Effect of austenitic texture on tensile behavior of lean duplex stainless steel with transformation induced plasticity (TRIP)

Materials Science & Engineering A 681 (2017) 114–120

Contents lists available at ScienceDirect

Materials Science & Engineering A journal homepage: www.elsevier.com/locate/msea

crossmark

Effect of austenitic texture on tensile behavior of lean duplex stainless steel with transformation induced plasticity (TRIP) ⁎

Jun-Yun Kanga, , Hoyoung Kima, Kyung-Il Kimb, Chang-Hoon Leea, Heung Nam Hanb, Kyu-Hwan Ohb, Tae-Ho Leea a

Korea Institute of Materials Science, 797 Changwon-daero, Seongsan-gu, Changwon, Gyeongnam 51508, Republic of Korea Department of Materials Science and Engineering and Research Institute of Advanced Materials, Seoul National University, 1 Gwanak-ro, Gwanak-gu, Seoul 08826, Republic of Korea b

A R T I C L E I N F O

A BS T RAC T

Keywords: Steel Austenite Mechanical characterization Martensitic transformation Texture

Mechanically induced martensitic transformation (MIMT) and consequent plastic flow behavior with respect to austenitic texture were investigated in a lean duplex stainless steel. Different grain sizes and textures with fixed phase fractions were obtained via varying the thermomechanical processes. Nearly random distribution of austenitic orientation exhibited a distinguished flow curve from the others with a major D {4 4 11}〈11 11 8〉 component due to more gradual enhancement of hardening by less martensitic transformation. In order to compare the susceptibility to the transformation with respect to individual austenitic orientations and the experimental textures, interaction energy between the imposed stress and transformation strain was calculated by a classical transformation and a crystal plasticity model. The results indicated that a larger stress imposed on the D component led to higher interaction energy and a steeper progress of MIMT observed in the textured materials.

1. Introduction Duplex stainless steels (DSS) have microstructures that consist of similar fractions of face centered cubic (fcc) austenite and body centered cubic (bcc) ferrite [1]. By virtue of constructive property combinations between the two constituent phases, they usually show an excellent balance in mechanical properties as well as corrosion resistance. They are used in many applications in chemical, petroleum, and atomic energy industries [2–5], and have progressively substituted for some classical austenitic stainless steels since the 1990s [6]. Lean DSSs have been developed to reduce the initial material cost in production and cost instability by reduction of expensive alloy elements [6–11]. As a major strategy to design lean compositions, inexpensive austenite stabilizers such as N and Mn have been added to lower the content of an expensive one, i.e., Ni [6–11]. In addition to the effect of austenite stabilization, Mn increases the solubility of the interstitial element N [12,13] which gives potent solid solution strengthening [13,14] and improves the resistance to pitting corrosion [13,15]. Therefore, in spite of the leaner compositions, some lean alloys reported superior mechanical properties and corrosion resistance [9– 11]. Recently, a few lean DSSs with exceptionally good tensile properties

⁎

by transformation induced plasticity (TRIP) were introduced [16–21]. In these alloys, the mechanically induced martensitic transformation (MIMT) in metastable austenite enhanced their strain hardening capacity, and the extended progress of MIMT to a large strain resulted in a very high tensile strength and ductility over 1 GPa and 60% respectively [18]. From the consideration on N content and its partitioning between the phases, stacking fault energy (SFE) which determined the deformation mechanisms of austenite was estimated to be in the range for MIMT [19,20]. Detailed microscopic analyses were performed to interpret the relationship between the progress of MIMT and tensile behavior, which confirmed the beneficial effect of MIMT on the excellent plasticity [20,21]. A number of studies followed to reveal the effect of various factors on this TRIP effect [21–24]. It is known that the strength and the ductility increased with an increasing content of N because of the increasing volume of mechanically induced martensite [21]. It was also reported that enhanced MIMT below room temperature increased uniform elongation [22], while an increased strain rate [23] and annealing temperature [24] suppressed MIMT. However, in spite of these studies, less focus was put on the probable effect of grain size, orientation or texture. In this article, the effect of austenitic texture on characteristic tensile behavior by TRIP is analyzed and discussed using a TRIP-aided lean DSS, which additionally

Corresponding author. E-mail address: fi[email protected] (J.-Y. Kang).

http://dx.doi.org/10.1016/j.msea.2016.11.001 Received 13 June 2016; Received in revised form 31 October 2016; Accepted 1 November 2016 Available online 03 November 2016 0921-5093/ © 2016 Elsevier B.V. All rights reserved.

Materials Science & Engineering A 681 (2017) 114–120

J.-Y. Kang et al.

Table 1 Chemical composition of the lean duplex stainless steel (wt%).

Table 2 Average phase fractions and grain sizes in equivalent circle diameter (ECD).

Cr

Mn

Mo

W

C

N

Si

Phase

18.28

5.68

2.38

0.39

0.035

0.300

0.11

α γ

contributes to the development of lean DSSs with tailored properties. 2. Experimental

CR120

HR30

41.1 2.72 58.9 3.31

42.4 9.82 57.6 10.27

42.5 9.10 57.5 13.54

ture (1050 °C). Considerable grain growth occurred in the prolonged annealing of CR120 in which the average grain diameter increased to more than three times from that of CR5. At a brief glance, HR30 exhibited the largest grain size in Fig. 1 because of some coarse grains. However, its average grain sizes were comparable to those of CR120 in Table 2. The broader grain size distribution in HR30 could be attributed to the omission of cold rolling, while the ratio of its maximum grain size to that of CR120 was less than 3 (80 µm in HR30 vs. 30 µm in CR120) which was less than the average grain size ratio of CR120 to CR5. Fig. 2(a) presents the tensile flow curves, and the average tensile properties are listed in Table 3. As expected from the grain size distributions in Fig. 1 and Table 2, CR5 had the highest stress evolution, followed by CR120. All the specimens exhibited very high tensile strength of over 800 MPa with large elongations exceeding 60%. Characteristic upward deflections of the flow curves were observed, which were more definite for CR5 and CR120 (indicated by the broken circle). The less definite deflection of HR30 led to a distinct shape of the curve, and the dissimilarity increased with strain (indicated by a double-sided arrow). Fig. 2(b) corresponds to the strain hardening rate obtained from Fig. 2(a). All the specimens experienced a transient increase in the hardening rate after their respective local minimum values, σb (marked with arrows). Fig. 2(c) is the normalization of Fig. 2(b) with the respective σb. It shows more clearly that HR30 exhibited later, slower and more gradual enhancement in hardening. This distinctive hardening behavior would explain the distinct shape of the flow curve as well as the increasing dissimilarity with strain. Figs. 3 and 4 present the orientation distribution function (ODF) of austenite and ferrite, respectively, in the φ2=45° section of the Euler space (notation by Bunge [26]), in which most of major texture components could be shown. For convenience, the major components found in this study are listed in Table 4. CR5 and CR120 had almost identical austenitic textures of moderate intensity as shown in Fig. 3. They were made up primarily of the D component with a very weak Goss component. As shown in Fig. 3(c), the peak ODF value for HR30 was too small, thus, the austenitic orientation distribution could be regarded as random. In Fig. 4, RC (rotated cube) was the common primary component of ferritic textures for all the specimens. CR5 and CR120 show the typical types of textures observed in many cold rolled and annealed ferrtic steels [27,28]. While the ferritic texture of CR5 more resembled cold rolling textures which were represented as a strong partial RD//〈110〉 fiber component, that of CR120 was closer to annealing textures with weakened RD//〈110〉 and enhanced ND//

The composition of the alloy is presented in Table 1. An ingot of 9 kg weight was cast using vacuum induction melting. It was reheated to 1200 °C, held for 2 h, hot rolled between 1100 and 950 °C and quenched in water. The thickness reduction in the hot rolling was 82.5% (from 40 mm to 7 mm). A part of the hot band was annealed at 1050 °C for 30 min, quenched in water, and denoted as HR30. The remaining parts were cold rolled by a thickness reduction of 82% (from 7 to 1.25 mm), also annealed at 1050 °C for 5 or 120 min and quenched. The former was denoted as CR5 and the latter as CR120. The designations of the above specimens simply represent the process prior to the annealing, i.e., hot rolling (HR) or cold rolling (CR), and the durations of the final annealing at 1050 °C, i.e., 5, 30 or 120 min. Uniaxial tensile tests of the specimens were conducted at room temperature using a universal test machine (Instron 5882) with a crosshead speed of 2 mm/min, i.e., an initial strain rate of 1.33×10−3 s−1. The preparation of the specimens and the test procedure followed the instructions in ASTM E8 [25]. The microstructures of the specimens were characterized using an electron backscatter diffraction (EBSD) system, Oxford Instruments NordlysNano detector with AZTEC software in a field emission scanning electron microscope (FESEM), JEOL JSM-7001F. EBSD mappings in the mid-thickness regions of the specimens were conducted on electropolished surfaces that were normal to the transverse direction (TD). This microtexture analysis presented the morphological characteristics of grains, fractions and textures of the two constituent phases, ferrite (α) and austenite (γ). The electropolishing was carried out using a commercial electropolisher (Struers LectroPol5) with a solution of 90 vol% ethanol and 10 vol% perchloric acid at −20 °C. For statistical reliability in the analyses, the total mapping area per specimen covered 0.8–3.2 mm2 depending on the grain size (at least 10,000 grains per phase). 3. Results The microstructures of the specimens are presented in Fig. 1 via the overlay images of phase, boundary and band contrast maps constructed from the EBSD mappings. The clustering of each phase and the consequent banded structures were observed. The average grain sizes and phase fractions are listed in Table 2. All the specimens were constituted by nearly the same phase fractions due to the same annealing temperature. It was clear that the minimum duration of annealing, i.e., 5 min for CR5, was sufficient to attain the fully annealed and equilibriated microstructure because of the applied high tempera-

(a)

Fraction (%) Grain size (μm) Fraction (%) Grain size (μm)

CR5

(b)

(c)

γ α GB / PB TB ND

100 μm

100 μm

100 μm

RD

Fig. 1. Microstructures according to the process conditions (overlay of phase, band contrast and boundary maps from EBSD): (a) CR5, (b) CR120, (c) HR30 (γ: austenite, α: ferrite, GB: grain boundary whose disorientation exceeds 3°, PB: phase boundary, TB: twin boundary, ND: normal direction, RD: rolling direction).

115

Materials Science & Engineering A 681 (2017) 114–120

J.-Y. Kang et al.

Fig. 2. Uniaxial tensile behaviors according to the heat treatments: (a) engineering stress-strain curves (note that the break on the vertical axis for better differentiation of the curves), (b) hardening rate (dσ/dε) curves, (c) normalization of (b) by the local minima (σb).

ferritic texture, we thought that a comparison between CR120 and HR30 would be interesting as they have apparently different austenitic textures. Indeed, HR30 exhibited a distinctive shape of the flow curve in Fig. 2(a). The lower stress level of HR30 in Fig. 2(a) may be accepted from the existence of some coarse grains in Fig. 1(c). However, it should be noted that the difference in grain size was less substantial than that of CR5 and CR120, as was stated in the previous section. The different ferritic texture could partly contribute to this lowered flow stress, while its contribution to the distinct shape of the flow curve was still questionable from the above comparison between CR5 and CR120. Therefore, it is reasonable to point out the last factor, i.e., the different austenitic texture as the major source for the distinct flow curve of HR30. The deformed microstructures in Fig. 5 provide a clearer insight into the reason for the different plastic flow behaviors of CR120 and HR30. In both specimens, a large fraction of original austenites was transformed to martensite by the tensile test. Thus, the transient enhancement of hardening and the resulting upward deflections of flow curves in Fig. 2 can be attributed to this characteristic deformation behavior of austenite, i.e., the progress of MIMT. It is generally known that similar transient enhancement in hardening is a typical sign for the operation of MIMT which leads to enhanced plasticity by TRIP [18–20,29]. In Fig. 5(a) larger fraction of austenite was retained in HR30 from the nearly identical initial fractions (i.e., approximately 58% in Table 2). The average remaining austenitic fractions in the uniformly strained volume were 15.0 and 26.2% respectively in CR120 and HR30, which is equivalent to the less extensive progress of MIMT in HR30 in spite of a larger strain to flow localization and fracture. As already mentioned, the key characteristics of HR30 were the delayed and less intense transient hardening in Fig. 2(b) and (c) which continuously enlarge the dissimilarity from CR120 in Fig. 2(a), more notably in the large strain regime ( > 20%). This must have originated

Table 3 Tensile properties (YS: yield strength evaluated with 0.2% proof stress, TS: ultimate tensile strength, UE: uniform elongation, TE: total elongation).

YS (MPa) TS (MPa) UE (%) TE (%)

CR5

CR120

HR30

572.9 952.5 59.3 65.6

516.2 929.8 61.7 68.5

491.7 850.0 65.7 77.4

〈111〉. In spite of the similar features with cold rolling textures of ferrite, it should be noted again that CR5 was fully annealed as already shown in Fig. 1(a). HR30 had somewhat distinct ferritic textures with more developed ND//〈001〉 fiber, while the maxima were still located at RC. 4. Discussion 4.1. Plastic flow behavior with respect to grain size and texture As shown in Fig. 2(a), CR5 and CR120 with identical austenitic texture had almost parallel flow curves after about 10% of tensile strain. Thus, it is clear that the differences in grain size and ferritic texture should have little influence on the shape of the flow curve. The hardening rate curves in Fig. 2(b) were very similar, and the normalized ones in Fig. 2(c) even overlapped until their concurrent onset of the transient enhancement in hardening. The small difference in stress level and hardening behavior would more likely be due to the substantial grain size difference (more than three times on average) rather than to the relatively less remarkable difference in ferritic texture. With the above consideration on the limited role of grain size and

0

Φ

φ1 (a) Max. 3.3

90

(b)

(c) Max. 3.6

Max. 1.6

90 Fig. 3. Orientation distribution functions (ODF) of austenite (φ2=45° section of Euler space, notation by Bunge, contour levels 1–2–3): (a) CR5, (b) CR120, (c) HR30 ( 〈11 11 8〉,

: Goss {1 1 0}〈0 0 1〉).

116

: D {4 4 11}

Materials Science & Engineering A 681 (2017) 114–120

J.-Y. Kang et al.

Max. 3.5

Max. 5.6

(b)

(a)

(c)

Fig. 4. ODFs of ferrite (contour levels 1–2–3–4–5): (a) CR5, (b) CR120, (c) HR30 (

Table 4 Major texture components found in the current work. Component

Euler angle (φ1, Φ, φ2) (deg.)

Miller index {h k l }〈u v w〉

γ

D Goss RC ND//〈111〉 RD//〈110〉 ND//〈001〉

(90, 27, 45) (90, 90, 45) (0, 0, 45), (90, 0, 45) (φ1, 55, 45) (0, Φ, 45) (φ1, 0, 45)

{4 {1 {0 {1 {h {0

Before After

4 11}〈11 11 8〉 1 0}〈0 0 1〉 0 1}〈1 1 0〉 1 1}〈u v w〉-fiber k l }〈1 1 0〉-fiber 0 1}〈u v w〉-fiber

1. 4

2 Iγ (220) + Iγ (311)

where I is the integrated intensity of the specified reflections, i.e., (211), (220) and (311) by the specified phases, i.e., α and γ. The estimated fractions in Table 5 generally exhibit good agreement with the corresponding ones in Table 1 and those in the above paragraph. More pronounced transformation in CR5 and CR120 is clearly seen. On the other hand, a few specimens, such as CR120 before the tensile test, exhibited considerable differences between the results by XRD and EBSD. The larger value by XRD was caused by a smaller Iα (211) due to

(a)

·····: ND//〈0 0 1〉).

CR5

CR120

HR30

57.5 16.5

70.0 17.8

58.4 31.2

The progress of MIMT depends on the externally applied stress state. This would be well represented in the comparison of uniaxial tension and compression applied on metastable austenite. It is generally known that tensile strain is more effective on the acceleration of MIMT than the compressive one [33,34]. On the other hand, there have been several reports on the dependency of MIMT on austenitic grain orientation [35–40], from which the dependency on texture could be speculated. The existence of a preference to a specific stress state, orientation or texture indicates that the driving force for MIMT should have definite anisotropy. In what follows, an analytical method to evaluate the driving force is briefly presented as a measure of the

(1)

2

: RD//〈1 1 0〉, ——: ND//〈1 1 1〉,

4.2. Susceptibility to MIMT as a function of austenitic orientation or texture

Iγ (220) + Iγ (311)

Iα (211)+1. 4

---

the different ferritic texture from CR5 in spite of a nearly identical austenitic texture. In the cases of considerable texture development as in the current study, it is known that general XRD-based methods are inaccurate in the measurement of phase volume fractions in spite of their superior representativeness from larger sampling volumes [31]. Thus, for this study, we preferred EBSD which directly identifies the phases of individual grains. As stated in the experimental section, a large sampling area of 0.8–3.2 mm2 which included at least 10,000 grains was scanned to complement the representativeness of EBSD. In this study, the results by EBSD should have sufficient reliability as well as much better consistency in the various textures.

from the austenitic volume which was more resistant to MIMT owing to the different grain size distribution or the texture. From the discussion in the preceding paragraph, it is clear that the nearly random texture of HR30 should be more influential on the distinct flow behavior. This is additionally supported by the remaining austenitic fraction in CR5, i.e., 14.9%, which was very close to that in CR120. The above results were reconfirmed from the estimated austenitic fractions by X-ray diffraction methods [30,31] as shown in Table 5. The fraction was calculated following the empirical equation which was suggested to take account of moderate textures [31,32] and produced the best consistency in the varying textures of this study.

Vγ =

: RC {0 0 1}〈1 1 0〉,

Table 5 Austenitic phase fractions (%) measured by XRD before and after the tensile test.

Phase

α

Max. 5.0

(b)

γ α ND 50 μm

50 μm

RD

Fig. 5. Microstructures in uniformly elongated volumes after the tensile tests to fracture (overlay of phase and band contrast maps): (a) CR120, (b) HR30 (remained austenite fraction: 16.6% and 29.1% for (a) and (b) respectively).

117

Materials Science & Engineering A 681 (2017) 114–120

J.-Y. Kang et al.

Fig. 6. Map (φ2=45° section of Euler space) of the orientation effect on mechanically induced martensitic transformation: (a) normalized interaction energy of transformation (U/σ0 ) under iso-stress condition, (b) normalized stress (σ11/τ0 ) and (c) normalized interaction energy (U/τ0 ) in the case of orientation-dependent stress evolution.

Fig. 7. Effect of texture on mechanically induced martensitic transformation: (a) normalized interaction energy of transformation under iso-stress condition, (b) normalized tensile stress and (c) interaction energy in the case of orientation-dependent stress evolution.

The subscript (m) indicates that the above tensors are represented in martensitic crystal coordinate. I is the identity matrix and the superscript T indicates the transpose of a matrix. εtr in the sample (i.e. reference) coordinate is finally obtained by the rotation of the above strain tensor with the orientation of a martensitic variant which can be obtained from the measured austenitic orientation (ga) and the corresponding variant of the orientation relationship (Δgi) [34,43].

susceptibility to MIMT. The influence of orientation or texture will also be explained. Thus, this discussion will be confined to the comparison of CR120 and HR30 which have different austenitic textures. With identical austenitic fractions and final annealing temperatures, the chemical part of the driving force should be the same in CR120 and HR30. Only consideration of the mechanical part, i.e., the mechanical interaction energy (U) between the imposed stress state (σ) and the transformation strain (εtr) [34], should suffice.

U i=σ : ε tr , i

ε tr , i=(∆giga ) ε(trm) (∆giga )T

(2)

In the above Eq. (1), the superscript i corresponds to the i-th variant of martensite. A positive value of U means a constructive interaction between σ and εtr, which increases the susceptibility to MIMT through the formation of the corresponding martensitic variant. εtr is obtained from the shape deformation (P1) by transformation,

P1=RBP

In Eq. (1), the orientation-dependency of U can be manifested via that of σ and εtr. Eq. (4) is the detailed description of the latter effect. This could be shown when a fixed (iso-) stress condition was assumed on all grain orientations, i.e.

⎡ σ11=σ0 0 0 ⎤ ⎥ σ=⎢ 0 0 0⎥ ⎢ ⎣ 0 0 0⎦

(3)

R, B and P respectively correspond to the rigid body rotation, Bain distortion and the lattice invariant shear from the Wechsler-LibermanRead (W-L-R) crystallographic theory for martensitic transformation [34,41,42]. With the lattice parameters of austenite and martensite and an assumption on their orientation relationship, R, B, P and consequently P1 can be obtained [34,43]. In this study, the most conventional Kurdjumov-Sachs (K-S) orientation relationship [44] was assumed to obtain them [34,43], although experimental ones usually exhibit small deviations from it because of their irrational nature [42,45,46]. The necessary lattice parameters were calculated based on the empirical equations by Cheng et al. [47] who gave relationships between the lattice parameters and the concentrations of C and N. The effect of other elements was ignored, as the influence of the two interstitial elements should be overwhelming especially in the given high-nitrogen steel. εtr represented in the martensitic crystal coordinate can be obtained from the above P1 in the same coordinate [34,43].

1 ε(trm) = [P1(T m) P1(m)−I ] 2

(5)

,for∀ga (6)

where σ0 is an arbitrary constant. Fig. 6(a) visualizes the distribution of tr the normalized U (U/σ0 , i.e., equivalent to ε11 ) in the orientation space under the iso-stress condition. With more focus on the nucleation of martensite, only the maximum values of U among the 24 K-S variants were considered. The major austenitic texture component of CR120 in Fig. 3(b), i.e., D, had the lowest U and should be less favorable for MIMT. Although this result can be supported by a similar one from a previous study [37], it should contradict the observation in Fig. 5. Therefore, the observed dependency of MIMT on austenitic texture in the comparison of CR120 and HR30 cannot be elucidated simply by the anisotropy in transformation strain due to texture. In fact, individual austenitic grains should be subjected to different stress states depending on their orientations, which also contributes to the orientation-dependency of MIMT. In an attempt to assess this factor, the varying stress state as a function of orientation can be calculated with a kind of simple Taylor-type plasticity model [48–50]. In the calculation, a simple stress state was assumed, i.e.,

(4) 118

Materials Science & Engineering A 681 (2017) 114–120

J.-Y. Kang et al.

⎡ σ11 (ga ) 0 0 ⎤ ⎥ σ=⎢ 0 0 0⎥ ⎢ ⎣ 0 0 0⎦

5. Conclusions (7)

In this study, lean DSS specimens with the same composition and phase constitution but different grain sizes and textures were prepared by varying the processing route. The specimens exhibited typical TRIP behavior due to the metastable austenites and resulted in high strengths and large elongations in the tensile tests. A stronger dependency of MIMT on austenitic texture than on grain size was deduced from the slower progress of MIMT and the distinct flow behavior of HR30 which had a distinct austenitic texture. The effect of orientation on the susceptibility to MIMT was evaluated with the classical theory of martensite crystallography. In the two different conditions of stress state, the interaction energy of transformation, which was the mechanical driving force for MIMT, exhibited different orientation- and texture-dependency.

where σ11 was a function of austenitic orientation, (ga); thus, it was different from grain to grain. An identical strain rate along the tensile direction, i.e., a constant ε̇11, was imposed on all the austenitic grains (or orientations), and 12 systems of {111}〈110〉 slip in the untransformed austenitic volume were considered. From these assumptions and the viscoplastic flow rule [50,51], σ11 was calculated by the following equation. 1

⎡ ⎤n ε11 ̇ ⎥ σ11=3τ0 ⎢ s s s s n ⎢⎣ γ0̇ ∑s m11 (2m11 − m22 − m33 ) ⎥⎦

(8)

τ0 and γ0̇ are the reference values of resolved shear stress and strain rate for {111}〈110〉 slip systems, respectively, and the latter was set to 1. ε̇11 is the applied strain rate along the tensile direction and was fixed at 1. n is the exponent in the viscoplastic flow rule that corresponds to the reciprocal of rate sensitivity, and the value of 19 was given following the routine choice for the deformation of metallic materials at room temperature [52,53]. Schmid tensor m of an arbitrary slip system s is defined by the following equation [50].

1 mijs= (nis bjs +njs bis ) 2

(1) Under the assumption of uniform stress irrespective of grain orientation, the primary texture component (D) in CR5 and CR120 had near minimum interaction energy. As a result, CR120 exhibited lower overall interaction energy than HR30 of comparable grain sizes and near-random austenitic texture, which was different from the observed larger susceptibility of the former to MIMT. (2) On the other hand, the heterogeneous evolution of stress was calculated using a simple Taylor-type plasticity model, which indicated near maximum stress evolution on the D component and consequently a larger overall stress in CR120. The resulting interaction energy substantially increased in the D component due to a large stress and the overall energy of HR30 became lower, which agreed well with the experimental observation.

(9)

where n and b are respectively the slip plane normal and slip direction of the corresponding slip system s. It should be noted that m is represented in the sample coordinate system, so it should be a function of orientation as n and b rotate according to orientations, which finally gives the orientation-dependency to σ11. Fig. 6(b) presents σ11 normalized with τ0 according to austenitic orientations after a very small tensile strain of 0.005. It shows an almost exactly opposite tendency to Fig. 6(a) which actually represents the anisotropy of transformation strain due to orientation. The interaction energy U could be recalculated under this heterogeneous stress condition and is presented in Fig. 6(c). The recalculated distribution of U was substantially different from the initial one in Fig. 6(a). As Fig. 6(c) can be regarded as a multiplication of Fig. 6(a) and (b), it is clear that the orientation-dependency of interaction energy is more affected by that of stress. The comparison of Figs. 3(b) and 6(c) suggests that the austenitic texture of CR120 is more favorable for MIMT, which now accords with the observation in Fig. 5. The above discussions on the orientation-dependency of MIMT sufficiently elucidated the observed texture-dependency. However, for the completeness of discussion, it is necessary to verify the above reasoning with respect to the experimental textures of CR120 and HR30. Fig. 7(a) shows the evolution of the sample-averaged (or overall) interaction energy under the iso-stress assumption with increasing strain and consequent rotation of austenitic texture. As speculated from Fig. 6(a), the overall interaction energy is higher in HR30, which contradicts the observation in Fig. 5. The evolution of the overall tensile stress and the interaction energy under the heterogeneous stress assumption are presented in Fig. 7(b) and (c), respectively. They ensure the lower level of stress and the consequent lower interaction energy of the austenitic volume in HR30, i.e., its lower susceptibility to MIMT, which determined its distinct plastic flow behavior in Fig. 2. The above results make it clear that the orientation- or texturedependency of MIMT should be primarily caused by the anisotropy in stress rather than that in transformation strain. It can be reasoned that the latter factor should be much weakened as there are a number of variants (24), i.e. choices to maximize the interaction energy for each austenitic orientation.

These analyses made it clear that the orientation- or texturedependency of MIMT was governed by heterogeneous distribution of stress according to grain orientation. Acknowledgement This work was funded by the Fundamental R & D Program of Korea Institute of Materials Science (KIMS) (PNK4680). HNH was supported by the Engineering Research Center (ERC) program the National Research Foundation of Korea funded by the Ministry of Education, Science and Technology (2015R1A5A1037627). References [1] Harvey D. Solomon, T.M. Devine Jr., Duplex Stainless Steels: A Tale of Two Phases, American Society for Metals, Metals Park, Ohio, 1982. [2] V. Muthupandi, P. Bala Srinivasan, S.K. Seshadri, S. Sundaresan, Effect of weld metal chemistry and heat input on the structure and properties of duplex stainless steel welds, Mater. Sci. Eng. A 358 (2003) 9–16. [3] J. He, G. Han, S. Fukuyama, K. Yokogawa, Tensile behaviour of duplex stainless steel at low temperatures, Mater. Sci. Technol. 15 (1999) 909–920. [4] R. Badji, B. Bacroix, M. Bouabdallah, Texture, microstructure and anisotropic properties in annealed 2205 duplex stainless steel welds, Mater. Charact. 62 (2011) 833–843. [5] R. Badji, T. Chauveau, B. Bacroix, Texture, misorientation and mechanical anisotropy in a deformed dual phase stainless steel weld joint, Mater. Sci. Eng. A 575 (2013) 94–103. [6] J.-C. Gagnepain, Duplex stainless steel: success story and growth perspectives, Stainless Steel World, December 2008, pp. 31–36 [7] M. Theofanous, L. Gardner, Experimental and numerical studies of lean duplex stainless steel beams, J. Constr. Steel Res. 66 (2010) 816–825. [8] Y.L. Fang, Z.Y. Liu, W.Y. Xue, H.M. Song, L.Z. Jiang, Precipitation of secondary phases in lean duplex stainless steel 2101 during isothermal ageing, ISIJ Int. 50 (2010) 286–293. [9] H. Sieurin, R. Sandström, E.M. Westin, Fracture toughness of the lean duplex stainless steel LDX 2101, Metall. Mater. Trans. A 37A (2006) 2975–2981. [10] T.-H. Lee, H.-Y. Ha, B. Hwang, S.-J. Kim, Isothermal decomposition of ferrite in a high-nitrogen, nickel-free duplex stainless steel, Metall. Mater. Trans. A 43 (2012) 822–832. [11] T.-H. Lee, H.-Y. Ha, J.-Y. Kang, B. Hwang, W. Woo, E. Shin, In situ and ex situ neutron diffraction study on deformation behavior of high-nitrogen, Ni-free duplex

119

Materials Science & Engineering A 681 (2017) 114–120

J.-Y. Kang et al.

transformation, Acta Metall. 1 (1953) 531–538. [34] H.N. Han, C.G. Lee, C.-S. Oh, T.-H. Lee, S.-J. Kim, A model for deformation behavior and mechanically induced martensitic transformation of metastable austenitic steel, Acta Mater. 52 (2004) 5203–5214. [35] I.V. Kireeva, Y.I. Chumlyakov, The orientation dependence of γ-α’ martensitic transformation in austenitic stainless steel single crystals with low stacking fault energy, Mater. Sci. Eng. A 481–482 (2008) 737–741. [36] B. Petit, N. Gey, M. Cherkaoui, B. Bolle, M. Humbert, Deformation behavior and microstructure/texture evolution of an annealed 304 AISI stainless steel sheet. Experimental and micromechanical modeling, Int. J. Plast. 23 (2007) 323–341. [37] A. Creuziger, T. Foecke, Transformation potential predictions for the stress-induced austenite to martensite transformation in steel, Acta Mater. 58 (2010) 85–91. [38] M.X. Zhang, P.M. Kelly, J.D. Gates, A model of stress induced martensitic transformation in Fe-Ni-C alloy, Mater. Sci. Eng. A 273–275 (1999) 251–256. [39] E. Nagy, V. Mertinger, F. Tranta, J. Sólyom, Deformation induced martensitic transformation in stainless steels, Mater. Sci. Eng. A 378 (2004) 308–313. [40] T.-Y. Liu, P. Yang, L. Meng, F.-Y. Lu, Influence of austenitic orientation on martensitic transformations in a compressed high manganese steel, J. Alloy. Compd. 509 (2011) 8337–8344. [41] M.S. Wechsler, D.S. Liberman, T.A. Read, On the theory of the formation of martensite, Trans. AIME 197 (1953) 1503–1515. [42] C.M. Wayman, The phenomenological theory of martensite crystallography: interrelationships, Metall. Mater. Trans. A 25A (1994) 1787–1795. [43] D.-W. Suh, H.N. Han, S.-J. Kim, Calculation of transformation plasticity during coherent transformation of steel, ISIJ Int. 46 (2006) 341–343. [44] G. Kurdjumov, G. Sachs, Uber den mechanismus tier Stahlhartung, Z. Phys. 64 (1930) 325–343. [45] G. Miyamoto, N. Takayama, T. Furuhara, Accurate measurement of the orientation relationship of lath martensite and bainite by electron backscatter diffraction analysis, Scr. Mater. 60 (2009) 1113–1116. [46] G. Miyamoto, N. Iwata, N. Takayama, T. Furuhara, Mapping the parent austenite orientation reconstructed from the orientation of martensite by EBSD and its application to ausformed martensite, Acta Mater. 58 (2010) 6393–6403. [47] L. Cheng, A. Böttger, Th.H. de Keijser, E.J. Mittemeijer, Lattice parameters of ironcarbon and iron-nitrogen martensites and austenites, Scr. Metall. Mater. 24 (1990) 509–514. [48] G.I. Taylor, Plastic strain in metals, J. Inst. Met. 62 (1938) 307. [49] Ph Lequeu, P. Gilormini, F. Montheillet, B. Bacroix, J.J. Jonas, Yield surfaces for textured polycrystals – I. crystallographic approach, Acta Metall. 35 (1987) 439–451. [50] L.S. Tóth, J.J. Jonas, D. Daniel, R.K. Ray, Development of ferrite rolling textures in low- and extra low-carbon steels, Metall. Trans. A 21 (1990) 2985–3000. [51] J.W. Hutchinson, Bounds and self-consistent estimates for creep of polycrystalline materials, Proc. R. Soc. A 348 (1976) 101–127. [52] R.A. Lebensohn, C.N. Tome, A self-consistent anisotropic approach for the simulation of plastic deformation and texture development of polycrystals: application to zirconium alloys, Acta Metall. Mater. 41 (1993) 2611–2624. [53] J.-Y. Kang, B. Bacroix, R. Brenner, Evolution of microstructure and texture during planar simple shear of magnesium alloy, Scr. Mater. 66 (2012) 654–657.

stainless steel, Scr. Mater. 67 (2012) 141–144. [12] R.D. Pehlke, J.F. Elliot, Solubility of nitrogen in liquid iron alloys: I. Thermodynamics, Trans. Metall. Soc. AIME 218 (1960) 1088–1101. [13] J.W. Simons, Overview: high-nitrogen alloying of stainless steels, Mater. Sci. Eng. A 207 (1996) 159–169. [14] E. Werner, Solid solution and grain size hardening of nitrogen-alloyed austenitic steels, Mater. Sci. Eng. A 101 (1988) 93–98. [15] M.O. Speidel, R.M. Pedrazzoli, High nitrogen stainless steels in chloride solutions, Mater. Perform. 31 (1992) 59–61. [16] M. Fujisawa, Y. Kato, T. Ujiro, CAMP-ISIJ, 21, 2008, pp. 602 [17] M. Fujisawa, Y. Kato, T. Ujiro, CAMP-ISIJ, 22, 2009, pp. 1163–1164 [18] C. Herrera, D. Ponge, D. Raabe, Design of a novel Mn-based 1 GPa duplex stainless TRIP steel with 60% ductility by a reduction of austenite stability, Acta Mater. 59 (2011) 4653–4664. [19] J.Y. Choi, J.H. Ji, S.W. Hwang, K.-T. Park, Strain induced martensitic transformation of Fe-20Cr-5Mn-0.2Ni duplex stainless steel during cold rolling: effects of nitrogen addition, Mater. Sci. Eng. A 528 (2011) 6012–6019. [20] J.Y. Choi, J.H. Ji, S.W. Hwang, K.-T. Park, TRIP aided deformation of a near-Nifree, Mn-N bearing duplex stainless steel, Mater. Sci. Eng. A 535 (2012) 32–39. [21] J.Y. Choi, J.H. Ji, S.W. Hwang, K.-T. Park, Effects of nitrogen content on TRIP of Fe-20Cr-5Mn-xN duplex stainless steel, Mater. Sci. Eng. A 534 (2012) 673–680. [22] N. Tsuchida, T. Kawahata, E. Ishimaru, A. Takahashi, Effects of temperature and strain rate on tensile properties of a lean duplex stainless steel, ISIJ Int. 54 (2014) 1971–1977. [23] J.Y. Choi, J. Lee, K. Lee, J.-Y. Koh, J.-H. Cho, H.N. Han, K.-T. Park, Effects of the strain rate on the tensile properties of a TRIP-aided duplex stainless steel, Mater. Sci. Eng. A 666 (2016) 280–287. [24] Q. Ran, Y. Xu, J. Li, J. Wan, X. Xiao, H. Yu, L. Jiang, Effect of heat treatment on transformation-induced plasticity of economical Cr19 duplex stainless steel, Mater. Des. 56 (2014) 959–965. [25] ASTM E8, Standard test methods for tension testing of metallic materials, ASTM International, West Conshohocken, PA, 2013. [26] V. Randle, O. Engler, Introduction to texture analysis: macrotexture, microtexture and orientation mapping, CRC Press LLC, Boca Raton, Florida 33431, 2000 [27] R.K. Ray, J.J. Jonas, R.E. Hook, Cold rolling and annealing textures in low carbon and extra low carbon steels, Int. Mater. Rev. 39 (1994) 129–172. [28] J.-Y. Kang, H.-C. Lee, S.-H. Han, Effect of Al and Mo on the textures and microstructures of dual phase steels, Mater. Sci. Eng. A 530 (2011) 183–190. [29] S.-J. Park, B. Hwang, K.H. Lee, T.-H. Lee, D.-W. Suh, H.N. Han, Microstructure and tensile behavior of duplex low-density steel containing 5 mass% aluminum, Scr. Mater. 68 (2013) 365–369. [30] ASTM E975, Standard practice for X-ray determination of retained austenite in steel with near random crystallographic orientation, ASTM International, West Conshohocken, PA, 2008. [31] C.F. Jatczak, Retained austenite and its measurement by X-ray diffraction, SAE Technical Paper Series 800426, SAE, PA, 1980, pp. 1–20 [32] R.L. Miller, A rapid X-ray method for the determination of retained austenite, Trans. ASM 57 (1964) 892–899. [33] J.R. Patel, M. Cohen, Criterion for the action of applied stress in the martensitic

120