Accepted Manuscript

Dislocation configurations through austenite grain misorientations

Arpan Das

PII: S0142-1123(14)00175-3DOI: http://dx.doi.org/10.1016/j.ijfatigue.2014.06.012Reference: JIJF 3402

To appear in: International Journal of Fatigue

Received Date: 10 March 2014Revised Date: 22 June 2014Accepted Date: 23 June 2014

Please cite this article as: Das, A., Dislocation configurations through austenite grain misorientations, InternationalJournal of Fatigue (2014), doi: http://dx.doi.org/10.1016/j.ijfatigue.2014.06.012

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Dislocation configurations through

austenite grain misorientations

Arpan Das

Fatigue & Fracture Group, Materials Science & Technology Division

CSIR - National Metallurgical Laboratory

(Council of Scientific & Industrial Research), Jamshedpur 831 007, India

E-Mail: dasarpan1@yahoo.co.in, Tel.: +91-(0)657 2345192, Fax: +91-(0)657 2345213

Abstract

In the present investigation, many strain controlled low cycle fatigue experiments of

austenitic stainless steel were carried out at various total strain amplitudes under

ambient temperature where the strain rate was kept constant. Dislocation cell

developed due to strain cycling was measured through extensive analytical

transmission electron microscopic investigation and the deformed austenite grains'

misorientation was measured through extensive electron back scattered diffraction

experiments. A strong connection has been established with the dislocation

substructures' configurations, the deformed austenite grains' misorientation and the

extents of induced phase transformation occurs while cyclic plastic deformation of

metastable austenite at various total strain amplitudes. It has been investigated that

with the increase in strain amplitude, dislocation cells are getting more uniform. It has

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also been found that with the increase in strain amplitude, dislocation cell size

decreases drastically towards the higher strain amplitudes.

Keywords

Misorientation, Dislocation substructures, Low cycle fatigue, Deformation induced

martensite, Austenitic stainless steel.

Introduction

Cyclic plastic deformation behaviour with the corresponding microstructural

characteristics and morphologies of nuclear grade AISI 304LN austenitic stainless steel

at various total strain amplitude has already been explored and reported by the present

author elsewhere [1, 2]. On the basis of deformation characteristics of this present alloy

and the corresponding experimental evidences, it is reasonable to consider dislocation

reactions with the grain boundaries and the austenite grain's misorientation as one of

the controlling micro--mechanisms of cyclic hardening-softening behaviour. At the

position of peak tensile stress (Figure 1 in [1]), the mobile dislocations pile-up against

the cell wall (shown in Figure 4 in [2]) and on the other hand, when the compressive

stress is applied externally, the dislocation moves in the reverse manner and gets

accumulated in the cell wall on the opposite direction. In this circumstance, the

dislocations are arrested at the cell wall for a very short period. The progressive

accumulation of dislocation pile-up during strain cycling and the corresponding

increase in the resistance of grain boundaries to the dislocation pile-up might be

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another source of initial hardening in addition to the rapid increase in the dislocation

density.

It has been well established that most of the austenitic stainless steels are unstable

upon deformation and transform in to deformation induced martensites (DIM) (i.e., ε

(hcp) and/or to α/ (bcc)) [2-7]. Present author has already shown the formation,

nucleation micro-mechanisms and the martensitic transformation sequences, i.e., γ (fcc)

→ ε (hcp), γ (fcc) → ε (hcp) → α/ (bcc) and γ (fcc) → α/ (bcc) after both tensile and

fatigue deformation of AISI 304LN stainless steel at various loading conditions under

ambient temperature. It was also found that DIM can nucleate at many microstructural

locations, e.g., shear-band intersection, isolated shear-band, shear band-grain boundary

intersection, grain boundary triple points etc. [2-7]. The magnetic response of the

cyclically deformed austenite at various strain amplitudes has also been documented in

literature [5]. Such solid state phase transformation during plastic deformation imparts

a good combination of strength and toughness to the metastable austenitic stainless

steels.

It has already been investigated that cyclic deformation alters the microstructure and

causes the instabilities which influence the cyclic plastic deformation with different

strain amplitudes imposed [1, 2, 5]. Fatigue life strongly depended on the extent of

martensite present in the matrix, strain amplitude imposed to the alloy and the initial

grain size of the material. Fatigue properties deteriorated on martensite formation,

owing to more crack initiating sites becoming available [5]. It has already been

investigated by the present author that the crack density measured on the fatigue

fracture surfaces increases drastically with increasing strain amplitude and there is a

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strong connection of it with the extent of DIM while low cycle fatigue (LCF) deformation

of metastable austenite [5].

It has also been reported by the present author that austenite grains are more

responsible for determining the cyclic plastic behaviour of the present alloy and with

the increase in strain amplitude, the activity of the single slip system decreases and that

of the multiple slip system increases [8]. The connection between the strain amplitude

dependencies of the organisation of dislocation cell substructures with the formation of

α/ (bcc) martensite during cyclic plastic deformation of austenite has already been

investigated by the present author elsewhere [1].

In the present investigation, an attempt has been made to correlate the dislocation

substructural configurations (i.e., shape, size etc.) with the corresponding deformed

austenite grains' misorientation data after LCF deformation of austenitic stainless steel

tested at various total strain amplitude under room temperature. With regard to the

cyclic softening characteristics of the alloy, the development of dislocation cell sub-

structures and the role of grain boundaries need to be taken into account. As mentioned

above, a high density of dislocations has been preferentially formed in the area adjacent

to the grain boundaries at the very early stage of cyclic deformation. Dislocation pile-up

against the austenite grain boundary has been frequently observed when the specimens

are cyclically exhausted for more number of cycles (i.e., at the lower strain amplitudes).

Evidently, interactions between dislocations and grain boundaries played an important

role in the course of strain cycling.

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Experiments

In order to test the hypothesis, a large number of LCF experiments at various total

strain amplitudes (∆εt) ranging from ±0.50 to ±1.60% have been done on smooth

cylindrical solid specimens of 14.00 mm gauge length and 7.00 mm gauge diameter.

Nuclear grade AISI 304LN austenitic stainless steel was used for the present

investigation. Chemical composition (wt. %) of the material is: C 0.03, Mn 1.78, Si 0.65, S

0.02, P 0.034, Ni 8.17, Cr 18.73, Mo 0.26, Cu 0.29, N 0.08 and the balance Fe. The Md30

temperature of the material at which 50% of the austenite transforms to martensite at a

true strain of 0.30, calculated from the equation of Angel [9], is found to be 2.8°C. Initial

austenite grain size of the material was found to be 70 µm.

Tests were conducted under ambient condition until complete fracture of the specimens

in a servo-electric Instron machine of 100 kN load capacity (8862) in laboratory air

environment. A triangular waveform with a constant strain rate of 0.01 s-1 was used for

cyclic straining. An axial extensometer of 12.5 mm gauge length was kept attached to

the specimen surface for controlling the test parameters. For the quantification of α/

(bcc) martensite formed in the gauge section of fatigued specimens during strain

cycling, magnetic measurement technique was employed. The as-received condition did

not indicate the presence of martensite in the alloy.

Specimens for electron back scattered diffraction (EBSD) experiments have been

obtained by the transverse slicing of the LCF failed specimens leaving 2-3 mm distance

from the fracture end so as to avoid the regions of excessive plastic deformation. EBSD

technique has been extensively employed for the measurement of the grain boundary

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characteristics for all the specimens. The parameters that are kept constant for all the

EBSD experiments are: scan area (350 µm x 200 µm), magnification (500 X) and step

size (0.5 µm). Several frames (6-9) were scanned for each specimen.

Analytical Transmission Electron Microscopy (TEM) investigation has also been carried

out for all the fatigue failed specimens in order to understand the evolution of phase

transformation characteristics and mechanisms, formation of dislocation sub-structures

and its connectivity with the austenite grain boundary misorientation under two beam

conditions at an operating voltage of 200 kV. The TEM foils for all the samples were cut

approximately 2.5 mm away from the fatigued fracture surface so as to avoid excessive

plastic deformation. There was no dislocation cell present in the as received

microstructure. Dislocation cell size has been measured on several bright field images

by standard linear intercept method for all the fatigue fractured specimens.

Results and Discussion

Figure 1 explains that with the increase in strain amplitude, number of cycles to failure

decreases abruptly as expected but on the other hand, the peak tensile stress increases

drastically. The two dimensional grain boundary connectivity (i.e., austenite grain

boundary triple point density) decreases with the increase in strain amplitude up to

±1.0% but beyond that it increases drastically. Dislocation cell size decreases drastically

with the increase in strain amplitude from ±0.85 to ±1.40%. Dislocation cell size data

indicates considerable variability in the dislocation cell size from one region to another.

The dislocation evolution is inhomogeneous, which is due to the grain boundary effect.

However, this is also reflective of the fact that all the bright field images of dislocation

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cells have not been taken at exactly the same conditions of material-beam orientation.

Recently Mayama et al. [10] investigated the strain amplitude dependent organisation

of dislocation substructures in cyclically deformed 316L stainless steel in their elegant

study. Dislocations are developed step-by-step at lower stain amplitudes and easily to

create cells substructures due to the multiple slip system activity at higher strain

amplitudes [8].

Figure 2 (a) shows the as received microstructure of 304LN austenitic stainless steel

showing a large number of annealing twins spread throughout and polygonal austenite

grains. Microstructural investigations have been performed on fatigue failed specimens,

revealing inhomogeneous distribution of α/ (bcc) martensite shown in Figure 2 (b),

which is mainly attributed to the local stress distribution and hence crystallographic

variant selection of martensite. According to Ye et al. [11], the increase in slip band

density and activation of more number of slip systems during cycling have also been

well documented to bear a direct correlation with strain amplitude dependent cyclic

hardening behaviour.

Figure 3 shows the extent of α/ (bcc) martensite as a function of imposed strain

amplitude. It has been seen from Figure 3 that with the increase in strain amplitude, α/

(bcc) martensite content increases drastically. Even though there is scatter in the data

points, the trend is increasing in nature. The scatter is primarily due to the fact that α/

(bcc) martensite does not form uniformly throughout the gauge length of the fatigued

specimen.

Austenite to DIM transformation is believed to be triggered when the susceptible

austenitic stainless steels are deformed at temperatures below Md30. Present author

reported that a number of factors, e.g., steel chemistry, stress state, stress, strain, strain

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rate, grain size, initial crystallographic microtexture, and temperature of deformation

influence the formation of DIM [12]. The present author also demonstrated that a large

amount of published data relating the fraction of DIM to plastic strain, in fact, can be

described in terms of the pure thermodynamic effect of applied stress [13].

The formation of α/ (bcc) martensite during cyclic loading strongly affects the cyclic

mechanical behaviour of various types of steels. Figure 4 shows the misorientation

profile of the undeformed (as received material) as well as the deformed austenite

grains at various total strain amplitude. It is to be noted that there are two peaks of

maximum relative frequency present for all the specimens (i.e., approximately at 1.5

and 59.5°). In between, there is no such peak observed. There is a systematic variation

of the relative frequency of the austenite grain boundary misorientations with the

imposed strain amplitude.

Figure 5 shows that with the increase in total strain amplitude, the extent of medium

angle grain boundary (i.e., MAGB = 10 - 30°) and high angle grain boundary (i.e., HAGB ≥

30°) fraction decreases drastically, but on the other hand, low angle grain boundary (i.e.,

LAGB ≤ 10°) fraction increases drastically. Dislocation cell size is also varying in the

same manner as with MAGB and HAGB fraction with the strain amplitude range of ±0.85

to ±1.40%. It is mainly attributed that the MAGB and HAGB help dislocation cell to

reduce drastically in the strain amplitude range from ±0.85 to ±1.40%. It is understood

from the figure that more the fraction of LAGB, the cell size is less and vice-versa.

Dislocation structures are found near the grain boundaries, and the dislocation

structure is low energy walls or cells inside the grain.

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According to Watanabe et al. [14], HAGB can slide more easily than low sigma

coincidence boundaries, as observed for Σ3 and Σ13 coincidence boundaries, which

showed significant slide hardening in aluminium. In general, the dissociation of lattice

dislocation at coincidence boundaries becomes easier with increasing the Σ value and

the easiest at high-energy random boundaries (conventionally with Σ value larger than

29). In other words, random boundaries can more easily absorb lattice dislocations and

produce sliding than low Σ coincidence boundaries and the LAGB.

According to Humphreys et al. [15], during recovery, the stored energy of the material is

lowered by dislocation movement and this recovery process is not a single

microstructural variation but a series of events. The observed dislocation configurations

are strongly dependent on the applied strain amplitude, as well as on the stacking fault

energy (SFE) of the material [16, 17]. Different morphologies of dislocation sub-

structures (i.e., cells, tangled dislocation, wall and channels) formed in the cyclically

deformed alloy at various total strain amplitudes which have been discussed by the

present author reported elsewhere [1, 2]. According to Kuhlmann-Wildsdorf et al. [18],

the dislocation cell substructure is the last transformation of the dislocation

arrangements generated in fatigue.

It has been clearly understood that the size, shape and morphologies of dislocation cells

are different with the strain amplitude imposed. This is mainly attributed to the

variation of strain accumulation during cyclic plastic deformation at various strain

amplitudes. According to Huang et al. [19], higher strain amplitude will induce multiple

slip systems to facilitate the formation of dislocation cell sub-structures during LCF

deformation. The poorly developed cells might be the result of dislocations from

different slip systems interacting and trapping each other at intersections. Ma and Laird

10

[20] have also pointed out that the dislocation structure changes from cells to loop

patches when the amplitude of loading changes from high to low. Long back, Feltner and

Laird [21] demonstrated different types of dislocation arrangements as a function of the

number of cycles to failure and the slip character of the material for cyclically deformed

polycrystalline fcc alloys. The value of Nf depend on the loading amplitude. According to

Laird et al. [22], higher strain amplitude induces multiple slip systems to facilitate the

formation of dislocation cell. The details of slip system activity during cyclic plasticity of

deformed austenite have been reported by present author elsewhere [8].

The observed dislocation configurations (Figure 6) are strongly dependent on the

employed strain amplitude, plastic strain accumulation as well as on the SFE of the

metastable alloy. Figure 6 (a-d) represents different morphologies and configurations of

dislocation substructures formed in the as received as well as in the cyclically deformed

austenite at various total strain amplitude. From this figure, it has been clearly

understood that the size, shape, configurations and morphologies of dislocation cells are

different with the nominal variation of imposed strain amplitude. Majority of

dislocations are actually distributed in the cell walls which are frequently referred as

sub cell boundaries. This is mainly attributed to the strain accumulation during the

cyclic plastic deformation at different strain amplitude and the induced phase

transformation. The common type of heterogeneous dislocation distribution in the

three dimensional cell structures develops under multiple slip conditions. Figure 7

shows the variation of dislocation cell size as a function of equivalent stress experienced

by the material. As the strain amplitude increases, dislocation cell size decreases

drastically at higher strain amplitudes range from ±0.85 to ±1.40% for the present

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material. This is mainly attributed to the austenite grain boundary misorientations and

the solid state martensitic transformation of the present alloy.

It has already been reported by the present author that with the increase in strain

amplitude, DIM formation increases which has been reported elsewhere [1, 2].

According to Raman et al. [17], dislocation tangles form during primary hardening and

the cell sub-structures are formed during secondary hardening. Owing to the

cumulative strain, the dislocations arrange themselves into relatively more stable

configurations (i.e., cell). The amount of DIM is significant by the time the material

attains the peak tensile stress. Hence, DIM forms much earlier than the dislocation cell

formed. Beyond ±0.85% strain amplitude, the dislocation cell size is decreased, but the

accumulation of strain increases with increasing strain amplitude, which generates

more DIM. Higher fraction of DIM triggers dislocation cells to grow further. According to

Huang et al. [19], the dislocation structures evolve with a strain amplitude decrease

from high to low, the low energy structure of walls, labyrinth walls, cells and

misorientation cells, which were formed at the higher strain amplitude, transfer to

dislocation structure of scattering walls, loop patches and the cell structures.

According to Koneva et al. [26], saturation value of dislocation cell size in most of the

polycrystalline fcc metals and alloys deformed at room temperature is slightly larger

than 0.10 µm and typically lies in the range of 0.20-0.60 µm. In austenitic stainless

steels, various kind of dislocation sub-structures have been observed, depending on the

nominal variation of strain amplitude imposed and the plastic strain accumulation

inside the material.

Figure 7 represents a clear comparison of dislocation cell size as a function of

equivalent stress of different fcc metals under various loading conditions at different

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temperatures. According to Challenger and Moteff [23], at 650°C, dislocation cell size

remains almost constant at various stress levels, while at 816°C, it decreases with

increase in stress for 304 austenitic stainless steel. They also performed fatigue tests for

316 austenitic stainless steel with temperature variation (i.e., 430°C, 650°C and 816°C)

and measured the dislocation cells size. At 430°C, cell size decreases with applied stress;

at intermediate and at higher temperatures (i.e., 650°C and 816°C respectively),

dislocation cell size decreases with equivalent stress drastically. A distinct transition

from rough dislocation cells at 430°C and 650°C to regular sub grains at 816°C have

been investigated by them. They also demonstrated that the dislocation cell size is the

characteristics of a given temperature and strain rate, and it has a direct influence on

the strain hardening capabilities of that material.

Ei-Madhoun et al. [25] investigated that stress and strain response and development of

dislocation substructures in deformed polycrystalline aluminium revealing that

saturation stress is linearly related to the inverse of dislocation cell size. Zhang et al.

[24] carried out many cyclic plastic deformation experiments on polycrystalline copper

at ambient temperature under cyclic shear. They investigated that during the transient

stage of dislocation cell formation, the stress amplitude is inversely proportional to the

dislocation cell size. This correlation is identical to that between the saturated stress

magnitude and the corresponding dislocation cell size. This is in agreement with the

present investigation.

From Figure 7, it is to be noted that the vast majority of the data (i.e., cell size) falls well

within 1.0 µm and it has been investigated that the saturation value is approximately

0.40 µm. A decrease in dislocation cell size corresponds to an increase in the average

scalar dislocation density. An excess dislocation density is rapidly accumulated in cell

13

walls, which results in cell misorientation. At the same time, the amount of dislocation

accumulation inside the cells remains low. With increase of strain amplitude, dislocation

density increases, cell size decreases, cell structure becomes better developed and cell

walls become more sharply defined. Deformation in any polycrystalline materials is

inherently inhomogeneous, which produces interaction stresses between grains and

dislocation structures on different slip systems within the grains, and these stresses can

promote the softening. According to Bassim et al. [27, 28], in the case of unidirectional

deformation, minimization of stored dislocation strain energy is the driving force, which

is indicated by the clearly much reduced dislocation density in the cell structure as

compared with the wall structure, and even more persuasively by the fact that the cells

nearly conform to the theoretically derived cell structure of minimum energy. With the

increase in strain, the cell wall width can decrease, increase or even remain constant in

different materials [21]. According to Huang et al. [19], the back force is larger than the

interior of the grain with a decrease in strain amplitude. According to them, the

dislocation development is faster at the grain boundaries and the twin boundaries due

to strain localization.

As strain amplitude increases, DIM fraction increases rapidly (Figure 3). Beyond the

strain amplitude of ±0.85%, dislocation cells are formed prominently. With the increase

in strain amplitude, dislocation cell size decreases abruptly (Figure 7). It has also been

found that the cell wall width increases drastically with the increase in strain amplitude.

According to Breedis [16], the deformation substructure in austenite influences the

subsequent nucleation of martensite on cooling to below the MS temperature. The

interaction of DIM with dislocation cells; shear bands with dislocation cells are shown at

different strain amplitude in Figure 8 (a-d). Figure 8 (a) shows the dislocation jungles at

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strain amplitude ±0.85%. Dislocation cells are observed at strain amplitude ±1.00%,

±1.20% and ±1.40% (Figure 8 (b-d)). Hence, the extent of DIM and their heterogeneous

distribution caused different dislocation cell configurations and characteristics. Hence,

there is a strong connection between DIM and dislocation cell configurations.

Conclusions

It appears that there is a systematic correlation of the grain boundary connectivity,

austenite grain misorientations and their types with the dislocation cell sub-structures'

configurations with the strain amplitude variation under cyclic plastic deformation of

metastable austenitic stainless steel. The present investigation also concludes that as

the strain amplitude increases, the dislocation cell sizes are getting more uniform in size

and there is an interaction between grain boundaries and DIM. It has also been found

that with the increase in strain amplitude, dislocation cell size decreases abruptly in the

range of higher strain amplitudes. It has also been investigated that with the increase in

strain amplitude, MAGB and HAGB fraction decreases drastically and on the other hand

LAGB fraction increases. DIM, grain boundary connectivity and their configurations are

the significant contributory factors in forming the dislocation cell substructures.

Acknowledgements

The author acknowledges the support and encouragement of Dr. S. Srikanth, Director,

CSIR-NML. The author also expresses his gratitude to Dr. S. Sivaprasad, Principal

Scientist for his assistance with the mechanical characterization. I also express my

15

gratitude to Dr. M. Ghosh, Senior Scientist of CSIR--NML, for helping in carrying out TEM

characterisation.

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List of Figures

Figure 1: Peak tensile stress, number of cycles to failure, grain boundary triple point

(GBTP) density and dislocation cell size as a function of strain amplitude imposed

during LCF deformation of metastable AISI 304LN stainless steel at room temperature.

AR - As Received.

Figure 2: (a) As received microstructure showing polygonal austenite grains and a large

number of annealing twins and (b) Cyclically deformed austenite showing the extent of

α/ (bcc) martensite formed in it and the dense shear bands.

Figure 3: The extent of α/ (bcc) martensite as a function of strain amplitude -

ferritescope measurement [1, 2].

Figure 4: Relative frequencies of austenite grain boundary misorientation profile during

LCF deformation of AISI 304LN stainless steel at various strain amplitude tested at

room temperature. In between there is no sharp peak.

Figure 5: Extents of undeformed and deformed austenite grain boundaries (i.e., LAGB,

MAGB and HAGB) fraction and dislocation cell size as a function of strain amplitude

imposed during LCF deformation of AISI 304LN stainless steel at room temperature. AR

- As Received.

Figure 6: Dislocation substructures observed by TEM bright field images: (a) as received

condition, (b) strain amplitude = ±0.85%, (c) strain amplitude = ±1.20% and (d) strain

amplitude = ±1.40%.

19

Figure 7: Dislocation cell size as a function of equivalent stress magnitude of some fcc

materials under various loading conditions at different temperatures. A - AISI 304 SS -

LCF at 650°C, B - AISI 304 SS - LCF at 816°C, C - AISI 316 SS - LCF at 430°C, D - AISI 316

SS - LCF at 650°C, E - AISI 316 SS - LCF at 816°C, F - Polycrystalline copper (textured

with grain size of 75 µm) - cyclic torsion at ambient, G - Polycrystalline copper (textured

with grain size of 75 µm) - tension-compression at ambient, H - Polycrystalline copper

(textured with grain size of 75 µm) - 90° out of phase non-proportional loading at

ambient, I - Polycrystalline copper (textured with grain size of 75 µm) - transient stage

at ambient, J - Polycrystalline copper (textured with grain size of 10 µm) - tension-

compression at ambient, K - Polycrystalline copper (textured with grain size of 10 µm) -

cyclic torsion at ambient, L - Polycrystalline copper (textured free with grain size of 75

µm) - tension--compression at ambient, M - Polycrystalline aluminium - LCF at ambient

and N - Present study. A - E (Challenger and Moteff [23]); F - L (Zhang and Jiang [24]); M

(Ei-Madhoun et al. [25]) [1].

Figure 8: Dislocation substructures and martensite/shear band interactions at strain

amplitude of (a) ±0.85%, (b) ±1.00%, (c) ±1.20% and (d) ±1.40%. A strong connection

of DIM with dislocation substructures is noted.

Figure1

Figure2

Figure3

Figure4

Figure5

Figure6

Figure7

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MATERIALS SCIENCE & TECHNOLOGY DIVISION

CSIR - National Metallurgical Laboratory

(Council of Scientific & Industrial Research)

Jamshedpur 831 007, India

Highlights

1. LCF experiments were done at various strain amplitudes under ambient.

2. Metastable austenitic stainless steel was chosen.

3. Dislocation cell size developed due to strain cycling was measured by TEM.

4. Austenite grain misorientation was measured by EBSD.

5. Dislocation cell size, austenite grains' misorientation and extent of DIM were

correlated.

Graphical Abstract