangle \) is ABCABC (Fig. 11.2, left). After the passage of the leading partial having the Burgers vector \( \frac{a}{6}\left[ {11\bar{2}} \right] \), it is modified to ABCACA (Fig. 11.2, middle). The passing of the trailing partial with the Burgers vector \( \frac{a}{6}\left[ {2\bar{1}\bar{1}} \right] \) reconstitutes the original stacking sequence (Fig. 11.2, right). The stacking fault is spanned between the partial dislocations.

Upon loading, the Burgers vectors of the partials interact with the external load, which modifies the movement of the partial dislocations and the widening of the stacking faults. This interaction was described by Copley [9] and Byun [10] as

In (11.3) and (11.4), \( \overrightarrow {{b_{1} }} \) and \( \overrightarrow {{b_{2} }} \) are the Burgers vectors of the partial dislocations, \( \overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\leftrightarrow}$}} {\tau } \) is the stress tensor, \( \hat{l} \) corresponds to the line vector of the dislocation, \( \hat{x} \) is the unit direction according to the setup in Fig. 11.3, \( x_{0} \) the separation distance of the partials and f₀ the lattice friction force. The different forces acting on the leading and trailing partial that are induced by the external stress are represented by the left-hand sides of (11.3) and (11.4) [11]. The SFE (\( \gamma_{\text{SF}} \)) pulls the partials together, whereas the repulsive interaction force due to their stress fields, i.e., \( \pm \frac{G}{{2\pi x_{0} }}\left[ {\left( {\overrightarrow {{b_{1} }} \cdot \hat{l}} \right)\left( {\overrightarrow {{b_{2} }} \cdot \hat{l}} \right) + \frac{{\left( {\overrightarrow {{b_{1} }} \times \hat{l}} \right)\left( {\overrightarrow {{b_{2} }} \times \hat{l}} \right)}}{1 + \nu }} \right] \), pushes the partials apart. The lattice friction against the dislocation movement (\( f_{0} \)) is equal for leading and trailing partial dislocation. Using these equations, the equilibrium of the dynamic force under an applied stress can be calculated. The maximum stress effect on the dissociation width is found for screw dislocations. For such dislocations, the separation distance \( x_{0} \) can be calculated as [10]:

Consequently, the dissociation distance between the partial dislocations is strongly affected by the SFE (\( \gamma_{\text{SF}} \)) and external stress (\( \tau_{zx} \)). Both effects are illustrated in Fig. 11.4, where the dependence of \( x_{0} \) on \( \tau_{zx} \) is plotted for several SFE values. The separation distance increases drastically above a critical stress level [10],at which the separation distance in (11.5) approaches infinity. In reality, the stacking fault extends through the entire grain. In materials with lower SFE, wide stacking faults are formed and the critical stress for quasi-infinite dissociation is lower than in materials with higher SFEs. Wide stacking faults are found in the microstructure of deformed austenitic CrMnNi steels and are the reason for their special mechanical behavior. As the SFEs of the austenitic CrMnNi steels with TWIP and TRIP effect range between 2 and 40 mJ/m² [12, 13], wide stacking faults form in their microstructure already at low deformations and affect the deformation behavior seriously.

The most important microstructure defects in metastable austenite are dislocations with the Burgers vectors \( \frac{a}{2}\langle 110\rangle \) and the stacking faults on the lattice planes \( \left\{ {111} \right\} \). Their configurations and interactions are depicted in the transmission electron microscopy (TEM) micrographs in Fig. 11.5, which were taken in an austenitic steel containing 16 wt% Cr, 7 wt% Mn, 9 wt% Ni, 1 wt% Si, 0.02 wt% C and 0.02 wt% N that was subjected to 2% deformation.

Nearly perfect dislocations (SFs with a very short dissociation width) are visible in area I of Fig. 11.5a, b. They stem from the Frank-Read-like dislocation sources [14]. One example of the Frank-Read source can be seen in the area II of Fig. 11.5a. Larger dissociation is observed for dislocations that are suitably oriented with respect to the applied force. The largely dissociated Shockley partial dislocations form stacking faults that are highlighted by red arrows in Fig. 11.5a. As the partial dislocations can only move on their slip planes, their cross slip to other planes is impeded and only possible, if the partials constrict and recombine. Furthermore, both perfect and partial dislocations are piling up at obstacles during plastic deformation (see, e.g., area I in Fig. 11.5b). These obstacles might be the stress fields produced by immobile dislocations or dislocation clusters as well as the grain boundaries. The pile-ups generate long-range stress fields, which enable further dislocation reactions like the cross-slip of screw dislocations [15].

If multiple slip systems are activated, which is generally the case for plastic deformation of polycrystalline metals, the dislocations can interact with SFs and specific dislocation reactions occur. Dissociated dislocations on intersecting slip planes form Lomer-Cottrell locks [16, 17] as seen in Fig. 11.5b, area II. These locks are generated, when stacking faults on different slip planes encounter. This can be illustrated by the edge-on stacking faults, which seem to stop the SFs on the other slip planes. The normal directions of the edge-on stacking faults lie in the plane of the TEM sample, thus they are visible just as thin lines in the TEM micrograph. Such locks immobilize SFs on both slip planes, which are now in a sessile configuration, and can cause further dislocation reactions or pile-ups, as the locks are obstacles for following dislocation slip. In Fig. 11.5b, area III, an intense interaction between dislocations and SFs near the grain boundary is obvious. The generation and slip of perfect dislocations, their dissociation, the formation of stacking faults and their widening are the microstructure phenomena that dominate the behavior of the metastable austenitic steels upon plastic deformation [18].

If three dislocations with different Burgers vectors meet on the same slip plane, then they form dislocation nodes [19], as shown in Fig. 11.5c. In the center of such a node, a small stacking fault is produced. This dislocation node behaves like a Lomer-Cottrell lock and persists, therefore, in a stable configuration, which can affect the slip or the formation of following dislocations and SFs [18, 19].

In contrast, the overlap of multiple SFs located on the same slip plane initiates the formation of deformation bands that are depicted in Fig. 11.5d. In this micrograph, the overlap of the parallel stacking faults and the presence of the bordering partial dislocations cause a change in the fringe contrast. The stacking faults accumulated within a deformation band are highly correlated. The deformation bands form first on a primary slip system that possesses the maximum Schmid factor and that experiences the highest shear stress. With increasing applied stress, the deformation bands widen, until they extend over the entire grain size. Concurrently, the increasing applied stress triggers the formation of deformation bands on secondary slip systems. In low-SFE austenitic steels, the formation of deformation bands is the most important deformation mechanism [20].

The characteristic microstructure features of the TRIP/TWIP steels are the amounts of original metastable γ-austenite and twinned austenite, ε-martensite and α′-martensite, the size of the grains or crystallites of the respective phase, the densities of microstructure defects (mainly dislocations and stacking faults), the preferred orientations of crystallites and the macroscopic or mesoscopic lattice deformations. The mechanisms of the microstructure defect formation and phase transformations were described in Sects. 11.2 and 11.3. Preferred orientation of crystallites is a result of local lattice rotations occurring during the plastic deformation. Macroscopic (elastic) lattice deformations stem from the external load, which is not relieved by the crystal plasticity. Mesoscopic elastic lattice deformations are induced by the interaction of neighboring grains or phases at their interfaces.

From the historical point of view, the first microstructure feature of interest in the TRIP steels was the amount of α′-martensite, as the progress of the martensitic phase transformation was related to the strength and the strain hardening of these steels [68]. For the quantification of the α′-martensite phase fraction, several methods were established. One of them utilizes the measurement of the magnetic permeability by a magnetic balance (ferritescope). The physical background of this method is that α′-martensite is a ferromagnetic phase, while austenite and ε-martensite are not ferromagnetic. The main drawbacks of the permeability measurement are that it cannot distinguish between α′-martensite and δ-ferrite,² and that the magnetization of α′-martensite depends on the strain. Hence, the ferritescope must be calibrated using a fully martensitic standard [69]. The advantage of the magnetic measurement is that it covers a large sample volume and provides a good statistics even for coarse-grained cast steels.

As ε-martensite and residual austenite are non-ferromagnetic phases, their amounts are typically quantified using diffraction methods like XRD and EBSD. For the phase identification, γ-austenite is described as an fcc phase (structure type Cu) with the lattice parameter about 3.59 Å, ε-martensite as a hcp phase (structure type Mg) with the lattice parameters a ≈ 2.54 Å and c ≈ 4.11 Å, and α′-martensite as a bcc phase (structure type W) with the lattice parameter about 2.87 Å. For the phase quantification, XRD uses the intensity ratios [70]. Nowadays, the phase quantification using XRD is usually carried out by employing the Rietveld analysis of the diffraction pattern [71, 72]. Phase quantification using EBSD is based on the comparison of the respective phase areas.

In comparison to the magnetic measurement, XRD and EBSD probe a significantly smaller sample volume. The penetration depth of X-rays (Cu Kα radiation) in TRIP/TWIP steels is about 8 µm, the irradiated area usually several mm². Typical information depth of the backscattered electrons in steels is about 70 nm (at the acceleration voltage of 20 kV), the analyzed area below 1 mm². Still, in most cases the amount of α′-martensite determined using XRD agrees very well with the values obtained from the magnetic measurement, as it is illustrated in Fig. 11.18 for several compression steps.

The quantification of the phase fractions using EBSD is generally biased by a low quality of the Kikuchi patterns in the regions that experienced a high local deformation, e.g., within the deformation bands. In such regions, the indexing of the Kikuchi patterns is frequently not possible, thus heavily deformed austenite and ε-martensite are not be considered for the quantitative phase analysis. For this reason, EBSD systematically underestimates the amount of ε-martensite, which contains a considerable amount of SFs. Furthermore, thin ε-martensite lamellae having a thickness below 100 nm cannot be resolved by EBSD, because the Kikuchi patterns from the ε-martensite lamellae are superimposed by the Kikuchi pattern from the surrounding (faulted) austenite. Finally, the α′-martensite fraction determined using EBSD in highly strained samples is overestimated at the expense of the deformed austenite, which is not recognized (because not indexed) due to a high defect density. Consequently, XRD provides a better accuracy in determining the ε-martensite fraction than EBSD. The influence of this effect is perceptible in Fig. 11.18, where the results of the quantitative phase analysis using EBSD and XRD are compared.

Another microstructure component, which is important for explanation and modelling of the mechanical behavior of the TWIP steels, is the twinned austenite [12, 73‐76]. However, as the strength of the steels is governed rather by the density of the twin boundaries restraining the dislocation slip [75] than by the volume fraction of the twins, the density of the twin boundaries is the relevant quantity, which has to be determined experimentally. However, due to the usually very fine morphology of the twins (thickness ~50 nm), neither SEM nor XRD can quantify the density of the twin boundaries accurately. The typically practiced EBSD orientation mapping [73, 77, 78] cannot account for the very fine twin structure, as its lateral resolution is limited. The twins can be more easily identified by electron channeling contrast (ECC). However, the ECC images are not commonly used as additional information for automated EBSD phase analysis.

The effect of the limited lateral resolution of EBSD on the result of the quantitative microstructure analysis is illustrated in Fig. 11.19. The ECC image reveals twin bundles, which are only partly recognized as twins in the corresponding EBSD mapping. In case of the not recognized twins, the measured Kikuchi pattern is a superposition of the Kikuchi patterns from the matrix and from twins that is indexed according to the dominant diffraction volume, which is the matrix. The only technique, which is capable of resolving the nanoscopic twin structures, is HRTEM (see, e.g., Figure 11.11). However, it is limited to small sampling sizes and therefore it suffers from the statistical unreliability.

The quantification of the twin density in austenite by XRD is difficult, as the twinning causes mainly an hkl-dependent asymmetry of the diffraction lines [30]. For low twin densities, the line asymmetry is relatively weak, because the shape of the diffraction lines from the fcc phase is dominated by the undisturbed austenite regions, while the contribution of the twins is negligible. Furthermore, the influence of the twinning on the line broadening and shift is small as compared to isolated stacking faults [33].

Still, XRD is capable of quantifying the density of isolated stacking faults in austenite and ε-martensite. In austenite, the isolated stacking faults affect both the positions and the broadening of diffraction lines as described in Sect. 11.2.3.2. In ε-martensite, the presence of isolated stacking faults leads to the broadening of diffraction lines \( \beta_{hkl}^{\text{SF}} \) with \( h - k = 3n \pm 1 \) that is equal to [30, 79]where \( l \) is the diffraction index, c the hexagonal lattice parameter and \( d_{hkl}^{*} \) the interplanar spacing in the reciprocal space. The densities of dislocations are determined from the hkl-dependent line broadening as well. The line broadening caused by dislocations is proportional to the square root of the dislocation density (\( \rho \)) and to the square root of the contrast factor of dislocations (\( \bar{C}_{hkl} \)) [80‐85]:

Further parameters affecting the magnitude of the line broadening in (11.15) are the Wilkens factor M, the Burgers vector b and the length of the reciprocal space vector (\( d_{hkl}^{*} \)). As the contrast factors describe the elastic response of the material on the presence of dislocations, they are basically calculated from the elastic constants of the material under study [82, 83, 86]. Nevertheless, Ungár et al. showed that for cubic and hexagonal materials, the hkl-dependence of the contrast factors must comply with the crystallographic anisotropy of the elastic constants [84, 87]. Therefore, it can be described by the respective crystallographic invariant:

The factors A and B characterize the degree of the crystallographic anisotropy. In the computer routines employed for the Rietveld refinement of the XRD patterns, the dependence of the dislocation-induced line broadening on the diffraction indices is calculated using the Popa model [88].

As discussed above, the knowledge of the SFE is crucial for the prediction of the deformation behavior of fcc metals and alloys, because it determines the occurring deformation mechanisms and consequently the strain hardening. In literature, various attempts to measure the SFE are reported that are mostly based on TEM or XRD methods. The most common TEM technique is the measurement of the separation distance of the partial dislocations [89‐92]. Usually, weak beam imaging is utilized to identify the dissociation distance between the partials, which amounts several nanometers and depends on the dislocation character (edge or screw). Indeed, detectable dissociation widths are found in materials with a relatively low SFE only. Another TEM approach examines extended dislocation nodes, in particular the curvature radius, from which the SFE is concluded [93‐96]. Some problems might arise from the delicate preparation of thin TEM foils, which can produce undefined strains in the area close to the investigated triangle dislocation node. Another source of systematic errors is a high sensitivity of the width of the dislocation nodes to the local concentration of the alloying atoms [90]. A general drawback of TEM is its limited statistical relevance.

The first technique for the SFE determination using XRD was developed by Dillamore [97, 98], who proposed obtaining SFE from the degree of the preferred orientation of crystallites, and directly from the ratio of two different texture components extracted from the pole figures. The idea behind this approach is that the formation of a crystallographic texture requires cross slip of perfect dislocations, which is a competing mechanism to the dislocation dissociation driven by a low SFE. This method can be applied for a wide range of SFEs, but is purely empirical and offers only a rough estimation of the SFE.

A more reliable XRD technique for the SFE determination is based on the analysis of the broadening and shift of the diffraction lines in XRD patterns of plastically deformed samples [99, 100]. Within this approach, the SFE (\( \gamma_{\text{SF}} \)) is proportional to the ratio of the squared dislocation-induced microstrain measured in the \( \langle 111\rangle \) direction \(\left( {\left\langle {\varepsilon _{111}^2} \right\rangle } \right)\) and the SF probability (\( \alpha \)):

The microstrain and the SF probability are determined from the line broadening and from the line shift, respectively, using the Warren model [30]. Further quantities in (11.18) are the shear modulus of austenite in the fault plane (\( G_{111} \)) and the lattice parameter (\( a_{0} \)). \( K_{111} \omega_{0} \) is a proportionality factor describing the relationship between the microstrain and the dislocation density, the dislocation character and the dislocation interaction [99]. This approach is commonly employed [101‐103] despite the problems with the determination of the proportionality factor \( K_{111} \omega_{0} \).

An alternative method for the SFE determination using XRD [104] is based on the proportionality between the SFE and the critical shear stress component (\( \tau_{zx} \)),that is valid for the formation of very wide stacking faults, [cf. (11.6)]. \( b_{p} = a_{0} \left| {\langle 211\rangle } \right|/6 \) is the magnitude of the Burgers vector of the partial dislocations. According to Copley and Byun [9, 10], the separation distance between partial dislocations follows from the balance of the forces that act on the partial dislocations terminating a stacking fault, and is given by:see also (11.5). In (11.20), \( \nu \) is the Poisson ratio and \( G \) the shear modulus. If the distance between the partials becomes ‘infinite’, the work resulting from the impact of the shear stress component \( \tau_{zx} \) on the partials must be in equilibrium with the stacking fault energy as described by (11.19). In the XRD approach from [104], the shear stress \( \tau_{zx} \) is calculated from a (uniaxial) internal stress \( \sigma_{x} \), which is needed to produce ‘infinitely’ wide SFs, and from the mean Schmid factor (\( M \)) that corresponds to the respective deformation state

The stress \( \sigma_{x} \) is proportional to the ‘residual’ elastic lattice deformation, which remains in the austenite after the plastic deformation. If the applied load is uniaxial and if the lattice deformation is measured in a direction perpendicular to this load [105], then the proportionality between stress and deformation is described bywhere \( s_{1}^{hkl} = - \nu^{hkl} /E^{hkl} \) is the X-ray elastic constant (XEC) of austenite. The indices hkl emphasize the crystallographic anisotropy of the elastic constants. As for cubic materials, the interplanar distances can be converted directly to the lattice parameters,the internal stress in fcc austenite can be determined from the measured lattice parameters \( a^{hkl}. \) However, as the presence of the stacking faults leads to additional shift of the diffraction lines, [cf. (11.10)], the lattice parameter affected by the internal stress and stacking faults has the form of [104, 105] \( a_{0} \) is the intrinsic lattice parameter of austenite (unaffected by internal stress and SFs), \( \alpha \) the SF probability and \( G_{hkl}^{\text{SF}} = \sum\nolimits_{af} { \pm \left( {h + k + l} \right)/\left[ {\left( {h^{2} + k^{2} + l^{2} } \right)m_{hkl} } \right]} \) the contrast factor of SFs from (11.10). In (11.24), the XEC \( s_{1}^{hkl} \) was replaced bywhereis the cubic invariant describing the crystallographic anisotropy of XECs. The last term in (11.24) describes the correction of the measured lattice parameters for instrumental aberrations, which cause a line shift \( \Delta \theta \). The fitting of measured lattice parameters with the function from (11.24) yields the intrinsic lattice parameter of austenite (\( a_{0} \)), the internal stress (\( \sigma_{x} \)) and the SF probability (\( \alpha \)). Finally, the internal stress is used for calculation of the SFE:

Another important method is the SFE calculation. Within the thermodynamic approach [23, 25, 106, 107], the SFE is calculated from the difference in the Gibbs energies of austenite and ε-martensite and from the strain and interface energies resulting from the faulting, see Sect. 11.2.3.1. The thermodynamic calculations are applied mainly to estimate the influence of certain alloying elements on the SFE. Nowadays, they are increasingly complemented by first-principles studies [24, 108]. However, if not based on experimental data, the modelled predictions often fail in giving reasonable trends, and show a systematic offset [107]. Therefore, the SFE calculations must be combined with experimental studies [92] or supported by other approaches like multivariate linear regression [109] or data driven machine-learning [110] in order to be verified.

The capability of XRD methods to track the microstructure changes in TRIP/TWIP steels during their plastic deformation was tested on samples containing 3, 6 and 9 wt% Ni (PM X4CrMnNi16-7-3, X3CrMnNi16-7-6, PM X2CrMnNi16-7-9) that possess different SFEs and consequently different stabilities of metastable austenite. One part of the in situ XRD experiments was performed with a laboratory source under bending the samples in a four-point bending apparatus (Fig. 11.20). Advanced synchrotron XRD experiments were carried out at the PETRA III/DESY beamline P07 in Hamburg (Germany) in a deformation dilatometer.

During the XRD measurement in the four-point bending apparatus from Fig. 11.20, the total deformation force and the amount of the bending are measured in addition to the XRD patterns. These quantities are converted into the mechanical tensile stress \( \sigma_{x}^{\text{mech}} \) and into the strain in the outer fiber \( \varepsilon_{x}^{\text{mech}} \) [105], respectively. The lattice parameters obtained from the line positions are plotted for selected deformation states as function of \( 3\Gamma _{hkl} \), cf. Fig. 11.21 and (11.24). In Fig. 11.21, the slope of the diagram is proportional to the internal stress \( \sigma_{x} \), the departure of the lattice parameters from the linear dependence scales with the SF probability. As the measured line positions were corrected using an internal standard, the line shift in (11.24) was set to zero for fitting (\( \Delta \theta = 0 \)).

The comparison of the measured lattice parameters with the lattice parameters fitted using (11.24) shows that the applied microstructure model is not valid for all deformation states (Fig. 11.21). While an excellent agreement between the measured and the calculated (fitted) lattice parameters was achieved for medium deformation states (Fig. 11.21b), the microstructure model cannot explain the anisotropy of the lattice parameters observed at the lowest and highest deformations (Fig. 11.21a, c). The reason for the observed discrepancies is the invalidity of the Warren model for short (Fig. 11.21d) and crossing (Fig. 11.21f) stacking faults. Consequently, the application of this microstructure model to the measured lattice parameters can be used for verification of the presence of wide but non-intersecting SFs.

In Fig. 11.22, the lattice parameters \( a_{0} \), the SF probabilities and the in-plane stresses (\( \sigma_{x} \)) are plotted against the strain in the outer fiber, and compared with the changes in the phase composition of the steel. As the intrinsic lattice parameter \( a_{0} \) is supposed to stay constant during the deformation, its increase observed for \( \varepsilon_{x}^{\text{mech}} \) < 2% and \( \varepsilon_{x}^{\text{mech}} \) > 6% is another indicator of the invalidity of the Warren SF model. Analogously, the apparently negative SF probability observed for \( \varepsilon_{x}^{\text{mech}} \) < 2% is related to the early stage of the SF formation (cf. Fig. 11.21d). From the difference of the stress values \( \sigma_{x} \), \( \sigma_{\parallel } \left( {311} \right) \) and \( \sigma_{\parallel } \left( {222} \right) \) in Fig. 11.22d, it can be supposed that the interaction of the local strain fields produced by partial dislocations in narrow SFs changes the crystallographic anisotropy of the SFs contrast factors. The SF crossing at larger deformations (\( \varepsilon_{x}^{\text{mech}} \) > 6%, cf. Fig. 11.21f) leads to an apparent change of the crystallographic anisotropy of XECs, which can be seen on the difference between \( \sigma_{\parallel } \left( {311} \right) \) and \( \sigma_{\parallel } \left( {222} \right) \). These stresses were calculated directly from the lattice deformations measured in the respective crystallographic direction:

The XECs, \( s_{1}^{{311}} = - 1.60 \times 10^{{ - 12}} \,{\text{Pa}}^{{ - {\text{1}}}} \), \( s_{1}^{222} = s_{1}^{111} = - 9.52 \times 10^{ - 13} \,{\text{Pa}}^{{ - {\text{1}}}}\) and \( s_{1}^{100} = s_{1}^{200} = - 2.17 \times 10^{ - 12} \) Pa⁻¹, were calculated using the Kröner approach [111] from the single-crystalline elastic constants of austenite, i.e., \( C_{11} = 1.975 \times 10^{11} \), \( C_{12} = 1.245 \times 10^{11} \) and \( C_{44} = 1.220 \times 10^{11} \) Pa that were taken from the Landolt-Börnstein database [112].

The comparison of the SF densities (Fig. 11.22c) with the phase compositions (Fig. 11.22a) and the corresponding TEM micrographs (Fig. 11.21d–f) confirmed that up to \( \varepsilon_{x}^{\text{mech}} \cong 2\% \), the deformation behavior of austenite is dominated by the formation and widening of SFs. For \( \varepsilon_{x}^{\text{mech}} \) above 2%, the SF density increases, which leads to the local ordering of SFs that is recognized by XRD as the ε-martensite formation. At the deformations above 6%, the SFs form also on crystallographically equivalent lattice planes \( \left\{ {111} \right\} \) and interact, which facilitates the formation of α′-martensite as explained in Sect. 11.3.

The validity range of the Warren model that was identified by the above routine was used for calculation of the SFE from the internal stress (\( \sigma_{x} \), \( \sigma_{\parallel } \left( {311} \right) \) or \( \sigma_{\parallel } \left( {222} \right) \)) and from the lattice parameter \( a_{0} \) measured by XRD. For the SFE calculation, (11.27) was employed. As the change in the preferential orientation of crystallites was negligible in this deformation range, the Schmid factors were assumed constant (independent of the deformation state) and obtained from the EBSD measurements that were carried out on non-deformed samples. The SFEs determined using this method were 17.5 ± 1.4 mJ m⁻² for the TRIP steel X3CrMnNi16-7-6 and 8.1 ± 0.9 mJ m⁻² for the TRIP steel X4CrMnNi16-7-3 [104], and 24.1 ± 2.5 mJ m⁻² for the TRIP steel X2CrMnNi16-7-9.

For a comprehensive description of the microstructure development during plastic deformation, the TRIP/TWIP steels PM X4CrMnNi16-7-3, X3CrMnNi16-7-6 and PM X2CrMnNi16-7-9 containing 3, 6 and 9 wt% Ni, respectively, were investigated using in situ synchrotron diffraction during compression [113]. In the non-deformed state, the samples had cylindrical shape (\( \varnothing \) 4 mm × 8 mm), and were fully austenitic and fine-grained. The synchrotron diffraction experiments were carried out at beamline P07 of PETRA III at DESY (Hamburg, Germany). The high energy and the short wavelength of the synchrotron radiation (100 keV, λ = 0.1235 Å) enabled measurements in transmission diffraction geometry, which is more appropriate for explanation of the bulk materials properties than the surface-sensitive laboratory XRD studies [114]. Furthermore, the short wavelength of the synchrotron radiation provided a broad coverage of the reciprocal space up towhich is beneficial for measurements in a broad range of the diffraction indices hkl, especially in materials with relatively small elementary cell. For austenite, nine diffraction peaks were recorded (up to 422). In (11.29), \( q \) is the maximum magnitude of the diffraction vector and \( d \) the minimum interplanar spacing that are accessible at the maximum diffraction angle \( 2\theta = 10^\circ \) and at the wavelength of 0.1235 Å. High flux of the synchrotron beam enables real in situ measurements. Relaxation effects in the sample during the acquisition of the individual diffraction patterns (measuring time about 1 s) are almost eliminated.

The samples were deformed in a deformation dilatometer (BÄHR DIL 850) until the maximum force, corresponding to a technical stress of 1590 MPa. The in situ compression was carried out in 35 quasi-static discrete load steps. The holding time between the deformation steps (approx. 1 s) resulted from the time that was needed for recording the diffraction patterns. The load direction was perpendicular to the direction of the primary synchrotron beam (Fig. 11.23). In this diffraction geometry, the angle Ψ between the load direction and the diffraction vector varies between \( 2\theta /2 \) and 90° along the Debye rings. The continuous change of the angle Ψ allows the determination of internal stresses and preferred orientations of crystallites in all present phases from a single 2D diffraction pattern.

For the analysis of the 2D diffraction patterns, the recorded images were integrated in 5° wide sections along the Debye rings in order to conserve the Ψ-dependent information. The 72 diffraction patterns (diffracted intensities versus diffraction angles for individual Ψ sections, see Fig. 11.24) were subjected to a coupled Rietveld refinement using MAUD [115, 116]. The microstructure models employed for the Rietveld refinement of individual diffraction patterns included: (i) anisotropic line broadening from perfect dislocations according to the Popa model [88], (ii) anisotropic line broadening and anisotropic line shift caused by SFs according to the Warren model [30] and (iii) anisotropic line shift caused by anisotropic elastic lattice deformation according to the Moment Pole Stress model [117]. In the Moment Pole Stress model, only the stress component \( \sigma_{33} \) was considered. The same elastic constants of the austenite were used like for the in situ XRD experiments during bending. Fractions of individual phases were determined after the diffracted intensities have been corrected for preferred orientations of crystallites using the Ψ dependence of the diffracted intensities [115, 118], because the texture correction improves significantly the reliability of the quantitative phase analysis [119].

Mechanical behavior of the Cr–Mn–Ni 16-7-x TRIP/TWIP steel samples during the compressive load is depicted in Fig. 11.25. The deformation and the applied force were measured by the dilatometer and converted to true stress and true strain. The material with the highest SFE (24.1 mJ/m²) and with the highest Ni content (9%) exhibits the lowest stress level and a nearly constant strain hardening. This kind of strain hardening is commonly associated with the TWIP effect [120]. The sample with the lowest SFE (8.5 mJ/m²) and lowest Ni content (3%) possesses the most pronounced strain hardening, which results in a sigmoidal flow curve that is characteristic for intense martensitic transformation [121]. In the sample containing 3 wt% Ni, the formation of ε-martensite begins at ca. 1% compression.

The maximum amount of ε-martensite (about 19 vol%) is reached at 20% deformation (Fig. 11.26). The α′-martensite forms at relatively low deformations. At the deformation of 15%, it becomes the dominant martensitic phase, which grows at the expense of austenite and ε-martensite at deformations exceeding 20%. In sample X2CrMnNi16-7-9, the formation of ε-martensite is delayed and the α′-martensite does not form up to a 40% compression. This dependence of the martensites formation on the Ni content is a result of a lower driving force for the martensitic transformation in materials with higher SFE that was discussed in Sects. 11.2.3 and 11.3. The sample containing 6% Ni (SFE = 17.5 mJ/m²) shows almost constant strain hardening like the steel X2CrMnNi16-7-9, while the development of the phase composition resembles the TRIP steel with 3 wt% Ni. However, the stress level in sample X3CrMnNi16-7-6 measured beyond the onset of the plastic deformation is clearly too high. The results of the diffraction analysis (see below) support the assumption that the high stress level is related to an incompletely recrystallized initial microstructure.

The \( \sigma_{33} \) component of the internal stress in austenite, which is parallel to the applied compression, increases during the sample compression (Fig. 11.27a), but is constantly lower than applied mechanical stress (cf. Fig. 11.25). The increase of \( \sigma_{33} \) indicates the strain hardening that is caused by the increase of dislocation density and thus by the increase of dislocation-induced microstrain (Fig. 11.28), and by the interaction of dislocations in austenite with the newly formed martensites [113].

The interplay of these effects can be illustrated on the lowest internal stress (Figs. 11.24 and 11.27a), lowest microstrain (Fig. 11.28) and delayed martensite formation (Fig. 11.26) in sample X2CrMnNi16-7-9. Weaker defect formation and retarded martensitic phase transformation are also the reasons for the smallest difference between the applied mechanical stress and internal (elastic) lattice stress in sample X2CrMnNi16-7-9 (Fig. 11.27b).

The largest difference between the mechanical stress and \( \sigma_{33} \) observed in sample X4CrMnNi16-7-3 for deformations beyond 7.5% suggests that newly formed martensites carry a significant part of the external load. In this deformation range, the amount of α′-martensite increases most quickly in the steel with lowest Ni content (sample X4CrMnNi16-7-3 in Fig. 11.26).

The stacking fault probabilities (SFPs, Fig. 11.29) correlate generally with the amount of ε-martensite (Fig. 11.26), because the ε-martensite is formed by the ordering of dense stacking faults, see Sect. 11.2. For this reason, both quantities are expected to increase with decreasing SFE. Still, at the lowest deformations, the SFs must be created before ε-martensite can form, thus the initial increase of SFP occurs always earlier, i.e., at lower strains than the onset of the ε-martensite formation. The steep increase of the SFP in samples X4CrMnNi16-7-3 and X3CrMnNi16-7-6 and the early onset of the ε-martensite formation indicate the dominant role of stacking faults as deformation mechanism. The unexpectedly high SFP in the deformed steel X3CrMnNi16-7-6 as compared with the SFP in the steel X3CrMnNi16-7-3 (Fig. 11.29) is caused by a higher density of dislocations in incompletely recrystallized initial sample X3CrMnNi16-7-6 (Fig. 11.28). The lowest SFPs were measured for the 9% Ni steel, because this steel possesses the highest SFE. Especially in this steel, the onset of the SF formation is slightly delayed (shifted to higher strains), because the initial deformation is realized by dislocation slip. Because of its higher SFE, the formation of twins is expected in this steel, but the presence of the twins cannot be evidenced easily from the diffraction data.

Although the formation of SFs and the martensitic transformations are the dominant deformation mechanisms in the TRIP steels, the role of perfect dislocations is not neglectable, because the perfect dislocations are the precursors of partial dislocations, SFs and ε-martensite (or twins in TWIP steels). In order to visualize the development of the dislocation density in the TRIP/TWIP steels during their plastic deformation, the squared microstrain \( \langle \varepsilon_{100}^{2} \rangle \) was plotted as a function of the true compression in Fig. 11.28. According to Wilkens [122], the squared microstrain is proportional to the dislocation density [cf. (11.15)]and can be determined directly from the dependence of the diffraction line broadening on the magnitude of the diffraction vector (\( \left| {\vec{q}} \right| = 2\pi d_{hkl}^{*} \)):

Additional contributions to the measured line broadening stem from the (small) crystallite size (\( K/D \)) and from stacking faults (\( \beta_{hkl}^{\text{SF}} \)), [cf. (11.14)].

In the steels containing 3 and 6% Ni, the dislocation-induced microstrain increases steeply during initial straining (Fig. 11.28). The offset of both curves is caused by the incompletely recrystallized initial microstructure of sample X3CrMnNi16-7-6 that contained a higher dislocation density. The higher dislocation density persists throughout the whole deformation process, and accounts for the higher SFP, higher lattice stress level and more intense ε-martensite formation in this sample. While the squared microstrain in steel X3CrMnNi16-7-6 increases almost linearly with increasing deformation, in the steel with a lower Ni concentration (X4CrMnNi16-7-3) the increase of the squared microstrain is reduced after ca. 9% compression, due to an intense stacking fault formation and martensitic transformation. The squared microstrain in the steel X2CrMnNi16-7-9 increases also almost linearly, but its increase is slower than in the steel X3CrMnNi16-7-6.

The comparison of the evolution of the dislocation-induced microstrain in the three steels under study suggests that the dislocation density and consequently the expected contribution of the dislocation slip to the plastic deformation decreases with decreasing SFE. Other deformation mechanisms such as the formation of stacking faults and phase transformations become dominant [113]. This change in the dominant deformation mechanism goes along with the transition from the TWIP to the TRIP behavior, and can be substantiated by microscopic studies using, e.g., ECCI and EBSD.

The ECCI and EBSD micrographs of the TRIP/TWIP steels deformed up to the maximum compression depicted in Fig. 11.30 show dislocation arrangements, stacking faults, deformation bands and α′-martensite nuclei. The characteristic microstructure features of the 3% Ni steel are pronounced deformation bands existing on several slip planes, single stacking faults and regions transformed to α′-martensite (Fig. 11.30a). The 6% Ni steel (Fig. 11.30b) exhibits similar features, which are finer scaled because of the incompletely recrystallized initial microstructure. Distinct dislocation structures and their mutual interactions can be seen in deformed steel X2CrMnNi16-7-9 (Fig. 11.30c), where some deformation bands become curved due to their intense interaction with the dislocation arrangements. As twins in austenite are hardly to be distinguished from ε-martensite using ECCI (see Sect. 11.4.1), the nature of the deformation bands and the relative density of the stacking faults within the bands were investigated by EBSD in the 9% Ni steel (Fig. 11.30d).

The formation of deformation bands plays a central role in the strain hardening of austenitic steels. As discussed above, the deformation bands accommodate dense SFs that serve as precursors of martensitic phase transformations and twinning in austenite. From the micromechanical point of view, the deformation bands produce strain fields, which interact with the microstructure defects existing outside of the deformation bands. This interaction is illustrated by the TEM image shown in Fig. 11.31, where a deformation band formed on the primary slip system acts as an obstacle for the motion of SFs and for the dislocation slip on the secondary slip systems. The interaction between the primary deformation band and the dislocations gliding on the secondary slip systems reduces the mean free path length of the dislocations [120, 123, 124], which is a phenomenon that is known as dynamic Hall-Petch effect.

A secondary stacking fault impinging a twin or deformation band must constrict, which means that the partial dislocations of the SF must recombine in order to be able to react with the stacking fault arrangement. Such a dislocation reaction is energetically unfavorable, and can only occur under a local stress concentration [125]. The interactions between deformation bands and other microstructure defects are illustrated exemplarily in Fig. 11.31, where the secondary stacking faults (\( \bar{1}11 \)) that are stopped at the deformation band on the (\( 1\bar{1}1 \)) plane seem to constrict partially, but a straight intersection of SFs located on the primary slip system by the SFs located on the secondary slip system is not observed.

Furthermore, the presence of the deformation bands inhibits the annihilation of nearly perfect dislocations having opposite Burgers vectors, as these dislocations are simply separated from each other. The annihilation of dislocations is additionally obstructed by their reduced cross-slip. The deformation bands also impede an arrangement of the dislocations in lower-energetic cell structures. Hence, the presence of deformation bands suppresses the dynamic recovery and enhances the dislocation storage capacity of the material. Dislocations accumulate in the interspace between the deformation bands much more than in materials without planar defects. This finding is confirmed by the continuous increase of the dislocation-induced microstrain measured by XRD in compressed steel PM X5CrMnNi16-6-9 (Fig. 11.32). The simultaneously increasing SF probability indicates that the stacking faults form during the whole deformation process, also on secondary slip systems, contribute continuously to a refinement of the microstructure, and thus maintain a high strain-hardening rate by reducing the mean free paths of gliding dislocations.

The interactions of microstructure defects discussed above can be found in deformation bands containing isolated SFs and concentrated SFs in form of ε-martensite and twins in austenite. Nevertheless, the extent of the interaction increases with the SF density, thus it is superior for imperfect twins. Correspondingly, enhanced strain hardening was reported for the TWIP steels showing no martensitic transformation [12, 120, 126].

If α′-martensite forms within the deformation bands, even enhanced strengthening is observed. The dislocation glide within the deformation bands is additionally obstructed by the newly formed phase boundaries. The mechanisms of the deformation band formation and the strengthening by the α′-martensite nucleation are summarized in Fig. 11.33.

During plastic deformation, the equilibrium dissociation width of beneficially oriented partial dislocations in austenite (1) is increased by external applied shear stress (2). New dislocations are generated and the deformation band forms (3), which is accompanied by conventional cold work strengthening. Formation of SFs and deformation bands on the secondary slip systems produces local strain fields that facilitate the nucleation of α′-martensite (4) having a specific volume of about 2.5% larger than austenite. The α′-martensite boundaries and the lattice strains resulting from the volume expansion are hard obstacles for the dislocation motion. They pin existing SFs, thus the further plastic deformation produces new (perfect) dislocations alongside the existing deformation band and leads to their dissociation (5). This explains the observed lateral growth of the deformation bands [40] and the high volume fraction of the ε-martensite of ≤ 25 vol% (Figs. 11.18 and 11.26) at moderate stages of straining.

A complex, heterogeneous microstructure is observed in deformed austenitic steels, even if they consist of equiaxed grains with unimodal grain-size distribution. As shown in the ECCI micrograph in Fig. 11.34, in some grains the stacking faults and deformation bands dominate, whereas other grains are free of planar defects and exhibit dislocation structures instead.

These differences in the deformation behavior can be explained by the orientation dependence of the stacking fault and deformation band formation, which follows from the dependence of the difference between the Schmid factors of the leading and trailing partials on the individual grain orientation (Fig. 11.35a). These partial dislocations experience different shear stresses, which depends on the orientation of their Burgers vector with respect to the direction of the external load [9]. From Fig. 11.35a, it can be concluded that the grains oriented with their \( \left\langle {001} \right\rangle \) direction nearly parallel to the applied compression should have the highest tendency to the stacking fault formation. In these grains, the leading partial dislocation has a clearly higher Schmid factor than the trailing one, thus the SFs are widened upon compression. For the grain orientations with a negative Schmid factor difference (Fig. 11.35a), the trailing partial dislocations move faster than the leading ones, thus the stacking fault is closed.

For the grains with negative difference of the Schmid factors of leading and trailing partial dislocation, this trend was confirmed by EBSD measurements, which revealed that grains with the orientations between \( \left\langle {101} \right\rangle \) and \( \left\langle {111} \right\rangle \) along the deformation direction were almost free of deformation bands (Fig. 11.35c, e). In Fig. 11.35c, these grains are highlighted. Figure 11.35e shows their orientation density distribution. The highest density of SFs and deformation bands should be observed for grain orientations with positive Schmid factor difference (Fig. 11.35a). However, this expectation was not confirmed experimentally, as the ECCI/EBSD measurement (Fig. 11.35d, f) revealed that the grains with the highest density of SFs and deformation bands have orientations between \( \left\langle {102} \right\rangle \) and \( \left\langle {113} \right\rangle \) with respect to the compression direction. The reason for this apparent discrepancy is that the dissociation of perfect dislocations must be preceded by their formation that is activated according to the Schmid factor from Fig. 11.35b. After the initiation of faulting, the grain orientation can still be rotated by dislocation slip (on secondary slip systems), producing the typical formation of a \( \left\langle {101} \right\rangle \) compression texture in fcc materials. This results in the observation of Fig. 11.35f that faulted grains are not sharply clustered around \( \left\langle {001} \right\rangle \), but rather found between \( \left\langle {102} \right\rangle \) and \( \left\langle {113 } \right\rangle \) orientations. The grains without stacking faults are oriented according to the \( \left\langle {101} \right\rangle \) fiber texture in compressive load direction.

Consequently, the orientation dependence of the stacking fault and deformation band formation in austenite is controlled by the Schmid factors of perfect dislocations and SFs, because the plastic deformation of austenite is activated by the formation of perfect dislocation and their dissociation. For compression, the interplay of these mechanisms favors the SF formation on the primary slip system for orientations between \( \left\langle {102} \right\rangle \), \( \left\langle {113} \right\rangle \) and \( \left\langle {001} \right\rangle \), while the formation of the deformation bands is delayed in grains having the orientations between \( \left\langle {101} \right\rangle \), \( \left\langle {111} \right\rangle \), \( \left\langle {113} \right\rangle \) and \( \left\langle {102} \right\rangle \). For tensile deformation, the favorable and unfavorable grain orientations are exchanged, because the sign of the Schmid factors of the partials switches with the inversion of the load direction.

The dependence of the stacking fault and deformation band formation on the local orientation of the austenite grains is no exclusive reason for the existence of complex heterogeneous microstructures that are typically observed in deformed austenitic steels. In general, the prevailing deformation mechanism in these steels depends on the SFE of austenite, which is, from the thermodynamic point of view, a function of the difference between the Gibbs energy of austenite and the Gibbs energy of ε-martensite (Sect. 11.2.3.1). As the difference of the Gibbs energies depends on the chemical composition of the steel, the deformation mechanisms are strongly influenced by the concentrations of the alloying elements. This is not only true on the macroscopic scale, where the SFE is generally affected by the overall chemical composition of the TRIP/TWIP steels (Sect. 11.4.3), but also on the microscopic scale, where local concentration fluctuations lead to a coexistence of deformation mechanisms even within individual grains [127].

Another result of the thermodynamic consideration of SFE is that the stacking fault energy increases with increasing temperature (through the temperature dependence of the Gibbs energies). The corresponding dependence of the deformation mechanisms on the temperature is illustrated in Fig. 11.36 for the steel composition X3CrMnNi16-6-6. From the XRD patterns, it can be seen that at the end of the uniform elongation the amount of the martensitic transformation decreases with increasing deformation temperature. As discussed in Sects. 11.2 and 11.3, both martensites (ε and α′) occur in deformation bands, which accommodate a high density of (ordered) SFs. With decreasing deformation temperature, the SFE decreases, which facilitates the formation of extended SFs and the transformation of austenite to ε- and α′-martensites. The sample deformed at −60 °C contains mainly α′-martensite. At higher temperatures (above room temperature), the increase of SFE with increasing deformation temperature hinders the SF formation. Above approx. 60 °C, the deformed steel X3CrMnNi16-6-6 consists predominantly of austenite. The diffraction peaks corresponding to the bcc phase that were observed above 100 °C stem from initial δ-ferrite, which is also present in small fractions from the primary ferritic solidification of the cast material.

The results of XRD phase analysis were complemented by the SEM/EBSD experiments (Fig. 11.37), which helped in visualization of the microstructure defects and their arrangement that are related to the change in the phase composition of the deformed samples.

It was confirmed that the martensites, which form at the deformation temperatures below 60 °C, grow first inside and later out of the (former) deformation bands (Fig. 11.37a, b, f and g). At deformation temperatures above 60 °C, the martensite formation is reduced, while the twinning of austenite and the formation and slip of perfect dislocations become the most important mechanisms of the plastic deformation (Fig. 11.37c, d, e, h, i and j). At the deformation temperature of 60 °C, all microstructure features, i.e., α′-martensite, SFs, ε-martensite and twins in austenite are present (Fig. 11.37c, h), which means that the deformation mechanisms facilitated by the formation of the respective microstructure feature coexist. At the deformation temperatures above 60 °C, the density of twins in austenite increases rapidly (Fig. 11.37d, i). As the twins act as obstacles for dislocation glide, the perfect dislocations are concentrated in the areas between the deformation bands consisting of twins (Fig. 11.37d, e). At 200 °C, twins are only scarcely observed and dislocation configurations indicate that the deformation was essentially carried by perfect dislocation slip (Fig. 11.37e, j).

The temperature dependence of the deformation mechanisms discussed above is depicted schematically in Fig. 11.38. The link between the deformation temperature and SFE (\( \gamma_{\text{SF}} \)) emphasizes that the deformation mechanisms are essentially controlled by the stacking fault energy. The SFE at room temperature was determined experimentally (Sect. 11.4.3). The increase of SFE with increasing temperature was calculated from the change of \( \Delta G^{\gamma \to \varepsilon } \) with temperature (Sect. 11.2.3.1).

The dislocation-induced plasticity is the fundamental deformation mechanism, thus its occurrence is highlighted by a grey hachure in the entire temperature range. At room temperature, the perfect dislocations dissociate quickly upon deformation, and form stacking faults. The stacking faults concentrate in deformation bands and form ε-martensite, below the critical temperature (M_D) also α′-martensite. Below the martensite start temperature (\( M_{s} \)), the formation of α′-martensite is further accelerated even without deformation. A high volume of α′-martensite at low (deformation) temperatures is one of the reasons for a high ultimate tensile stress (UTS in Fig. 11.38). Another reason for the increase of UTS with decreasing deformation temperature is the reduction of the mean free path of dislocations in the deformation bands by the successive nucleation of α′-martensite crystallites (cf. Sect. 11.5.1).

In contrast to UTS, which decreases monotonously with increasing deformation temperature, the uniform elongation (UE) shows pronounced maximum between room temperature and 150 °C, which corresponds to the SFE range between 15 and 34 mJ/m². In this temperature/SFE range, an intensified formation of ε-martensite and twins was observed that was already reported for various austenitic stainless steels in literature [59, 128]. The high amount of local shear approaching \( 0.35 \left( { \cong \sqrt 2 /4} \right) \) and \( 0.71 ( \cong \sqrt 2 /2) \) for ε-martensite and twins, respectively, which is stored within the deformation bands because of the high SF density (see Sect. 11.2.3.1), contributes significantly to the overall dislocation based plasticity.

The alteration of deformation mechanisms with the temperature is also responsible for the change of the shape of the stress-strain curve and for the magnitude of the strain hardening (Fig. 11.39). The correlation between Figs. 11.38 and 11.39 confirms that the α′-martensite formation is a very effective hardening mechanism.