1 Introduction

Steels exhibiting twinning-induced plasticity (TWIP) and transformation-induced plasticity (TRIP) are favored due to their unique combination of high stress and elongation. Their industrial processing involves shape giving, during which texture development and phase transformations occur simultaneously (besides other deformation mechanisms). Therefore, a detailed understanding of the underlying mechanisms and their interaction is of great importance. When austenite is mechanically deformed, crystallographic texture develops. When it undergoes transformation, the product phase (ferrite, acicular ferrite, bainite, ε martensite, α′ martensite) is also textured. Since the crystal orientation of the new phase is obtained through phase transformation, the term “transformation texture” was introduced. Transformation texture is governed by the texture of prior austenite, the crystallographic correspondence between austenite and the product phase, and stress. While the first two determine all possible orientations of the new crystals, the latter specifies which orientations actually form among all. This is called “variant selection”. Miyaji et al.[1] showed that variant selection acts simply due to geometrical non-uniformity even if external load is absent. Since then, the role of variant selection in different steel types has been recognized by many authors.[2,3,4] To predict the texture of the product phases, models had been established based on the observed {111}γ||{011}α′, \( \langle 1\bar{1}0\rangle_{\upgamma } ||\langle 1\bar{1}1\rangle_{\upalpha \prime } \) orientation relations.[5,6,7,8,9] When it comes to describing the texture of austenite, difficulties arise. First, calculating the austenite texture is rather complicated, since one specific crystal orientation of the product phase can be inherited from multiple parent orientations.[2,3,4] This problem was resolved with promising results by the method of Tomida et al.[8] which specifies that the orientation relation of a nucleating ferrite and two adjoining austenite grains is fulfilled. Second, the texture of austenite can only be measured if there is a notable amount of retained austenite. In such case, it is possible to directly observe orientation relations between the parent and product phases. The orientation relationship between γ and α′ phases[10] and texture evolution during tensile tests[11,12] or rolling and annealing[13,14,15,16,17,18] were studied by many authors. In some of these works, conclusions were deduced based on electron backscattered diffraction (EBSD) analysis,[10,11,15] while in others it was done on orientation distribution function (ODF) synthesis.[11,12,13,14,15,16,17,18] Both methods define texture through the orientation of unit cells, i.e., texture components.[19,20] However, due to variant selection, martensite formations occur preferably on those γ{111} planes—within an austenite unit cell—which are directed favorably with respect to applied stress or constraint stress.[1,2,3,4,21] On the macroscopic scale, consequently, a series of γ{111} planes with favored orientations undergo transformation, while non-favored oriented planes do not. This predicts that due to variant selection, the resulting texture cannot be accurately characterized in terms of unit cell orientations. The aim of the present work is to describe the role of variant selection associated with deformation induced γ → ε and γ → α′ transformations in the final texture of TWIP/TRIP steels with different Cr content. At first, the case of uniaxial tensile loading is considered.

2 Materials and Methods

Steels exhibiting both TWIP and TRIP behavior with Cr content of 0.07, 2.26 and 6.12 (wt pct) were produced and provided in the form of hot-rolled rods by the TU Bergakademie Freiberg. The compositions of the examined steels are given in Table I.

Table I Composition of the Examined Steels
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Cylindric tensile test specimens with diameter of 5 mm and samples for differential scanning calorimeter (DSC) examinations were machined from the hot-rolled rods. Afterwards, specimens were solution treated at 1273 K (1000 °C) in a resistance heating furnace under argon atmosphere for 30 minutes and subsequently quenched in room temperature water. According to XRD phase analysis, as-quenched (AQ) samples of all three steel types consisted of thermally induced ε martensite and γ austenite (Figure 1).

Fig. 1
figure 1

XRD spectra of the as-quenched samples

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The ε ↔ γ transformation temperatures were obtained with a Netzsch 204 heat flux DSC. The cylindric samples had 5 mm diameter and ~ 2 mm thickness. DSC scans were performed under Ar atmosphere using 10 K/min scan speed. The DSC curves and the determined transformation temperatures are shown in Figure 2. The ε ↔ γ transformation temperatures are summarized in Table II. The start and finish temperatures refer to the ε ↔ γ transformations.

Fig. 2
figure 2

DSC curves and transformation temperatures of the as-quenched samples

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Table II The ε ↔ γ Transformation Temperatures of the As-Quenched Samples
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Tensile tests were performed at different temperatures with an Instron 5982 universal mechanical tester equipped with a specimen furnace. Prior to loading, specimens were heated up to 573 K (300 °C) and held for 30 minutes to obtain pure austenitic state. Afterwards, the specimens were cooled down to the test temperatures, namely: 473 K, 453 K, 433 K, 413 K, 398 K, 383 K (200 °C, 180 °C, 160 °C, 140 °C, 125 °C, 110 °C), and room temperature and they were loaded till fracture. Subsequently, cross-section samples were prepared from the gauge section of the tensile test specimens for transmission electron microscopy (TEM) and X-ray diffraction (XRD) texture examinations. Specimens for TEM examinations were prepared by ion beam milling. TEM examinations were carried out with a FEI Tecnai G2 equipment with ASTAR system. Samples were embedded in epoxy resin and mechanically polished. XRD measurements were carried out with a Bruker D8 Advance type diffractometer equipped with Eulerian cradle and CoKα X-ray source, operating with 40 kV tube voltage and 40 mA tube current. The length of the applied line focus was 20 mm while its width was a few mm depending on the Bragg-angle, meaning that the full cross-section of the samples were examined during measurements. Incomplete pole figures were measured to θ = 75 deg tilting and were defocus corrected. Figure 3. shows the diffracting {hkl} plane series with a general orientation within a cylindrical sample. Here, θ is the angle between the normal of the {hkl} plane series (N) and the direction of applied stress (σ1). On the presented pole figures, the center of the pole figures (θ = 0 deg) correspond to the axis of applied stress (σ1) and θ increases radially.

Fig. 3
figure 3

The diffracting {hkl} plane series within a cylindrical specimen. θ is the angle between the normal of the {hkl} plane series (N) and the direction of applied stress (σ1)

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Recalculated pole figures were obtained using the harmonic method and positivity refinement.[19,22] Orientation distribution functions (ODF) were calculated with the equipment’s own software, TexEval. From the data of pole figures, the ratio of net intensity at the θ = 70 deg directions (summarized from 50 to 75 deg) and at θ = 0 deg direction (from 0 to 20 deg) of γ{111} and α′{110} pole figures were calculated (Zγ{111} and Zα′{110}, respectively). Note that on the 111 standard projection, 1 pole is at θ = 0 deg and 3 poles can be found at θ = 70 deg.[20] Thus, the theoretical value of Zγ{111} is 3 in the case of 〈111〉 fiber texture if variant selection does not take place. Vice versa, notably different values for Zγ{111} suggest that variant selection took place. In addition, the value of Z is close to 1 for all 〈hkl〉 poles in the case of a randomly oriented structure.

3 Results

Figure 4 shows the true stress–true strain curves of the steel tensile tested at different temperatures. According to XRD phase analysis, tensile-tested samples consisted of austenite, ε martensite and α′ martensite.

Fig. 4
figure 4

True stress-true strain curves obtained at different temperatures from the examined steels (a) Steel 0.07, (b) Steel 2.26[23] and (c) Steel 6.12

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In Figure 5, TEM phase maps taken from the cross-section of Steel 0.07 (Figure 5(a)), Steel 2.26 (Figure 5(b)) and Steel 6.12 (Figure 5(c)) tensile tested at 398 K (125 °C) can be seen. On the images, cyan-colored areas correspond to austenite, red corresponds to ε martensite and green to α′ martensite. Note that the examined volume is too small to give reliable information about the relative amount of the present phases.

Fig. 5
figure 5

Cross-section TEM phase maps of (a) Steel 0.07, (b) Steel 2.26 and (c) Steel 6.12 tensile tested at 398 K (125 °C). Cyan: γ austenite, red: ε martensite, green: α′ martensite (Color figure online)

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3.1 Texture

Figure 6 shows the sections of the obtained XRD plots from which the Bragg angles of the γ{111}, ε{002} and α′{110} reflections were determined. The relative heights of the reflections change with test temperature due to the developing texture of the phases.

Fig. 6
figure 6

XRD plots obtained at different temperatures from the examined steels (a) Steel 0.07, (b) Steel 2.26 and (c) Steel 6.12

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The developed fiber texture of the γ phase is clearly seen on the PHI = 0 deg ODF cuts taken from the steels tested at 453 K (Figure 7).

Fig. 7
figure 7

The PHI1 = 0 ODF cuts of the γ phase, obtained from of (a) Steel 0.07, (b) Steel 2.26 and (c) Steel 6.12 tested at 453 K

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Figure 8 shows the measured γ{111} (a, d, g, j, m, p), ε{002} (b, e, h, k, n, q) and α′{110} (c, f, I, l, o, r) XRD pole figures of the steel tensile tested at different temperatures. Pole density (measured intensity) is proportional to the color saturation of the pole figures.

Fig. 8
figure 8

Measured γ{111} (a, d, g, j, m, p), ε{002} (b, e, h, k, n, q) and α′{110} (c, f, i, l, o, r) pole figures of Steel 0.07, Steel 2.26 and Steel 6.12 tensile tested at 473 K (200 °C) and at room temperature (Color figure online)

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In Figures 8(a), (g) and (m), it can be seen that at 473 K (200 °C), the γ{111} poles appear at θ ≈ 0 deg and at θ ≈ 70 deg. The poles at θ ≈ 0 deg are from those γ{111}θ = 0 deg planes that are closely parallel with the cross-section (perpendicular to the tensile axis), while poles at θ ≈ 70 deg are tilted with 70 deg relative to the tensile axis. In other words, the γ〈111〉 fiber texture formed during tensile loading which is in agreement with the literature. However, at 473 K (200 °C), the pole densities are high at θ ≈ 0 deg and low at θ ≈ 70 deg, while at room temperature (313 K and 298 K, they are high at θ ≈ 70 deg, and low at θ ≈ 0 deg (Figures 8(d), (j), and (p)). On the ε{002} pole figures taken from 473 K (200 °C) high pole densities can only be observed at θ ≈ 70 deg directions, and more uniform distributions are found at room temperature (313 K and 298 K, Figures 8(b), (h), (n) and (e), (k), (q), respectively). In Figures 8(c), (i), and (o), the α′{110} pole figures from 473 K (200 °C) also have high pole densities at the θ ≈ 70 deg directions. At 313 K and 298 K (40 °C and 25 °C), however, the pole distributions are completely random (Figures 8(f), (l), and (r)). The above shown pole figures correspond to the highest and the lowest test temperatures and provide only qualitative information about the pole distributions. To quantitatively show the pole density variation of γ and α′ phases in the whole temperature range of all three steels, the ratio (Z) of measured intensity at θ ≈ 70 deg and θ ≈ 0 deg of γ{111} and α′{110} pole figures for all three steels are shown in Figure 9.

Fig. 9
figure 9

Net intensity ratio (Z) of the ~ 70 and 0 deg directions of the γ{111} and α′{110} pole figures vs test temperature of (a) Steel 0.07, (b) Steel 2.26 and (c) Steel 6.12

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As seen in Figure 9, both Zγ{111} and Zα′{110} strongly vary with test temperature. In the case of Steel 0.07, the theoretical value of 3 is obtained for Zγ{111} below 413 K (Figure 9(a)). This means that Zγ{111} is identical to the 111 standard projection. However, Zγ{111} decreases from 400 K and goes below 1 at high temperatures. The value below 3 means that within the 〈111〉 textured austenite unit cells, the ~ 70 deg oriented γ{111}θ = 70 deg planes underwent phase transformation, while the γ{111}θ = 0 deg planes did not. For the other two steels, Zγ{111} is between 3 and 1 at low temperatures suggesting that more γ{111}θ = 70 deg planes transformed than γ{111}θ = 0 deg planes. At higher temperatures, similarly to Steel 0.07, Zγ{111} decreases below 1. For α′ martensite, Zα′{110} is notably larger than 1 at high temperatures and it is around 1 at low temperatures. Accordingly, at high temperatures, α′{110} planes are dominantly parallel with the ~ 70 deg directions and are randomly oriented at low temperatures. Zε{002} was not calculated since thermally induced ε (with random orientations) also could form (thermally formed ε was present at some test temperatures) besides the stress/strain-induced ε. Furthermore, it will be shown later that theoretically stress/strain-induced ε martensite can only form at γ{111}θ = 70 deg planes.

4 Discussion

To understand the fine details of the developed texture, the effect of variant selection accompanying the occurring phase transformations are taken into account. To introduce the contribution of external stress to martensitic transformations, the mechanical driving force (U) of the γ → α′ and γ → ε transformations were calculated according to (1) after Patel and Cohen[5] and Seetharaman,[24] where σ1 is the applied stress, δ is the dilatation component and s is the shear component of the transformation deformation. For the γ → α′ transformation, values of δ = 0.03 and s = 0.26 were used,[21] while in the case of γ → ε, the transformation deformation is a simple shear with δ = 0 and s = 1/√2.[25] The dependency of U on θ is plotted in Figure 10.

Fig. 10
figure 10

The absolute value of mechanical driving force (U) of the γ → α′ and γ → ε transformations per applied stress (σ1) vs the angle between tensile direction and normal of the habit plane (θ)

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$$ U = \frac{{\sigma_{1} }}{2}\left( {\delta + \delta \cos 2\theta + s\sin 2\theta } \right). $$
(1)

In Figure 10, it can be seen that both Uγ → α′/σ1 and Uγ → ε/σ1 are maximal at θ ≈ 45 deg. However, since the austenite phase developed a 〈111〉 texture, habit planes are only available at the θ = 0 deg and θ ≈ 70 deg orientations. From Figure 10, it is also apparent that Uγ → α′/σ1 is almost 3 times larger at θ ≈ 70 deg (0.087) than at θ ≈ 0 deg (0.030). According to this, stress/strain-induced α′ martensite plates form preferably on γ{111}θ = 70 deg planes at higher temperatures, where the chemical driving force is weak.[24] As the γ{111} → α′{110} transformation occurred along the γ{111}θ = 70 deg planes, the γ{111}θ ≈ 70 deg pole density decreased, while that of α′{110}θ ≈ 70 deg increased. (Consequently, Zγ{111} decreased while Zα′{110} increased.) At low temperatures, where the chemical driving force is increased, the γ → α′ transformation was activated also on the γ{111}θ = 0 deg planes where the mechanical contribution is weaker. In that case, γ → α′ transformation occurred in both γ{111}θ = 70 deg and γ{111}θ = 0 deg planes. Consequently, γ{111} pole density is decreased and α′{110} poles appear at both θ ≈ 0 deg and θ ≈ 70 deg directions. In the case of ε martensite, Uγ → ε/σ1 is notable at θ ≈ 70 deg (0.227) and it is 0 at θ = 0 deg. Thus, stress/strain-induced ε formation can occur only on γ{111}θ = 70 deg habit planes, regardless of test temperature. Therefore, stress/strain-induced ε {002} poles appear only at θ ≈ 70 deg. (Note that ε can also form thermally without any preferred orientation.) It was also seen that for Steel 0.07, the theoretical pole distribution of the 111 standard projection was obtained at low temperatures, while this was not the case for Steel 2.26 and Steel 6.12. This can be the result of two factors. First, \( M_{\text{s}}^{\varepsilon } \) is the highest of Steel 0.07 (407 K compared to 396 K and 378 K). Thus, it can be assumed that most thermally induced, randomly oriented ε and consequently, the least stress/strain induced, 〈002〉θ = 70 deg oriented ε formed in the 0.07 pct Cr steel compared to the other two. As a result, the effect of the γ{111}θ = 70 deg → {002}θ = 70 deg transformation on the γ{111}θ = 70 deg pole density was the least pronounced in Steel 0.07. Second, the effect of Cr content on the stacking fault energy could play a role in the texture development. This, however, needs further investigation.

5 Summary

After uniaxial tensile tests performed at different temperatures on steels with varying Cr content showing TWIP/TRIP behavior it was shown that the γ〈111〉 and α′〈110〉 fiber texture developed and the γ{111} || ε{001} || α′{011} crystallographic correlation (more precisely, close to the γ{111} || α′{011} correlation) was observed which is in agreement with the literature.[5,6,7,8,9] However, notable differences were observed in diffracted γ{111} and α′{110} intensities between the θ = 70 deg and θ = 0 deg directions at various test temperatures. The mechanical contribution of the stress/strain-induced γ → ε and the γ → α′ transformations were calculated and it was concluded that the observed intensity differences are caused by variant selection which accompanies the stress/strain-induced γ → ε and γ → α′ transformations. It is shown that at higher temperatures, α′ martensite plates form preferably on γ{111} planes that are oriented θ ≈ 70 deg with respect to the tensile direction, while at lower temperatures, plates form on all available γ{111} planes. It is also shown that stress/strain-induced ε martensite can only form on θ ≈ 70 deg γ{111} planes, while thermally induced ε forms on every available γ{111} planes.