Content uploaded by Azdiar A. Gazder
Author content
All content in this area was uploaded by Azdiar A. Gazder on Nov 21, 2022
Content may be subject to copyright.
This article has been accepted for publication and undergone full peer review but has not
been through the copyediting, typesetting, pagination and proofreading process, which may
lead to differences between this version and the Version of Record. Please cite this article as
doi: 10.1002/adem.202200891.
This article is protected by copyright. All rights reserved
Void formation and crack propagation in a Cr-Mn-N metastable austenitic
stainless steel during bending
Hamidreza Kamali1,*, Haibo Xie1, Hongyun Bi2, E Chang2, Haigang Xu2, Haifeng Yu2, Zhengyi Jiang1, Azdiar
A. Gazder3
1 School of Mechanical, Materials, Mechatronic and Biomedical Engineering, University of Wollongong, Wollongong
NSW 2522, Australia
2 Baosteel Research Institute, Baoshan Iron & Steel Co., Ltd., Shanghai 200431, China
3 Electron Microscopy Centre, University of Wollongong, Wollongong NSW 2500, Australia
Abstract
Microstructure evolution via deformation-induced martensitic transformation, void formation, and crack
propagation were investigated in a metastable austenitic Cr-Mn-N stainless steel for up to 90° bending using
a combination of electron backscattering diffraction and parent grain reconstruction. Stress-strain
heterogeneity and stress triaxiality studied using finite element analysis revealed that the inner and outer radii
were in approximately uniaxial compressive and tensile stress states, respectively with the outer radius
showing higher values for von Mises and principal stresses, and equivalent strain. Voids were observed at
both, austenite/αʹ-martensite and αʹ/αʹ-martensite interfaces. Parent grain reconstruction applied to the 90°
bending sample revealed that cracks at αʹ/αʹ-martensite interfaces tend to propagate predominantly along
intergranular parent austenite grain boundaries. It was also found that both, intra-granular and inter-granular
cracks in parent austenite tend to propagate between αʹ-martensite child-child grains comprising the same
crystallographic packets. This is the first study of its kind to comprehensively show this phenomenon. A
representative example of intergranular crack propagation within a ‖ normal direction (ND) oriented
parent austenite grain was also demonstrated.
Keywords: electron backscattering diffraction (EBSD); transformation induced plasticity (TRIP); twinning
induced plasticity (TWIP); phase transformation; steel; martensite; parent grain reconstruction.
1. Introduction
Transformation- and twinning-induced plasticity (TRIP-TWIP) metastable austenitic stainless steels
possessing low stacking fault energy ( ~ 12-18 mJ.m-2) are studied extensively due to their unique
mechanical response and superior energy absorption abilities [1]. Their deformation mechanisms comprise
slip, twinning and/or martensitic transformation from face-centred cubic (fcc) metastable austenite to
Accepted Article
15272648, ja, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/adem.202200891 by University Of Wollongong University of Wollongong Library, Wiley Online Library on [21/11/2022]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License
Corresponding Author: Hamidreza Kamali, E-mail: hk207@uowmail.edu.au
This article is protected by copyright. All rights reserved
hexagonal close-packed (hcp) ɛ-martensite and/or body-centred tetragonal (bct, or approximated as body-
centred cubic (bcc) when tetragonality is negligible) αʹ-martensite [2, 3].
Although extensive research on the deformation behaviour of TRIP-TWIP steels during uniaxial tension and
in-plane compression has been undertaken (e.g. Refs. [4, 5]), fewer studies have investigated their performance
during bending (e.g. Refs. [6, 7]). While production processes, in which the steel has been developed for, are
principally involved with bending type deformations. This is a subject of some interest as the Bauschinger
effect, which is the result of different operative stress states, leads to heterogeneous microstructure evolution
throughout the bending zone [8].
The response of TRIP-TWIP steels during bending was initially studied by Fei and Hodgson [9] and Shan et
al. [10], when springback was evaluated by varying processing parameters including blank thickness, Young’s
modulus and die gap. Subsequently, the work of Kim and Lee [11] was the first to consider the effects of
constituent phases on springback. Following that, several studies characterised the variation in phase fractions
of bending samples (e.g. Refs. [6, 12, 13]) while Ogawa et al. [14] and He et al. [15] investigated the effects
of alloying elements on the variations in phase fractions. More recently, some of the present co-authors studied
microstructure and micro-texture evolution [16], the orientation dependence of deformation-induced
martensitic transformation [7], and effects of strain rate on the microstructure and micro-texture evolution [17]
in a TRIP-TWIP steel during bending.
Although uniaxial tensile testing is a common approach to experimentally evaluate voids and crack
propagation, it is inadequate to explain voids and crack propagation during bending [18]. In this context, the
effect of deformation-induced martensitic transformation on the fracture resistance was reported as favourable
in a Fe-34Mn-10Co-10Cr (at.%) high-entropy steel [19] and a Fe-9Mn-3Ni-1.4Al (wt.%) martensitic steel
[20], and unfavourable in a Fe-0.2C-10.4Mn-2.9Al metastable austenitic steel [21] and a low-alloy TRIP steel
[22].
In a medium-Mn steel, Steineder et al. [23] reported a reduction in the fracture strain with lower austenite
stability. This was correlated with the influence of deformation-induced martensitic transformation on fracture
concealment and creation [20], localised work hardening, and stress triaxiality [22]. Jacques et al. [24]
suggested that the volume expansion upon the formation of αʹ-martensite leads to dislocation pile-ups at
austenite (γ)/αʹ-martensite interfaces that reduce the interfacial energy and result in interface separation.
Sites where voids form are described as areas of strain incompatibility between austenite and αʹ-martensite
[19], or within the αʹ-martensite phase [21]. In agreement with the latter study, Eskandari et al. [25] reported
on void formation and coalescence at the intersection of αʹ-martensite plates in a Fe-21Mn-2.5Si-1.6Al-0.11C
(wt.%) TRIP-TWIP steel. Given these contrasting conclusions, a clearer understanding of void formation and
crack propagation in a TRIP-TWIP steel during bending is currently unavailable.
Accepted Article
15272648, ja, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/adem.202200891 by University Of Wollongong University of Wollongong Library, Wiley Online Library on [21/11/2022]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License
Corresponding Author: Hamidreza Kamali, E-mail: hk207@uowmail.edu.au
This article is protected by copyright. All rights reserved
Thus, this work focuses on highly localised void formation and crack propagation in a Cr-Mn-N metastable
austenitic stainless steel during bending. Moreover, this study analyses microstructure evolution during
deformation-induced martensitic transformation via electron backscattering diffraction (EBSD). Finite
element (FE) analysis is used to illustrate stress-strain heterogeneity within the bending zone. The EBSD maps
were coupled with a novel parent grain reconstruction approach to determine crack propagation routes in parent
austenite grains.
2. Material and methods
2.1. Experimental procedure
A metastable austenitic stainless TRIP-TWIP steel with the nominal composition of Fe-0.07C-0.35Si-9.28Mn-
1.10Ni-14.70Cr-0.16N-1.49Cu-0.04P (wt.%) was received after (i) heating to 1120 °C for 5 minutes, (ii) hot
rolling at 1120 °C, (iii) water quenching, and (iv) 10% thickness reduction via cold rolling at room temperature.
X-ray diffraction results reported in Ref. [16] show that before cold rolling, the microstructure was fully
austenitic, i.e. free of thermally-induced martensite.
This steel in the mentioned condition is typically used for continuous square pipe forming applications. As
shown in Fig. 1, the continuous square pipe forming process bends the sheet by 90° in 4 positions along the
transverse direction (TD) with the bend region running along the sheet rolling direction (RD). It is during such
bending operations that cracks are frequently reported in industries.
To mimic the above industrial process under laboratory conditions, 20 mm wide and 100 mm long specimens
were wire cut from the 2.80 mm thickness strip as per the AS 2505.1-2004 (R2017) standard. The setup and
experimental conditions related to bending are detailed in Fig. 1. A punch displacement of 23 mm (parallel to
the sheet normal direction - ND) on a universal testing machine operating in speed control mode at 10 mm/min
resulted in a bending angle of 90° after springback. To facilitate an understanding of how the microstructure
evolves half-way through bending, a half stroke of 11.50 mm resulting in a bending angle of 48° after
springback was also considered.
For microstructure analysis, the face containing the sheet ND and TD was mechanically polished using 1200,
2400 and 4000 grit silicon carbide abrasive papers. Thereafter, the face was electropolished on a Struers
Lectropol-5 using an electrolyte of 330 ml methanol, 330 ml butoxyethanol and 40 ml perchloric acid operating
at 50 V, ~1.2 mA for 90 s.
A JEOL JSM-7001F field emission gun scanning electron microscope operating at 15 kV accelerating voltage,
~6.5 nA probe current and 12 mm working distance was coupled with an Oxford Instruments Nordlys-II(S)
EBSD detector and the Aztec v4.1 software suite. In the rectangles denoted by green, blue, and red colours in
Fig. 1, EBSD maps covering an area of 80 × 60 µm2 were acquired with a step size of 0.05 µm. The area
highlighted in the green rectangle corresponds to the 0° bending (Fig. 3). Alternatively, the areas highlighted
Accepted Article
15272648, ja, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/adem.202200891 by University Of Wollongong University of Wollongong Library, Wiley Online Library on [21/11/2022]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License
Corresponding Author: Hamidreza Kamali, E-mail: hk207@uowmail.edu.au
This article is protected by copyright. All rights reserved
by the blue and red rectangles denote the inner and outer radii of the bending samples, respectively, which in
turn lie within the compression and tension zones of the bending sample, respectively (Figs. 4 and 5).
Care was taken to ensure that the EBSD maps were collected from the same position with respect to the inner
and outer radii of the bending samples (d ≈ 200 µm). EBSD maps containing tear-drop shaped voids and crack
propagation were acquired using a finer step size of 0.02 µm within the orange rectangle located close to the
outer radius of 90° bending sample (Figs. 8-10). The methodology of FE analysis is detailed in Appendix A.
2.2. Analytical procedure
Post-processing of the EBSD maps was undertaken using the Oxford Instruments HKL Channel-5 software
suite and involved removing wild orientation spikes, filling in non-indexed (or zero solutions) via extrapolation
up to eight neighbours and removing orientation data with band contrast value less than 50. As per the ISO
13067 recommendation, pixel groupings less than 10 were neglected when defining substructures with
boundary misorientation ≥ 2°.
Low-angle boundaries (LABs) and high-angle boundaries (HABs) are defined as misorientation angles (θ)
between 2° ≤ θ < 15° and 15° ≤ θ, respectively. Σ3 twin boundaries in fcc austenite (60°/) are only
considered for misorientations between 57.5°≤ ≤ 61.5°. The latter range is smaller than the 6° limit identified
by the Palumbo–Aust criterion (i.e.
) [26].
extension twins denoted as
~86°/
are shown with a 5° deviation [27].
The intragranular heterogeneity of plastic deformation was assessed via kernel average misorientation (KAM)
maps using a 3×3-pixel square filter. A critical subgrain angle of 2° was used to disregard subgrain boundaries.
A log-normal probability distribution was fitted to the relative frequency distribution of KAM values [28], and
expressed as follows:
(1)
where, is the KAM value, and are the median and width of the log-normal distribution,
respectively. and are the mean and standard deviation, respectively, and are expressed as follows:
(2)
(3)
2.3. Procedure for reconstruction of parent austenite grains
Parent grain analysis was conducted in MATLAB using MTEX, an open-source crystallographic toolbox [29]
and ORTools, an add-on function library [30]. Since the computational approach to parent grain reconstruction
Accepted Article
15272648, ja, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/adem.202200891 by University Of Wollongong University of Wollongong Library, Wiley Online Library on [21/11/2022]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License
Corresponding Author: Hamidreza Kamali, E-mail: hk207@uowmail.edu.au
This article is protected by copyright. All rights reserved
is based on grain-level EBSD map data, the initial parameters for grain reconstruction are of importance [30].
Accordingly, αʹ-martensite child grains were identified by a Voronoi decomposition using a threshold angle
of 3° (a value that is small enough to avoid large orientation gradients while being large enough to disregard
orientation noise within individual αʹ-martensite child grains) and only considering groupings of 4 pixels or
more.
In the present study, metastable austenite comprises the parent phase and both, ɛ-martensite and αʹ-martensite
are the child phases. However, for the specific purpose of the parent grain reconstruction of the EBSD maps
obtained from the outer radius of the 90° bending sample (Figs. 9 and 10), child grains refer exclusively to αʹ-
martensite. The parent grain reconstruction process begins by computing a map-based orientation relationship
(OR) between the αʹ-martensite child and parent (austenite) phases via iterative refinement of an ideal OR that
serves as the closest starting match (Figs. 9d and 10e).
Using a graph-based approach, neighbouring grains are connected by edges that are weighted by the
probabilities of them belonging to the same parent grain. The probability is computed by a cumulative
Gaussian distribution with a given mean value of 2.5°, which describes the misfit of the misorientation between
αʹ-martensite child-child grains compared to the theoretical αʹ-martensite child-child misorientation, and a
standard deviation of 2.5°.
Subsequently, a Markov clustering algorithm, which simulates random walks across all nodes connecting
neighbouring grains, is applied to identify clusters of strongly connected grains based on the calculated
probability. The precision of the clustering between nodes of strong and weak interactions is controlled by an
inflation parameter (here 1.6), such that higher inflation values result in more clusters with weak interactions
and vice-versa. Following the identification of the clusters that are likely to belong to the same parent grain,
they are transformed to parent orientations by applying the inverse OR to each αʹ-martensite child grain
orientation in the cluster.
Since it is likely that αʹ-martensite child grains with high disorientations to the OR are assigned to the wrong
cluster, and small clusters are also likely to return an uncertain parent orientation, the disorientation and cluster
size are evaluated after the calculation of the parent orientation. Consequently, clusters with disorientations
greater than 5° or smaller than 20 pixels are reverted to αʹ-martensite child grains.
Subsequently, the remaining reconstructed parent grains serve as the “nuclei” in an iterative nuclei-growth
algorithm such that, the boundary misorientations of all possible parent orientations of a αʹ-martensite child
grain with neighbouring parent grains are computed and voting probabilities are assigned. A threshold angle
of 2.5° is set as the misorientation angle between a neighbouring parent orientation and the reconstructed
parent orientation at which the probability is 50%.
Cleaning the parent grain microstructure involves merging fragmented grains with a threshold of 7.5° which
is the maximum allowed misorientation angle between neighbouring grains and merging small grain within a
specific maximum area of 40 pixels. Ultimately, the EBSD data of the reconstructed parent phase is generated
Accepted Article
15272648, ja, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/adem.202200891 by University Of Wollongong University of Wollongong Library, Wiley Online Library on [21/11/2022]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License
Corresponding Author: Hamidreza Kamali, E-mail: hk207@uowmail.edu.au
This article is protected by copyright. All rights reserved
from the EBSD data of the αʹ-martensite child phase. For a more detailed explanation of parent grain
reconstruction, please refer to Ref. [30]. The code for reconstruction of parent austenite grains is provided in
Appendices B.
3. Results
3.1. Microstructure development during bending
Fig. 2 shows contour plots of the von Mises stress, principal stresses and equivalent plastic strain obtained
from FE analysis (refer to Appendix A for details) at 90° bending to visualise stress-strain heterogeneity across
the sample cross-section. The FE analysis does not include a material model as the phase transformation
undergone by this material system cannot be accounted for in such mathematical models. Thus, the sole aim
of the FE analysis is to provide the reader with a visual aid to understand the distribution of stress and
equivalent plastic strain during bending. The overall stress distribution matches that expected for the bending
of an isotropic beam [31]. The innermost node located at the inner radius along the bending axis returned a
maximum von Mises stress of 570 MPa (Fig. 2a) and maximum equivalent plastic strain of 0.07 (Fig. 2e)
whereas the outermost node located at the outer radius returned a maximum von Mises stress of 792 MPa and
maximum equivalent plastic strain of 0.16.
As shown in Fig. 2b, the principal stress , perpendicular to the loading axis, indicates approximately -595
MPa and 782 MPa in the inner and outer radii, respectively. On the other hand, the principal stress , parallel
to the loading axis (Fig. 2c), indicates low stresses of approximately -28 MPa and -18 MPa in the inner and
outer radii, respectively. The principal stress , perpendicular to the x and y axes (Fig. 2d), is approximately
zero throughout the bending zone.
The stress triaxiality (, Eq. 4) is defined as the ratio of the hydrostatic stress, , to the von Mises equivalent
stress, . It is used to determine the relative degree of hydrostatic stress in a given stress state [32]. Fig. 2f
shows the distribution of stress triaxiality along the bending axis. Extracting the parameters from FE analysis
for 90° bending, the stress triaxiality at the inner and outer radii are -0.36 and 0.32, respectively. Accordingly,
the stress states operative in the inner and outer radii may be approximated as close to uniaxial compression
( <
) and uniaxial tension (
), respectively.
(4)
In Figs. 3a, 4a, 4b, 5a and 5b, the grey, green and blue colours for the austenite, ɛ and αʹ-martensite phases,
respectively, are superimposed on to the band contrast maps. As shown in Fig. 3a, the microstructure of the 0°
bending sample comprises austenite grains with the following characteristics: (i) annealing twins carried over
from prior processing, (ii) stacking faults characterised by striations without any boundary misorientation
along them, (iii) stacking faults that form deformation twins, (iv) ɛ-martensite forming in plate-like
morphologies across austenite grains and located within annealing and/or deformation twins, and (v) αʹ-
Accepted Article
15272648, ja, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/adem.202200891 by University Of Wollongong University of Wollongong Library, Wiley Online Library on [21/11/2022]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License
Corresponding Author: Hamidreza Kamali, E-mail: hk207@uowmail.edu.au
This article is protected by copyright. All rights reserved
martensite forming predominantly within ɛ-martensite plates and to some extent, within austenite grains. Thus,
in the 0° bending sample, the dominant phase transformation route was γ → ɛ → αʹ (Fig. 3a inset 1) with some
instances of γ → αʹ also visible.
Figs. 4a and 4b show phase maps of inner and outer radii, respectively, in the 48° bending sample. For the
localised areas mapped by EBSD, the outer radius illustrates a higher fraction of deformation-induced
martensite, compared to the inner radius, as shown in Figs. 5a and 5b for the inner and outer radii of the 90°
bending sample, respectively. In the inner and outer radii of the 48° and 90° bending samples, both phase
transformation routes, γ → ɛ → αʹ and γ → αʹ, were also visible. In this regard, areas with lower KAM values
tended to continue showing γ → ɛ → αʹ transformation (Fig. 5a inset denoted by the red dashed rectangle)
whereas areas with higher KAM values tended to show direct γ → αʹ transformation (Fig. 5b inset denoted by
the red dashed rectangle). Both phenomena resulted in the recorded increasing area fraction of αʹ-martensite
as a function of increasing bending angle (Fig. 5g).
As shown in Fig. 5g, the fraction of austenite reduced from ~85% in the 0° bending sample to ~50% in the
outer radius of the 90° bending sample. Conversely, the fraction of αʹ-martensite increased from ~2% in the
0° bending sample to ~38% in the outer radius of the 90° bending sample. In the case of ɛ-martensite, its phase
fraction was the highest in the 0° bending sample, following which it decreased with increasing bending angle.
Since this study only contains EBSD maps, the distribution of phases is calculated on the basis of their localised
area fractions only. These local values are not reflective of the volume fractions of the various phases across
the bulk sample cross-section.
The formation of stacking faults during the early stages of deformation of low austenitic steels have
frequently been observed using transmission electron microscopy (e.g. Refs. [33, 34]), and EBSD (e.g. Ref.
[35]). Thereafter, the dissociation of Shockley partial dislocations to an infinite distance results in the
formation of deformation twins and subsequently the phase transformation of the twin to ɛ-martensite [36].
On account of the low of the present alloy (~15 mJ.m-2 based on the empirical equation proposed by
Pickering [37]) and based on observations from previous EBSD work [35], the striations observed in the EBSD
maps (e.g. Figs. 3a inset (2) within the red rectangle and 3c) are more attributable to stacking faults as they
tend to lack misorientation across them. Moreover, these stacking faults are also observed to transform to
deformation twins (e.g. within the black dashed rectangle insets in Figs. 4f and 5f) and/or ɛ-martensite (e.g.
within the black dashed rectangle insets in Figs. 4a and 5a) at 48° and 90° bending angles.
Figs. 3c, 4e, 4f, 5e and 5f show grain boundary misorientation distribution between austenite grains such that
the boundaries in red denote Σ3 (60°/) twin boundaries with the rotation axis notation for the fcc crystal
reference frame shown in corresponding insets. The γ/ɛ and γ/αʹ boundaries are shown in black.
Annealing twins are shown: (i) within the dashed black rectangle in Fig. 3a by their straight lines that extend
either across the entire width of austenite grains or, into the austenite grain interiors, and (ii) by the red colour
of the same straight boundaries in Fig. 3c and the maxima in their rotation axis in the Fig. 3c inverse pole
figure inset denoting a coherent <111>/60° boundary misorientation between the twin and the austenite grain.
Accepted Article
15272648, ja, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/adem.202200891 by University Of Wollongong University of Wollongong Library, Wiley Online Library on [21/11/2022]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License
Corresponding Author: Hamidreza Kamali, E-mail: hk207@uowmail.edu.au
This article is protected by copyright. All rights reserved
In the outer radii of the 48° and 90° bending samples shown in Figs. 4f and 5f, respectively, the development
of twins is also observed where the deformation twins (within the black dashed rectangles) tend to form from
stacking faults. The latter are seen as dark striations in band contrast maps without boundary misorientation
along them.
Fig. 6 shows the area fraction of grain boundary evolution between neighbouring subgrains and grains of the
same phase. The length-dependence of misorientation angles was removed by assigning one point per
boundary to ensure statistical comparison. As shown in Figs. 6a, 6b and 6c for austenite, ɛ and αʹ -martensite,
respectively, the area fraction of LABs increased progressively with consistently higher values for the outer
radius compared to the inner radius, in conjunction with a continuous decline in the area fraction of HABs
including Σ3 twin boundaries in austenite and
extension twins in ɛ-martensite. LABs comprise
dislocation arrays, and an increase in their population is indicative of deformation accommodation [38]. While
the
extension twin boundaries are absent in the EBSD map of the outer radius, it does not
mean they are not present in the outer radius area entirely.
The heterogeneity in deformation accommodation is illustrated by KAM maps (Figs. 3b, 4c, 4d, 5c, and 5d).
In the 0°, 48° and 90° bending samples, strain gradients tend to concentrate along: (i) some of the striated
stacking faults and deformation twins within austenite grains, (ii) along boundaries and triple junctions
between austenite grains, and (iii) areas of phase transformation to ɛ and αʹ -martensite. Observations (i) and
(ii) are indicative of the softer and predominant austenite phase accommodating most of the deformation
imposed during cold rolling (in the case of the 0° bending sample) and subsequent bending. The KAM maps
of the inner (Figs. 4c and 5c) and outer (Figs. 4d and 5d) radii for the 48° and 90° bending samples show the
tendency of higher KAM values for the outer radius.
For austenite, ɛ and αʹ -martensite, the frequency distributions versus KAM values () and the mean local
KAM value () were calculated using Eqs. 1 and 2, and are illustrated in Fig. 7 and their insets, respectively
[35, 39]. For all phases, the varying magnitudes of rightward peak shifts towards higher KAM values and the
widening of their relative frequency distributions can be ascribed to the heterogeneity in accumulated strain.
3.2. Void formation and crack propagation
The location where the voids and cracks are perceived in the outer radius after 90° bending are denoted by the
orange rectangle in Fig. 1. Fig. 8 shows two instances of typical tear-drop shaped voids at γ/αʹ interfaces. The
voids are typically located within an austenite grain (Fig. 8a) or between austenite grains (Fig. 8c), and
comprise a mix of blunt-rounded and sharp-straight interfaces which are shown by yellow and red arrows,
respectively. The phase maps in Figs. 8a and 8c reveals αʹ-martensite in the vicinity of blunt-rounded bottom
interfaces, whereas remnant austenite neighbours αʹ-martensite between the sharp-straight top interfaces.
The coincidence of blunt-rounded interfaces in conjunction with a higher fraction of αʹ-martensite is indicative
of the cracking conquest phenomenon resulting from martensitic transformation. As per the KAM maps in
Accepted Article
15272648, ja, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/adem.202200891 by University Of Wollongong University of Wollongong Library, Wiley Online Library on [21/11/2022]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License
Corresponding Author: Hamidreza Kamali, E-mail: hk207@uowmail.edu.au
This article is protected by copyright. All rights reserved
Figs. 8b and 8d, the αʹ-martensite in the vicinity of the blunt-rounded bottom interfaces showed relatively
lower KAM values whereas the γ/αʹ interfaces in the vicinity of the sharp-straight top interfaces possess
considerably higher strain gradients along their lengths.
Fig. 9a is representative of crack propagation in αʹ-martensite (white arrows) located in a region close to the
outer radius of 90° bending sample within the orange rectangle shown in Fig. 1. To understand crack
propagation, parent austenite grains were reconstructed for this map (refer to Section 2.3 for details). Fig. 9b
shows the IPF-z map of remnant austenite superimposed on to the band contrast map before parent grain
reconstruction, with the remnant austenite mostly belonging to the ‖ND and ‖ND fibres.
It is well-known that an orientation relationship (OR) derived from an EBSD map may deviate from ideal and
rational orientation relationships (ORs) described by geometrically perfect sets of parallel planes and directions
[40]. Fig. 9c shows that the parent austenite and αʹ-martensite child boundary misorientation distribution had
a single peak at ~45°, indicating that one OR was responsible for γ → αʹ transformation. In Fig. 9d, the αʹ-
martensite child-child grain boundary disorientation from the map-based OR is plotted alongside the
disorientations from the ideal Kurdjumov-Sachs (K-S, ,
[41]) and Nishiyama-
Wassermann (N-W, ,
[42]) ORs. Since the fit between the map-based and K-
S ORs are closer, the latter OR was chosen as the starting guess and iteratively refined [43]. The refined OR,
defined as the
and , matches the map-based OR and was 3.8° disoriented
from the ideal K-S OR. For the refined OR the angular deviation from parallelism between parent-αʹ-martensite
child planes and directions was 1.2° and 1.3°, respectively.
Figs. 9e and 9f show the variants and crystallographic packets form along the crack propagation path. Via K-
S OR, an austenite grain can transform into four kinds of crystallographic packets where in a crystallographic
packet, the αʹ-martensite grains share the same habit plane (), and six variants of αʹ-martensite [44]. In
this area, the αʹ-martensite reveals the appearance of all four crystallographic packets that among all, the
crystallographic packet id four appears to be dominant with a higher frequency for the variant id nineteen,
especially along the crack propagation path.
The reconstruction of parent austenite grains progressed as per the steps outlined in Section 2.3. After parent
grain reconstruction, the IPF-z map of the reconstructed parent austenite grains in Fig. 9g clearly shows that
the crack propagated across a triple junction of ‖ND, ‖ND and ‖ND oriented parent austenite
grains. The crack segment marked as (1) in Fig. 9b took place between the ‖ND and ‖ND austenite
grains (red arrows) whereas the crack segment marked as (2) occurred along the ‖ND and ‖ND
grains (green arrows), and the crack segment marked as (3) occurred along the ‖ND and ‖ND grains
(blue arrows).
Fig. 10 shows another instance of crack propagation located in a region close to the outer radius of 90° bending
sample within the orange rectangle shown in Fig. 1. The phase map shown in Fig. 10a illustrates that most of
the austenite in the vicinity of the crack transformed to αʹ-martensite. This is clearly seen in Fig. 10b which is
Accepted Article
15272648, ja, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/adem.202200891 by University Of Wollongong University of Wollongong Library, Wiley Online Library on [21/11/2022]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License
Corresponding Author: Hamidreza Kamali, E-mail: hk207@uowmail.edu.au
This article is protected by copyright. All rights reserved
a magnified view of the area within the dashed green rectangle in Fig. 10b. Despite the high strain gradient
revealed in the KAM map (Fig. 10c), there was remnant austenite near the fracture surface (marked by red
arrows in Fig. 10b). In this case, the crack was deflected and propagated through the closest αʹ-martensite
grains.
To track the path of crack propagation, the parent austenite grains were once again reconstructed. Fig. 10d
shows that the parent-αʹ-martensite child boundary misorientation has a single peak at ~45°, indicating that
one OR was responsible for γ → αʹ transformation. The αʹ-martensite child-child boundary disorientation
returned the smallest deviation for the K-S OR (Fig. 10e). Thereafter, the K-S OR was iteratively refined such
that the refined OR, defined as the
and
, was 3.1° disoriented from the rational
K-S OR. The angular deviation from parallelism between parent-αʹ-martensite child planes and directions was
1.2° and 1.3°, respectively. Subsequently, the reconstruction of parent austenite grains progressed as per the
steps outlined in Section 2.3.
Fig. 10f shows the overlaid crack on the IPF-z map of reconstructed austenite grains. A combination of
intergranular and intragranular crack propagation is seen along the crack path. In the region denoted by the
dashed rectangle (1), intergranular crack propagation occurred along parent austenite grain boundaries between
‖ND and ‖ND oriented austenite grains. Following that, in the region denoted by the black dashed
rectangle (2), intragranular crack propagation through a ‖ND grain is clearly observed.
Figs. 10g and 10h show the maps of variant and crystallographic packets of αʹ-martensite formed within the
‖ND austenite grain, respectively. This study is one of the first to clearly show that cracks propagate
intra-granularly within parent austenite grains (as shown in Fig. 10h) and inter-granularly along parent
austenite grain boundaries (as shown in Fig. 9f), with the interfaces in both cases sharing the same
crystallographic packet.
4. Discussion
4.1. Microstructure development during bending
Similar to Fig. 2 of the present study, He et al. [15] used FE analysis and reported the propensity along the
bending axis for the outermost node to sustain higher von Mises stress and equivalent plastic strain values
compared to the innermost node. This stress-strain heterogeneity is responsible for the higher fraction of
deformation-induced martensite in the outer radius region compared to its inner radius counterpart.
The operative stress states can also affect the operation of deformation mechanisms, i.e. twinning and/or
transformation -induced plasticity. For example, Gussev et al. [45] reported that the deformation twinning was
the dominant deformation mechanism under uniaxial tension compared to its equivalent plastic strain under
uniaxial compression. Saleh et al. [46] established that not all of the twinning systems are activated
during the uniaxial compression of a TRIP-TWIP steel subjected to cyclic tension-compression tests and that
the yield stress is intrinsically lower in uniaxial tension cycles compared to compression cycles.
Accepted Article
15272648, ja, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/adem.202200891 by University Of Wollongong University of Wollongong Library, Wiley Online Library on [21/11/2022]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License
Corresponding Author: Hamidreza Kamali, E-mail: hk207@uowmail.edu.au
This article is protected by copyright. All rights reserved
Based on the FE analysis, the stress states operative in the inner and outer radii are approximated as uniaxial
compression and tension, respectively. The higher equivalent plastic strain as well as the approximately
uniaxial tensile stress state in the outer radius may be the reason for the higher fraction of deformation twinning
in austenite compared to the inner radius (Fig. 6a).
The presence of
extension twins, which are synonymous with the simultaneous activation of
pyramidal and basal slip [47], were extensively detected in the inner radius (Fig. 6b). Focusing on TRIP-TWIP
steels, Pramanik et al. [48] detected the presence of
extension twins in an Fe-17Mn-3Al-2Si-
1Ni-0.06C steel deformed under plane strain compression and cold-rolling at room temperature. They
explained that the
extension twins are formed by the non-planar dissociation of a perfect
dislocation into twinning partial dislocations in the pyramidal plane and partial dislocations.
Focusing on bending deformation, the same tendency was reported by Wang et al. [49] during bending of a
rolled AZ31 Mg alloy with hcp structure where the extension twins were observed in the inner radius region.
Similar extension twins formed in a rolled Mg alloy with basal texture subjected to uniaxial compression
parallel to the TD or RD direction. Interestingly, extension twinning was suppressed in the same alloy [50]
under tensile loading parallel to the same directions.
4.2. Voids and crack propagation
In medium-Mn metastable austenitic steels (e.g. Ref. [51]) and dual-phase steels (e.g. Ref. [52]), voids are
commonly reported at γ/αʹ interfaces. Sun et al. [21] concluded that the formation of deformation-induced
martensite and the high stress/strain localisations at γ/αʹ interfaces are the main reasons behind, and not the
consequence of, voids and crack propagation.
In this study, however, we observed that not all voids at γ/αʹ interfaces propagated as cracks; most probably
on account of the cracking conquest phenomenon resulting from martensitic transformation and the formation
of blunt-rounded interfaces in the vicinity of γ/αʹ interfaces (Fig. 8). The cracking conquest phenomenon was
also observed in the vicinity of blunt-rounded interfaces of inclusion-induced voids in a metastable Fe-35Mn-
10Co-10Cr (wt.%) high-entropy alloy [19].
Previous studies on TRIP steels reported that crack propagated along αʹ/αʹ interfaces or within αʹ-martensite,
or in both locations in equal proportions. In our study, however, the parent austenite grain reconstruction
clearly illustrates that cracks at αʹ/αʹ interfaces or within αʹ-martensite mostly propagate along intergranular
parent austenite grain boundaries (Figs. 9g and 10f). This can be attributed to the high strain gradient perceived
at austenite grain boundaries at the onset of deformation (Figs. 3b, 4c and 4d). That is to say, upon further
deformation, deformation-induced martensite starts to nucleate and grow at the vicinity of the austenite grain
boundaries resulting in a high KAM value, which is indicative of a higher density of GNDs [19], at the
austenite grain boundaries. The highly localised strain at the parent austenite grain boundaries enables the
Accepted Article
15272648, ja, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/adem.202200891 by University Of Wollongong University of Wollongong Library, Wiley Online Library on [21/11/2022]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License
Corresponding Author: Hamidreza Kamali, E-mail: hk207@uowmail.edu.au
This article is protected by copyright. All rights reserved
formation of voids. As the deformation continues, the nucleated voids start to grow and coalesce, leading to
the crack observed along the austenite grain boundaries (Figs 9 and 10).
The schematic shown in Fig. 11 is a representation of the void formation and crack propagation sequence in
the outer radius. Being the predominant phase, austenite undergoes slip, twinning (not shown in the schematic)
and concurrent deformation-induced martensitic transformation to accommodate the deformation imposed
during bending. Following martensite formation, load partitioning between austenite and ɛ and αʹ -martensite
occurs; with the latter two phases accommodating some of the imposed deformation. Thereafter, the large
strain incompatibility between austenite and αʹ-martensite and/or the volume expansion upon martensitic
transformation leads to void formation at localised γ/αʹ and αʹ/αʹ interfaces. While the cracking conquest
phenomenon retards crack propagation at γ/αʹ interfaces via blunt-rounded interfaces, the sharp-straight
interfaces at αʹ/αʹ interfaces, located at parent austenite grain boundaries, enable intergranular crack
propagation. Continued propagation of the crack, mostly through αʹ/αʹ interfaces located at parent austenite
grain boundaries or through parent austenite grins, leads to fracture and failure of the bending sample.
5. Conclusions
In this study, microstructure evolution via deformation-induced martensitic transformation, void formation
and crack propagation were studied in a metastable austenitic Cr-Mn-N stainless steel subjected to up to 90°
bending using EBSD and parent grain reconstruction. Voids were identified as forming at both, γ/αʹ and αʹ/αʹ
interfaces. The blunt-rounded interfaces at γ/αʹ interfaces did not enable crack propagation due to the cracking
conquest phenomenon. this study is one of the first to clearly show that cracks propagate intra-granularly
within parent austenite grains and inter-granularly along parent austenite grain boundaries, with the interfaces
in both cases sharing the same crystallographic packet. To a lesser extent, intergranular crack propagation was
also found in a ‖ND oriented parent austenite grain.
Acknowledgement
The financial support from Baosteel-Australia Joint Research and Development Centre (BAJC) under the
project BA-18007 is acknowledged. The JEOL JSM-7001F was funded by the ARC – Linkage, Infrastructure,
Equipment and Facilities grant LE0882613. The Oxford Instruments 80 mm2 X-Max EDS detector was funded
via the 2012 UOW Major Equipment Grant scheme.
Conflict of interest
None.
Data availability
The raw/processed data required to reproduce the findings cannot be shared at this time as the data also forms
part of an ongoing study.
Accepted Article
15272648, ja, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/adem.202200891 by University Of Wollongong University of Wollongong Library, Wiley Online Library on [21/11/2022]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License
Corresponding Author: Hamidreza Kamali, E-mail: hk207@uowmail.edu.au
This article is protected by copyright. All rights reserved
Appendix A. Methodology of FE analysis
The local strains and corresponding stresses at the critical nodes during bending were determined using FE
analysis in ABAQUS/Implicit. Data was imported from tensile testing of as-received sheets before bending.
A full model was created and meshed using the three-dimensional (3D) ten-node quadratic tetrahedron
(C3D10) that were refined at the bending zone using adaptive remeshing module (Fig. A. 1). The upper and
support rollers were modelled as discrete rigid. The overall number of nodes and elements were 17817 and
11494, respectively. The Coulomb friction model, which is to relate the critical shear stress, , across an
interface to the contact pressure, p, between the contacting bodies ( ), was assumed to be operative
between surfaces in contact where was the coefficient of friction and set as 0.1 [15].
Appendix B. Code for reconstruction of parent austenite grains
%% Grains are calculated with a 3° threshold
[grains,ebsd.grainId] = calcGrains(ebsd('indexed'), 'angle', 3*degree);
% EBSD data in small grains are removed
ebsd(grains(grains.grainSize < 4)) = [];
% Grains are recalculated from the remaining data ...
[grains,ebsd.grainId] = calcGrains(ebsd('indexed'),'angle',3*degree);
% ... and grain boundaries are smoothed
grains = smooth(grains,5);
%% defining and refining parent-to-child orientation relationship
job = setParentGrainReconstructor(ebsd,grains,Ini.cifPath);
% giving an initial guess for the OR: Kurdjumow-Sachs
job.p2c = orientation.KurdjumovSachs(job.csParent, job.csChild);
% ... and refine it based on the fit with boundary misorientations
job.calcParent2Child;
% checking the disorientation with K-S and N-W
KS = orientation.KurdjumovSachs(job.csParent,job.csChild);
NW = orientation.NishiyamaWassermann(job.csParent,job.csChild);
plotHist_OR_misfit(job,[KS,NW],'legend',{'K-S','N-W'});
% Plotting information about the OR
ORinfo(job.p2c);
Accepted Article
15272648, ja, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/adem.202200891 by University Of Wollongong University of Wollongong Library, Wiley Online Library on [21/11/2022]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License
Corresponding Author: Hamidreza Kamali, E-mail: hk207@uowmail.edu.au
This article is protected by copyright. All rights reserved
%% reconstructing parent microstructure with a graph-based approach
job.calcGraph('threshold',2.5*degree,'tolerance',2.5*degree);
job.clusterGraph('inflationPower',1.6);
% ... and calculating the parent orientations
job.calcParentFromGraph;
%% removing badly reconstructed clusters
job.revert(job.grains.fit > 6*degree | job.grains.clusterSize < 20)
%% filling in unreconstructed regions by voting algorithm iterating 8 times
for k = 1:8
% compute votes
job.calcGBVotes('p2c','threshold',k*2.5*degree);
% compute parent orientations from votes
job.calcParentFromVote
end
%% cleaning reconstructed grains
% - merging grains with similar orientation
job.mergeSimilar('threshold',7.5*degree);
% - and merging small inclusions into larger grains
job.mergeInclusions('maxSize',40);
%% analysing variants and crystallographic packets
plotPDF_variants(job);
job.calcVariants;
plotMap_variants(job,'grains','linewidth',2);
plotMap_packets(job,'grains','linewidth',2);
%% plotting reconstructed parent EBSD
parentEBSD = job.calcParentEBSD;
% plotting grain boundaries superimposed on to the reconstructed EBSD map
figure; plot(parentEBSD(job.csParent),parentEBSD(job.csParent).orientations);
hold on;
plot(job.grains.boundary,'lineWidth',1)
hold off;
Accepted Article
15272648, ja, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/adem.202200891 by University Of Wollongong University of Wollongong Library, Wiley Online Library on [21/11/2022]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License
Corresponding Author: Hamidreza Kamali, E-mail: hk207@uowmail.edu.au
This article is protected by copyright. All rights reserved
References
[1] O. Grässel, L. Krüger, G. Frommeyer, and L. Meyer, "High strength Fe–Mn–(Al, Si) TRIP/TWIP steels
development—properties—application," International Journal of plasticity, vol. 16, no. 10-11, pp. 1391-1409,
2000.
[2] G. Frommeyer, U. Brüx, and P. Neumann, "Supra-ductile and high-strength manganese-TRIP/TWIP steels for
high energy absorption purposes," ISIJ international, vol. 43, no. 3, pp. 438-446, 2003.
[3] D. T. Pierce, J. A. Jiménez, J. Bentley, D. Raabe, C. Oskay, and J. Wittig, "The influence of manganese
content on the stacking fault and austenite/ε-martensite interfacial energies in Fe–Mn–(Al–Si) steels
investigated by experiment and theory," Acta Materialia, vol. 68, pp. 238-253, 2014.
[4] S. Pramanik, A. A. Gazder, A. A. Saleh, D. B. Santos, and E. V. Pereloma, "Effect of uniaxial tension on the
microstructure and texture of high Mn steel," Advanced Engineering Materials, vol. 20, no. 11, p. 1800258,
2018.
[5] I. Souza Filho, K. Zilnyk, M. Sandim, R. Bolmaro, and H. Sandim, "Strain partitioning and texture evolution
during cold rolling of AISI 201 austenitic stainless steel," Materials Science and Engineering: A, vol. 702, pp.
161-172, 2017.
[6] E. Ishimaru, H. Hamasaki, and F. Yoshida, "Deformation-induced martensitic transformation behavior of type
304 stainless steel sheet in draw-bending process," Journal of Materials Processing Technology, vol. 223, pp.
34-38, 2015.
[7] H. Kamali et al., "Deformation mechanism and texture evolution of a low-Ni Cr-Mn-N austenitic stainless
steel under bending deformation," Materials Science and Engineering: A, p. 140724, 2020.
[8] A. Mandal et al., "Cold-bending of linepipe steel plate to pipe, detrimental or beneficial?," Materials Science
and Engineering: A, vol. 746, pp. 58-72, 2019.
[9] D. Fei and P. Hodgson, "Experimental and numerical studies of springback in air v-bending process for cold
rolled TRIP steels," Nuclear engineering and design, vol. 236, no. 18, pp. 1847-1851, 2006.
[10] T. Shan, S. Li, W. Zhang, and Z. Xu, "Prediction of martensitic transformation and deformation behavior in
the TRIP steel sheet forming," Materials & Design, vol. 29, no. 9, pp. 1810-1816, 2008.
[11] S. Kim and Y. Lee, "Effect of retained austenite phase on springback of cold-rolled TRIP steel sheets,"
Materials Science and Engineering: A, vol. 530, pp. 218-224, 2011.
[12] P. Seemann, S. Kurz, and P. Gümpel, "Martensite formation in a new manganese alloyed metastable austenitic
steel (AISI 200-series)," Journal of Alloys and Compounds, vol. 577, pp. S649-S653, 2013.
[13] J. Van Beeck, V. Kouznetsova, and M. Van Maris, "The mechanical behaviour of metastable austenitic steels
in pure bending," Materials Science and Engineering: A, vol. 528, no. 24, pp. 7207-7213, 2011.
[14] T. Ogawa, M. Koyama, C. C. Tasan, K. Tsuzaki, and H. Noguchi, "Effects of martensitic transformability and
dynamic strain age hardenability on plasticity in metastable austenitic steels containing carbon," Journal of
Materials Science, vol. 52, no. 13, pp. 7868-7882, 2017.
[15] J. He, X. Guo, J. Lian, S. Münstermann, and W. Bleck, "Delayed cracking behavior of a meta-stable austenitic
stainless steel under bending condition," Materials Science and Engineering: A, vol. 768, p. 138470, 2019.
[16] H. Kamali et al., "Microstructure and texture evolution of cold-rolled low-Ni Cr–Mn–N austenitic stainless
steel during bending," Journal of Materials Science, vol. 56, no. 10, pp. 6465-6486, 2021.
[17] H. Kamali et al., "Effects of strain rate on the microstructure and texture evolution of a TRIP-TWIP metastable
austenitic stainless steel during bending," Journal of Materials Science, pp. 1-19, 2022.
[18] C. Suppan, T. Hebesberger, A. Pichler, J. Rehrl, and O. Kolednik, "On the microstructure control of the
bendability of advanced high strength steels," Materials Science and Engineering: A, vol. 735, pp. 89-98,
2018.
[19] S. Wei, J. Kim, and C. C. Tasan, "Boundary micro-cracking in metastable Fe45Mn35Co10Cr10 high-entropy
alloys," Acta Materialia, vol. 168, pp. 76-86, 2019.
[20] M. Koyama et al., "Bone-like crack resistance in hierarchical metastable nanolaminate steels," Science, vol.
355, no. 6329, pp. 1055-1057, 2017.
[21] B. Sun et al., "Revealing fracture mechanisms of medium manganese steels with and without delta-ferrite,"
Acta Materialia, vol. 164, pp. 683-696, 2019.
[22] G. Lacroix, T. Pardoen, and P. J. Jacques, "The fracture toughness of TRIP-assisted multiphase steels," Acta
Materialia, vol. 56, no. 15, pp. 3900-3913, 2008.
[23] K. Steineder, D. Krizan, R. Schneider, C. Béal, and C. Sommitsch, "On the Damage Behavior of a 0.1 C6Mn
Medium‐Mn Steel," steel research international, vol. 89, no. 9, p. 1700378, 2018.
[24] P. Jacques, Q. Furnemont, T. Pardoen, and F. Delannay, "On the role of martensitic transformation on damage
and cracking resistance in TRIP-assisted multiphase steels," Acta materialia, vol. 49, no. 1, pp. 139-152, 2001.
[25] M. Eskandari, A. Zarei-Hazanki, M. Mohtadi-Bonab, A. Odeshi, and J. Szpunar, "Microstructure and texture
evolution in 21Mn–2.5 Si–1.6 Al–Ti steel subjected to dynamic impact loading," Materials Science and
Engineering: A, vol. 622, pp. 160-167, 2015.
[26] G. Palumbo and K. Aust, "Structure-dependence of intergranular corrosion in high purity nickel," Acta
Metallurgica et Materialia, vol. 38, no. 11, pp. 2343-2352, 1990.
Accepted Article
15272648, ja, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/adem.202200891 by University Of Wollongong University of Wollongong Library, Wiley Online Library on [21/11/2022]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License
Corresponding Author: Hamidreza Kamali, E-mail: hk207@uowmail.edu.au
This article is protected by copyright. All rights reserved
[27] J. Chen, W.-n. Zhang, Z.-y. Liu, and G.-d. Wang, "Microstructural evolution and deformation mechanism of a
Fe-15Mn alloy investigated by electron back-scattered diffraction and transmission electron microscopy,"
Materials Science and Engineering: A, vol. 698, pp. 198-205, 2017.
[28] D. N. Githinji, S. M. Northover, P. J. Bouchard, and M. A. Rist, "An EBSD study of the deformation of
service-aged 316 austenitic steel," Metallurgical and Materials Transactions A, vol. 44, no. 9, pp. 4150-4167,
2013.
[29] F. Bachmann, R. Hielscher, and H. Schaeben, "Texture Analysis with MTEX–Free and Open Source Software
Toolbox, Solid St. Phen., 160, 63–68, doi: 10.4028," ed, 2010.
[30] F. Niessen, T. Nyyssönen, A. A. Gazder, and R. Hielscher, "Parent grain reconstruction from partially or fully
transformed microstructures in MTEX," arXiv preprint arXiv:2104.14603, 2021.
[31] G. Kress and C. Thurnherr, "Bending stiffness of transversal isotropic materials," Composite Structures, vol.
176, pp. 692-701, 2017.
[32] Y. Bao and T. Wierzbicki, "On fracture locus in the equivalent strain and stress triaxiality space," International
Journal of Mechanical Sciences, vol. 46, no. 1, pp. 81-98, 2004.
[33] X. Feaugas, "On the origin of the tensile flow stress in the stainless steel AISI 316L at 300 K: back stress and
effective stress," Acta materialia, vol. 47, no. 13, pp. 3617-3632, 1999.
[34] H. Beladi, G. S. Rohrer, A. D. Rollett, V. Tari, and P. D. Hodgson, "The distribution of intervariant
crystallographic planes in a lath martensite using five macroscopic parameters," Acta materialia, vol. 63, pp.
86-98, 2014.
[35] A. A. Saleh, E. V. Pereloma, and A. A. Gazder, "Microstructure and texture evolution in a twinning-induced-
plasticity steel during uniaxial tension," Acta materialia, vol. 61, no. 7, pp. 2671-2691, 2013.
[36] S. Martin, S. Wolf, U. Martin, L. Krüger, and D. Rafaja, "Deformation mechanisms in austenitic TRIP/TWIP
steel as a function of temperature," Metallurgical and Materials Transactions A, vol. 47, no. 1, pp. 49-58,
2016.
[37] F. Pickering, "“Proceedings of Stainless Steels 84”, Goeteborg, 1984," 1985.
[38] E. Tochigi, A. Nakamura, N. Shibata, and Y. Ikuhara, "Dislocation Structures in Low-Angle Grain Boundaries
of α-Al2O3," Crystals, vol. 8, no. 3, p. 133, 2018.
[39] M. Calcagnotto, D. Ponge, E. Demir, and D. Raabe, "Orientation gradients and geometrically necessary
dislocations in ultrafine grained dual-phase steels studied by 2D and 3D EBSD," Materials Science and
Engineering: A, vol. 527, no. 10-11, pp. 2738-2746, 2010.
[40] A. B. Greninger and A. R. Troiano, "The mechanism of martensite formation," JOM, vol. 1, no. 9, pp. 590-
598, 1949.
[41] G. Kurdjumow and G. Sachs, "Über den mechanismus der stahlhärtung," Zeitschrift für Physik, vol. 64, no. 5-
6, pp. 325-343, 1930.
[42] Z. Nishiyama, Martensitic transformation. Elsevier, 2012.
[43] T. Nyyssönen, P. Peura, and V.-T. Kuokkala, "Crystallography, morphology, and martensite transformation of
prior austenite in intercritically annealed high-aluminum steel," Metallurgical and Materials Transactions A,
vol. 49, no. 12, pp. 6426-6441, 2018.
[44] T. Furuhara, H. Kawata, S. Morito, and T. Maki, "Crystallography of upper bainite in Fe–Ni–C alloys,"
Materials Science and Engineering: A, vol. 431, no. 1-2, pp. 228-236, 2006.
[45] M. N. Gussev, J. T. Busby, T. S. Byun, and C. M. Parish, "Twinning and martensitic transformations in nickel-
enriched 304 austenitic steel during tensile and indentation deformations," Materials Science and Engineering:
A, vol. 588, pp. 299-307, 2013.
[46] A. A. Saleh et al., "An in-situ neutron diffraction study of a multi-phase transformation and twinning-induced
plasticity steel during cyclic loading," Applied Physics Letters, vol. 106, no. 17, p. 171911, 2015.
[47] R. L. Bell and R. W. Cahn, "The dynamics of twinning and the interrelation of slip and twinning in zinc
crystals," Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, vol. 239,
no. 1219, pp. 494-521, 1957.
[48] S. Pramanik, A. A. Gazder, A. A. Saleh, and E. V. Pereloma, "Nucleation, coarsening and deformation
accommodation mechanisms of ε-martensite in a high manganese steel," Materials Science and Engineering:
A, vol. 731, pp. 506-519, 2018.
[49] L. Wang, G. Huang, T. Han, E. Mostaed, F. Pan, and M. Vedani, "Effect of twinning and detwinning on the
spring-back and shift of neutral layer in AZ31 magnesium alloy sheets during V-bend," Materials & Design,
vol. 68, pp. 80-87, 2015.
[50] B. Song, R. Xin, G. Chen, X. Zhang, and Q. Liu, "Improving tensile and compressive properties of magnesium
alloy plates by pre-cold rolling," Scripta Materialia, vol. 66, no. 12, pp. 1061-1064, 2012.
[51] J. Han et al., "The effects of prior austenite grain boundaries and microstructural morphology on the impact
toughness of intercritically annealed medium Mn steel," Acta Materialia, vol. 122, pp. 199-206, 2017.
[52] Q. Lai et al., "Damage and fracture of dual-phase steels: Influence of martensite volume fraction," Materials
Science and Engineering: A, vol. 646, pp. 322-331, 2015.
Accepted Article
15272648, ja, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/adem.202200891 by University Of Wollongong University of Wollongong Library, Wiley Online Library on [21/11/2022]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License
Corresponding Author: Hamidreza Kamali, E-mail: hk207@uowmail.edu.au
This article is protected by copyright. All rights reserved
Accepted Article
15272648, ja, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/adem.202200891 by University Of Wollongong University of Wollongong Library, Wiley Online Library on [21/11/2022]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License
Corresponding Author: Hamidreza Kamali, E-mail: hk207@uowmail.edu.au
This article is protected by copyright. All rights reserved
Figures
Figure 1 Experimental setup of the bending tests. The boxed regions indicate regions from which EBSD
maps were acquired. d ≈ 200 µm is the distance of the regions from the edge of the bending samples. The
green rectangle denotes the region where the EBSD map was acquired in the 0° bending sample. The blue
and red rectangles highlight the inner and outer radii of the bending samples, respectively. The orange
rectangle marks the region where the EBSD maps of voids and crack propagation were acquired in 90°
bending.
Accepted Article
15272648, ja, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/adem.202200891 by University Of Wollongong University of Wollongong Library, Wiley Online Library on [21/11/2022]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License
Corresponding Author: Hamidreza Kamali, E-mail: hk207@uowmail.edu.au
This article is protected by copyright. All rights reserved
Figure 2 FE results showing (a) von Mises stress, principal stresses (b) , (c) , (d) , (e) equivalent
plastic strain, and (f) distribution of stress triaxiality along the bending axis. In Fig. 2f, the horizontal axis
shows the position of the nodes along the bending axis where stress triaxiality is calculated. Moreover, the
grey region in Fig. 2f indicates the areas away from the studied region for the distribution of stress triaxiality.
Accepted Article
15272648, ja, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/adem.202200891 by University Of Wollongong University of Wollongong Library, Wiley Online Library on [21/11/2022]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License
Corresponding Author: Hamidreza Kamali, E-mail: hk207@uowmail.edu.au
This article is protected by copyright. All rights reserved
Figure 3 Microstructure of the 0° bending sample using (a) austenite, ɛ- and αʹ-martensite phase map in grey,
green and blue, respectively, superimposed on to the band contrast map, (b) KAM map for all three phases,
and (c) grain boundary misorientation angle distribution with inset showing Σ3 () twin boundaries
in red for the austenite phase. Inset (1) shows the γ → ɛ → αʹ sequence during deformation-induced
martensitic transformation. Inset (2) illustrates the striations that are attributable to stacking faults where at
some point – within the red rectangle – transformed to ɛ-martensite.
Accepted Article
15272648, ja, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/adem.202200891 by University Of Wollongong University of Wollongong Library, Wiley Online Library on [21/11/2022]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License
Corresponding Author: Hamidreza Kamali, E-mail: hk207@uowmail.edu.au
This article is protected by copyright. All rights reserved
Figure 4 Microstructure of the 48° bending sample showing (a,b) phase maps superimposed on to the band
contrast maps of the inner and outer radii, respectively, (c,d) KAM maps of the inner and outer radii,
respectively, for all three phases, and (e,f) grain boundary misorientation angle distribution with inset
showing Σ3 () twin boundaries in red for the austenite phase in the inner and outer radii,
respectively. Figs. 4a and 4f insets illustrate the striations transformed to ɛ-martensite and deformation twins,
respectively.
Accepted Article
15272648, ja, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/adem.202200891 by University Of Wollongong University of Wollongong Library, Wiley Online Library on [21/11/2022]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License
Corresponding Author: Hamidreza Kamali, E-mail: hk207@uowmail.edu.au
This article is protected by copyright. All rights reserved
Figure 5 Microstructure of the 90° bending sample showing (a,b) phase maps superimposed on to the band
contrast maps of the inner and outer radii, respectively, (c,d) KAM maps of the inner and outer radii,
respectively, for all three phases, (e,f) grain boundary misorientation angle distribution with inset showing
Σ3 () twin boundaries in red for the austenite phase in the inner and outer radii, respectively, and
(g) phase fraction evolution. Figs. 5a and 5f insets denoted by the back dashed rectangles illustrate the
striations transformed to ɛ-martensite and deformation twins, respectively. In Figs. 5a and 5b insets denoted
Accepted Article
15272648, ja, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/adem.202200891 by University Of Wollongong University of Wollongong Library, Wiley Online Library on [21/11/2022]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License
Corresponding Author: Hamidreza Kamali, E-mail: hk207@uowmail.edu.au
This article is protected by copyright. All rights reserved
by the red dashed rectangles illustrate areas with lower KAM values tended to continue showing γ → ɛ → αʹ
transformation and areas with higher KAM values tended to show direct γ → αʹ transformation, respectively.
Figure 6 Grain boundary area fraction in (a) austenite, (b) ɛ-martensite and (c) αʹ-martensite.
Accepted Article
15272648, ja, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/adem.202200891 by University Of Wollongong University of Wollongong Library, Wiley Online Library on [21/11/2022]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License
Corresponding Author: Hamidreza Kamali, E-mail: hk207@uowmail.edu.au
This article is protected by copyright. All rights reserved
Figure 7 KAM relative frequency distribution in (a) austenite, (b) ε-martensite, and (c) αʹ-martensite. The
mean KAM values of the phases are shown in insets of their corresponding plot.
Accepted Article
15272648, ja, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/adem.202200891 by University Of Wollongong University of Wollongong Library, Wiley Online Library on [21/11/2022]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License
Corresponding Author: Hamidreza Kamali, E-mail: hk207@uowmail.edu.au
This article is protected by copyright. All rights reserved
Figure 8 (a, b) and (c, d) are two examples of typical voids occurring at γ/αʹ interfaces within the 90°
bending sample. (a, c) are band contrast maps with the γ, ɛ-martensite and αʹ-martensite phases
superimposed in grey, green and blue, respectively. (b, d) are KAM maps for all three phases. Figs. 8a and
8c show typical voids located within an austenite grain and between austenite grains, respectively. The blunt-
rounded and sharp-straight interfaces are denoted by yellow and red arrows, respectively.
Accepted Article
15272648, ja, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/adem.202200891 by University Of Wollongong University of Wollongong Library, Wiley Online Library on [21/11/2022]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License
Corresponding Author: Hamidreza Kamali, E-mail: hk207@uowmail.edu.au
This article is protected by copyright. All rights reserved
Figure 9 A representative crack propagation in the outer radius of the 90° bending sample showing (a) phase
map superimposed on to the band contrast map, (b) IPF-z map of austenite superimposed on to the band
contrast map, (c) parent-αʹ-martensite child boundary misorientation distribution histogram, (d) αʹ-martensite
child-child grain disorientation histogram, αʹ-martensite (e) variant and (f) crystallographic packet ids maps,
and (g) IPF-z map of the reconstructed austenite.
Accepted Article
15272648, ja, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/adem.202200891 by University Of Wollongong University of Wollongong Library, Wiley Online Library on [21/11/2022]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License
Corresponding Author: Hamidreza Kamali, E-mail: hk207@uowmail.edu.au
This article is protected by copyright. All rights reserved
Figure 10 Another crack propagation in the outer radius of the 90° bending sample showing (a) phase map,
(b) phase map within the green frame denoted in (a) superimposed on to the band contrast map, (c) KAM
map for all three phases, (d) parent-αʹ-martensite child boundary misorientation distribution histogram, (e)
αʹ-martensite child-child grain disorientation histogram, (f) IPF-z map of reconstructed parent austenite
grains shown in (a), and αʹ-martensite (g) variant and (h) crystallographic packet ids maps.
Accepted Article
15272648, ja, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/adem.202200891 by University Of Wollongong University of Wollongong Library, Wiley Online Library on [21/11/2022]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License
Corresponding Author: Hamidreza Kamali, E-mail: hk207@uowmail.edu.au
This article is protected by copyright. All rights reserved
Figure 11 Schematic representation of voids and crack propagation sequence in the outer radius of the 90°
bending sample.
Figure A. 1 Finite element model of bending setup shown in Fig. 1. The inset shows adaptive meshing in the
bending zone.
Void formation and crack propagation are studied in TRIP-TWIP steel during bending. EBSD and
parent grain reconstruction used for characterisation of cracking sites. Voids are identified as
Accepted Article
15272648, ja, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/adem.202200891 by University Of Wollongong University of Wollongong Library, Wiley Online Library on [21/11/2022]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License
Corresponding Author: Hamidreza Kamali, E-mail: hk207@uowmail.edu.au
This article is protected by copyright. All rights reserved
forming at both, γ/αʹ and αʹ/αʹ interfaces. At γ/αʹ interfaces, cracking conquest observed due to
martensitic transformation. Both, intra-granular and inter-granular cracks in parent austenite tend to
propagate between αʹ-martensite child-child grains comprising the same crystallographic packets.
Accepted Article
15272648, ja, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/adem.202200891 by University Of Wollongong University of Wollongong Library, Wiley Online Library on [21/11/2022]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License
A preview of this full-text is provided by Wiley.
Content available from Advanced Engineering Materials
This content is subject to copyright. Terms and conditions apply.
