#### 2.1. Sample and Experiment

The data used in this study were the same data reported in our previous study, (PART I) [

6] and were obtained by in situ neutron diffraction experiments during tensile deformation using iMATERIA at the Japan Proton Accelerator Research Complex, Materials and Life Science Experimental Facility (J-PARC MLF, Ibaraki, Japan). Although detailed explanations of the samples, experiments, and analysis are described in PART I, some essential parts are described in

Section 2.1.

Commercial SUS 304 stainless steel was used as the sample. The tensile test was conducted at a constant crosshead speed of 0.3 mm/min at room temperature (300 K). The diffraction data were acquired every 1800 s and were used for the analysis. The increment in the strain every 1800 s corresponded to approximately 0.02–0.025.

The diffraction patterns of the steel sample were recorded at 132 observation points, using iMATERIA. The 132 diffraction patterns were simultaneously fitted by considering the texture, using the Rietveld texture analysis (RTA) method. Consequently, some properties of the materials were obtained. In Part I, the mechanical response of the steel sample was discussed based on the development of the phase fractions and line profile parameters. Herein, the mechanical properties of the steel sample were discussed based on the textures of the formed phases, which were simultaneously determined with the aforementioned parameters.

The RTA was conducted using the MAUD software (Trento, Italy) (ver. 2.9.3). [

7] The entropy-modified Williams–Imhof–Matthies–Vinel (E-WIMV) was applied as the orientation distribution function (ODF) calculation method, with a 5° resolution for austenite and

α’ martensite, and 10° resolution for

ε martensite. At this stage, we did not assume any sample symmetry. For further analysis, the ODFs were calculated from the pole figures exported from the MAUD software, using the MTEX toolbox (ver. 5.3.1) on MATLAB (2020a) [

8]. Hereafter, the Euler angles are expressed based on the Bunge’s definition [

9]. For the hexagonal close-packed

ε martensite, the crystal basis was set such that

x was parallel to

$\left[2\overline{1}\overline{1}0\right]$, that is, the

a axis of the unit cell. The ODF plots in the Euler space were calculated with an orthorhombic sample symmetry.

EBSD measurements were conducted by using a scanning electron microscope (Hitachi SU5000, Tokyo, Japan) equipped with an EDAX OIM system. The microstructures of the steel sample were observed in the mid layer parallel to the sheet plane.

#### 2.2. Numerical Analysis of the Transformation Orientation Relationships

To determine the texture components of the three phases, simple transformation texture calculations were conducted. For the

γ→

ε DIMT, the two phases exhibit the Shoji–Nishiyama (S–N) orientation relationship, that is,

${\left(111\right)}_{\gamma}\parallel {\left(0001\right)}_{\epsilon}$ and

${\left[\overline{1}01\right]}_{\gamma}\parallel {\left[2\overline{1}\overline{1}0\right]}_{\epsilon}$. This transformation can be assumed to be a simple shear on the

$\left\{111\right\}\langle \overline{2}11\rangle $ slip system. Therefore, the orientation of the

ε phase was obtained by rotating the

z and

x of the crystal basis corresponding to the

${\left[111\right]}_{\gamma}$ and

${\left[\overline{1}01\right]}_{\gamma}$. This rotation can be expressed by using Euler angles as follows:

$\left({45}^{\xb0}+{90}^{\xb0}i,{54.74}^{\xb0},{60}^{\xb0}j\right)$, where

i = 0, 1, …, 3 and

j = 0, 1, …, 5. Although the variations of

j fall in the equivalent orientation, each corresponds to the activation of different

$\left\{111\right\}\langle \overline{2}11\rangle $ slips. The rotation matrix (

R_{1}) was calculated from the set of the Euler angles. The crystal orientation of the

γ phase (

${g}_{\gamma}$) was also represented by using the rotation matrix (

${G}_{\gamma}\left({g}_{\gamma}\right)$), which is defined by the Euler angles [

9]. Hence, the orientation of the

ε phase (

${G}_{\epsilon}$) can be calculated as follows:

Consequently, the inverse manipulation can be obtained by applying the inverse rotation matrix:

This can be used to observe the origin of the orientation of the product.

The transformation texture was calculated by applying Equation (1) to all the orientations of the γ austenite phase. In this study, the γ→ε DIMT was estimated by using the transformation texture calculations. First, the ODF of the γ matrix was discretized into 5000 orientations. Subsequently, from each matrix orientation, 24 variants were calculated for the ε phase. These variants corresponded to $\left\{111\right\}\langle \overline{2}11\rangle $ slip systems, considering the directional signs, that is, $\left[\overline{2}11\right]$ and $\left[2\overline{1}\overline{1}\right]$ were separately considered. Consequently, the ε phase formed by the six systems on a certain {111} plane had the same crystal orientation. However, they were treated separately for the subsequent Schmid factor considerations. By integrating 120,000 (i.e., 24 × 5000) orientations without any weight, a transformation texture with no variant selection rule was obtained.

To observe the effect of the Schmid factors of the $\left\{111\right\}\langle \overline{2}11\rangle $ systems on the variant selection, the Schmid factor was applied as the weight of the ODF integration process. The Schmid factors can be negative for certain slip systems. This indicates that the activation of the system produced a compressive strain in the selected tensile direction. Hence, the system was inactive during the tensile deformation, and the corresponding weight was set to zero. The aforementioned discretization and reintegration of the ODF were conducted by using the MTEX toolbox.

The consideration of the

γ→

α’ or

ε→

α’ DIMT was more complicated than that of the

γ→

ε DIMT, owing to the large lattice distortion and deviation from the exact Kurdjumov–Sachs (K–S) orientation relationship,

${\left(111\right)}_{\gamma}\parallel {\left(011\right)}_{{\alpha}^{\prime}}$,

${\left[\overline{1}01\right]}_{\gamma}\parallel {\left[\overline{1}\overline{1}1\right]}_{{\alpha}^{\prime}}$. The total lattice distortion matrix (

${P}_{1}$) can be expressed as follows [

1]:

where

R_{2} is the rigid body rotation matrix,

B is the Bain distortion, and

P is the complementary shear.

B was calculated by using the lattice parameters of the

γ and

α’phases. In this study, we used

a_{0} = 0.35945 nm for

γ and a = c = 0.28743 nm for

α’ based on the results of the neutron diffraction analysis. Because the lattice parameter of martensite was determined under stress, it may contain certain errors. However, the first three digits should be reliable. Therefore, the

R_{2},

P, and

P_{1} were determined such that the total distortion exhibited an invariant plane, and the direction followed the Bowles–Mackenzie theory [

10], as explained in the book by Nishiyama [

1]. As

B and

P have no effect on the crystal orientation, the orientation of the

α’ martensite can be calculated with

R_{2} and the Bain coordinate transformation.