Dynamic interactions of twinning, grain boundaries, and dislocation in deformed body-centered cubic iron under high strain rates

Abstract

Understanding of dynamical responses and mechanical characteristics of metals and alloys at high strain rates holds significant importance in fundamental physics and optimizing the performance capabilities of materials. During high-speed impact scenarios, materials may be subjected to high pressure and plastic deformation, which have the potential to modulate their mechanical attributes. In this study, high-speed planar impact experiments were conducted to investigate the progressive alterations in the microstructures and mechanical properties in coarse-grain body-centered cubic (bcc) iron subjected to high-strain-rate (approximately 2.60–3.89 × 10⁶ s⁻¹) impact reaching approximately 15 GPa in a one-stage light-gas gun. The nanoindentation tests show that the nano-hardness of the post-shock iron improves 1.5 times from approximately 1.75–2.70 GPa. Microscopic analyses of the post-shock bcc-iron show no significant grain refinement but a noticeable increase in the twin boundaries (TBs) and low angle grain boundaries (LAGBs) proportion with increasing shock pressure. Therefore, the interaction between TBs, LAGBs, and dislocations in post-shock iron grains plays an important role in mediating its mechanical properties. Our findings serve as possible guidance for exploring the mechanical properties of single-crystalline and poly-crystalline iron-based materials, such as steel, with optimized mechanical performance.

Full text

Dynamic interactions of twinning, grain
boundaries, and dislocation in deformed
body-centered cubic iron under high strain rates
Cite as: J. Appl. Phys. 135, 155102 (2024); doi: 10.1063/5.0193215
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Submitted: 21 December 2023 · Accepted: 31 March 2024 ·
Published Online: 17 April 2024
Canlian Tang,
1
Bo Gan,
1
Yukai Zhuang,
1
Zhipeng Gao,
2
and Youjun Zhang
1,3,a)
AFFILIATIONS
1
Institute of Atomic and Molecular Physics, Sichuan University, Chengdu 610065, China
2
China Academy of Engineering Physics, Institute of Fluid Physics, Mianyang 621900, China
3
Key Laboratory of High Energy Density Physics and Technology of Ministry of Education, Sichuan University,
Chengdu 610065, China
a)
Author to whom correspondence should be addressed: zhangyoujun@scu.edu.cn
ABSTRACT
Understanding of dynamical responses and mechanical characteristics of metals and alloys at high strain rates holds significant importance
in fundamental physics and optimizing the performance capabilities of materials. During high-speed impact scenarios, materials may be
subjected to high pressure and plastic deformation, which have the potential to modulate their mechanical attributes. In this study, high-
speed planar impact experiments were conducted to investigate the progressive alterations in the microstructures and mechanical properties
in coarse-grain body-centered cubic (bcc) iron subjected to high-strain-rate (approximately 2.60–3.89 × 10
6
s
−1
) impact reaching approxi-
mately 15 GPa in a one-stage light-gas gun. The nanoindentation tests show that the nano-hardness of the post-shock iron improves
1.5 times from approximately 1.75–2.70 GPa. Microscopic analyses of the post-shock bcc-iron show no significant grain refinement but a
noticeable increase in the twin boundaries (TBs) and low angle grain boundaries (LAGBs) proportion with increasing shock pressure.
Therefore, the interaction between TBs, LAGBs, and dislocations in post-shock iron grains plays an important role in mediating its mechan-
ical properties. Our findings serve as possible guidance for exploring the mechanical properties of single-crystalline and poly-crystalline
iron-based materials, such as steel, with optimized mechanical performance.
© 2024 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution (CC BY) license
(https://creativecommons.org/licenses/by/4.0/). https://doi.org/10.1063/5.0193215
I. INTRODUCTION
Severe plastic deformation can induce lattice distortion, which
subsequently causes alterations in the microstructures of metals.
These modifications encompass the processes of grain refinement
and the incorporation of structural imperfections, such as twins, tex-
tures, and dislocations.
1–3
These refined grains and defects possess
the capability to modify the hardness, corrosion resistance, and other
exceptional mechanical properties of metals.
4,5
As a result, grain
refinement, surface defects between two adjacent grains, and twins
can play a crucial role in influencing the plastic deformation behavior
and mechanical characteristics of materials.
6–8
Numerous studies
have indicated that metals can be strengthened by grain refinement.
9
Nevertheless, the effects of defects in metals, including TBs, LAGBs,
and dislocations, on their mechanical behavior remain limited and
constrained, thereby impeding a comprehensive understanding of
the microstructure–property relationship in metals.
For bcc metals and alloys, the deformation twin is known as
an extreme deformation mode that occurs when dislocations are not
enough to carry the plastic strain.
10–12
Twinning is a typical mode
of strain energy relaxation with a unique displacive manner as com-
pared with dislocation slip. Many dislocations can lead to a reduc-
tion in the static strength of metals. Meanwhile, TBs can hinder
dislocation motion and, thus, act as stable interfaces for strengthen-
ing metals.
13,14
As an important deformation mode that competes
with dislocation slip, TBs in metals can also enhance the properties
of metals, such as strength, hardness, and ductility, due to their
minimal grain boundary energy.
14–17
Therefore, we chose a typical
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bcc transition metal, iron (Fe), to investigate how interacts between
its twins, grain boundaries, and dislocations in the grains during
deformation without grain refinement under high strain rates.
18
Iron, the most abundant transition metal on the Earth and a
primary constituent in the cores of terrestrial planets
19,20
holds
considerable significance in industrial applications due to its excep-
tional ductility, high strength, ease of alloying, and magnetism.
21–23
Extensive studies have been conducted to investigate the physical
and mechanical properties of iron under extreme pressure–temper-
ature conditions.
24–26
One of the important investigations focuses
on comprehending the relationships between microstructures and
bulk mechanical properties of iron subjected to severe plastic defor-
mation, which holds great significance in the development of new
advanced materials.
Because of the high stacking fault energy, it is challenging to
generate twins in bulk bcc iron via the growth methods or mechan-
ical deformation strategies.
27
Most experimental investigations on
deformation twins have primarily focused on alloys and nanoscale
bcc metals.
28–30
The studies on twins in pure bcc metals, however,
have mainly emphasized theoretical approaches.
12,28,31
Dieter
32
reported that the density of deformation twins increases in shocked
iron as the strain rate intensifies. Then, dynamic deformation twin-
ning is observed in shock-deformed bcc-iron,
33
where the volume
fraction of twins monotonically increases from 0 to about 4%. It is
interesting to note that plasticity is not primarily influenced by
twinning when the shock pressure is below 25 GPa.
34
High strain
rate impact experiments have been proven to be an effective tech-
nique for generating twinning in bcc metals. However, the
FIG. 1. (a) Schematic diagram of shock experiments by planar impact; (b) the SEM map of the initial sample; (c) XRD patterns of the starting and recovered iron from
shock compression; (d) typically particle velocity profile measured at the free surface of iron under planar impact of approximately 613 m/s by Fe flyer, where the final pres-
sure could be reached in ∼30 ns. Hugoniot elastic limit (HEL) of the shock-compressed iron was observed at ∼50 m/s.
35
XRD peaks of the initial and recovered iron could
all be indexed with a bcc phase structure.
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TABLE I. Planar impact conditions and experimental results for polycrystalline iron under shock compression. Note: Pand Tare the Hugoniot pressure and temperature in the
iron sample under single shock compression, respectively; εis the estimated strain rate of iron under shock compression in this study.
40
H
d
is the hardness of the recovered
samples; R
s
is the residual stress of the recovered samples.
No. Sample/flyer w(km/s) P
H
(GPa) T(K) ε(×10
6
s
−1
)H
d
(GPa) R
s
(GPa)
1(initial) …0 0 300 0 1.75(3) −
2 Fe/Fe 0.512(1) 10.0(2) 329(7) 2.60 1.91(8) −0.077(3)
3 Fe/Fe 0.594(1) 11.8(2) 335(8) 3.05 2.17(7) −0.182(6)
4 Fe/Fe 0.683(1) 13.7(3) 342(10) 3.53 2.61(6) −0.387(9)
5 Fe/Fe 0.746(2) 15.1(3) 347(10) 3.89 2.70(5) −0.763(14)
FIG. 2. Nanoindentation tests of the post-shock irons recovered from varied pressures: (a) the typical loading and unloading profile curves for three random points con-
ducted on a cross-sectional sample, characterized by a shock pressure of 15.1 GPa, (b) the average data of the loading/unloading-depth profile curves, (c) hardness distri-
bution, and (d) residual stress of post-shock irons. It is evident that the nano-hardness and residual stress values exhibit varying for the samples processed at different
strain rates.
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contribution of twins and LAGBs to the mechanical properties of
bcc metals remains highly mysterious.
In this study, a high-speed impact method was employed to
establish experimental conditions conducive to high strain rates.
We conducted a series of shock recovery experiments on large-
grain pure iron with an average grain size exceeding 1000 μm.
The changes in the microstructures and mechanical properties
of the post-shock iron were then analyzed. Our results show that
many twinning and low-angle grain boundaries (hybrid low-
energy interface architectures) were introduced into shocked
iron. Meanwhile, the post-shock iron from 15 GPa shows an
approximately 54% increase in nano-hardness. Our findings
indicate that the increase in twins and LAGBs could be a
primary contributor to elevating the hardness of post-iron. This
study underscores the significance of deformation twinning and
LAGBs in bcc-iron as a mechanism for enhancing mechanical
properties, emphasizing its effectiveness comparable to tradi-
tional grain refinement techniques.
II. MATERIAL AND EXPERIMENTAL METHODS
A coarse-grained polycrystalline iron sample, with a chemical
purity exceeding 99.9%, was chosen as the starting material for the
specimen. The grains in this material possessed sizes greater than
1000 μm. Shock compression experiments were carried out utilizing
a one-stage light-gas gun with 24-mm diameter at the Institute of
Atomic and Molecular Physics, Sichuan University. A schematic
representation of the shock procedure is depicted in Fig. 1(a), and
the post-shock samples were recovered. Prior to the experiments,
the iron specimens were precision-cut into discs measuring approx-
imately 12 mm in diameter and 2 mm in thickness. Both surfaces
of the initial specimens were meticulously polished to achieve a
mirror-like finish. Additionally, pure iron served as the flyer plate,
characterized by dimensions of approximately 23 mm in diameter
and 2 mm in thickness. The impact velocity of the flyer plate was
accurately measured using an electromagnetic method with an
uncertainty of approximately 0.5%.
36,37
The shock pressure (P
H
) was determined using the imped-
ance matching method,
38,39
specifically: P
H
=ρ
0
u
s
u
p
=ρ
0
(C
0
+λu
s
)
u
p
,whereρ
0
represents the sample’s initial density, u
s
denotes the
shock wave velocity, u
p
is the particle velocity, and C
0
and λrep-
resent the fitted factors. The C
0
and λfor bcc iron was deter-
mined to be 4.63 km/s and 1.33, respectively, so the Hugoniot
parameters used for iron are u
s
= 4.63 + 1.33u
p
(km/s) with a
density of 7.875 g/cm
3
.
35
In this experiment, the flyer plate was
identical to the sample, and the experimental setup followed a
symmetrical impact configuration, resulting in up being half of
the impact velocity (w).Thespecificimpactconditionsare
detailed in Table I, where the iron was subjected to shock pres-
sures and strain rates ranging from 10 to 15 GPa and 2.60 to
3.89 × 10
6
s
−1
, respectively.
The post-shock samples were sectioned into cross section
(1 mm in size) parallel to the direction of impact.
Nanoindentation tests were conducted employing a Nano Test
FIG. 3. The geometrically necessary dislocations density maps of (a) starting iron, and post-shock irons from (b) 10.0, and (c) 15.1 GPa. Color scale indicates the disloca-
tion densities in the starting and post-shock iron. Global GND density distribution based on corresponding mapping results in (d)–(f ). The dislocation density of recovered
samples is proportional to pressure, resulting in hardening of pure irons after deformation.
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Vantage system from Micro Material. Three random points were
selected on the cross section of each sample for nanoindentation
measurements, which were then averaged. A maximal force of
50 mN was applied, with a loading-unloading cycle lasting 20 s
and a 2-s pause at maximum load. It is noteworthy that the
spacing between indentations (40 μm) exceeded three times the
characteristic length of residual imprints (<10 μm), which prevents
perturbations arising from the mechanically affected zone of adja-
cent tests. Subsequently, the microstructures, grain size, and dislo-
cation density of the post-shock iron were comprehensively
examined using electron backscatter diffraction (EBSD) with two
distinct indexation step sizes. A step size of 3 μm was used for
broader-scale observations, whereas a finer step size of 0.5 μmwas
employed to detect finer grains.
In addition, x-ray diffraction (XRD), energy dispersive spec-
trometer (EDS), and scanning electron microscope (SEM) measure-
ments were carried out to ascertain the crystal structure, elemental
component, and uniformity of initial samples, respectively. The
SEM map verified the homogeneity of the initial pure iron sample
[Fig. 1(b)]. As shown in Fig. 1(c), XRD peaks of starting and post-
shock samples are in good agreement with the standard peaks of
the bcc-iron. The intensity of the (110) peak of compressed irons is
significantly reduced compared to that of the starting iron, likely
due to the introduction of many dislocations under high strain
rates.
41
III. RESULTS AND DISCUSSION
A. Nano-hardness of post-shock bcc-iron
Considering the limitations imposed by the sample size, nano-
indentation measurements have emerged as a preferred technique
for ascertaining the nano-hardness of materials on a microscale.
Figure 2(a) illustrates typical load/unload-depth curves of post-
shock irons. A comparison of load/unload-depth curves in starting
and post-shock irons reveals that the post-shock irons exhibit shal-
lower profiles [Fig. 2(b)]. Moreover, the loading depth gradually
decreases with the increasing strain rate. Consequently, the nanoin-
dentation tests indicate that the nano-hardness of post-shock iron
rises with pressure, peaking at 2.70 GPa [Fig. 2(c)], recovered from the
highest shock pressure of 15.1 GPa. In addition, the residual stress of
the post-shock samples can be derived from the nanoindentation mea-
surement [Fig. 2(d)], which suggests that the samples subjected to
shock show an improved capacity to resist deformation.
Previous studies have shown that the hardness of pure iron at
room temperature ranges from 170 HV (1.7 GPa) to 260 HV
(2.5 GPa) for grain sizes ranging from 1500 to 200 nm.
42–44
Meanwhile, in this study, the nano-hardness of post-shock iron
reached 2.7 GPa. Our findings indicate that the effect of the interac-
tion between twinning and dislocations on the mechanical behavior
of polycrystalline materials is similar in importance to that of the
grain refinement mechanism. The improvement of mechanical prop-
erties of post-shock iron may be linked to the augmentation of
FIG. 4. Grain/sub-grain boundary maps (upper) and histograms (below) of the cross section of post-shock iron from different pressures: (a) and (d) 0; (b) and (e) 10.0; (c)
and ( f) 15.1 GPa. Black, green, and red lines in maps indicate high angle (θ≥15°), low angle (2° ≤θ< 15°), and near-twin boundaries in terms of the Brandon crite-
rion,
55
respectively; The black arrow indicates the direction of impact. The number of low angle grain boundaries and twin boundaries is proportional to pressure, and no
refined grains are found.
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twinning, LAGBs, and dislocation density, achieved by integrating
TBs and LAGBs statistics and dislocation density. The increase in
residual stress in the sample is likely due to the development of com-
pressive stresses that can resist impact deformation after the sample
has undergone plastic deformation.
B. Dislocation density in post-shock bcc-iron
To quantitatively study the dislocation density changes of post-
shock iron, the Kernel Average Misorientation (KAM) method was
adopted to determine the local misorientation based on the EBSD
orientation data.
45,46
The geometrically necessary dislocations
(GND) can be obtained from the measured local crystal orientations
on the specimen surface. The KAM could present the average mis-
orientation between a given point and its nearest neighbors in a
grain. Any local misorientation angle calculated greater than 3° was
excluded in this analysis. Therefore, the KAM histogram was used
to evaluate the plastic strain in the post-shock samples. The local
misorientation at a region measuring 300 × 300 nm
2
was then deter-
mined by analyzing its 24 surrounding points,
Δθi¼1
nXn
j¼1jθsur
jθij, (1)
where θ
i
shows the local misorientation at the point “i”and θsur
jrep-
resents the misorientation at its neighboring point “j.”To infer the
GND density information, a simple method based on the strain gra-
dient theory was adopted,
47
ρGND ¼2Δθi
ub ¼BΔθi, (2)
where ρ
GND
represents the GND density at the point of interest; Δθ
i
is the local misorientation; ushows the unit length of the point
FIG. 5. The {100} pole figures (left) and inverse pole figures (right) of post-shock bcc-iron from different pressures: (a) and (b) 0; (c) and (d) 10.0; (e) and (f ) 15.1 GPa.
Color scale indicates the texture strength in the starting and post-shock iron. The maximum intensity of pole figures and inverse pole figures exhibits a gradual decrease
from 24.7 and 5.3 to 21.4 and 3.3, respectively, as the pressure increases. Additionally, there is a gradual increase in the variety of textures observed.
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(300 nm); and brepresents the Burgers vector (0.248 nm for iron).
48
B= 2.688 × 10
16
m
−2
is a constant for iron. The distribution of GND
density for each post-shock sample is expected (Fig. 3).
The KAM mappings and their corresponding KAM values vs
frequency for all samples are depicted in Figs. 3(a)–3(f ), respec-
tively. The observed high kernel values are found in post-shock
samples rather than in the initial sample, and the GND density var-
iation increases with the degree of compression. This phenomenon
can be classified as a genuine deformation, as opposed to a mere
measurement error.
49,50
The histograms reveal that the initial
sample spans a broad range with a relatively low concentration of
GNDs. As a result, the dislocation density within the post-shock
samples is significantly elevated. Notably, the average GND density
increases to 1.67 × 10
16
m
−2
in post-shock iron from the shock
pressure of 15.1 GPa, which signifies a 65% enhancement relative
to the initial material’s density.
The source of dislocations is activated by stress concentration
of stacked dislocations at grain boundaries.
51,52
Due to the presence
of a low dislocation density in the initial sample, the samples
underwent a dislocation surge and slip phenomenon during the
deformation process. Lattice deformation is expected to occur in
the microstructure of iron during shock compression, resulting in
the increase of dislocation density. Beyond a critical point, interac-
tions among the dislocations can hinder their mobility, making the
material deformation more difficult. During deformation,
dislocations can intersect, forming new dislocation loops. These
loops then interact with other dislocations, triggering a reorganiza-
tion of the existing dislocation network. This complex process of
recombination ultimately may lead to the annihilation of certain
dislocations.
53,54
Furthermore, the material exhibits a cellular sub-
structure, which is characterized by the presence of high-density
dislocation walls. Indeed, the formation of sub-grain boundaries
with lower orientation angles is attributed to the recombination of
high-density dislocations.
C. Sub-grain boundaries in post-shock bcc-iron
The formation and evolution of grain/sub-grain boundaries in
post-shock irons were investigated based on EBSD analyses. The
grain/sub-grain boundary (GSB) includes high angle grain
boundaries (HAGBs) between 15° and 62.8° and LAGB between
2° and 15°, as well as TBs [Figs. 4(a)–4(c)]. The GSB maps show
that the grain size of the post-shock iron was not significantly
changed. However, a conspicuous abundance of densely popu-
latedLAGBsandTBswasobservedwithinallgrainsafterthe
impact-induced deformation [Figs. 4(b) and 4(c)]. These LAGBs
can be attributed to the rearrangement and migration of accu-
mulated dislocations.
Grain boundaries, which serve as origins of dislocations, could
produce slip bands and, thus, contribute to the occurrence of
FIG. 6. The three-dimensional (a)–(c) and ɸ2 = 45° (d)–( f) of orientation distribution function sections for bcc iron, at (a) and (d) 0, (c) and (e) 10.0, (c) and ( f) 15.1 GPa.
An increase in the diversity of texture types coupled with a significant decrease in strength.
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LAGBs along these boundaries. This, in turn, leads to an associated
rise in stress levels, generating areas of strain concentration at these
grain boundaries. LAGBs tend to initially appear near HAGBs,
which is closely related to the motion of dislocations and slip
systems.
56
Therefore, the substructures were likely formed in grains
that possess a higher quantity of GNDs.
The distribution histograms of grain/sub-grain boundary for
post-shock irons from different pressures are illustrated in
Figs. 4(d)–4(f ), where the term “Correlated”signifies the misorien-
tation calculated employing adjacent data points, the
“Uncorrelated”lines indicate misorientation calculated based on
random data points from the scan, and the “Random”lines repre-
sent the theoretically calculated random misorientation distribution
of a purely random texture.
57
The misorientation angles in the
“Correlated”data in the initial sample are distributed evenly across
the range from 2° to 62° [Fig. 4(d)]. Nevertheless, the highly
deformed samples exist many low misorientation angles, which
FIG. 7. The band slope images of post-shock irons recovered from the shock pressure of 10.0 (left) and 15.1 GPa (right). Theoretical traces of two slip planes of grain A
and B: (a) 10.0; (b) 15.1; (c) and (e) (110); (d) and (f ) (

110), (g) and (i) (112); (h) and ( j) (123). The slip band L1 and L2 belong to grain A, and the slip band L3 and L4
are in grain B.
TABLE II. Mean Schmid factors of the three slip planes at the 111hidirectionof the
starting and post-shock irons.
Slip plane 0 GPa 10.0 GPa 15.1 GPa
{110} 0.422 0.438 0.458
{112} 0.430 0.446 0.476
{123} 0.438 0.459 0.475
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were lower than 5° [Figs. 4(e) and 4(f )], similar findings were
reported in other studies.
58,59
The variation tendency of LAGBs is
consistent with maps. Meanwhile, the deviation between the
“Uncorrected”line and “Random”curve indicates the presence of
preferred orientations in the examined samples.
Figure 5 illustrates the process of texture change with increas-
ing shock pressure via {100} pole figures (PF) and inverse pole
figures (IPF). As evident from the presented figures, a clear reduction
in the intensity of texture orientation was observed as the strain rate
rises. The initial sample exhibits a weak cubic texture characterized
by the presence of {111} 011
hi
orientation and 101
hi
fiber orientation
[Fig. 5(a)], and it exhibits the highest 223
hi
fiber orientation
strength. However, the fiber with an index of 223hiunderwent trans-
formation in the deformed samples, which gradually transfers
toward the 001
hi
orientation ( 223
hi
fiber →113
hi
fiber →114
hi
fiber). The emergence of the new {001} 100
hi
orientation and 111
hi
fiber orientation is observed in samples subjected to high pressures.
Additionally, the maximum intensity of the {001} 100hiorientation
decreases as the shock pressure and strain rate increases.
The three-dimensional [Figs. 6(a)–6(c)] and the ɸ2 = 45° sec-
tions [Figs. 6(d)–6(f )] of the orientation distribution function
(ODF) are presented to investigate the potential changes in textures
before and after deformation of iron. Despite the textures in iron
are relatively weak, the changes between the initial and shocked
samples can still be observed. Specifically, the intensity of texture
orientation noticeably decreases as pressure increases, which aligns
with the findings of PFs and IPFs. Furthermore, the initial sample
no longer exhibits the rolling texture, and instead, the {111} texture
is found in the sample recovered from the shock pressure of
10.0 GPa. The decrease in intensity of texture suggests a shift
toward a more random orientation of the shocked material, thereby
facilitating the initiation of multiple slip systems and subsequent
plastic deformation.
60,61
When a dislocation moves along a specific direction on the
slip plane, it leaves a trace, called a slip trace. This slip trace can be
used to identify the slip system of the material. Traditional slip
theory posits that the slip system with the highest Schmid Factor
(SF) is the initial one to undergo slip. The determination of the
activation state of the slip system necessitates the computation of
the SFs linked to different slip systems. The activation of slip
systems in polycrystalline materials is governed by the maximum
shear stress and the interplay among adjacent grains. Therefore, in
situations where the SFs of two slip systems are high and converg-
ing during the deformation process, conventional approaches prove
inadequate in accurately determining the slip system that is initially
activated.
As depicted in Figs. 7(c) and 7(d), grain A exhibits an orienta-
tion characterized by two crystal planes, namely, (110) and (

110).
We have observed that the theoretical trace of the (110) plane in
grain A is parallel to L
2
, while the theoretical trace of the (

110)
plane is parallel to L
1
. The slip system of grain B was also verified
utilizing the identical method, as shown in Figs. 7(e) and 7(f ).It
can be inferred that the formation of slip bands L
1
and L
2
is attrib-
uted to the displacement of the slip system along the (

110) and
(110) slip planes, respectively. It is noteworthy that the SFs within
the grains demonstrate a consistent behavior across the crystal
planes that belong to the same family. This similarity can be attrib-
uted to the close proximity of the loading direction of the shock
FIG. 8. The texture component maps (left) and inverse pole figures (right) of
post-shock irons recovered from different shock pressures: (a) and (b) 10.0, (c)
and (d) 15.1 GPa. Note: The red arrow in the left images points toward the
texture inside the twin, which is consistent with the direction shown in the right
images.
FIG. 9. Schematic diagram of the formation of low angle grain boundaries and
twins: (a) In regions that are remote from grain boundaries, (b) the distribution
of defects at location (a) after impact compression, (c) in areas proximal to grain
boundaries, (d) the distribution of defects at location (b) after impact compres-
sion. In the figures, black, gray, green, and red lines represent grain boundaries,
dislocations, LAGBs, and twins, respectively.
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wave to L
1
and L
2
. Therefore, we analyzed the strength of only one
slip plane, where Figs. 7(g)–7( j ) illustrates the theoretical traces of
the slip planes (112) and (123) in grain A and B, respectively.
Our results indicate that three slip systems of bcc-iron were
activated during high-speed impact, necessitating an assessment of
their SFs. The average SFs for these slip planes, corresponding to
the 111hicrystallographic direction under varying pressures, are
presented in Table II. By comparing the three slip systems, it was
observed that the activation of the {123} 111
hi
slip system serves as
the primary mechanism during high-speed impact in the initial
sample.
D. Twinning in bcc-iron under high strain rates
The occurrence of twinning was not observed in previous
studies on the microplastic deformation and low strain rate behav-
ior of polycrystalline iron.
62–65
Twinning in single-crystalline iron
is likely to occur under the conditions of exceptionally high strain
rates and low temperatures, preceding the plastic deformation.
66
In
this study, a significant number of deformation twins and LAGBs
were observed in the post-shock irons [Figs. 4(b) and 4(c)]. The
statistical analyses reveal that the length fraction of the TBs in iron
recovered from 10.0 and 15.1 GPa is 9.79% and 21.30%, respec-
tively. Additionally, a weaker 111hifiber texture was observed in
the impacted samples, which could be attributed to the occurrence
of abundant twinning along the migration front of the abnormally
growing grains (Fig. 8).
67
The formation of twins can lead to a diminished strength in
the crystallographic texture of compressed samples, while simulta-
neously mitigating stress concentrations that arise from the com-
plexities of dislocation slip. Twins are more likely to form near
grain boundaries due to grain deformation, which causes relative
slip between grains and subsequent slip of dislocation lines or
planes and results in the formation of twinning structures.
68,69
FIG. 10. Example of twin type in post-shock iron recovered from 15.1 GPa: (a) Diagram of Euler angle2 of a locally enlarged view in the sample; T1 and T2 represent the
quilted twin structure; T3 expresses the “apparent crossing”twin structure; T4 and T5 show the double twin structure. (b) The geometrically necessary dislocations density
maps, the red arrow refers to the highest point of dislocation density, which is located at the intersection of twins. (c) The misorientation of {112} 111
hi
deformation twins
(No. 1–14) boundaries of the dashed line in (a), and the misorientation of twins is 60°. (d) The sizes of {112} 111
hi
deformation twins of No. 1–14 in (c), and the average
size of twins are 1.5 μm.
Journal of
Applied Physics ARTICLE pubs.aip.org/aip/jap
J. Appl. Phys. 135, 155102 (2024); doi: 10.1063/5.0193215 135, 155102-10
©Author(s)2024

Figure 9 illustrates the notable emergence of LAGBs and twin
structures within the deformed iron. Regions without grain bound-
aries primarily underwent deformation through the formation of
these small-angle boundaries upon a single impact, while twin was
mainly formed in the vicinity of grain boundaries.
A significant number of 60° {112} 111
hi
deformation twins
were observed with an average size of 1.5 μm in the post-shock iron
[Figs. 10(c) and 10(d)]. Through careful analysis, three distinct
microstructural features have been observed in relation to twin–
twin interaction [Fig. 10(a)]. These features include the quilted
twin structure (T1 and T2), the “apparent crossing”twin structure
(T3), and the double twin structure (T4 and T5). The quilted twin
structure is normally formed through the transmission and inter-
ruption of multiple twin mutations. A crossing twin structure
occurs when one twin intersects another by following a secondary
twinning path within the crystal lattice. The double twin structure
refers to the occurrence of a secondary twin formation within a
primary twin domain. Twin knots play a distinctive role in twin-
ning and detwinning during deformation, influencing local stress
fields and playing a crucial part in their development. These factors
inevitably impact the mechanical characteristics of materials,
including strain hardening, crack initiation, and resistance to
failure.
70,71
During the dynamic process of impact compression, the mate-
rial experiences a proliferation of dislocations, which accumulate
and coalesce, leading to the formation of LAGBs. In contrast to
HAGBs, twin boundaries exhibit a higher degree of coherence and
are less likely to cause significant lattice distortion. This inherent
structural compatibility makes twin boundaries particularly effec-
tive in promoting the transfer of dislocation plasticity, thereby
enhancing the material’s capacity to withstand deformation under
stress.
72
The dislocation density is found to be significantly higher
near the TBs and at the interactions of twins [Fig. 10(b)]. This phe-
nomenon occurs due to the interaction of twinning, which leads to
the formation of twin–twin boundaries. These boundaries have a
significant impact on the twin and its growth process, which could
enhance the dislocation strength by impeding twin reproduction
and growth.
73–75
IV. CONCLUSION
In this paper, the deformation behavior of large-grain pure
iron was studied under high strain rates (∼10
6
s
−1
), with shock
pressures reaching approximately 15 GPa. The main conclusions
are summarized as follows:
(1) The nano-hardness of post-shock iron increases by 1.5 times,
rising from around 1.75 to 2.70 GPa.
(2) As strain rates increase, the proportion of low-angle grain
boundaries rises in shocked-iron, a phenomenon closely
related to dislocation movement within grains. Our analyses
suggest that the entanglement and stacking resulting from dis-
location interactions lead to the formation of low-angle grain
boundaries, which, in turn, could hinder the movement of
dislocations.
(3) The density of geometrically necessary dislocations is the
highest around twin boundaries in post-shock iron, especially
at the intersections of twins. As a result, a significant number
of twin boundaries impede dislocation movement.
(4) The post-shock iron retains its initial bcc configuration with
grain sizes minimal change. Consequently, the increase in its
nano-hardness primarily hinges on the existence of twins and
low-angle grain boundaries after shock.
ACKNOWLEDGMENTS
We thank L. Y. Zhou, Y. F. Zhang, W. H. Song, J. Wu, and
Q. M. Wang for the shock experiments. This work was supported
by the National Natural Science Foundation of China (No.
42074298), the National Key Laboratory of Shock Wave and
Detonation Physics (No. 2022JCJQLB05701), the Sichuan Science
and Technology Program (No. 2023NSFSC1910), and the
Institutional Research Fund from Sichuan University (No.
2022SCUNL102).
AUTHOR DECLARATIONS
Conflict of Interest
The authors have no conflicts to disclose.
Author Contributions
Canlian Tang: Writing –original draft (equal). Bo Gan: Writing –
review & editing (equal). Yukai Zhuang: Writing –review &
editing (equal). Zhipeng Gao: Writing –review & editing (equal).
Youjun Zhang: Writing –review & editing (equal).
DATA AVAILABILITY
The data that support the findings of this study are available
within the article.
REFERENCES
1
X. D. Zhang, N. Hansen, Y. K. Gao, and X. X. Huang, Acta Mater. 60, 5933
(2012).
2
I. Brooks, P. Lin, G. Palumbo, G. D. Hibbard, and U. Erb, Mater. Sci. Eng. A
491, 412 (2008).
3
B. Sułkowski and R. Chulist, Mater. Sci. Eng. A 749, 89 (2019).
4
X. L. Zhou, Z. Q. Feng, L. L. Zhu, J. N. Xu, L. Miyagi, H. L. Dong,
H. W. Sheng, Y. J. Wang, Q. Li, and Y. M. Ma, Nature 579, 67 (2020).
5
Y. Q. Li, P. Shen, H. M. Zhang, K. Dong, Y. Deng, X. W. Chen, and Z. S. Cui,
Mater. Des. 210, 110057 (2021).
6
J. Jeong, M. Alfreider, R. Konetschnik, D. Kiener, and S. H. Oh, Acta Mater.
158, 407 (2018).
7
Y. Zhang, N. R. Tao, and K. Lu, Scr. Mater. 60, 211 (2009).
8
Y. D. Wei, H. C. Liao, and S. H. Huo, Int. J. Fatigue 166, 107293 (2023).
9
A. Chokshi, A. Rosen, J. Karch, and H. Gleiter, Scr. Metall. 23, 1679 (1989).
10
X. Z. Liao, Y. H. Zhao, S. G. Srinivasan, Y. T. Zhu, R. Z. Valiev, and
D. V. Gunderov, Appl. Phys. Lett. 84, 592 (2004).
11
Y. T. Zhu, X. Z. Liao, and X. L. Wu, Prog. Mater. Sci. 57, 1 (2012).
12
C. Huang, X. H. Peng, T. Fu, X. Chen, H. G. Xiang, Q. B. Li, and N. Hu,
Mater. Sci. Eng. A 700, 609 (2017).
13
Z. Cheng, H. F. Zhou, Q. H. Lu, H. J. Gao, and L. Lu, Science 362, eaau1925
(2018).
14
L. Lu, Y. F. Shen, X. H. Chen, L. H. Qian, and K. Lu, Science 304, 422 (2004).
15
Y. J. Wei, H. J. Gao, X. Y. Li, L. Lu, and K. Lu, Nature 464, 877 (2010).
Journal of
Applied Physics ARTICLE pubs.aip.org/aip/jap
J. Appl. Phys. 135, 155102 (2024); doi: 10.1063/5.0193215 135, 155102-11
©Author(s)2024

16
L. Lu, X. Chen, X. Huang, and K. Lu, Science 323, 607 (2009).
17
Y. J. Tian, B. Xu, D. L. Yu, Y. M. Ma, Y. B. Wang, Y. B. Jiang, W. T. Hu,
C. C. Tang, Y. F. Gao, K. Luo, Z. S. Zhao, L. M. Wang, B. Wen, J. L. He, and
Z. Y. Liu, Nature 493, 385 (2013).
18
D. L. Zou, L. Zhen, Y. Zhu, C. Y. Xu, W. Z. Shao, and B. J. Pang, Mater. Sci.
Eng. A 527, 3323 (2010).
19
T. Sakai, T. Kondo, E. Ohtani, H. Terasaki, N. Endo, T. Kuba, T. Suzuki, and
T. Kikegawa, Geophys. Res. Lett. 33, L15317, https://doi.org/10.1029/
2006GL026868 (2006).
20
L. Dubrovinsky, N. Dubrovinskaia, F. Langenhorst, D. Dobson, D. Rubie,
C. Geßmann, I. A. Abrikosov, B. Johansson, V. I. Baykov, and L. Vitos, Nature
422, 58 (2003).
21
R. Z. Valiev and I. V. Alexandrov, Nanostruct. Mater. 12, 35 (1999).
22
I. V. Alexandrov and R. Z. Valiev, Scr. Mater. 44, 1605 (2001).
23
R. Z. Valiev, Y. V. Ivanisenko, E. F. Rauch, and B. Baudelet, Acta Mater. 44,
4705 (1996).
24
D. Alfè, Phys. Rev. B 79, 060101 (2009).
25
Y. Ivanisenko, R. Z. Valiev, and H.-J. Fecht, Mater. Sci. Eng. A 390, 159
(2005).
26
C. T. Seagle, E. Cottrell, Y. W. Fei, D. R. Hummer, and V. B. Prakapenka,
Geophys. Res. Lett. 40, 5377, https://doi.org/10.1002/2013GL057930 (2013).
27
S. Ogata, J. Li, and S. Yip, Phys. Rev. B 71, 224102 (2005).
28
J. W. Xiao, L. Y. Zhu, R. Wang, C. Deng, Z. X. Wu, and Y. T. Zhu, Mater.
Today 65, 90 (2023).
29
D. Ma, H. J. Xu, J. L. Ding, Y. Shen, and T. Zhang, Mater. Sci. Eng. A 862,
144489 (2023).
30
L. G. Zhao, G. X. J. Chen, H. Zheng, S. F. Jia, K. X. Li, R. H. Jiang, L. Li,
Y. Zhang, H. Y. Peng, P. L. Zhao, Z. Y. Huang, and J. B. Wang, J. Mater. Sci.
Technol. 144, 235 (2023).
31
G. Sainath and A. Nagesha, Comput. Mater. Sci. 210, 111449 (2022).
32
G. E. Dieter, Strengthening Mechanisms in Solids (ASM, Metals Park, OH,
1962), Vol. 279.
33
J. N. Johnson and R. W. Rohde, J. Appl. Phys. 42, 4171 (1971).
34
C. Wehrenberg, D. McGonegle, C. Bolme, A. Higginbotham, A. Lazicki,
H. J. Lee, B. Nagler, H.-S. Park, B. A. Remington, and R. E. Rudd, Nature 550,
496 (2017).
35
L. M. Barker and R. E. Hollenbach, J. Appl. Phys. 45, 4872 (1974).
36
B. Gan, Y. J. Zhang, Y. Q. Huang, X. H. Li, Q. M. Wang, J. Li, Y. K. Zhuang,
Y. Liu, and G. Jiang, Geophys. Res. Lett. 48, e2021GL094446, https://doi.org/
10.1029/2021GL094446 (2021).
37
Y. Q. Huang, M. Q. Hou, B. Gan, X. H. Li, D. W. He, G. Jiang, Y. J. Zhang,
and Y. Liu, J. Geophys. Res. 127, e2021JB023645, https://doi.org/10.1029/
2021JB023645 (2022).
38
S. S. Penner, J. Quant. Spectrosc. Radiat. Transfer 76, 235 (2003).
39
Y. B. Zel Dovich and P. Raizer Yu, Physics of Shock Waves and High-
Temperature Hydrodynamic Phenomena (Courier Corporation, 2002).
40
R. F. Smith, R. W. Minich, R. E. Rudd, J. H. Eggert, C. A. Bolme, S. L. Brygoo,
A. M. Jones, and G. W. Collins, Phys. Rev. B 86, 245204 (2012).
41
Y. Yang, Z. Jiang, C. Wang, H. B. Hu, T. G. Tang, H. S. Zhang, and Y. N. Fu,
Mater. Sci. Eng. A 731, 385 (2018).
42
B. Q. Han, E. J. Lavernia, and F. A. Mohamed, Metall. Mater. Trans. A 34,71
(2003).
43
Y. Yan, Y. Qi, Q.-W. Jiang, and X.-W. Li, Acta Metall. Sin. (Engl. Lett.) 28,
531 (2015).
44
Y. Ding, J. H. Jiang, and A. D. Shan, Mater. Sci. Eng. A 509, 76 (2009).
45
M. Calcagnotto, D. Ponge, E. Demir, and D. Raabe, Mater. Sci. Eng. A 527,
2738 (2010).
46
P. Chen, S. C. Mao, Y. Liu, F. Wang, Y. F. Zhang, Z. Zhang, and X. D. Han,
Mater. Sci. Eng. A 580, 114 (2013).
47
L. P. Kubin and A. Mortensen, Scr. Mater. 48, 119 (2003).
48
Q. Liu, L. M. Fang, Z. W. Xiong, J. Yang, Y. Tan, Y. Liu, Y. J. Zhang, Q. Tan,
C. C. Hao, L. H. Cao, J. Li, and Z. P. Gao, Mater. Sci. Eng. A 822, 141704
(2021).
49
A. Kundu, D. P. Field, and P. Chandra Chakraborti, Mater. Sci. Eng. A 773,
138854 (2020).
50
A. J. Wilkinson, Scr. Mater. 44, 2379 (2001).
51
V. Moorthy, T. Jayakumar, and B. Raj, Int. J. Pressure Vessels Piping 64, 161
(1995).
52
R. C. Bill, J. R. Frederick, and D. K. Felbeck, J. Mater. Sci. 14, 25 (1979).
53
E. I. Galindo-Nava, J. Sietsma, and P. E. J. Rivera-Díaz-del-Castillo, Acta
Mater. 60, 2615 (2012).
54
L. H. Wang, Z. Zhang, E. Ma, and X. D. Han, Appl. Phys. Lett. 98, 051905
(2011).
55
A. H. King and S. Shekhar, J. Mater. Sci. 41, 7675 (2006).
56
N. Saeidi, F. Ashrafizadeh, B. Niroumand, and F. Barlat, Mater. Des. 87, 130
(2015).
57
Z. G. Liu, P. J. Li, L. T. Xiong, T. Y. Liu, and L. J. He, Mater. Sci. Eng. A 680,
259 (2017).
58
L. Tan, X. Y. Zhang, Q. Sun, J. P. Yu, G. J. Huang, and Q. Liu, Mater. Sci. Eng.
A699, 247 (2017).
59
Z. F. Yan, D. H. Wang, X. L. He, W. X. Wang, H. X. Zhang, P. Dong, C. H. Li,
Y. L. Li, J. Zhou, Z. Liu, and L. Y. Sun, Mater. Sci. Eng. A 723, 212 (2018).
60
T. Walde and H. Riedel, Mater. Sci. Eng. A 443, 277 (2007).
61
A. Styczynski, C. Hartig, J. Bohlen, and D. Letzig, Scr. Mater. 50, 943 (2004).
62
Q. Q. Tian, H. Y. Luo, R. Yi, X. F. Fan, Y. Ma, D. Q. Shi, and J. J. Gao, Mater.
Sci. Eng. A 771, 138645 (2020).
63
S. Descartes, C. Desrayaud, and E. F. Rauch, Mater. Sci. Eng. A 528, 3666
(2011).
64
D. Tumbajoy-Spinel, X. Maeder, G. Guillonneau, S. Sao-Joao, S. Descartes,
J.-M. Bergheau, C. Langlade, J. Michler, and G. Kermouche, Mater. Des. 147,56
(2018).
65
D. Tumbajoy-Spinel, S. Descartes, J.-M. Bergheau, V. Lacaille, G. Guillonneau,
J. Michler, and G. Kermouche, Mater. Sci. Eng. A 667, 189 (2016).
66
M. J. Tang and J. Marian, Acta Mater. 70, 123 (2014).
67
P. Cizek, A. Sankaran, E. F. Rauch, and M. R. Barnett, Metall. Mater. Trans. A
47, 6655 (2016).
68
X. Y. Li, Z. Zhang, and J. W. Wang, Prog. Mater. Sci. 139, 101160
(2023).
69
X. Y. Li, Q. Zeng, and J. W. Wang, Scr. Mater. 220, 114930 (2022).
70
P. A. Juan, C. Pradalier, S. Berbenni, R. J. McCabe, C. N. Tomé, and
L. Capolungo, Acta Mater. 95, 399 (2015).
71
C. Liu, F. Roters, and D. Raabe, Acta Mater. 242, 118444 (2023).
72
Y. J. Song, T. X. Li, X. Q. Fu, Z. J. Zhang, G. Sheng, Y. H. Zhu, Y. P. Lu, and
Q. Yu, J. Alloys Compd. 947, 169522 (2023).
73
Q. Yu, Y. Y. Jiang, and J. Wang, Scr. Mater. 96, 41 (2015).
74
M. Koyama, E. Akiyama, K. Tsuzaki, and D. Raabe, Acta Mater. 61, 4607
(2013).
75
C. A. Stein, A. Cerrone, T. Ozturk, S. Lee, P. Kenesei, H. Tucker, R. Pokharel,
J. Lind, C. Hefferan, R. M. Suter, A. R. Ingraffea, and A. D. Rollett, Curr. Opin.
Solid State Mater. Sci. 18, 244 (2014).
Journal of
Applied Physics ARTICLE pubs.aip.org/aip/jap
J. Appl. Phys. 135, 155102 (2024); doi: 10.1063/5.0193215 135, 155102-12
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