Nanocrystalline structure formation under severe plastic deformation and its influence on mechanical properties
Consideration is given to the distinction between nanocrystal strengthening and Hall−Petch grain size strengthening which varies linearly with d−1/2. The important role of grain boundary structure in the strengthening formation of nanomaterials is emphasized. Static and dynamic recoveries are the ma...
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Донецький фізико-технічний інститут ім. О.О. Галкіна НАН України
2005
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irk-123456789-701042014-10-29T03:01:44Z Nanocrystalline structure formation under severe plastic deformation and its influence on mechanical properties Podrezov, Yu.M. Consideration is given to the distinction between nanocrystal strengthening and Hall−Petch grain size strengthening which varies linearly with d−1/2. The important role of grain boundary structure in the strengthening formation of nanomaterials is emphasized. Static and dynamic recoveries are the main reasons limiting the minimal size of structural elements under deformation in high-deformed materials. Structural relaxation proceeding by the recovery mechanism during both the plastic deformation and unloading causes loss of strengthening in high-deformed materials. At the initial stage of repeated deformation the recovered cell structure interacts with moving dislocations in a special way. In the microdeformation level the hardening stress is practically independent of previous deformation degrees in a wide interval of deformation. The usual increase of strengthening with rise of deformation is observed only from the yield point. 2005 Article Nanocrystalline structure formation under severe plastic deformation and its influence on mechanical properties / Yu.M. Podrezov // Физика и техника высоких давлений. — 2005. — Т. 15, № 1. — С. 11-18. — Бібліогр.: 15 назв. — англ. 0868-5924 PACS: 62.20.Fe http://dspace.nbuv.gov.ua/handle/123456789/70104 en Физика и техника высоких давлений Донецький фізико-технічний інститут ім. О.О. Галкіна НАН України |
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Consideration is given to the distinction between nanocrystal strengthening and Hall−Petch grain size strengthening which varies linearly with d−1/2. The important role of grain boundary structure in the strengthening formation of nanomaterials is emphasized. Static and dynamic recoveries are the main reasons limiting the minimal size of structural elements under deformation in high-deformed materials. Structural relaxation proceeding by the recovery mechanism during both the plastic deformation and unloading causes loss of strengthening in high-deformed materials. At the initial stage of repeated deformation the recovered cell structure interacts with moving dislocations in a special way. In the microdeformation level the hardening stress is practically independent of previous deformation degrees in a wide interval of deformation. The usual increase of strengthening with rise of deformation is observed only from the yield point. |
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Podrezov, Yu.M. Nanocrystalline structure formation under severe plastic deformation and its influence on mechanical properties Физика и техника высоких давлений |
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Podrezov, Yu.M. |
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Podrezov, Yu.M. |
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Nanocrystalline structure formation under severe plastic deformation and its influence on mechanical properties |
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Nanocrystalline structure formation under severe plastic deformation and its influence on mechanical properties |
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Nanocrystalline structure formation under severe plastic deformation and its influence on mechanical properties |
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Nanocrystalline structure formation under severe plastic deformation and its influence on mechanical properties |
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Nanocrystalline structure formation under severe plastic deformation and its influence on mechanical properties |
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nanocrystalline structure formation under severe plastic deformation and its influence on mechanical properties |
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Донецький фізико-технічний інститут ім. О.О. Галкіна НАН України |
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2005 |
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http://dspace.nbuv.gov.ua/handle/123456789/70104 |
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Nanocrystalline structure formation under severe plastic deformation and its influence on mechanical properties / Yu.M. Podrezov // Физика и техника высоких давлений. — 2005. — Т. 15, № 1. — С. 11-18. — Бібліогр.: 15 назв. — англ. |
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Физика и техника высоких давлений |
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AT podrezovyum nanocrystallinestructureformationundersevereplasticdeformationanditsinfluenceonmechanicalproperties |
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2025-07-05T19:24:49Z |
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1836836181337178112 |
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Физика и техника высоких давлений 2005, том 15, № 1
11
PACS: 62.20.Fe
Yu.M. Podrezov
NANOCRYSTALLINE STRUCTURE FORMATION
UNDER SEVERE PLASTIC DEFORMATION
AND ITS INFLUENCE ON MECHANICAL PROPERTIES
Institute for Problems of Materials Sciences, NAS of Ukraine
3, Krzhizhanovsky Str., Kiev, 03142, Ukraine
Consideration is given to the distinction between nanocrystal strengthening and
Hall−Petch grain size strengthening which varies linearly with d−1/2. The important role
of grain boundary structure in the strengthening formation of nanomaterials is empha-
sized. Static and dynamic recoveries are the main reasons limiting the minimal size of
structural elements under deformation in high-deformed materials. Structural relaxation
proceeding by the recovery mechanism during both the plastic deformation and unload-
ing causes loss of strengthening in high-deformed materials. At the initial stage of re-
peated deformation the recovered cell structure interacts with moving dislocations in a
special way. In the microdeformation level the hardening stress is practically independent
of previous deformation degrees in a wide interval of deformation. The usual increase of
strengthening with rise of deformation is observed only from the yield point.
Introduction
The creation of new high deformation methods offers ample scope for both the
strain hardening theory and deformed materials structure engineering. Equal-
channel angular pressing (ECAP) method was created by Segal [1]. Simple shear
uniform deformation of high intensity can be achieved on a 15×15×150 mm mac-
rosample without changing its sizes (Fig. 1). Another method based on the defor-
mation by twist extrusion (TE) scheme was proposed by Beygelzimer [2] (Fig. 2).
The creation of uniform shear deformation without size changing allows to carry
out repeated deformed treatment in the different (or the same) direction of defor-
mation and, as a result, to control structure formation process under high defor-
mation degrees.
The achievement of high strength in deformed materials with nanostructure is
essentially a more complicated task than it follows from the microscopic theory of
strength. According to the models of this theory, strength of materials is related
with structural element dimension by Hall−Petch equation σт = σ0 + kуd
−1/2 or its
Holt variation for cells materials σт = σ0 + kуd
−1. The extrapolation to nanoscale of
Физика и техника высоких давлений 2005, том 15, № 1
12
Fig. 1. ECAP scheme [1]
Fig. 2. Deformation by TE [5]
grain or cell dimension theoretically predicts a very high strength of nanocrystal-
line materials. But experimental results demonstrate essentially worse situation.
A.W. Tompson [3] reviewed experimental data from variety of investigations ob-
tained on high-deformed armco-Fe wires. Relation between flow stress increment
σ − σ0 and substructure size is shown in Fig. 3. In this graph we add our data ob-
tained on armco-Fe deformed by ECAP.
Important conclusions about interrelation of structural evolution and strength-
ening of high-deformed materials follow from these results. Firstly, it is the
change of strengthening mechanism from grain size sensitivity (Hall−Petch equa-
tion) to cell size sensitivity (Holt equation) at critical grain size d < 0.4 µm. Sec-
ondly, it is the theoretical possibility to
obtain superhigh strengthening in nano-
crystalline armco-Fe. It follows from
experimental data (see dashed line) that
extrapolation of experimental data to
nanostructure sizes (10 nm) gives, for
such material, the value of yield point of
approximately 6000 MPa. But the thread
conclusion restricts such possibility. Dif-
ficulty is amplified due to the fact that
the cell or subgrain size in armco-Fe
obtained by different methods of severe
plastic deformation (rolling, drawing,
EC-pressure) cannot be less than 100
nm. As a result, the yield point for such
material is only 1000 MPa [3−6].
Fig. 3. Effect of cell size on yield point of
high-deformed armco-Fe after ECAP (1)
and wire drawing (2) [4]
Физика и техника высоких давлений 2005, том 15, № 1
13
Experimental procedure
In order to explain the restriction of structural dispersion in deformed materials care-
ful investigations of deformed substructure by TEM were carried out. More important
experimental work was published by Langford and Cohen [6] who investigated high-
deformed armco-Fe wires. Practically the same results were obtained in our work,
where severe plastic deformation in armco-Fe was produced by rolling and ECAP.
Results and discussion
The following expression for f, the fraction of the initial number of cells in a
cross section at any given deformation power can be written
)](exp[ in
in
ee
N
Nf −−= , (1)
where Nin is the initial number of cells per unit cross-sectional area as formed at
some early strain ein and N is the number of cells per unit cross-sectional area at
some subsequent strain e. Measurements of N have been made during the defor-
mation and corresponding values of f versus e are plotted in Fig. 4. As it can be
deduced from Fig. 4, f is near unity both for wire drawing and for rolling defor-
mation under low and medium deformation degrees. This result is in a good
agreement with the Tailor−Pallany law: both bulk material and structural elements
(grains, cell) have the same shape under deformation. Since ECAP is a process
capable of producing plastic deformation without causing substantial change in
geometric shape of billet, the cell size of ECAP deformed iron at the medium de-
formation degrees is substantially higher.
Under high deformation power principal changing in f(e) dependence takes
place. There is the large decrease in f throughout the subsequent elongation, signi-
fying that substantial dynamic recovery is operative during the cell refinement.
This means that many cells are being lost from the structure simultaneously with
cross-sectional reduction of the re-
maining cells. It is clear that cell wall
migration constitutes a very important
aspect of the structural changes and
the critical deformation degree ec, un-
der which changing in f(e) dependence
takes place, is a very important mag-
nitude. Cell size evolution under de-
formation is accompanied by the in-
creasing of cell misorientation.
According to Tompson’s model [3]
of structural evolution, static and dy-
namic recoveries are the main reasons
limiting the minimal size of structural
elements under deformation in high-
Fig. 4. The dependence of f-parameter on
deformation degree e: • − rolling, ∆ − ECAP,
ο − wire drawing [4]
Физика и техника высоких давлений 2005, том 15, № 1
14
deformed materials. On one hand, many cells are being lost from the structure
during this process, on the other hand, the recovery process promotes boundary
perfection and increases misorientation of cells. But this model cannot explain the
existence of critical deformation degree ec, which characterizes start or strong ac-
tivation of this process.
Rybin [7] proposed the disclination model of severe plastic deformation. This
model is based on the analysis of micromechanical stress arising around a dislo-
cation during plastic deformation. According to this model, plastic deformation in
crystals is developed by moving dislocation at a low and medium deformation.
But after transformation of substructure from dislocation forest to cells at ei ~ 0.2
a change of deformation mechanism takes place and severe deformation is evoked
by generation of disclination modes without diminution in subgrain size.
Calculation in the framework of disclination model gives critical cell size ~ 0.2 µm
for BCC metals. As far as the critical cell size depends on some physical constants
(Burgers vector, elastic modulus, stacking fault energy), for some FCC metals its
value is essentially lower. It is in a good agreement with recent experimental data,
obtained on ECAP deformed Ni and Al where the average size of structural ele-
ment was 30−50 nm [8]. The disclination theory predicts monotonic rise of
misorientation with the increasing of deformation power and does not imply any
spatial features of mechanical behaviour of high-deformed materials after critical
deformation ec.
Near the critical deformation ec there is the change in the mechanical behavior
of materials [9]. The parabolic strain hardening which was observed at the low
and medium deformation degrees was followed by the linear stage of deformation
at high deformation degrees. The growth of the fracture toughness for specimens
with cracks introduced into the plane per-
pendicular to the plane of deformation
was shown.
Mechanical behavior near critical de-
formation ec was observed in high-
deformed armco-Fe after ECAP. The
growth of the fracture toughness for
specimens with cracks introduced into the
plane perpendicular to the plane of de-
formation was shown, and the decreasing
of the fracture characteristic for speci-
mens with cracks introduced into the
plane parallel to the plane of deformation
was observed (Fig. 5). The increasing of
the deformation degree (e > ec) promotes
the change of the failure mechanism as:
quasi-cleavage → quasi-cleavage with
delamination. On the contrary, transition
Fig. 5. Fracture toughness of strained
iron: 1, 2 − rolling; 3, 4 − ECAP (1, 3 −
crack introduced into the plane perpen-
dicular to the plane of deformation; 2, 4
− crack introduced into the plane paral-
lel to the plane of deformation)
Физика и техника высоких давлений 2005, том 15, № 1
15
from the parabolic stage of strain hardening to the linear one is not related with
the change of the deformation mechanism. Therefore the processes occurring near
critical deformation ec are very important and must be investigated more carefully.
The noted features of structure formation in deformed materials predetermine
regularities of designing their mechanical properties. Analysis of strengthening
curves for a deformed material is made usually basing on structural changes occur-
ring in the material at its continuous loading. And it is assumed that each successive
structural condition follows from the evolution of the previous one, and a change of
the deforming stress is a consequence of the evolution. Structure sensitive models of
strain hardening have been described in detail by many authors [10−12].
Practically the same approaches are used to analyze structural sensitivity of me-
chanical properties of prestrained materials [5]. Widely used is the known postulate
of mechanics that deforming stress being achieved in a material at repeated defor-
mation corresponds exactly to deforming stress achieved in it at the unloading mo-
ment at initial deformation. This postulate does hold well in the range of low and
medium deformation degrees for materials which have not susceptibility to recov-
ery process [13]. For example, it was verified enough really in Al−Ti−Cr intermet-
allic specimens in our experiments under uniaxial compression tests, Fig. 6,a. But
this postulate does not hold for materials which have inclination to recovery. Such
results were obtained in aluminium (Fig. 6,b) which is inclined to recovery. Strain
hardening curve obtained by single loading compression test (Fig. 6,b, curve 1) was
compared with curves obtained after repeated deformation (second deformation −
curve 2, third deformation − curve 3 and fourth deformation − curve 4). Experi-
mental data show that prestrained materials have both lower yield point and lower
strain hardening coefficient than it follows from the postulate.
a b
Fig. 6. Stress-strain curves of Al−Ti−Cr alloys (a) (1, 2 – continuous deformation, 3 –
repeated deformation) and of pure Al (b) (1, 2 – continuous deformation, 3−5 − repeated
deformation)
Физика и техника высоких давлений 2005, том 15, № 1
16
Unfortunately, due to the fact that conditions of uniaxial deformation are lim-
ited by friction and size effects under compression and by neck formation process
under tension, it is impossible to verify the postulate at high deformation powers
(more than e = 0.4). Therefore, in order to obtain strain hardening curve of high-
deformed aluminium in unified loading condition we have made repeated grinding
of lateral faces of a specimen deformed by single compression. As a result, the
specimen was put into shape of rectangle and tested by repeated compression.
This strain hardening curve (curve 5) lies essentially lower than single one (curve
1) but its start position coincides with the end of last curves obtained by repeated
compression (curve 4). Since the summary hardening curve of predeformed mate-
rials could be obtained by mating results of consecutive loading cycles, but be-
cause of recovery process its strain hardening coefficient may be essentially lower
than one obtained under continuous loading.
In titanium specimens we obtained similar effects [14]. Strain hardening curves
obtained by uniaxial tension (subject to neck formation moment) and data on
hardening of the material after high-deformed rolling were compared (Fig. 7). In
this case, the hardening is stronger essentially for the specimens tested in continu-
ous loading than that for the specimens tested in reloading of predeformed mate-
rial. In particular, failure stress of 1600 MPa is achieved under uniaxial tension of
pure titanium. In high-deformed rolled titanium the stress never exceeds 600−700
MPa. Undoubtedly, a difference of both loading conditions and of specimen tex-
ture should be taken into account in this case. However only these factors do not
in any case explain essential difference in titanium properties in conditions of
continuous loading and pre-deformation states.
Larikov [15] explains the recovery process by increasing the mobility of screw
dislocation components and, as a result, activation of cross slip in plastic defor-
mation mechanism. The processes of structural relaxation proceeding by recovery
mechanism both during plastic deformation and during unloading seem to be the
most important factors to promote loss of strengthening in high-deformed materials.
We analyzed microplasticity curves of
predeformed rolled molybdenum speci-
mens (range of deformation degrees
9−75%). It was found (Fig. 8) that at the
initial stage of repeated deformation mi-
croplasticity stress-strain diagrams are
insensitive to pre-deformation degrees
(and therefore to structural state of de-
formed materials). In the microdeforma-
tion level at 10−5, 10−4 and 5·10−4 defor-
mation degrees (Fig. 9) the deformation
stress is practically the same for all inves-
tigated materials. Differences start to be
noticeable at 2·10−3 (yield point). And only
Fig. 7. Stress-strain curves for Ti: ■ –
tension, ● – rolling
Физика и техника высоких давлений 2005, том 15, № 1
17
Fig. 8. Microplasticity curves of molybdenum deformed by rolling to different deforma-
tion degrees, %: 1 − initial, 2 – 9, 3 – 13, 4 − 23, 5 − 39, 6 − 53, 7 – 63, 8 − 68, 9 – 73
Fig. 9. Stress-prestrain dependences of molybdenum deformed by rolling for different mi-
croplasticity levels: ◊ − 5·10−3, − 2·10−3, ▼ − 1·10−3, ▲ − 5·10−4, ● − 1·10−4, × − 1·10−5
at comparatively high repeated deformation degree 5·10−3 the stable increase of
stress with the rise of deformation is observed. Obviously, the hardening curves
obtained at microdeformation levels cannot be explained in the framework of tra-
ditional structural model. In the initial stage of repeated deformation the recovered
cells structure interacts with the moving dislocation in a spatial way.
These data are important for creation of an adequate model of mechanical be-
haviour of high-deformed materials, and may be useful in the explaining of
anomalous dependence of fracture toughness on deformation power of materials
tested in ductile-brittle transition temperature range (see Fig. 5). In this case, the
laws of interaction of dislocations being emitted from a crack tip with primary
structure, in conditions when number of the dislocations is not too large, should be
accounted for.
Conclusions
Cells or subgrain size in armco-Fe obtained by different methods of severe
plastic deformation (rolling, drawing, EC-pressure), cannot be less than 100 nm.
As a result, the yield point for such material is only 1000 MPa. Static and dynamic
recovery are the main reasons limiting the minimal size of structural elements un-
der deformation in high-deformed materials.
The change of mechanical behavior near critical deformation ec was observed
in high-deformed armco-Fe after ECAP .The growth of the fracture toughness for
specimens with cracks introduced into the plane perpendicular to the plane of de-
formation was shown, and the decreasing of the fracture characteristic for speci-
mens with cracks introduced into the plane parallel to the plane of deformation
was observed. Increasing of the deformation degree (e > ec) promotes the change
of the failure mechanism as: quasi-cleavage → quasi-cleavage with delamination.
Физика и техника высоких давлений 2005, том 15, № 1
18
Postulate of mechanics, that deformation stress being achieved in a material at
repeated deformation corresponds exactly to deformation stress achieved in it at
unloading moment at the initial deformation, does hold well for materials which
have no susceptibility to recovery process. But this postulate does not hold for
materials which have inclination to recovery. Structural relaxation proceeding by
recovery mechanism both during plastic deformation and during unloading pro-
motes loss of strengthening in high-deformed materials.
In the initial stage of repeated deformation the recovered cells structure inter-
acts with the moving dislocation in a spatial way. In the microdeformation level,
the hardening stress is practically independent of previous deformation degrees in
the wide interval of deformation. Usual increase of strengthening with rise of de-
formation is observed only starting from the yield point (e = 0.002).
The author wishes to thank Prof. S. Firstov and Dr. M. Danylenko for fruitful
discussion. I also thank Dr. D. Verbylo who assisted in the experiments.
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