Strain-induced martensite formation in austenitic stainless steel

Mitsuhiro Okayasu • Hironobu Fukui •

Hiroaki Ohfuji • Tetsuro Shiraishi

Received: 28 November 2012 / Accepted: 27 April 2013 / Published online: 8 May 2013

� Springer Science+Business Media New York 2013

Abstract In situ measurements of the strain-induced

martensitic transformation (SMTs) of SUS304 stainless

steel that takes place during tensile loading at room tem-

perature were performed around the notch of a dumbbell-

shaped specimen where high stress concentration occurs.

Even in the low plastic strain regime, with loading to 0.2 %

proof stress (r0.2), some SMTs occurred. However, the area

fraction of the Fe-a0-martensite phase did not increase

significantly even when the sample was loaded to the

ultimate tensile strength (rUTS). After the rUTS point, the

total fraction of the Fe-a0 phase increased dramatically to

the fracture point (rf). The phase textures of Fe-a0 and Fe-cwere almost equal at (rUTS - rf)/2, and the Fe-a0 phase

was observed over almost the entire measurement area

around the notch at the rf point. However, the area fraction

of the Fe-a0 phase at the rf point decreased far away from

the fracture surface, to an extent that the total fraction of

the Fe-a0 phase was almost the same as that of the Fe-cphase in an area about 1.7 mm from the fracture face.

Different martensite characteristics were detected in the

stainless steel, depending on the applied load level. This

was attributed to the severity of deformation. In particular,

deformation twinning, created around rUTS, and severe

plastic deformation before fracture make a strong Fe-a0

phase. Details of this phenomenon are interpreted using

various approaches, including electron backscatter dif-

fraction analysis and finite element analysis.

Introduction

Austenitic stainless steels have received special attention

because of their use for various engineering components,

such as in power plants and the automobile industries, owing

to their excellent machinability, high corrosion resistance,

high strength and high ductility. However, although

austenitic stainless steels have high material ductility, this is

significantly affected by strain-induced martensitic trans-

formations (SMTs). A variety of stainless steel components

are produced by mechanical processes including stretching,

drawing and bending, all of which cause severe plastic

deformation [1]. Experimental and numerical approaches

have been used to attempt to understand the stress–strain

characteristics in stainless steel components [2, 3]. It is

believed that austenite phases in some stainless steels are

metastable owing to the presence and amount of Cr and Ni,

both of which lead to a SMT when the stainless steel is

subjected to plastic deformation. The life of stainless steel

components in service is generally a function of the severity

of this plastic deformation. Consequently, an examination of

plastic strain characteristics in these stainless steels is of

considerable importance, and several techniques have been

proposed to observe the localised plastic deformation zone

[4]. It is believed that austenitic stainless steels exhibit sig-

nificant work hardening, resulting in the transformation from

metastable austenite to martensite [5]. It is also considered

that a marked increase in elongation occurs when martensites

are formed during the deformation, which is called trans-

formation-induced plasticity [6]. The volume fraction of

austenite to martensite transformation depends on the strain

level, temperature and strain rate [3].

Zong-yu et al. [7] investigated the influence of pre-

transformed martensite on the work hardening behaviour of

metastable SUS304 austenitic stainless steel. One of their

M. Okayasu (&) � H. Fukui � T. Shiraishi

Department of Materials Science and Engineering, Ehime

University, 3 Bunkyo-cho, Matsuyama, Ehime 790-8577, Japan

e-mail: okayasu.mitsuhiro.mj@ehime-u.ac.jp

H. Ohfuji

Geodynamics Research Center, Ehime University,

2-5 Bunkyo-cho, Matsuyama, Ehime 790-8577, Japan

123

J Mater Sci (2013) 48:6157–6166

DOI 10.1007/s10853-013-7412-8

results was that the work hardening exponent of the

stainless steel decreases with an increase of pre-trans-

formed martensite. SUS304 stainless steel is a typical

austenitic stainless steel and is known to exhibit considerable

work hardening; hence a pre-strained-type stainless steel

would be expected to show a martensitic transformation

[1]. In the study by Dan et al. [5], a constitutive model for the

transformation-induced plasticity accompanying the SMT

was developed. The increase in the number of nucleation

sites in austenite owing to plastic deformation is formulated

as an increase of the shear band intersection. The nucleation

site probability is dependent not only on the stress state,

plasticity strain and temperature of the environment but also

on the strain rate. During their analysis of the tensile process

at a strain rate of 0.001 s-1, an increase in temperature led to

a slow martensite transformation. The shear band, driving

force and parameter-a0 transformation also decrease when

the deformation temperature is higher [5]. This is because the

shear band intersection is reduced at higher temperature,

resulting in weak plasticity-induced transformation. Beese

and Mohr examined the effect of the stress state on the

transformation kinetics of stainless steel sheets (301LN) at

room temperature using newly developed experimental

techniques for simple shear and large strain in-plane com-

pression. Their experimental results indicated that the mar-

tensite transformation kinetics cannot be described solely by

a monotonically increasing function of stress triaxiality. For

instance, less martensite is developed under equibiaxial

tension compared with uniaxial tension for the same increase

in equivalent plastic strain [8].

To date, several studies have systematically investigated

the SMT characteristics of austenitic stainless steels, along

with relevant information used to explain their material

characteristics. Although some significant information has

been reported, it is believed that further study is required to

obtain more effective SMT characteristics for these stainless

steels. This is especially true, as the SMT characteristics

have been examined mainly using X-ray diffraction, TEM

and magnetic permeability measurements, [9–11] which

may not show clear phase textures, e.g. with two-dimen-

sional images. In the present study, in situ measurements of

SMT behaviour were made during tensile loading, and the

effects of deformation and crystal orientation characteristics

on the SMT behaviour were investigated using electron

backscatter diffraction (EBSD) analysis.

Experimental procedures

Materials and experiments

The study reported used a commercial SUS304 stainless

steel plate, produced by a hot-rolling process, with

chemical composition Fe–Ni8.6–Cr18.4–Si0.45–Mn1.8–

Mo0.3–S0.03–C0.08 (wt%). The SUS304 was annealed at

1150 �C for 2 h and air-cooled to remove any residual

stresses. The stainless steel consisted of an austenite phase

with a mean grain size of 92 lm in diameter. Figure 1

shows a test specimen. The specimens were machined into

the form of rectangular dumbbell shapes with two notches.

The reason for the notches was to measure the SMT

characteristics in the same area and similar stress level.

Specimens were machined by a wire electric discharge

machine. The stress concentration rate in the specimens

around the notches was about Kt = 2.4 [12]. In this case,

the specimen surfaces were finished with a smooth level of

Ra = 1.6 to reduce the stress concentration arising from

tool marks. It should be pointed out that the material

properties of the notched specimens are different from

those of standard smooth tensile specimens. In this case,

the ductility of the sample would be reduced by the notch

effect [13].

Tensile tests were conducted using an electro-servo-

hydraulic system with 50 kN capacity. The applied load

and strain were measured with a commercial load cell and

a strain gauge, respectively. After a specimen was loaded

to several specific loading points, the SMT characteristics

of the specimen were examined adjacent to the notch tip

(A0, see Fig. 1), where relatively high stress concentration

occurs. Note first that the area A0 does not have the highest

stress concentration, owing to the area being about 1 mm

away from the notch tip. The reason for this measurement

was to obtain clear SMT characteristics during the tensile

tests. In fact a clear SMT cannot be obtained in the area of

the sample adjacent to the notch tip (the highest stress

concentration area) because of severe material damage.

This examination was carried out only at room temperature

(about 293 K) as a first approach even though the SMT is

sensitive to sample temperature [14]. The crystal

2

6.5

2

R1

t = 5 12.5

175

57

R12.5

20

Measurement area (A’)1

Fig. 1 Schematic illustration of the test specimen

6158 J Mater Sci (2013) 48:6157–6166

123

orientation characteristics were investigated by EBSD

analysis, using a high-resolution electron microscope

(JSM-7000F, JEOL Ltd). Based upon an analysis of the

EBSD patterns, the phase textures (Fe-a0 and Fe-c phases)

of the matrix were determined using HKL Channel 5

software. The main measurement conditions for this anal-

ysis were as follows: the sample was tilted to an angle of

70�, and an accelerating voltage of 15 kV, beam current of

5 nA and measurement step size of 4 lm were used. The

sample surfaces for this examination were polished for

about 2 h to mirror level in a vibro-polisher using colloidal

silica. The polishing process was executed carefully with a

low applied load so as to reduce sample damage.

Finite element analysis

To investigate the stress–strain distribution in the test

specimen of SUS304 stainless steel after tensile loading,

finite element analysis was conducted using ANSYS soft-

ware. In this analysis, a two-dimensional finite element

simulation with 8-node quad elements was employed. The

finite element analysis model was designed to simulate the

actual specimen, as shown in Fig. 1. The mesh size of the

model was set to 0.05 mm, giving a total of 3251 quadri-

lateral solid elements. To identify the plastic strain levels in

this analysis, the option of bilinear kinematic hardening

was selected, in which the initial slope of the stress–strain

relationship is taken as the Young’s modulus of the

material. After the yield point, the curve continues along a

second slope defined by the tangent to the curve. Based on

our experimental results, the following material properties

were determined: Young’s modulus E = 210 GPa, tangent

modulus T = 1105 MPa, Poisson’s ratio m = 0.3 and yield

strength r0.2 = 290 MPa. Note that, in this case, the yield

strength was defined as the stress value at which 0.2 %

permanent deformation occurs.

Results and discussion

Figure 2 displays representative tensile stress (r)–strain (e)curves for our SUS304 stainless steel. Because the speci-

men has notches, its tensile properties are different from

those of a standard smooth specimen, i.e. there is a notch

effect. We have examined the tensile properties of the

smooth specimen in addition to those of the notched one,

and it appears that both ultimate tensile strength and

Young’s modulus are almost the same, but the strain to

failure for the notched specimen is slightly lower compared

to the smooth specimen. This is because the presence of

triaxial stress field and steep stress (such as arise at a notch)

gradients with the notch effect results in a change of

ductility.

In the present study, several specimens were loaded to

the specific loading (or strain) points labelled A, B, C, D, E

and F in Fig. 2. Point A is the specimen without any

applied load, i.e. 0 N. Points B, D and F are the yield point

r0.2, ultimate tensile strength rUTS and fracture point rf,

respectively. Finally, points C and E are at load levels of

(rUTS - r0.2)/2 and (rUTS - rf)/2, respectively. It should

be noted that, in the tensile test, the applied load was

applied at a low strain rate of about 0.0005 s-1, which is

much lower than that used in previous studies [15, 16]. The

A

B

C

D

E

F

0 10 20 30 40 50

Strain, %

0

100

200

300

400

500

600

700

Ten

sile

str

ess,

MPa

Fig. 2 Tensile stress–strain curve for the SUS304 stainless steel

Sample A

Sample B

Sample C

Sample D

Sample E

Sample F

10mm

Fig. 3 Photographs of the test specimens after loading to the specific

points shown in Fig. 2

J Mater Sci (2013) 48:6157–6166 6159

123

reasons behind the low strain rate are (i) to create a clear

SMT [3, 17] and (ii) to easily control the load level at the

specific points (points A–F). The effect of strain rate on

SMT characteristics has been investigated by Das et al.

[17]. One of their conclusions is that the total volume

fraction of martensite decreases when the strain rate is

increased because of the enhancement of sample temper-

ature. Talonen et al. [18] have also similarly reported that

more strain-induced a0-martensite is formed in steel at a

lower strain rate and higher Md30 temperature. The Md30

temperature of our stainless steel approximated using

Gladman’s formula is 11.7 �C, i.e. 497–462(C ? N)–

Sample A Sample B

Sample C Sample D

Sample E Sample F

50µm

001 101

111

Fig. 4 Crystal orientation maps of the SUS304 stainless steels after loading to the specific points shown in Fig. 2 (Color figure online)

6160 J Mater Sci (2013) 48:6157–6166

123

9.2(Si)–8.1(Mn)–13.7(Cr)–20(Ni)–18.5(Mo), which is

similar to that for a related stainless steel [19]. However, an

opposite trend for SMT is obtained in the stainless steel

after impact loading tests, in which the volume fraction of

martensite increases with increasing strain rate, i.e.

8 9 102 to 4.8 9 103 s-1 [20]. The increase in martensite

volume fraction caused by the increase of strain rate can

lead to high strength, where a high dislocation density

would be introduced into the austenite to accommodate the

martensite volume expansion [21]. Figure 3 shows photo-

graphs of the specimens after loading to the specific points

mentioned above. The different degrees of permanent

deformation around the notches can clearly be seen,

especially after the material yields (samples C–F), while no

clear deformation can be observed in sample B. In sample

D, severe deformation occurs because it undergoes necking

α’-phase

γ -phase

50µm

Sample A

Sample C

Sample B

Sample E

Sample D

Sample F

Fig. 5 Orientation imaging microscopy maps for samples A–F (Color figure online)

J Mater Sci (2013) 48:6157–6166 6161

123

[12], and more severe deformation occurs in samples E and

F. In previous reports, similar load–strain relationships

were obtained for the appropriate stainless steel, where

high strain increases the severity of the martensitic trans-

formation [22].

Figure 4 depicts the crystal orientation maps obtained at

points A–F. The colour level of each pixel in the crystal

orientation map is defined according to the deviation of the

orientation measured from the direction parallel to ND (see

the colour key of the stereographic projection). Moreover,

the dark areas in this analysis are associated with regions in

which data cannot be collected. This is because of the

severe material damage, e.g. collapse of microstructure and

micro-cracks. Austenite grains can be clearly seen in the

SUS304 stainless steel when it is loaded to an extent less

than the ultimate tensile strength. On the other hand, some

twinning-like deformation zones are observed in sample D,

as indicated by the circles. The grain formations in samples

E and F are seen to have collapsed to tiny regions and

randomly distributed crystal orientation caused by more

severe slip deformation. Basically, the crystal orientation in

samples A–D is different depending on the grain, whereas

this cannot be seen clearly in samples E and F.

Figure 5 shows orientation imaging microscopy maps for

samples A–F, and Fig. 6 shows the variations of the area

fraction of Fe-a0-martensite and Fe-c phases as a function of

tensile strain. Note that the measurement areas displayed in

Fig. 5 are the same as those shown in Fig. 4. It is clear that a

strong texture of Fe-c is apparent until the samples are

strained to about 40 %, at which point the total area fraction

of Fe-c is about 85 % (samples A–D). It is interesting to

mention first that even if a relatively high strain (e = 40 %)

is present in sample D, the SMT is weak. In addition, the

characteristics of Fe-a0-martensite formation for sample D

(Fig. 5) are different from those for samples A, B and C. For

example, several Fe-a0 phase colonies are obtained for

sample D, and the Fe-a0 phase can be detected, with many

tiny regions (dot-like formations), for samples B and C, as

indicated by the dashed circles. This contrasting martensitic

characteristic will be discussed later. In the present study, the

total area fraction of the Fe-a0 phase apparently increases

with increasing strain level beyond e = 40 % (or rUTS),

during which the phase textures of Fe-a0 and Fe-c are similar

(Fe-a0 = 55 % and Fe-c = 45 %) at e = 45 % (sample E).

In sample F, almost the whole measurement area is charac-

terised by the presence of the Fe-a0-martensite phase

(Fe-a0 & 80 %). Interestingly, corresponding results were

reported by Ogata et al. [14], where there is no clear SMT in

SUS316L until a strain level of 40 %. In another report, the

volume fraction of martensite increased sharply when the

sample was strained to about 25–50 %, which was dependent

on the strain rate: the higher the strain rate, the lower the

volume fraction of martensite [17]. Although the strain levels

used in previous studies to alter the texture are close to our

result, further study will be required, because notched

specimens were employed in our approach. A different result

was also reported by Spencer et al. [23], where the stainless

steel was virtually saturated with a0-martensite before

necking (i.e. r\ ultimate tensile strength), which may be

affected by the experiments being conducted at the lower

temperature of 77 K [12, 23]. An interesting approach was

used by Hecker et al. [24]. They investigated the SMT

characteristics for 304 stainless steel using the von Mises

effective strain criterion, which gives a reasonable correla-

tion of transformation kinetics under general strain states: the

principal effect of increased strain rate was obtained at

strains greater than 0.25 [24].

Consideration should be given as to whether micro-

cracks affect SMT or not in the present study. In general,

the micro-cracks would be created by the following pro-

cess: micro-voids are created during the earlier failure

process, and their coalescence occurs as the load becomes

greater than the ultimate tensile strength [25]. Because of

stress relaxation, caused by micro-crack generation, this

could be a significant factor in the SMT characteristics. It is

considered that micro-cracks are created during the tensile

tests especially in samples E and F. Since the data col-

lection rate in the EBSD analysis was decreased for the

samples loaded to points E and F as mentioned for Figs. 4

and 5, this occurrence may be attributed to the micro-

cracks. However, further study will be required in the future.

It is also considered that the nucleation of a0-martensite

is always confined to microscopic shear bands, including

strain, faults and twin intersections [11]. Details of those

microstructural effects on the martensite transformation are

discussed below.

0 10 20 30 40 50

Strain, %

0.1

0

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

Rat

e of

are

a fr

actio

n fo

r α ’

-an

d γ -

phas

e

A

A

B

B

C

C

D

D

E

E

F

F

α’-phase

γ -phase

Fig. 6 Variation of the area fraction of Fe-a0-martensite and Fe-cphase as a function of the tensile strain, obtained on the basis of Fig. 5

6162 J Mater Sci (2013) 48:6157–6166

123

Figure 7 depicts the lattice strain distribution in samples

A–F. In this case, the lattice strain was defined by the

crystal orientation angle. It is seen that there are different

strain distribution characteristics. Compared to the orien-

tation imaging microscopy maps in Fig. 5, the severe strain

is randomly distributed in the area of Fe-a0 phase, which

may be associated with severe plastic deformation [6].

In addition, lattice strain, which is related to SMT, is

enhanced in twins, although that strain is at a low level as

indicated by the dashed circles. From this result, SMT can

be attributed to two different strain patterns: plastic

deformation and twin formation. Note that although there

are deformation twins in samples B and C as indicated by

the circles, those are not attributed to SMT [26]. This is

because those twins are not created during the tensile

loading.

50µm

Sample A

Sample C

Sample B

Sample E

Sample D

Sample F

0 1 2 3 4 5 6 7°

Fig. 7 Strain distribution defined with crystal orientation angle (Color figure online)

J Mater Sci (2013) 48:6157–6166 6163

123

Several researchers have investigated the associated

SMT characteristics of SUS304 stainless steels. In the

study by Shen et al. [15] it is made clear that a high fraction

of martensite phase is obtained in related stainless steels

when loaded at a lower strain rate of 3 9 10-3. Further-

more, they found, using careful TEM observations, that

stacking faults and twins preferentially occur before mar-

tensitic nucleation and both e-martensite and a0-martensite

are observed in the deformed microstructures. The pres-

ence of a0-martensite is attributed to the twinning defor-

mation and the presence of e-martensite to the plastic

deformation [15]. It is generally considered that the twin-

ning deformation occurs most readily in steels subjected to

high strain rate and/or low temperature conditions [12].

The observation of SMT, obtained with the low strain rate

of 3 9 10-3 in the study by Shen et al. [15], might be

related to the texture of the e-martensite. From the above

information, it may be considered that strong SMT,

obtained in previous study after tensile tests at a lower

temperature [22], is influenced by the twinning deforma-

tion, thus resulting in a0-martensite formation [15, 22].

Interesting results were further reported by Shen et al.

[15], who showed that different kinds of martensite can be

formed. Alpha prime martensite is mainly formed when

high loads are applied to the sample, e.g. loads greater than

the ultimate tensile strength, as for our samples D, E and F.

In contrast, e-martensite is observed when the loading is

less than about (rUTS - r0.2)/2, which is the case for our

samples B and C. As mentioned in the discussion of Fig. 5,

the texture of Fe-a0-martensite formation is different in our

SUS304 when it is loaded with more than or less than the

ultimate tensile strength (samples B and C vs. sample D).

This difference in texture may be attributed to the different

degree of martensite formation. In addition, for sample D,

the Fe-a0-martensite phases seem to be distributed mainly

in the twinning deformation zones, as evident from Figs. 4

and 5. It has been reported that mechanical twinning could

give a0-martensite resulting from uniaxial tensile tests at

room temperature [27], where the formation of the

mechanical twin structure was detected at a strain level of

e = 0.4 [27]. This result is similar to that for sample D (at

rUTS). Note that a Luders band front may have given sig-

nificant SMT because of the high initial dislocation density

especially in samples D and E [23], but this cannot be

clarified in the present study, and will be studied in the

future.

The Fe-a0 and Fe-c phases were further investigated

after the tensile tests. Figure 8 shows the orientation

imaging microscopy map recorded for sample F around the

notch and fracture surface (crack), and Fig. 9 shows the

variation of the area fraction of the Fe-a0 and Fe-c phases

as a function of the distance from the fracture surface. A

high concentration of the Fe-a0-martensite phase is detec-

ted near the crack, which could be a result of the high

plastic strain. The area fraction of the Fe-a0 phase

Crack surface

0.1mm α’-phase

γ -phase

Crack

Measurement zone

1mm

0.7 mm

Fig. 8 Orientation imaging microscopy map in the SUS304 stainless steels in the region of the crack surface (Color figure online)

0 1 2 3 4

0.1

0

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

Rat

e of

are

a fr

actio

n fo

r α

’-an

d γ -

phas

e

Distance from the crack surface, mm

γ -phase

α ’-phase

Fig. 9 Variation of the area fraction of Fe-a0 and Fe-c phase as a

function of the distance from the crack surface, obtained on the basis

of Fig. 8

6164 J Mater Sci (2013) 48:6157–6166

123

decreases in the area far away from the crack face. The

total area fraction of the Fe-a0 phase is almost the same as

that of the Fe-c phase in the area about 1.7 mm from the

crack face. In the study by Huang et al. [21] variation of the

area fraction of martensite was similarly examined, and

the area fraction of Fe-a0 and Fe-c phases was almost the

same in the area about 5 mm away from the fracture surface,

which is slightly different from our findings. This may be

attributed to the different specimen geometry, namely with

or without notches. An associated experiment was also

carried out by Nakajima et al. They investigated the

occurrence of SMT in SUS304 stainless steels after fatigue

tests (cyclic loading), but no clear SMT was detected in their

sample adjacent to fatigue cracks [28]. The reason behind

this may be the weaker plastic deformation, arising from the

high cyclic loading speed of 53 Hz.

Figure 10 displays the plastic strain distribution

obtained by finite element analysis. In this analysis, the

specimen was loaded to its ultimate tensile strength of

695.9 MPa, i.e. rUTS. This analysis reveals high plastic

strain in the sample adjacent to the notch owing to the high

stress concentration, and the plastic strain level decreases

in the area far away from the notch (Fig. 10). The value of

the plastic strain in area A0 (Fig. 10) is found to be about

48 %, and this value is relatively close to the experimen-

tally obtained strain level after loading with more than the

ultimate tensile strength, e.g. points E and F (Fig. 2). Note

that area A0 is the same area as that used for the EBSD

measurements (Fig. 1). This numerical approach suggests

that SMT in associated SUS304 stainless steels can occur

to a great degree when the sample is strained by more than

40 %.

Conclusions

A SMTs in SUS304 stainless steel near a notch was

examined using an electron backscattering diffraction

approach. The results obtained were as follows:

(1) Even if low strain at the r0.2 point occurs, a slight

increase of the Fe-a0-martensite fraction is obtained.

The total area fraction of the Fe-a0-martensite phase

at the rUTS point is almost the same as that at the r0.2

point. After loading at greater than rUTS (or

e [ 40 %), the area fraction of the Fe-a0 phase

increases dramatically, although the phase textures of

Fe-a0 and Fe-c are almost the same as at (rUTS - rf)/2.

In addition, the Fe-a0-martensite phase is formed over

almost the entire region at rf.

(2) The characteristics of the Fe-a0-martensite phase are

apparently different, depending on the sample. For

example, many tiny fractions of the Fe-a0 phase are

distributed in the un-twinning deformation zones

when the sample is subjected to a load of less than

(rUTS - r0.2)/2, whereas several Fe-a0-martensite

colonies are formed in the twinning deformation

zones when the load is greater than rUTS. In this case,

two main factors are observed to affect the Fe-a0-martensite phase: (i) twinning deformation and (ii)

severe plastic deformation. In particular, deformation

twinning is created around rUTS and severe plastic

deformation is detected before fracture.

(3) A high area fraction of the Fe-a0-martensite phase is

detected near the notch, but the area fraction of the

Fe-a0 phase decreases in the area far away from the

crack surface. The total fraction of the Fe-a0 phase is

almost the same as that of the Fe-c phase in an area

about 1.7 mm from the crack surface.

Acknowledgement This study was technically supported by Mr.

Yuki Sato at Akita Prefectural University in Japan.

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