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The influence of strain rate on the microstructure transition
of 304 stainless steel
A.Y. Chen
a,b
, H.H. Ruan
b
, J. Wang
b
, H.L. Chan
b
, Q. Wang
b
,Q.Li
c
,J.Lu
d,⇑
a
School of Material Science & Engineering, Shanghai Institute of Technology, 201400, People’s Republic of China
b
Department of Mechanical Engineering, The Hong Kong Polytechnic University, Hong Kong, People’s Republic of China
c
Physics Department, The Chinese University of Hong Kong, Hong Kong, People’s Republic of China
d
Department of Manufacturing Engineering and Engineering Management, City University of Hong Kong, Hong Kong, People’s Republic of China
Received 28 December 2010; received in revised form 4 March 2011; accepted 5 March 2011
Available online 28 March 2011
Abstract
In the top-down approach to tailor the microstructures of materials via plastic deformation, the strain rate plays a significant role.
This paper systematically investigates the deformation mechanisms of 304 stainless steel subjected to surface impacts over a wide range of
strain rates (10–10
5
s
1
). Based on comprehensive analysis of X-ray diffraction and electron microscopy observations, we found that the
strain rate between 10 and 10
3
s
1
only activated dislocation motions and a0-martensite transformations, resulting in nanocrystallines
and ultra-fine grains. However, higher strain rates (10
4
–10
5
s
1
) produced a high density of twin bundles with nanoscale thickness in
the bulk material. The transition from dislocation-mediated mechanism to twinning-mediated mechanism was interpreted in terms of
the magnitude of the applied stress, which was calculated from the explicit finite-element simulation with the use of the Johnson–Cook
model. A critical twinning stress, determined from the infinite separation of Shockley partials, renders the transition point. Deformation
twinning occurs when the applied stress exceeds this critical twinning stress. Larger stress leads to thinner and denser twin lamellae. Con-
versely, the stress below the transition point can only induce dislocation motions and a0-martensite transformations.
Ó2011 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.
Keywords: Austenitic stainless steels; Microstructure formation mechanism; Phase transformation; Deformation twinning; Strain rate
1. Introduction
Over the past decades, substantial grain refinement from
micrometer to submicrometer or nanometer scale has been
achieved by various technologies, leading to significant
improvement in strength of these materials over their
coarse-grained (CG) counterparts. These technologies can
be classified into top-down approaches and bottom-up
approaches. Severe plastic deformation (SPD) methods
are the main top-down approach used to produce ultra-
fined grains (UFG, d<1lm) and nanocrystalline grains
(NC, d< 100 nm) in bulk materials by exploiting large
plastic strains under low strain rates [1]. The grain-refine-
ment mechanisms of most SPD processes are principally
dislocation subdivision [2], twin fragmentation [3,4] and
phase transformation [5]. It is generally agreed that the
equilibrium grain size obtained via dislocation subdivision
is not on the nanometer scale (i.e. <100 nm) but generally
on the submicron scale. The twin fragmentation and phase
transformation of the materials with low stacking fault
energy (SFE) are supplementary mechanisms enabling fur-
ther refinement of grains to the nanometer scale [5].
Apart from SPD, another kind of top-down approach
involves surface nanostructuring, which includes shot peen-
ing [6], shock loading [7], laser shock processing [8], ballis-
tic impacting [9] and surface mechanical attrition treatment
(SMAT) [10]. In these processes, the surface layer of a
material is subjected to high-strain-rate deformation, pro-
ducing nanostructures on the surface and a high density
1359-6454/$36.00 Ó2011 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.
doi:10.1016/j.actamat.2011.03.005
⇑
Corresponding author.
E-mail address: jianlu@cityu.edu.hk (J. Lu).
www.elsevier.com/locate/actamat
Available online at www.sciencedirect.com
Acta Materialia 59 (2011) 3697–3709
of crystalline defects in the subsurface layers, resulting in a
much smaller plastic deformation than that produced by
SPD [11]. The nanostructuring mechanisms involved in
these techniques have been extensively discussed [8,12–
14]. For example, Zhang et al. [14] pointed out that the sur-
face nanostructures of AISI 304 SS after SMAT resulted
from planar dislocation arrays and twin–twin intersections.
Gray [15] observed microtwins in face-centered cubic Al–
Mg alloys after explosive loading at surface, which can
hardly be twinned under low strain rate due to the very
high SFE. These studies showed the preferential occurrence
of deformation twinning rather than dislocation slip at
higher strain rates.
Nanotwinned (NT) materials have been a focus of
research for their novel properties, such as good conductiv-
ity and thermal stability [16–19]. Recent discoveries have
shown that a high density of twins can not only promote
the subdivision of grains to the nanometer scale but also
can introduce significant strengthening [16,17]. These find-
ings shed light on a new way to enhance metallic material,
i.e. by introducing substantial twins. However, bulk NT
materials can only be produced by bottom-up approaches,
e.g. electrodeposition [16,17] in the form of thin-film. A
top-down approach is in practice more favorable since it
can produce bulk NT materials. Strain rate is then one of
the key factors. The present study of strain-rate effect spans
two extreme cases: either very low strain rates (smaller than
10 s
1
, e.g. SPD) or extremely high strain rates (larger than
10
5
s
1
, e.g. laser shock or blast loading). The effect of
moderate strain rate has not been investigated.
The main objective of this study is to provide an in-
depth understanding of the microstructural evolution and
deformation mechanism under a moderate range of strain
rates from 10 to 10
5
s
1
. Since deformation twinning and
dislocation slip are competitive mechanisms, understand-
ing the nature of the influence of strain rate on microstruc-
ture evolution becomes crucial for developing nanotwinned
or nanocrystallized materials [20]. The main objectives of
this study are: (i) to provide an in-depth understanding
of the microstructural evolution and deformation mecha-
nism over a wide range of strain rates, i.e. 10–10
5
s
1
;
and (ii) to establish a quantitative relationship between
strain rate and deformation mechanism, especially on the
slipping–twinning transition. AISI 304 stainless steel (SS)
sheet was used as the testing material. The effects of strain
rate on the formation of nanograins and nanotwins are
elaborated in Section 3, followed by a discussion of the
transition of the deformation mechanism from dislocation
slip to twinning in Section 4.
2. Experimental procedures
The chemical composition of AISI 304 SS is: 0.04 C,
0.49 Si, 1.65 Mn, 7.8 Ni, 16.8 Cr, 0.37 Mo and the balance
Fe (all in mass%). Both surfaces of 304 SS specimens
(70 mm 50 mm 1 mm) were treated by either low-
speed SMAT (SMAT-L) or high-speed SMAT (SMAT-
H), in which the average impact velocities of the balls are
about 0.5 and 10 m s
1
[21], respectively. Detailed process-
ing parameters are given in Table 1. In order to reflect the
macroscopic plastic strain of the material after SMAT, the
residual strain is defined by e¼4
3lnðV0
VfÞ, where V
0
and V
f
are the initial and final volume of the treated samples,
respectively [11]. To estimate the plastic strain rate induced
by ball impact, a simulation model has been developed and
applied to 304 SS. A detailed description was given in Refs.
[21–23].
The samples for the tensile tests were cut into dog-bone
shapes with a gauge length of 30 mm and a width of 6 mm,
and tested at room temperature at a strain rate of
6.7 10
4
s
1
. Four specimens were tested to confirm the
repeatability. X-ray diffraction (XRD) was performed to
determine the phase composition using a Philips Xpert
X-ray diffractometer with Cu Karadiation. The XRD
analyses were carried out along the cross-sectional direc-
tion. The samples were carefully prepared by mechanical
polishing from the surface to reach the desired depths.
The volume fraction of different phases was estimated from
the peak integrated intensities I
h,k,l
after background sub-
traction. The cross-sections of the specimens were etched
by 2 ml HF + 3 ml HNO
3
+95ml H
2
O and observed by
field emission scanning electron microscopy (SEM) using
a Hitachi S-4200 microscope. Transmission electron
microscopy (TEM) observations were made with a JEM
2010 microscope with an operating voltage of 200 KV.
Plane-view and cross-sectional TEM foils were prepared
in the same way as in Ref. [14] and ion-thinned at low tem-
perature. Since the treated specimens exhibited depth-
dependent microstructures, we used different approaches
to obtain quantitatively the distributions of grain size
and twin spacing. Specifically, for the SMAT-L sample,
the size of grain within the depth of 100 lm was measured
from dark-field TEM images. The sizes of the dislocation
cell (DC) and the CGs were respectively measured from
bright-field TEM images and SEM images for the other
regimes. For the SMAT-H sample, the spacing between
twin boundaries (k) was measured from dark-field TEM
images and high-resolution (HR) TEM images within the
depth of 200 lm and from bright-field TEM images and
Table 1
Processing parameters of SMAT.
Samples SMAT parameters
Vibrating frequency (Hz) Impact velocity (m s
1
) Ball material Diameter of ball (mm) Treatment time (min) Residual strain
SMAT-L 50 0.5 GGr15 8 40 0.07
SMAT-H 20,000 10 Bearing steel 3 15 0.2
3698 A.Y. Chen et al. / Acta Materialia 59 (2011) 3697–3709
SEM images for the other regimes. The twin density (TD)
at different depths was estimated by calculating the area
fraction of grains containing twins with k<1lm. The dis-
location density (DD) was measured from HRTEM images
with inverse Fourier transformation (IFT).
3. Microstructure
Multiple deformation mechanisms, such as dislocation
motion, twinning and phase transformation, can be trig-
gered in different strain-rate ranges in austenitic stainless
steel. In this paper, the SMAT-L sample is deformed under
strain rates ranging from 5 10
3
s
1
at the surface to
20 s
1
at the center. In contrast, the strain rate of the
SMAT-H sample varies from 1.2 10
5
to 2 10
4
s
1
.
The dominant deformation mechanism varies from disloca-
tion gliding to martensite transformation and then to
deformation twinning with increasing strain rate, which
resulted in the UFG and NC material in the SMAT-L sam-
ple and the nanotwins in the SMAT-H sample. In the fol-
lowing subsections, we shall elaborate the evidence of these
transitions.
3.1. The cross-sectional morphology
A remarkable distinction between the microstructures of
the SMAT-L and SMAT-H samples can be observed by
SEM after etching the cross-sections. The SMAT-L sam-
ple, as shown in Fig. 1a, exhibits non-uniform deformation
bands, densely arranged within a depth of 80 lm from the
surface, then quickly vanishing after another 70 lm. The
grains in the regime close to the surface are mainly UFG,
as shown in the inset of Fig. 1a. In contrast, the cross-sec-
tional morphology of SMAT-H sample exhibits a large
number of aligned shear bands inside grains with predom-
inant spacing much less than 1 lm, as shown in Fig. 1b. It
is worth emphasizing that these finely spaced shear bands
were abundant at all depths of the material, indicating
the efficiency of the SMAT-H process in altering the micro-
structure of the bulk stainless steel. It is further noted that
the shear bands can parallelly cut through the whole grains
(indicated by the solid arrow) or intersect at an angle of
about 70°(indicated by the dashed arrow). The differences
in the morphologies of the two samples imply that the
deformation mechanism changes with the change of strain
rate.
3.2. a0-Martensite transformation
Fig. 2 shows XRD patterns of the as-received, SMAT-
L and SMAT-H samples. The as-received 304 SS is pri-
marily composed of caustenite (fcc) and a small amount
of a0-martensite (bcc). The a0-martensite transformation
occurs in both SMAT-L and SMAT-H samples, as
shown in Fig. 2a and b, respectively. However, the
amount of a0-martensite differs significantly after the
two treatments, as shown in Fig. 2c. The a0-martensite
forms more easily during the low-strain-rate SMAT-L
process than during the high-strain-rate SMAT-H pro-
cess. The volume fraction of a0-martensite in the surface
of the SMAT-L sample is as high as 95%, as shown in
Fig. 2c, which is consistent with Ref. [14]. It is further
shown that the volume fraction of a0-martensite gradu-
ally reduces to the original value of about 6% at a depth
of 180 lm. However, the volume fraction of a0-martensite
in the SMAT-H sample is much smaller, varying from
about 23% at the surface to 6% at a depth of 150 lm.
It is therefore conjectured that the a0-martensite transfor-
mation is impeded by the SMAT-H process, which can
be attributed to the specific deformation mechanism
induced by the high strain rate.
3.3. Nanograins in SMAT-L sample
Nanograins formed on the surface of the SMAT-L
sample (Fig. 3a) are a0-martensite with random crystallo-
graphic orientations, indicated by the corresponding
selected-area diffraction pattern (SAED) shown in
Fig. 3b. Fig. 3c shows that the surface grain size is in
the range of 2–100 nm, and the mean grain size is
approximate 10 nm. At a depth of 50 lm from the
surface, both a0-martensite phase and c-austenite phase
Fig. 1. Cross-sectional SEM observations of (a) SMAT-L and (b) SMAT-H samples.
A.Y. Chen et al. / Acta Materialia 59 (2011) 3697–3709 3699
are observed, as illustrated in Fig. 3d–g. This result is
consistent with the XRD analysis. Fig. 3e and f are
dark-field TEM images diffracted from the spots “B”
and “C”in the SAED pattern in Fig. 3d, showing the
equiaxed grains of a0-martensite and c-austenite, respec-
tively. The mean grain size of a0-martensite is about
60 nm, much smaller than that of the c-austenite
(200 nm), as shown in Fig. 3g. The nanosized a0-martens-
ite is still the primary component at this depth. However,
the larger c-austenite grains are uniformly distributed
among them, resulting in a bimodal grain size distribu-
tion. It is noted that no other phase can be observed
under TEM and XRD, indicating that only c!a0trans-
formation occurs in SMAT-L sample. In comparison, the
surface microstructures of the SMAT-H sample are
shown in Fig. 4. Both a0-martensite and c-austenite
phases can be identified in Fig. 4a. Nevertheless, both
the mean grain sizes and distribution ranges, as summa-
rized in Fig. 4b, are much larger than those of the
SMAT-L sample. Combined with the XRD analysis,
the above comparison indicates that the higher strain
rate is not effective in reducing grain size due to hinder-
ing effect of the a0-martensite transformation, but is nev-
ertheless the main mechanism producing nanograins in
the SMAT-L sample.
With increasing depth, the grain size of the SMAT-L
sample gradually increases from a few nanometers to hun-
dreds of nanometers within 150 lm. At depths of 150–
350 lm, a large number of DCs with a high density of tan-
gled dislocations is observed in most grains, as shown in
Fig. 5. Some microtwins can also be found at depths of
200–300 lm, but the number of microtwins is small in com-
parison with that of the DCs. To recapitulate, the micro-
structures of the SMAT-L sample are characterized by a
multi-modal grain size distribution with a dual-phase struc-
ture. For the whole thickness, the volume fraction of NC
and UFG material is about 30%; CGs with submicron-
sized DCs comprise the remaining volume.
3.4. Nanotwins in the SMAT-H sample
In contrast to the NC/UFG structure of the SMAT-L
sample, the SMAT-H sample possesses more complex
microstructures, which are primarily austenite nanotwins
as well as a small fraction of a0-martensite and e-martensite
(hcp). Fig. 6a is a bright-field TEM image revealing a large
number of deformation twins at a depth of 50 lm. These
deformation twins mostly nucleate from grain boundaries
and grow into the grain interior. Some of them do not
transect the entire grain but terminate in the grain interior.
Fig. 6c shows the magnification of the circled area in
Fig. 6a. The SAED pattern of Fig. 6c, indexed in Fig. 6b,
shows composite diffractions of c-austenite, twin, e-mar-
tensite and a0-martensite with the zone axis ½
110c==
½1
10twin==½11
20e==½1
11a0:This orientation relationship
is the well-known Kurdjumov–Sachs (K–S) relationship.
The dark-field images in Fig. 6d–f are obtained from diffrac-
tion spots “1”,“2”and “3”in Fig. 6b, showing the mor-
phologies of nanotwins, e-martensite and a0-martensite,
respectively. Fig. 6d shows dense bundles of nanoscale
twins with large numbers of dislocations. Statistical mea-
surements indicate that the twin thickness kvaries between
2 and 50 nm, with an average value of about 20 nm, as
shown in the inset of Fig. 6d. These NT structures are
found in most grains. Fig. 6e shows e-martensite platelets
of very small thickness (45 nm). It is identified that the
impact-induced {0 0 0 1} habit plane of e-martensite phase
matches the orientation relationship ½11
20e==½
110c. The
Fig. 2. (a and b) XRD patterns of the as-received, SMAT-L and SMAT-H samples, respectively; (c) phase content at different depths of the SMATed
samples.
3700 A.Y. Chen et al. / Acta Materialia 59 (2011) 3697–3709
morphology of a0-martensite can be classified into two
types, as indicated in Fig. 6f. The first type comprises
martensite laths of submicron thickness distributed along
twin lamellae (marked by a01). The second is island-shaped
a0-martensite inside twin lamellae (marked by a02). These
a0-martensite islands originate from the fragmentation of
deformation twins. In studying the high-strain-rate
compression of stainless steel, Staudhammer et al. [24]
designated both types of a0-martensite as stress-assisted
martensite, whose shape is different from that of strain-
induced material. The statistical distribution of the thick-
ness of a0-martensite lath is given in the inset of Fig. 6f.
The average thickness is about 120 nm. In the subsurface
layer of SMAT-H sample, e-martensite and a0-martensite
phases are found, and we speculate that the deformation
mechanisms occurring in this layer are mainly deformation
Fig. 3. Nanostructures of the SMAT-L 304 SS: (a) bright-field TEM image; (b) selected-area electron diffraction (SAED) pattern; (c) statistical
distribution of grain size on the surface, respectively. (d)–(g) Nanostructure at a depth of 50 lm from the surface: (d) bright-field TEM image and SAED
pattern; (e and f) dark-field TEM images corresponding to the diffraction zone marked “B”and “C”in the SAED pattern of (d), respectively. (g) Statistical
distribution of grain size of a0-martensite and c-austenite phase, respectively.
A.Y. Chen et al. / Acta Materialia 59 (2011) 3697–3709 3701
twinning, followed by some c!etransformation and
twin !atransformations.
In order to investigate the details of nanotwins and nano
e-martensite, HRTEM observations of the outlined region
in Fig. 6c are shown in Fig. 7.Fig. 7a shows that the twin is
composed of several atomic layers about 11 nm thick. As
indicated in the inset of Fig. 7a, strong diffraction spots
appear with respect to the {1 1 1} plane, and diffuse spots
in the [1 1 1] direction, indicating the formation of defor-
mation twins and stacking faults on the {1 1 1} plane.
The corresponding inverse Fourier transform (IFT) image
(Fig. 7b) exhibits high-density dislocations inside the nano-
twin lamellae and at twin boundaries, which is distinct
from the growth twin structure where less dislocation exists
[17]. Some of these dislocations are found to be Shockley
partial dislocations. A twinning mechanism by partial dis-
location dissociation has been predicted by molecular
dynamics simulations in nanocrystalline Al [25] and exper-
imentally evidenced in nanocrystalline aluminum [26] and
copper [27].Fig. 7c and the associated IFT image
(Fig. 7d) show the coexistence of e-martensite grains, twin
lamellae and stacking faults. The e-martensite phase is not
detected in the XRD patterns of the SMAT-H sample,
since they are exceptionally small and scarce. The TEM
image and HRTEM images clearly reveal that e-martensite
platelets are a few nanometers in size. The e-martensite
platelets and deformation twins are formed by different
stacking sequences of stacking faults on close-packed
planes. The change in stacking sequence of the close-
packed (1 1 1) planes from ABCABC to ABABAB is
achieved by passing partial Shockley dislocations of Bur-
gers vector 1=6½11
2con every two (1 1 1)
c
planes [28].
The sequence of stacking faults is irregularly overlapped
at first and then changes gradually to the regular sequence.
Correspondingly, the diffraction pattern changes from fcc
matrix to broadened streaks first, and then to the pro-
nounced intensity maxima appearing on these streaks. This
procedure is clearly shown in Fig. 7e–g, where the SAED
patterns and IFT images are taken at square regions
“A”,“B”and “C”in Fig. 7c, respectively. The above
Fig. 4. Microstructures of the SMAT-H 304 SS at surface: (a) bright-field TEM; (b) SAED pattern; (c) statistical distribution of grain size.
Fig. 5. (a) Bright-field TEM images and the SAED pattern of the SMAT-L samples at a depth of 300 lm, showing the UFG dislocation cells (DCs). (b)
Grain size/DC distribution in the SMAT-L sample.
3702 A.Y. Chen et al. / Acta Materialia 59 (2011) 3697–3709
observations show that the deformation twinning is usually
accompanied by e-martensite transformation at high strain
rates, corroborating the c!nanotwin/e-martensite !a0-
martensite transformation sequence occurring in the
SMAT-H sample, in contrast to the direct c!a0-martens-
ite transformation observed in the SMAT-L sample.
Intersections of two twinning systems are also observed
at large depths. A typical twin–twin intersection observed
at a depth of 300 lm is shown in Fig. 8a, in which the
angle between the primary and the conjugate twins is
70.5°, corresponding to the simple shear sliding of a=ffiffiffi
2
p
in the ½
110plane. The overall microstructure of
SMAT-H sample features the high density of twins in
the entire thickness of the sheet with kfrom a few nano-
meters in the subsurface to hundreds of nanometers in the
center. A large number of dislocations were also found
associated with these deformation twins. They are also
the deformation byproduct, which can on the one hand
assist the formation of twins and on other hand impede
twin growth, as will be discussed in Section 4.2. The cru-
cial structure parameters of the twinned materials, i.e. dis-
tributions of the twin thickness kand the twin density
(TD), are shown in Fig. 8b. The value of kvaries from
20 nm at a depth of 50 lm to about 350 nm in the center.
Fig. 6. TEM images of SMAT-H sample at 50 lm depth: (a) bright-field TEM; (b) SAED pattern and indexed pattern, showing the e-martensite (hcp), a0-
martensite (bcc), and twin (fcc) with the zone axis of ½
110c==½1
10twin==½11
20e==½1
11a0; (c) bright-field TEM of the magnification of the circle regime in
(a); (d)–(f) dark-field TEM images, corresponding to the diffraction patterns “1”,“2”and “3”in (b), respectively; The insets of (d)–(f) are the statistical
distribution of lath thickness of a0-martensite phase, e-martensite phase and twins.
A.Y. Chen et al. / Acta Materialia 59 (2011) 3697–3709 3703
Correspondingly, the twin density varies from about 65%
at a depth of 50 lm to 40% in the center. Similar nano-
scale twins were observed in various steels after other
mechanical processes, such as laser-shocked 304 SS, ECA-
Ped 316L SS and cold-worked austenite steel [8,29,30].
However, the deformation twins produced by the present
high-strain-rate process have the smallest thickness and
the largest density, which spreads to all the depths of
the bulk material.
3.5. Mechanical properties
Mechanical properties are the embodiment of a mate-
rial’s microstructure. Corresponding to the depth-
dependent microstructures discussed above, we investigated
the depth-dependent hardness, which is summarized in
Fig. 9a for both SMAT-L and SMAT-H samples. The max-
imum hardness of the SMAT-L specimen is 502 MPa at the
surface, which is mainly attributed to the strengthening of
Fig. 7. HRTEM images of the SMAT-H sample at a depth of 50 lm from surface: (a and b) HRTEM image and the corresponding inverse Fourier
transformation (ITF) image viewed from the [011] zone axis, showing deformation nanotwins and dislocations inside the twin; (c and d) HRTEM image
and the corresponding ITF image viewed from the [011] zone axis, showing deformation nanotwins and e-martensite, indicated by white lines and orange
lines, respectively; (e)–(g) high magnification of the rectangle A, B, C in (c), showing the austenite, twin and e-martensite, respectively.
3704 A.Y. Chen et al. / Acta Materialia 59 (2011) 3697–3709
nanograins, especially the nanosized a0-martensite grains.
The microhardness then decreases to the original value of
the as-received 304 SS (200 MPa) at a depth of 180 lm
due to the decrease in volume fraction of the a0-martensite
and the increase in grain size. This result is consistent with
the microstructures of the SMAT-L steel. However, for the
SMAT-H sample, since the deformation twins remain
abundant even in the middle layer, the whole bulk material
was notably strengthened and the microhardness varies
from 495 MPa at the surface to about 274 MPa at the
center.
Fig. 9b shows the tensile curves of the as-received,
SMAT-L and SMAT-H samples. In most cases, the mate-
rials processed by SPD exhibit very high strength but gen-
erally low ductility regardless of processing temperature
[1,30,31]. However, with our process, a good combination
of high yield strength and high ductility has been achieved,
which is most likely due to the higher strain-hardening
capacity, as shown in the inset of Fig. 9b. The superior
mechanical properties can be attributed to the complex
microstructure induced by the SMAT processes, such as
the bimodal grain size distribution as shown in Figs. 5b
and 8b. In this case, the nanosized grains provide the very
high strength, while the micronsized grains provide the sig-
nificant strain-hardening capacity through dislocation pile-
up as discussed in Refs. [32,33].
It is noted that the SMAT-H sample is stronger than the
SMAT-L sample, which is in agreement with the hardness
result. The reason for this difference between the SMAT
materials is that the SMAT-H process can induce large
numbers of deformation twins at all depths of the material,
whereas the SMAT-L process can only affect down to
180 lm. The deformation twins induced by the SMAT-H
process play a similar role as grain boundaries in blocking
dislocation motions [16,17]. Thus the more abundant and
finer the twins, the higher the strength.
4. Discussions
Table 2 summarizes the microstructures and deforma-
tion mechanisms produced by the two SMAT process.
From the above microstructure analysis, we note that: (i)
deformation twinning is predominant at strain rates of
10
4
–10
5
s
1
; (ii) a0-martensite transformation can be
Fig. 8. (a) Bright-field TEM images and the corresponding SAED pattern of the SMAT-H samples at a depth of 300 lm, showing the intersection of
twins; (b) twin density and kdistributions in the SMAT-H sample.
Fig. 9. Mechanical properties of the SMAT samples and as-received 304 SS: (a) hardness distribution with depth; (b) engineering stress–strain curves. The
inset shows true stress–strain curves.
A.Y. Chen et al. / Acta Materialia 59 (2011) 3697–3709 3705
retarded at high strain rates; (iii) the dislocation subdivi-
sion can only achieve UFG, and the a0-martensite transfor-
mation is necessary to obtain nanograins (d< 100 nm). In
the following, we seek an interpretation of this strain-rate
effect by assuming that different deformation mechanisms
are induced by different stress levels.
Christian and Mahajant [7] postulated that the necessary
condition for deformation twinning in fcc metals is that the
local stress resulting from stress concentration should be ele-
vated to levels higher than the critical twinning stress (CTS).
Byun et al. [34] examined the relationship of the equivalent
stress and the deformation-induced microstructure in 316
LN stainless steels by using a disk-bend method. The exper-
imental and theoretical results demonstrated that austenitic
steels deform by twinning when a sufficiently high stress (i.e.
larger than CTS) can be reached irrespective of which load-
ing method is used [31,35–37]. The CTS can be achieved by
dynamic strain aging, large plastic strain and/or high strain
rate [18,34]. Although the existence of the CTS for fcc mate-
rial has been well recognized, the tendency to substitute
twinning for slip, and the actual magnitude of the twinning
stress, has been less studied, especially the strain-rate depen-
dence of twinning stress.
4.1. Critical twinning stress
The occurrence of dislocation substructures and twins is
influenced by the width of partial dislocation separation
caused by the resolved shear stress s[29,35,37]. Dissocia-
tion of a perfect dislocation on {1 1 1} plane into two
Shockley partial dislocations can be expressed as
a
2½1
10¼a
6½2
1
1þa
6½1
21, where a
2½1
10,a
6½2
1
1and
a
6½1
21are the Burgers vectors of the perfect, the leading
and the trailing partial dislocations, respectively. Byun
[35] showed that in low-SFE materials, the equilibrium sep-
aration distance wof Shockley partials depends on the SFE
c
SFE
and the shear stress s, which is given by:
w¼Gb2
p
pð2rSFE sbpjsin h2sin h1jÞ
cos h1cos h2þsin h1sin h2
ð1vÞ
;ð1Þ
where b
p
is the value of the Burgers vector of a Shockley
partial dislocation, Gis the shear modulus, vis Poisson’s
ratio, h
1
and h
2
are respectively the angles of the Burgers
vectors of the leading and trailing partial dislocations
referring to the Burgers vector of the perfect dislocation.
Eq. (1) indicates that the width of a stacking fault in-
creases with increasing shear stress and approaches infin-
ity when the shear stress exceeds a critical value. This
situation corresponds to the scenario that only the lead-
ing partial dislocations emit from the highly stressed re-
gion, which is the necessary condition for deformation
twinning. Therefore, the stress for the infinite separation
of Shockley partials can be regarded as the CTS, which
satisfies:
ð2rSFE sCTS bpjsin h2sin h1jÞ ¼ 0:ð2Þ
Since the resolved shear stress sis maximized when the
angles h
1
and h
2
are 30°and 30°, respectively, corre-
sponding to perfect dislocation dissociation on the
{1 1 1} plane [37], the CTS is simplified by:
sCTS ¼2cSFE
bp
:ð3Þ
By assuming an average Schmid factor 0.326 for poly-
crystalline stainless steel, the critical equivalent stress (r
T
)
for twinning can be given by:
rT¼6:13 cSFE
bp
:ð4Þ
For the 304 stainless steel (c
SFE
=16mJm
2
,and
b
p
=0.147 nm), Eq. (4) predicts the critical equivalent
stress for twinning to be about 584 MPa. The exact critical
Table 2
Microstructure characteristics of the SMAT-L and SMAT-H samples.
Sample Depth (lm) SR
a
(10
4
)RS
b
(10
2
)DD
c
(10
16
m
12
) TEM microstructures Deformation mode
SMAT-L 0 0.4 1.0 35 Nano a0c!a0
50 0.5 1.7 40 Nano a0(P
d
), nano cc!dislocation
100 0.01 1.3 23 UFG c(P), UFG a0, pile-up
dislocation
c!twin
300 0.002 0.4 – Tangled dislocations (P), twins,
SMAT-H 0 9 5.3 5 UFG c(P), UFG a0, pile-up
dislocation
c!twin
50 12 6.6 2 Nanotwins (P), nano a0, nano e,
tangled dislocation
c!a0
c!e
100 7 6.8 2 Nanotwins (P), nano a0, nano e,
tangled dislocations
c!twin !a0
c!e!twin
300 2 4.2 – UFG twins (P), nano e, tangled
dislocations
c!dislocation
a
SR, Strain rates.
b
RS, Residual strain.
c
DD, Dislocation density.
d
P, Primary constituent.
3706 A.Y. Chen et al. / Acta Materialia 59 (2011) 3697–3709
equivalent stress should vary with Schmid factor for differ-
ent slip systems [38]. When the resolved shear stress reaches
CTS, the slipping–twinning transition occurs.
To quantitatively analyze the stress experienced by the
material during SMAT, the empirical rate-sensitivity John-
son–Cook model [39] was adopted:
rT¼½AþBen1þCln
_
e
_
e0
;ð5Þ
where r
T
is equivalent stress, eis equivalent plastic strain, _
e
is plastic strain rate, _
e0is the reference strain rate for a qua-
si-static test, nis the work-hardening exponent, and A,B,C
and mare constants. The parameters for 304 SS are
A= 300 MPa, B= 1.477 MPa, n= 0.72, C= 0.02,
_
e0¼103[22,23]. We established an axisymmetric model
and simulated the normal impact of a rigid ball onto the
sample surface. The contour maps of equivalent stresses
are plotted in Fig. 10a and b for SMAT-L and SMAT-H
processes, respectively. The equivalent stress in the
SMAT-L sample is in the range of 280–560 MPa, as shown
in Fig. 10a, which is lower than the critical equivalent stress
for deformation twinning. However, the equivalent stress
in the SMAT-H sample is apparently higher than the crit-
ical equivalent stress. The equivalent stress is as high as
1 GPa to a depth of 50 lm and then gradually decreases
to 590 MPa in the center, as shown in Fig. 10b. The exper-
imental observation matches the theoretical calculation,
confirming that our estimation of critical twinning stress
is reasonable. Comparing the stress distribution (Fig. 10)
with the TEM observations (Figs. 5–8), the deformation
mechanisms may be correlated to the stress level as: (i) dis-
location slip is dominant at the equivalent stress lower than
400 MPa (corresponding to strain rates smaller than
10
2
s
1
); (ii) a0-martensite transformation is activated in
the stress range of 400–560 MPa (corresponding to strain
rates of 10
2
–10
3
s
1
); and (iii) deformation twins are initi-
ated at stresses higher than 584 MPa (corresponding to
strain rates larger than 10
4
s
1
). Since the plastic strain in
the SMAT process is very small, as given in Table 1, much
smaller than that of SPD processes, we shall consider that
these stress levels are mainly attributed to the different
strain rates.
4.2. Critical twinning nucleus size
Formation of stable deformation twins comprises nucle-
ation of twin embryos and their subsequent growth when
the applied stress is larger than the CTS. The critical twin
nucleus thickness, k
c
, depends on the twin boundary energy
(c
TB
) and the driving stress of twin nucleation. The relation
between k
c
and the equivalent stress is given by [20,36]:
kc¼5p
4
GcTB
r2
T
:ð6Þ
Eq. (6) indicates that the twin nucleus size is inversely
proportional to the stress. Due to the uncertainties of
c
TB
, we select values of c
TB
in the range of 2c
SFE
–10c
SFE
as introduced in Ref. [36]. Comparing the nucleus size with
the experimentally measured twin size, as shown in Fig. 11,
can be seen that the measured kis close to k
c
at high stress
but considerably deviates from k
c
at low stress. Venables
[40] pointed out that the resistance to twin growth increases
with the dislocation density. Therefore larger dislocation
density leads to thinner twins. It is observed that the dislo-
cation density in the SMAT-H sample is 2510
16
m
2
up to a depth of 100 lm (shown in Table 2), even higher
than that produced by other SPD processes [11,41]. Such
high dislocation density may impede the growth of twins.
In addition, larger strain rates usually imply smaller life-
times [21], limiting the time for the growth of twins. The
spatial and temporal limitation under high strain rates
results in a very small twin thickness. Conversely, for the
lower strain rate and smaller stress, the twin nucleus has
plenty of room and time to grow, resulting in an increase
in the difference between the measured twin thickness and
the calculated thickness of the twin nucleus shown in
Fig. 11.
Moreover, it should be noted that the twin lamellae are
so fine that no further fragmentation of the deformation
twins occurs. Most of the nanotwins were simply parallel
Fig. 10. Contour map distributions of equivalent stress in (a) SMAT-L and (b) SMAT-H samples.
A.Y. Chen et al. / Acta Materialia 59 (2011) 3697–3709 3707
aligned in the gains. In previous reports, deformation twins
play a significant role in refining grains via the interactions
of twin bundles and dislocations, resulting in the formation
of nanograins, as evidenced in dynamically plastically
deformed copper [4] and ECAPed SS [5]. In our case, the
high density of nanotwins remains stable during the
SMAT-H process. The preservation of nanotwins is attrib-
uted to the high strain rate, large dislocation density and
very small strain. As discussed above, the high strain rate
induces much finer twin lamellae and a larger twin density,
resulting in nanotwin stability. However, the almost strain-
free deformation caused by SMAT may be the most impor-
tant reason for the formation of nanotwins instead of NC
grains since no obvious macroscopic plastic deformation
cuts the twin lamellae, which is the fundamental difference
from the large strain in the SPD processes.
4.3. Nanocrystalline formation
An obvious strain rate effect on the refinement of initial
CG to NC and UFG microstructures occurs at strain rates
of 10–10
3
s
1
. Two mechanisms operate: (i) dislocation
activities, such as accumulation, interaction, tangling and
spatial rearrangement; and (ii) a0-martensite transforma-
tion. With mechanism (i), refinement of CG is dominated
by dislocation slip to form various dislocation structures,
including DCs, walls and geometrically necessary bound-
aries [4,41]. The DCs gradually transform into subgrains
with the eventual grain size determined by the DC size.
The size of DC (d
DC
) depends upon the shear stress (s)
according to [41]:
dDC ¼KGb
ðss0ÞKGb
sKGb
0:326 rT
;ð7Þ
where Kis a constant (normally taken as 10) [41], and s
0
is
the internal frictional resistance to the relative sliding of
atomic layers. The d
DC
is calculated to be 0.8–1.6 lm when
the applied external stress varies from 560 to 280 MPa.
This means that grains resulting from dislocation activity
cannot be finer than 0.8 lm. Therefore, a0-martensite trans-
formation must operate to produce finer grains. Figs. 2, 3
and 8a show that 70% of nanosized grains (d< 100 nm)
are a0-martensite in the SMAT-L sample. This result sug-
gests that a0-martensite transformation is more effective
in refining grains down to the nanometer scale. The
stress-mediated a0-martensite transformation requires the
assistance of dislocation pile-up [34]. At a limited strain,
a sufficient density of dislocations should be induced by
large strain rates. Up to a depth of 100 lm in the SMAT-
L sample, the dislocation density is 2.3–4 10
17
m
2
,
which is even larger than that of other nanocrystalline met-
als,—for example, the dislocation density is about 10
10
m
2
in shock-loaded 316L SS and about 10
15
m
2
in Cu after
multiple impacts at low temperature [11,41]. Such high dis-
location density promotes the a0-martensite nucleation to
form nanograins. However, the a0-martensite transforma-
tion is retarded by the further elevated strain rate, as ob-
served in the SMAT-H sample. This can partly be
attributed to the elevated temperature in the high-strain-
rate deformation [42]. A similar phenomenon was also
found by strain-controlled tensile testing [43,44]: the a0-
martensite transformation occurred at smaller strains with
higher strain rates and then diminished as the strain rate in-
creased further. In the strain-controlled quasi-static tensile
test, a0-martensite transformation occurs at a stress of over
400 MPa after significant strain hardening [42,43]. This
indicates that the critical stress for the nucleation of a0-
martensite must be around 400 MPa under either the
stress-mediated or the strain-mediated process. For 304
SS at zero plastic strain, this stress corresponds to a strain
rate of 10
2
. In noting that a strain rate larger than 10
4
leads
to nanotwins, we conclude that strain rates of the order of
10
2
–10
3
are the most effective way to induce a0-martensite
transformation and nanograins.
5. Conclusions
The influence of strain rate on microstructure and
mechanical properties of the 304 SS are systematically
investigated. The transition from dislocation slip to defor-
mation twinning is analyzed. The results are summarized as
follows:
(1) Deformation mechanisms via c!twin, c!a0and
c!ehave been observed under high strain rates of
10
4
–10
5
s
1
, and deformation twinning is dominant.
In contrast, dislocation activities and the direct
c!a0transformation are the dominant deformation
mechanisms under lower strain rates of 10–10
3
s
1
.
(2) An analytical model is proposed to calculate the crit-
ical twinning stress, which is 584 MPa for 304 SS,
corresponding to a strain rate of 10
4
s
1
. By compar-
ing the stress distributions obtained by finite-element
simulation and the microstructure observation, it is
confirmed that the critical twinning stress accurately
Fig. 11. The dependence of critical twin thickness (k
c
) and twin density
with equivalent stress in the SMAT-H sample.
3708 A.Y. Chen et al. / Acta Materialia 59 (2011) 3697–3709
delineates the transition from dislocation slip to
deformation twinning. We further conjecture that
a0-martensite transformation occurs in a medium
stress range of about 400–500 MPa (corresponding
to strain rates of 10
2
–10
3
s
1
). If the equivalent stress
is lower than 400 MPa, dislocation activities are
dominant.
(3) If the applied stress is much larger than the CTS,
which can be achieved with a sufficiently high strain
rate (say 10
5
s
1
), a large density of deformation
twins with thicknesses as small as 20 nm can be pro-
duced. These nanoscale twins do not grow after
nucleation owing to spatial and temporal limitations.
Therefore, the thickness of these nanotwins agrees
with the theoretical estimate of the size of the twin
nucleus.
(4) Dislocation activities can only form UFGs and/or
ultra-fine DCs, while a0-martensite transformation
forms nanoscale grains. For a limited plastic strain,
a strain rate in the range of 10
2
–10
3
s
1
can produce
a very large dislocation density (about 10
17
m
2
),
leading to a large number of nucleation sites for a0-
martensite transformation. Nevertheless, the higher
strain rate tends to impede a0-martensite transforma-
tion due to deformation twinning.
Acknowledgements
The authors are grateful to the Research Grant Council
(RGC) for the financial support of grant number CityU8/
CRF/08 and the Hong Kong Innovation and Technology
Commission (ITC) for financial support of the research
project (No. ITP/004/08NP).
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