Constitutive behavior and microstructural evolution of FeMnSiCrNi shape memory alloy subjected to compressive deformation at high temperatures

Materials and Design 182 (2019) 108019

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Constitutive behavior and microstructural evolution of FeMnSiCrNi shape memory alloy subjected to compressive deformation at high temperatures Shuyong Jiang a, Yu Wang b, Yanqiu Zhang a,⁎, Xiaodong Xing a, Bingyao Yan b a b

College of Mechanical and Electrical Engineering, Harbin Engineering University, Harbin 150001, China College of Materials Science and Chemical Engineering, Harbin Engineering University, Harbin 150001, China

H I G H L I G H T S

G R A P H I C A L

A B S T R A C T

• Strain-compensation constitutive equation of FeMnSiCrNi alloy was established. • All the deformed FeMnSiCrNi alloys were composed of γ austenite and ε martensite. • h1122i fiber texture in ε martensite of deformed FeMnSiCrNi alloy was observed.

a r t i c l e

i n f o

Article history: Received 22 April 2019 Received in revised form 3 July 2019 Accepted 4 July 2019 Available online 05 July 2019 Keywords: Shape memory alloy FeMnSiCrNi alloy Constitutive behavior Microstructure evolution Plastic deformation

a b s t r a c t Constitutive behavior and microstructural evolution of FeMnSiCrNi shape memory alloy (SMA) subjected to compressive deformation at high temperatures were investigated based on the different deformation conditions. According to Arrhenius type equation, the constitutive equation of FeMnSiCrNi SMA was constructed according to strain compensation, where material parameters vary with increasing strain. The involved constitutive equation can effectively predict the flow stress during dynamic recrystallization (DRX) of FeMnSiCrNi SMA. All the compressed FeMnSiCrNi samples consist of ε martensite and γ austenite. In addition, dislocations, stacking faults and austenite twins were also found in the deformed FeMnSiCrNi samples. Owing to the occurrence of DRX, the grain size increases with increasing deformation temperature. Furthermore, with increasing deformation temperature, the fraction of large angle grain boundaries increases while the one of low angle grain boundaries decreases. Deformation temperature also affects the texture of FeMnSiCrNi SMA. With increasing deformation temperature, 〈110〉 texture becomes weak gradually in the γ austenite, but 〈001〉 texture and cube texture are intensified gradually along with the onset of 〈110〉 and 〈111〉 fiber textures. Moreover, ε martensite possesses h1122i fiber texture. © 2019 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http:// creativecommons.org/licenses/by-nc-nd/4.0/).

1. Introduction ⁎ Corresponding author. E-mail address: [email protected] (Y. Zhang).

FeMnSi-based shape memory alloys (SMAs) have caught many people's attention because they possess shape memory effect (SME),

https://doi.org/10.1016/j.matdes.2019.108019 0264-1275/© 2019 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

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Fig. 1. Microstructures of solution-treated FeMnSiCrNi SMA: (a) Grain size distribution; (b) Grain boundary distribution.

which stems from a martensite transformation from face-centered cubic (FCC) structure to hexagonal close-packed (HCP) structure [1,2]. It can be stated that FeMnSi-based SMAs are a class of smart materials that are investigated most widely after the onset of NiTi-based SMAs. Because of low production cost and good workability, FeMnSi-based SMAs become the best candidates for substituting NiTi-based SMAs in the civil engineering. For example, FeMnSi-based SMAs can be applied for manufacturing pipe coupling in the civil structure [3]. However, unfortunately, the shape recovery strain of FeMnSi-based SMAs is smaller than that of NiTi-based SMAs. Therefore, many researchers have been dedicated to enhancing or improving the SME of FeMnSi-based SMAs by means of adding alloying elements. As a consequence, many kinds of FeMnSi-based SMAs were developed. Among all the FeMnSi-based SMAs, FeMnSiCrNi SMAs are especially concerned because they possess high corrosion resistance, superior mechanical properties and stable stress-induced martensite transformation ability [4–7]. Thermalmechanical processing is another approach to enhancing or improving the SME of FeMnSi-based SMAs [8–10]. In particular, plastic working at elevated temperatures is an indispensable procedure to make FeMnSiCrNi SMAs into the products employed in the civil engineering fields. As a result, it is of great importance to understand flow behavior of FeMnSiCrNi SMAs suffering from plastic working at high temperatures. It is well known that the

constitutive equation is a crucial approach of describing the flow behavior of metals experiencing plastic deformation at high temperatures, and it is able to establish the relationship among stress, temperature, strain and strain rate [11–13]. Among all the constitutive models, Arrhenius type equation is a phenomenological constitutive model to be most widely used for describing high-temperature flow behavior of metals [14–17]. However, Arrhenius type equation does not take into consideration the influence of strain on flow stress since it is assumed that the steady flow stress does not vary with increasing true strain. In fact, the flow stress varies with increasing true strain during high-temperature plastic flow of metal materials since it is closely related to microstructural evolution of metals based on dynamic recrystallization (DRX). As a consequence, many researchers have established the strain-compensation constitutive model, which takes into account the influence of strain on flow stress based on Arrhenius type equation. The constitutive model based on strain compensation has been successfully applied for predicting flow behavior of metals, such as NiTi SMA [18], Ni-based superalloy [19], aluminum alloy [20–24], magnesium alloy [25] and steel [26]. In the present study, the purpose of the work is to develop the strain-compensation constitutive equation of a FeMnSiCrNi SMA based on Arrhenius type equation for describing the flow behavior of the alloy subjected to plastic deformation at high temperatures.

Fig. 2. TEM micrographs of solution-treated FeMnSiCrNi SMA: (a) Bright field image indicating ε martensite and stacking faults (SFs); (b) diffraction pattern of selected area in (a) indicating the orientation relationship between γ austenite and ε martensite.

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Fig. 3. Compressive stress-strain curves for FeMnSiCrNi SMA at various deformation conditions: (a) 850 °C; (b) 900 °C; (c) 950 °C; (d) 1000 °C.

Furthermore, the microstructures of FeMnSiCrNi SMA subjected to hot deformation were characterized so as to further reveal the corresponding plastic deformation mechanism. Texture evolution of FeMnSiCrNi SMA is dependent on microstructural evolution, where the correlation of texture type with microstructural evolution is established as well.

2. Materials and methods The FeMnSi-based SMA studied in the present investigation is composed of five elements, including Fe, Mn, Si, Cr and Ni, where the nominal weight fractions of the five elements are 66%Fe, 15%Mn, 5%Si, 9%Cr and 5%Ni, respectively. In the subsequent text, the above FeMnSi-based SMA is termed as FeMnSiCrNi SMA. Firstly, a cast ingot with the above composition was manufactured via vacuum induction melting. Subsequently, the cast ingot was subjected to homogenizing annealing for 12 h at 1000 °C in the vacuum heat treatment furnace. Then, the cast ingot was subjected to plastic working by means of free forging and consequently it was made into a bar. Finally, the forged bar was sealed in the vacuum quartz tube and it underwent solution treatment for 2 h at 850 °C.

Scanning electron microscope (SEM) along with energy dispersive spectrometer (EDS) was used in order to examine the genuine chemical composition of the solution-treated FeMnSiCrNi SMA. It can be found that the solution-treated FeMnSiCrNi SMA exhibits an approximately homogeneous composition. Based on the average value in the selected zones, it can be verified that the chemical composition of the solution-treated FeMnSiCrNi SMA is approximately 66.09%Fe, 14.80%Mn, 4.99%Si, 9.08%Cr and 5.04%Ni. Sixteen samples for compression test were fabricated from the solution-treated FeMnSiCrNi SMA bar. The FeMnSiCrNi SMA samples, in which the diameter is 6 mm and the proportion of the height to the diameter is 1.5, were compressed on the AG-Xplus universal material testing machine. In the compression test, the reduction in height is 60%. The deformation temperatures were selected as 850, 900, 950 and 1000 °C, respectively. The strain rates were determined as 0.0005, 0.005, 0.05 and 0.5 s−1, respectively. Transmission electron microscope (TEM) characterization was implemented to investigate the microstructures in the solution-treated FeMnSiCrNi SMA sample as well as in the four FeMnSiCrNi SMA samples which were compressed at the strain rate of 0.005 s−1 and the temperatures of 850, 900, 950 and 1000 °C, respectively. In addition, the

Table 1 Peak stresses for FeMnSiCrNi SMA in different deformation conditions (MPa). _ −1 ε/s

lnε_

0.5 0.05 0.005 0.0005

−0.6931 −2.9957 −5.2983 −7.6009

T/°C 850

900

950

1000

283.5992 206.2477 165.569 105.8491

223.2235 164.2866 123.4821 76.1732

195.6608 147.4224 88.4287 58.4672

165.6015 105.8327 68.3389 43.8053

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Fig. 4. Data graphs for calculating the material constants according to experimental data: (a) obtaining n value; (b) obtaining β value; (c) modifying n value; (d) obtaining Q value.

microstructures of the corresponding solution-treated and four compressed FeMnSiCrNi SMA samples were characterized by electron back-scattering diffraction (EBSD). 3. Results and discussion 3.1. Microstructures of solution-treated FeMnSiCrNi SMA Fig. 1 indicates microstructures of the solution-treated FeMnSiCrNi SMA based on EBSD, where grain size distribution and grain boundary distribution are captured. Fig. 2 shows TEM micrographs of the solution-treated FeMnSiCrNi SMA. It can be found from Fig. 2 that the solution-treated FeMnSiCrNi SMA consists of γ austenite and ε martensite. Furthermore, the orientation relationship between the two struc-

deformation temperature. Consequently, the constitutive equation for the FeMnSiCrNi SMA is able to be described by the Arrhenius type equation, namely
Q n ε_ ¼ A½ sinhðασ Þ exp − Þ RT

ð1Þ

_ σ, T, Q and R are the strain where A, α and n are the material constants, ε, rate (s−1), the flow stress (MPa), the absolute temperature (K), the activation energy (J·mol−1) and the universal gas constant (8.314 J·mol−1·K−1), respectively.

tures is ½110γ ==½2110ε . In addition, a lot of stacking faults appear in the matrix of γ austenite. 3.2. Establishment of constitutive equation The true stress-strain curves of the FeMnSiCrNi SMA under uniaxial compression are obtained for the purpose of describing the flow behavior of the alloy at high temperatures, as shown in Fig. 3. It can be noted that like most metals, the FeMnSiCrNi SMA is also a kind of strain rate sensitive material at high temperatures. In other words, the flow stress of the FeMnSiCrNi SMA increases with the increase of strain rate. In addition, it is evident that flow stress of the FeMnSiCrNi SMA decreases with the increase of deformation temperature. According to the flow characteristic of the FeMnSiCrNi SMA at high temperatures, the dynamic recrystallization (DRX) is confirmed to have occurred along with plastic deformation of the FeMnSiCrNi SMA. According to the stress-strain curves in Fig. 3, the plastic flow of the FeMnSiCrNi SMA is found to depend on both the strain rate and the

Fig. 5. Data graph for calculating the value of A according to lnZ − ln [sinh(ασ)] relationship.

S. Jiang et al. / Materials and Design 182 (2019) 108019

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Fig. 6. Variation of material constants with true strain: (a) α; (b) n; (c) Q; (d) A.

When the flow stress is at the low level, Eq. (1) can be approximately represented by
 −Q ε_ ¼ A1 σ n exp ; ασ ≤0:83373 RT

ð2Þ

where A1 remains a material constant and A1 = Aαn. When the flow stress is at the high level, Eq. (1) is able to be approximately expressed as
 −Q ε_ ¼ A2 expðβσ Þ exp ; ασ ≥1:60944 RT

ð3Þ

A where A2 and β remain the material constants and A2 ¼ n , β = nα. 2 Generally, the relationship between strain rate and temperature is able to be described by Zener-Hollomon parameter Z, which is able to be represented by the following equation. Z ¼ ε_ exp




Q RT

 ð4Þ

By introducing the parameter Z into Eq. (1), Eq. (5) is then obtained. Z ¼ A½ sinhðασ Þ

n

Q ln ε_ ¼ ln A1 þ n ln σ − RT

ð7Þ

According to Eq. (7), the value of n is determined as 6.06882 by linear fitting method according to the involved experimental data (Fig. 4 (a)). For the purpose of solving the value of α, it is necessary to gain β value at first. In the same manner, natural logarithm of Eq. (3) is taken so as to obtain the following equation, namely ln ε_ ¼ ln A2 þ βσ−

Q RT

ð8Þ

In the similar way, the value of β is determined by linear fitting method according to the corresponding experimental data (Fig. 4 (b)).

ð5Þ

Eq. (5) can be further transformed into the following form, namely vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi9 8 u > > 1 u
2 > > > >
 u þ < 1 Z n t Z n þ 1= ln σ¼ > > α A A > > > > ; :

By simplifying Eq. (1), the values of A, α, n and Q are able to be obtained based on the experimental data from the stress-strain curves, where the peak stress is adopted, as shown in Table 1. Consequently, the constitutive equation of the FeMnSiCrNi SMA during hot deformation can be further solved. Taking natural logarithm for Eq. (2) is able to result in the following equation, namely

ð6Þ

Accordingly, Eq. (6) is the constitutive equation described by the parameter Z.

Table 2 Coefficient values of fifth-order polynomials in Eq. (14). α

n

Q

lnA

α0 = −0.01138 α1 = −0.03871 α2 = 0.1672 α3 = −0.33.12 α4 = 0.30467 α5 = −0.10729

n0 = 4.13976 n1 = −1.98628 n2 = 7.20937 n3 = −14.91931 n4 = 18.10188 n5 = −8.00468

Q0 = 3,134,613 Q1 = 1,576,947 Q2 = −4,148,687 Q3 = 2,800,254 Q4 = 2,261,044 Q5 = −2,027,492

A0 = 26.69652 A1 = 17.40413 A2 = −53.87584 A3 = 60.76838 A4 = −13.03156 A5 = −6.85738

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Fig. 7. Comparison between experimental and predicted compressive stress-strain curves of FeMnSiCrNi SMA at various deformation conditions: (a) 0.5 s−1; (b) 0.05 s−1; (c) 0.005 s−1; (d) 0.0005 s−1.

As a result, the value of β is 0.0475775. Accordingly, the value of α is further calculated as 7.84 × 10−3 MPa−1. In addition, the value of n needs to be further modified, so it is necessary to taking natural logarithm of Eq. (1). As a consequence, a new formulation shown in Eq. (9) is established.

After all the material constants are solved, the constitutive equation of FeMnSiCrNi SMA is described by the following equation. h  i4:4761 −3:5002533  105 exp ε_ ¼ 1:3505  1013 sinh 7:84  10−3 σ RT

!

ð12Þ Q ln ε_ ¼ ln A þ n ln ½ sinhðασ Þ− RT

ð9Þ

Based on the aforementioned linear fitting method, the value of n is further modified as 4.47611 according to Fig. 4 (c). For solving the value of Q, it is necessary to differentiate T−1 in Eq. (9) at the unchangeable strain rate. Therefore, Q can be expressed as follows:

Q ¼ nR


 ∂ ln ½ sinhðασ Þ ∂T −1

ε_

ð10Þ

As the modified values of n and R have been solved, the value of Q is calculated as 3.5002533 × 105J ⋅ mol−1 based on the fitting value resulting from Fig. 4 (d). For solving the value of A, it is necessary to take natural logarithm of Eq. (5) and thus Eq. (11) is gained. ln Z ¼ ln A þ n ln ½ sinhðασ Þ

ð11Þ

Based on Eq. (11), the involved experimental data are used for linear fitting as is indicated in Fig. 5 and the value of lnA becomes 30.23408. Finally, the value of A is determined as 1.3505 × 1013.

The constitutive equation of FeMnSiCrNi SMA is described in the form of Zener-Hollomon parameter, namely σ¼

1 7:84  10−3

8 <
ln

Z

: 1:3505  1013

1=4:47611

sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi9
2=4:47611 = Z þ þ1 ; 1:3505  1013

ð13Þ It can be found from Eq. (1) that Arrhenius model is not capable of reflecting the relationship between the strain and the flow stress. In fact, the FeMnSiCrNi SMA cannot exhibit an absolutely steady flow during plastic deformation at high temperatures. When DRX occurs, in particular, the flow stress frequently varies with increasing true strain. Therefore, it is of great importance to take into account the strain compensation. In other words, the material constants α, n, Q and A are no longer unchangeable, and they shall vary with increasing true strain. The values of α, n, Q andA are calculated based on the various stresses corresponding to the various strains, which range from 0 to 0.9 at the interval of 0.05. The corresponding calculation method is completely identical to the aforementioned one based on the peak stress. Consequently, the involved calculation results are illustrated in Fig. 6. For the purpose of further describing the dependence of the material constants on the strain mathematically, the four fifth-order polynomials are obtained by fitting the calculated values in Fig. 6, as shown in

S. Jiang et al. / Materials and Design 182 (2019) 108019

Eq. (14). The corresponding coefficient values are indicated in Table 2.

V

α ¼ α 0 þ α 1 ε þ α2 ε2 þ α 3 ε3 þ α4 ε4 þ α 5 ε5 2

3

4

n ¼ n0 þ n1 ε þ n2 ε þ n3 ε þ n4 ε þ n5 ε

ð14Þ

5

Q ¼ Q 0 þ Q 1 ε þ Q 2 ε2 þ Q 3 ε3 þ Q 4 ε4 þ Q 5 ε5

7

Consequently, the comparison between the experimental and predicted flow stresses is performed, as illustrated in Fig. 7, where the predicted flow stresses are found to agree well with the experimental ones. 3.3. Microstructures of deformed FeMnSiCrNi SMA

ln A ¼ A0 þ A1 ε þ A2 ε2 þ A3 ε3 þ A4 ε 4 þ A5 ε5

By combining Eq. (1) with Eq. (14), the flow stress can be predicted with respect to any deformation condition where true strain, deformation temperature and strain rate are known.

In order to further reveal the microstructures of all the four FeMnSiCrNi samples compressed at the strain rate of 0.005 s−1, the corresponding TEM micrographs are illustrated in Figs. 8, 9, 10 and 11. It can be found from Fig. 8 that there are ε martensite, γ austenite, a

Fig. 8. TEM micrographs of FeMnSiCrNi sample deformed at 850 °C: (a) Bright field image showing γ austenite phase and a high density of dislocations; (b) diffraction pattern of selected area in (a) showing γ austenite phase; (c) bright field image showing austenite twin, a high density of dislocations and stacking faults (SFs); (d) diffraction pattern of selected area in (c) showing austenite twin; (e) bright field image showing ε martensite variants (ε1 and ε2); (f) diffraction pattern of selected area in (e) showing ε martensite phase.

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Fig. 9. TEM micrographs of FeMnSiCrNi sample deformed at 900 °C: (a) Bright field image showing ε martensite variants (ε1 and ε2) and stacking faults (SFs); (b) diffraction pattern of selected area in (a) showing γ austenite phase; (c) bright field image showing ε martensite, austenite twin and a high density of stacking faults (SFs); (d) diffraction pattern of selected area in (c) indicating the orientation relationship between γ austenite and ε martensite.

Fig. 10. TEM micrographs of FeMnSiCrNi sample deformed at 950 °C: (a) Bright field image showing ε martensite variants (ε1 and ε2), dislocations and stacking faults (SFs); (b) diffraction pattern of selected area in (a) showing ε martensite phase; (c) bright field image showing ε martensite variants (ε1 and ε2), austenite twin and a high density of stacking faults (SFs); (d) diffraction pattern of selected area in (c) indicating the orientation relationship between γ austenite and ε martensite.

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Fig. 11. TEM micrographs of FeMnSiCrNi sample deformed at 1000 °C: (a) Bright field image showing ε martensite variants (ε1 and ε2); (b) diffraction pattern of selected area in (a) showing γ austenite phase; (c) bright field image showing ε martensite variants (ε1 and ε2), austenite twin and a high density of stacking faults (SFs); (d) diffraction pattern of selected area in (c) indicating the orientation relationship between γ austenite and ε martensite.

Fig. 12. EBSD microstructures of FeMnSiCrNi samples deformed at the various temperatures: (a) 850 °C; (b) 900 °C; (c) 950 °C; (d) 1000 °C.

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Fig. 13. Distribution of rotation angle in FeMnSiCrNi samples deformed at the various temperatures: (a) 850 °C; (b) 900 °C; (c) 950 °C; (d) 1000 °C.

Fig. 14. Schmid factor distribution of FeMnSiCrNi samples deformed at the various temperatures: (a) 850 °C; (b) 900 °C; (c) 950 °C; (d) 1000 °C.

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Fig. 15. Inverse pole maps of γ austenite phase in the FeMnSiCrNi samples deformed at the various temperatures: (a) 850 °C; (b) 900 °C; (c) 950 °C; (d) 1000 °C.

high density of dislocations and plenty of stacking faults in the FeMnSiCrNi sample deformed at 850 °C. Furthermore, austenite twins are captured in Fig. 8 (c). In particular, ε martensite variants are observed in Fig. 8 (e). In the same manner, ε martensite variants, γ austenite, stacking faults and austenite twins appear in the other three deformed FeMnSiCrNi samples as well. The existence of ε martensite variants means that ε martensite belongs to thermally-induced one rather than stress-induced one [7–9]. The similar results are also observed in the other three deformed FeMnSiCrNi samples. However, the dislocations are reduced a lot in the other three deformed FeMnSiCrNi samples. This means that dislocations decrease with the increase of deformation temperature, which is due to the fact that dynamic recrystallization occurs in the FeMnSiCrNi SMA at elevated temperatures. However, it is not denied that dislocations are still observed in the FeMnSiCrNi sample subjected to plastic deformation at higher temperature, as shown in Fig. 10(a). In addition, it can be found from Figs. 9, 10 and 11 that the orientation relationship between ε martensite and γ austenite in the deformed FeMnSiCrNi samples is

still ½110γ ==½2110ε , which is frequently observed in FeMnSi-based SMAs [27,28]. It has been accepted that deformation twinning and dislocation slip are the principal plastic deformation mechanisms in the metal materials. However, deformation twinning usually takes place in the conditions of the higher strain rates or the lower temperatures because the critical resolved stress (CRS) for deformation twinning is lower than the one for dislocation slip [29]. At the high temperatures, slip system is easier to be activated than twinning nucleation since the CRS for dislocation slip is lower than the one for deformation twinning. In other words, deformation twinning is difficult to occur at the high temperatures [30]. In our work, we do not provide a direct experiment evidence that austenite twin is a product of deformation twinning during hot deformation of the FeMnSiCrNi SMA. As a consequence, dislocation slip is dominant during hot deformation of the FeMnSiCrNi SMA. For the purpose of further investigating the deformation mechanism of the aforementioned deformed FeMnSiCrNi samples, the

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Fig. 16. Orientation distribution functions (φ2 = 45°) of γ austenite phase in the FeMnSiCrNi samples subjected to compression at the various temperatures: (a) 850 °C; (b) 900 °C; (c) 950 °C; (d) 1000 °C; (e) standard stereographic projection of some key orientations (Cube, Copper, Brass and Goss represent the corresponding textures, respectively).

corresponding microstructures are characterized using EBSD, as illustrated in Figs. 12 and 13. It can be noted from Fig. 12 that the grain size increases with the increase of deformation temperature. For the FeMnSiCrNi sample deformed at 1000 °C, in particular, the grain size grows very substantially, where some elongated grains arise. Furthermore, it can be observed from Fig. 13 that with the increase in the deformation temperature, the fraction of large angle grain boundaries increases while the one of low angle grain boundaries decreases. It can be envisaged that the dependence of grain size and grain boundary on deformation temperature is closely

associated with DRX of the FeMnSiCrNi SMA at elevated temperatures. It is well known that dynamic recrystallization deals with the nucleation and growth of crystal. Furthermore, the nucleation of the dynamically recrystallized grains is closely related to the dislocation density since dynamic recrystallization does not take place without reaching a threshold of dislocation density [31,32]. Therefore, dislocation slip is an indispensable mechanism of plastic deformation in the FeMnSiCrNi SMA subjected to hot deformation. Consequently, according to EBSD data, Schmid factor distribution of the four deformed FeMnSiCrNi SMA samples is obtained, as indicated

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Fig. 17. Inverse pole maps of ε martensite phase in the FeMnSiCrNi samples subjected to compression at the various temperatures: (a) 850 °C; (b) 900 °C; (c) 950 °C; (d) 1000 °C.

in Fig. 14. Schmid factor is calculated on the basis of the grains containing γ austenite, without considering the grains consisting of ε martensite, since ε martensite results from subsequent martensitic transformation and thus it does not participate in plastic deformation at high temperatures. Consequently, the grains containing ε martensite are represented by the white zone shown in Fig. 14. It is well known that the larger value of Schmid factor contributes to plastic deformation of metal materials since it enables the grains to be a soft orientation in which dislocation slip is easier to take place [33,34]. It can be found from Fig. 14 that so far as all the four deformed FeMnSiCrNi SMA samples are concerned, most grains containing γ austenite possess the larger value of Schmid factor, which facilitates their subsequent plastic deformation. For the purpose of further investigating the orientation characteristic of the grains in the four deformed FeMnSiCrNi SMA samples, the corresponding inverse pole figures and orientation distribution functions are obtained based on EBSD data, as shown in Figs. 15–18, respectively. It is generally accepted that inverse pole figure is frequently used for characterizing the texture of polycrystalline metal materials, but it is not able to accurately describe the texture components due to the limitation of two-dimensional stereographic projection. Therefore,

orientation distribution function is another more effective method for characterizing the texture of polycrystalline metal materials by describing the frequency at which particular orientations occur in a threedimensional orientation space, namely Euler space. In the present work, standard stereographic projection of ε martensite is calculated based on the Bunge system, where each component g(ϕ1, ϕ, ϕ2) is defined by the angles ϕ1, ϕ and ϕ2 corresponding to a rotation with respect to Z-X-Z axes [35]. Consequently, the crystal planes {hkil} and the crystal directions buvtwN, which are used to represent the texture, can be expressed by g(ϕ1, ϕ,ϕ2), namely 2 3 2 pffiffiffi 2 3 h pffiffiffi sinφ2 sinφ 6k7 6 7 ¼ 4 3−1 0010− 3−1 000c=a4 cosφ sinφ 5 2 4i5 2 2 2 2 cosφ l

ð15Þ

2

3 2 2 3 u cosφ1 cosφ2 − sinφ1 sinφ2 cosφ 6v7 6 7 ¼ 4 2 −1 002 02 −1 000c=a4 − cosφ sinφ − sinφ cosφ cosφ 5 1 2 1 2 4t 5 3 3 3 3 3 sinφ1 sinφ w

ð16Þ

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Fig. 18. Orientation distribution functions (φ2 = 60°) of ε martensite phase in the FeMnSiCrNi SMA samples deformed at the various temperatures: (a) 850 °C; (b) 900 °C; (c) 950 °C; (d) 1000 °C; (e) standard stereographic projection of some key orientations.

It can be found from Figs. 15 and 16 that for the FeMnSiCrNi SMA sample deformed at 850 °C, γ austenite phase possesses the stronger 〈110〉 texture and the relatively weaker 〈001〉 texture in the compression direction, which corresponds to normal direction (ND). However, with increasing deformation temperature, 〈110〉 texture becomes weak gradually, but 〈001〉 texture is intensified gradually. In addition, it can be noted from Fig. 16 that with the increase in the deformation temperature, cube texture becomes stronger and stronger, and 〈110〉

and 〈111〉 fiber textures are formed. The phenomenon indicates that deformation temperature has a significant impact on texture of γ austenite in the FeMnSiCrNi SMA. Furthermore, the texture of γ austenite in FeMnSi-based SMA significantly influences SME of the alloy. Druker et al. stated that certain crystallographic textures may facilitate a better shape recovery in the case of minor applied stresses [36]. Kwon et al. found that the volume fraction of 〈101〉 texture component contributes to the increase of shape recovery strain [37]. Arabi-Hashemi et al.

S. Jiang et al. / Materials and Design 182 (2019) 108019

proposed that texture has an influence on the formation of recovery stresses [38]. Therefore, it is of great significance to deeply investigate the texture of FeMnSi-based SMA [38]. It can be found from Fig. 17 that ε martensite phase possesses h2112i texture and h1011i texture in the compression direction, which corresponds to ND. It is obvious that h2112i and h1122i belong to the same family of crystal direction. Therefore, according to orientation distribution functions illustrated in Fig. 18, it can be proposed that the texture type of ε martensite should be h1122i fiber texture. The ε martensite is formed by shearing the γ austenite along the 〈112〉 directions on

15

and cube texture are intensified gradually along with the onset of 〈110〉 and 〈111〉 fiber textures. In addition, ε martensite possesses h1 122i fiber texture. CRediT authorship contribution statement Shuyong Jiang:Conceptualization, Methodology, Writing - original draft, Supervision, Funding acquisition. Yu Wang:Investigation, Software. Yanqiu Zhang:Validation, Writing - review & editing, Funding acquisition. Xiaodong Xing:Investigation. Bingyao Yan:Investigation.

the f111g planes, so there is a certain orientation relationship between γ austenite and ε martensite, namely f111gγ ==f0001gε and h112iγ == h1010iε [39]. Consequently, when γ austenite is transformed into ε martensite, the 〈110〉 direction of γ austenite is converted to the h1120i direction of ε martensite, namely h110iγ ==h1120i . Furthermore, γ austenite possesses 〈001〉 texture in the normal direction, which is inclined to 45° angle about the 〈110〉 direction, and in the ε martensite, the angle between h1120i and h1122i is 54.7°. The difference between the two angles is about 10°. Accordingly, the h1122i direction of ε martensite is approximately parallel to the normal direction, so it can be stated that ε martensite possesses h1122i fiber texture. 4. Conclusions 1) Constitutive equation of the FeMnSiCrNi SMA according to Arrhenius type equation was established as

−3:5002533  105 Þ by means of expð RT compression test, where the temperature range is 850–1000 °C and the strain rate range is 0.0005–0.5 s−1. The constitutive equation can describe the flow behavior of the FeMnSiCrNi SMA during hot deformation. The flow stress increases with the increase of strain rate, but it decreases with the increase of deformation temperature. The flow stress of the FeMnSiCrNi SMA at high temperatures frequently varies with the increase of true strain. It is of great importance to take into account the strain compensation during plastic flow of the FeMnSiCrNi SMA at high temperatures. Consequently, the material constants α, n,Q and A in the Arrhenius type equation shall vary with increasing true strain. According to Arrhenius model based on strain compensation, the flow stress of the FeMnSiCrNi SMA is able to be predicted with respect to any deformation condition where true strain, deformation temperature and strain rate are known. Consequently, the predicted values of flow stresses agree well with the experimental ones. There exist γ austenite and ε martensite in the FeMnSiCrNi samples subjected to hot deformation. Stacking faults as well as austenite twins are also observed in the deformed FeMnSiCrNi samples. A high density of dislocations appears in the FeMnSiCrNi sample subjected to deformation at the relatively lower temperature. In other words, dislocations decrease with the increase of deformation temperature. However, dislocation slip remains the principal mechanism responsible for plastic deformation of the FeMnSiCrNi SMA at high temperatures. Dynamic recrystallization takes place during plastic deformation of the FeMnSiCrNi SMA at high temperatures. As a consequence, the grain size increases with the increase of deformation temperature. In addition, with the increase of deformation temperature, the fraction of large angle grain boundaries increases while the one of low angle grain boundaries decreases. The deformation temperature affects the texture of the FeMnSiCrNi SMA as well. With increasing deformation temperature, 〈110〉 texture becomes weak gradually in the γ austenite, but 〈001〉 texture 4:4761

½ sinhð7:84  10−3 σ Þ

2)

3)

4)

5)

ε_ ¼ 1:3505  1013

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