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Deformation in nanocrystalline materials
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Deformation in nanocrystalline materials
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Deformation in nanocrystalline materials
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Deformation in nanocrystalline materials
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Deformation in nanocrystalline materials
Superplasticity
Superplasticity the ability of a material to
sustain large plastic deformation has been
demonstrated in a number of metallic,
intermetallic and ceramic systems. Conditions
considered necessary for superplasticity are a
stable fine-grained microstructure and a
temperature higher than 0.5 Tm (where Tm is the
melting point of the matrix). Superplastic
behaviour is of industrial interest, as it forms
the basis of a fabrication method that can be
used to produce components having complex shapes
from materials that are hard to machine, such as
metal matrix composites and intermetallics. Use
of superplastic forming may become even more
widespread if lower deformation temperatures can
be attained.
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Deformation in nanocrystalline materials
Superplasticity
Stress-strain data obtained at constant strain
rates and temperatures. Shown are stress-strain
curves for electrodeposited nickel (a), aluminium
alloy 1420-Al processed by severe plastic
deformation (b). Note the transition from low
plasticity to superplasticity in (a) between 280
C and 350 C, the high strain rates in (b).
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Deformation in nanocrystalline materials
Superplasticity
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Deformation in nanocrystalline materials
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Deformation in nanocrystalline materials
shear bands
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Deformation in nanocrystalline materials
shear bands
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Deformation in nanocrystalline materials
Dislocation emission
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Deformation in nanocrystalline materials
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Deformation in nanocrystalline materials
Very high values of the yield stress (see point
(i)) are thought to be related to the effect of
GBs as obstacles for movement of lattice
dislocations being carriers of plastic flow in
grain interiors. That is, grain refinement causes
lattice dislocation movement to be hampered and
the yield stress to be increased. This statement
is in agreement with classical representations on
the strengthening effect of GBs in conventional
coarse grained polycrystals, described by the
standard HallPetch relationship. However,
mechanically loaded nanocrystalline materials
exhibit deviations from the conventional grain
size strength relationship at very small grain
sizes with dlt30 nm see point (ii). This abnormal
HallPetch relationship is a remarkable
manifestation of specific behavioral features of
nanocrystalline solids.
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Deformation in nanocrystalline materials
Lattice dislocation slip and diffusional
deformation modes occur in, respectively, large
grains (with dislocation signs) and small
(shaded) grains
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Deformation in nanocrystalline materials
Many efforts have been made to describe
theoretically the abnormal HallPetch
relationship in nanocrystalline materials. In
early theoretical studies, models of
nanocrystalline materials as two-phase composites
with nanograin interiors and GBs being component
phases have been dominant. They describe the
yield stress t and account for the macroscale
phenomena (i) and (ii) in nanocrystalline
materials, using the so-called rule of mixture.
In this approach, the yield stress t of a
nanocrystalline material is some weighted sum
(mixture) of the yield stresses characterizing
the grain-interior and grain-boundary phases,
which strongly depends on the volume fraction of
the GB phase and, therefore, the grain size d.
The yield stress of the grain-boundary phase is
assumed to be lower than that of the
grain-interior phase, in which case the rule of
mixture describes the deviations from the
conventional HallPetch relationship in
accordance with experimental data.
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Deformation in nanocrystalline materials
Such models deal with macroscopically averaged
characteristics and use the volume fraction of
the GB phase as the control parameter. They do
not account for the nanoscale phenomena (v)(vii)
related to evolution of defects and GB
structures, and cannot be effective in explaining
the new macroscale phenomena (iii) and (iv) that
definitely need to be described in terms of
defects and transformations of GB structures.
There are several theoretical models that
describe physical mechanisms of plastic flow in
nanocrystalline materials and deal with evolution
of defects (lattice dislocations, GB
dislocations, vacancies) and transformations of
GB structures, that occur in mechanically loaded
nanocrystalline materials.
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Deformation in nanocrystalline materials
In the framework of this approach, several models
exploit the idea of lattice dislocation motion in
grain interiors as the basic deformation
mechanism in nanocrystalline materials, which is
modified (compared to that in coarse grained
polycrystals) as a result of nanoscale effects.
At the same time, the generic idea of most models
is that the GB phase provides the effective
action of deformation mechanism(s) in
nanocrystalline materials, which is (are)
different from the lattice dislocation mechanism
realised in conventional coarse-grained
polycrystals. In the context of this generic
idea, the dominant role of the lattice
dislocation mechanism causes the grain refinement
to strengthen a coarse-grained material, in which
case a classical HallPetch relationship (1) is
valid.
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Deformation in nanocrystalline materials
At the same time, when the deformation mechanisms
associated with the active role of GBs
effectively come into play, the grain refinement
will weaken a specimen this is the case for
nanocrystalline materials with small grain sizes
(dlt30 nm). The theoretical models under
consideration are distinguished by their
identification of the deformation mechanism(s)
inherent to GBs and their description of the
competition between these mechanisms and the
conventional lattice dislocation slip. The
following plastic deformation mechanisms are
commonly treated as those associated with the
active role of GBs and the nanoscale structure,
effectively competing with the lattice
dislocation mechanism in nanocrystalline
materials GB sliding, GB diffusional creep,
triple junction diffusional creep and rotational
deformation
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Deformation in nanocrystalline materials
Nanoscale and interface effects on lattice
dislocation slip
Theoretical models are considered based on
conventional lattice dislocation slip in
nanograin interiors as the dominant deformation
mechanism in nanocrystalline materials, as with
coarse-grained polycrystals. In the framework of
this approach, experimentally documented
deviations from conventional deformation
behaviour (in particular, the HallPetch
relationship) in nanocrystalline materials are
explained as those related to the influence of
grain size reduction and high-density ensembles
of GBs on the formation lattice dislocation
pile-ups in grain interiors and the penetration
of lattice dislocations through GBs in such
materials.
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Deformation in nanocrystalline materials
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Deformation in nanocrystalline materials
Nanoscale and interface effects on lattice
dislocation slip
Despite the good correspondence between
theoretically predicted t(d) dependences and
experimental data, all the models which are based
on the representation of the lattice dislocation
mechanism of plastic flow in nanocrystalline
materials meet the question if the lattice
dislocations exist and play the same role in
nanograin interiors as with conventional coarse
grains. The existence of lattice dislocations in
either free nanoparticles or nanograins composing
nanocrystalline aggregates is energetically
unfavourable, if their characteristic size,
nanoparticle diameter or grain size, is lower
than some critical size which depends on such
material characteristics as the shear modulus and
the resistance to dislocation motion. The models
based on the lattice dislocation slip are
effective in explaining the deformation behaviour
of nanocrystalline materials with grain size
dlt30100 nm.
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Deformation in nanocrystalline materials
Deformation modes associated with enhanced
diffusion along grain boundaries and their triple
junctions
The deformation mechanisms associated with
enhanced diffusion along GBs and their triple
junctions in nanocrystalline materials will be
considered, with the combined effects of the
competition between various deformation
mechanisms (depending on the grain size) and
distribution of grain size on the deformation
behaviour of nanocrystalline materials taken into
account. This model, based on the idea of
competition between lattice dislocation slip, GB
diffusional creep (Coble creep) and bulk
diffusional creep is summarized below. The
assumptions in this model are
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Deformation in nanocrystalline materials
Deformation modes associated with enhanced
diffusion along grain boundaries and their triple
junctions
1. It is assumed that polycrystals with a
relatively large average grain size obey the
classical HallPetch relation (1). 2. At the
other extreme for very small grain sizes, it is
assumed that Coble creep is active and that the t
versus d relationship is given by tcA/d Bd3
(2) where B is both temperature and
strain-rate dependent. The additional term A/d
(the threshold term) can be large if d is in the
nanometer range. For intermediate grain sizes,
both mechanisms might be active if the specimen
has a range of grain size distribution. 3. The
statistical nature of the grain sizes in a
polycrystal is taken into consideration. 4.
Finally, it is assumed that a grain size d
exists at which value the classical HallPetch
mechanism switches to the Coble creep mechanism
thptc at dd.
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Deformation in nanocrystalline materials
Deformation modes associated with enhanced
diffusion along grain boundaries and their triple
junctions
Thus this model uses conventional HallPetch
strengthening for larger grains and Coble creep
with a threshold stress for smaller grains. In a
material with a distribution of grain sizes, a
fraction of the grains deform by a lattice
dislocation slip process and the rest by vacancy
transport. As the average grain size decreases,
the fraction deforming by slip decreases and the
overall response changes from strengthening to
softening. The exact form of the yield stress
against grain size curve depends on the relative
values of the HallPetch slope k, the
conventional Coble constant B, the threshold
constant A and the width of the grain size
distribution.
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Deformation in nanocrystalline materials
Deformation modes associated with enhanced
diffusion along grain boundaries and their triple
junctions
The model of Masumura is supported by results of
computer modelling of plastic deformation
processes in nanocrystalline materials,
indicating the essential contribution of Coble
creep to these processes. Also, it should be
noted that Masumura et al. have suggested a new
general approach to the description of the
mechanical characteristics of deformed
nanocrystalline materials, which takes into
account a distribution in grain size and suggests
the simultaneous action of different deformation
mechanisms in a mechanically loaded sample. For
instance, with a distribution in grain size,
recently a theoretical model has been suggested
describing a contribution of the deformation
mechanism associated with triple junction
diffusion to plastic flow in nanocrystalline
materials. In recent years, it has definitely
been recognized that triple junctions of GBs have
structure and properties different from those of
the GBs that they adjoin.
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Deformation in nanocrystalline materials
Deformation modes associated with enhanced
diffusion along grain boundaries and their triple
junctions
In particular, as it has been shown in
experiments, the triple junction diffusion
coefficient Dtj highly (by three or more orders)
exceeds the GB diffusion coefficient Dgb in
polycrystalline materials. Also, following
experimental data, creep associated with enhanced
diffusion along triple junctions contributes to
plastic flow of coarse-grained polycrystalline
aluminium. With these experimental data, Fedorov
et al. suggested that triple junction diffusion
is capable of playing a very important role in
plastically deformed nanocrystalline materials
where the volume fraction of triple junctions of
GBs is extremely high. Actually, triple junction
tubes characterized by high values of the
diffusion coefficient form a continuous network
distributed throughout a nanocrystalline material
(Fig. 3a).
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Deformation in nanocrystalline materials
Deformation modes associated with enhanced
diffusion along grain boundaries and their triple
junctions
When a mechanical load is applied to a
nanocrystalline specimen, atoms/vacancies are
pumped with a high velocity along the continuous
network of triple junctions. Atoms/vacancies move
from one quadruple point to its neighboring
quadruple point along a triple junction and then
to a new neighboring quadruple point, and so on.
(This process resembles a conventional GB
diffusional creep Coble creep which consists
of numerous events each being a stress-driven
mass transfer from one triple junction to its
neighboring junction along a GB plane bounded by
these junctions.) Thus, directional diffusional
creep along the continuous triple junction
network occurs resulting in the macroscopic
plastic deformation of a nanocrystalline
specimen.
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Deformation in nanocrystalline materials
Deformation modes associated with enhanced
diffusion along grain boundaries and their triple
junctions
In the illustrative case shown in Fig. 3bd,
triple junction tubes provide a diffusional mass
transfer from lateral to upper and bottom free
surfaces of a nanocrystalline specimen under
tensile deformation.
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Deformation in nanocrystalline materials
Deformation modes associated with enhanced
diffusion along grain boundaries and their triple
junctions
Diffusional deformation modes a continuous
network of triple junction tubes (lines) in
cylindrical nanocrystalline specimen points
where triple junction tubes enter free surfaces
are shown as filled circles bd inhomogeneous
creep occurring through enhanced diffusion along
triple junction tubes in nanocrystalline specimen
(shown schematically) triple junction tubes
provide mass transfer from lateral to both upper
and bottom free surfaces of cylindrical specimen
under uniaxial tension e homogeneous bulk
diffusional creep.
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Deformation in nanocrystalline materials
Deformation modes associated with enhanced
diffusion along grain boundaries and their triple
junctions
Fedorov et al. suggested a theoretical model
describing the yield stress dependence on grain
size in fine-grained materials, based upon
competition between conventional dislocation
slip, GB diffusional creep and triple junction
diffusional creep. The model takes into account
also a distribution in grain size. As has been
shown that the contribution of triple junction
diffusional creep increases with reduction of
grain size, causing a negative slope for the
HallPetch dependence in the range of small
grains (see curve 1 in Fig. 4). These results
have been compared with experimental data for
copper and have been shown to be in rather good
agreement (Fig. 4).
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Deformation in nanocrystalline materials
Deformation modes associated with enhanced
diffusion along grain boundaries and their triple
junctions
Fig4 Yield stress s as a function of inverse
square root of average grain size d in copper
experimental data along with calculated values
are shown solid and dashed curves correspond to
model calculations with contribution of triple
junction diffusional creep, respectively, taken
and not taken into account classical HallPetch
dependence is shown as dotted line
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Deformation in nanocrystalline materials
Grain boundary sliding
Now it will be discussed GB sliding as the
deformation mechanism that effectively competes
with the conventional lattice dislocation slip
and diffusional deformation modes in
nanocrystalline materials. The GB sliding occurs
via the motion of mobile GB dislocations with
Burgers vectors being tentatively parallel to the
boundary planes. Triple junctions of GBs, where
the boundary planes with various orientations
join together, serve as obstacles for the GB
dislocation motion. When GB dislocations overcome
the obstacles, they and GB structures undergo
transformations that accompany and accommodate
the GB sliding.
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Deformation in nanocrystalline materials
Grain boundary sliding
There are several models that describes GB
sliding. Now it will be considered a theoretical
model which involves representations of the GB
sliding in a description of the experimentally
detected fact that the t(d) relationship in
nanocrystalline materials shows two different
behaviours, depending on their processing. In the
range of small grain sizes, heat-treated
materials exhibit inverse Hall Petch behaviour
(softening with reduction of grain size), whereas
the yield stress or hardness of as-prepared
materials slightly increases or saturates at
grain size dlt10 nm showing little or no inverse
HallPetch behaviour (Fig. 5).
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Deformation in nanocrystalline materials
Grain boundary sliding
Fig5 Comparison of theoretical predictions (solid
and dashed curves) with experimental dependences
HV(d-1/2) obtained by Volpp et al. for
as-prepared (open boxes) and heat-treated (filled
boxes) nanocrystalline materials, respectively
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Deformation in nanocrystalline materials
Grain boundary sliding
This difference in the deformation behaviour
between heat-treated and as prepared
nanocrystalline materials is related to the
difference between their defect structures.
Different defect structures in heat-treated and
as-prepared materials cause the effective action
of different deformation modes occurring as a
result of grain refinement. In particular, the
contribution of GB sliding is expected to be high
in as-prepared materials commonly characterized
by a high density of lattice and GB dislocations
which enhance GB sliding processes. On the other
hand, heat treatment is capable of suppressing GB
sliding, in which case diffusional deformation
modes effectively come into play.
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Deformation in nanocrystalline materials
Grain boundary sliding
Let us consider a nanocrystalline specimen
fabricated in highly non-equilibrium conditions.
Most of the fabrication routes produce highly
defected GBs. In particular, GBs with an excess
density of GB dislocations carriers of GB
sliding often exist in as fabricated
nanocrystalline materials (Fig. 6a). When a
mechanical load is applied to the specimen,
mobile GB dislocations (with Burgers vectors
being parallel to GB planes) move causing GB
sliding. Some of the moving GB dislocations
annihilate when they meet GB dislocations having
Burgers vectors of opposite sign (Fig. 6b). Other
GB dislocations are stopped at triple junctions
of GBs, that represent effective obstacles for
dislocation movement (Fig. 6b). In general, GB
dislocations stopped near a triple junction are
capable of overcoming the junction obstacle by a
dislocation reaction when the shear stress
reaches some critical value (Fig. 6c).
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Deformation in nanocrystalline materials
Grain boundary sliding
Fig6 Grain boundary sliding at triple junctions.
(a) grain boundary dislocation ensemble in
as-prepared nanocrystalline specimen (b) grain
boundary dislocations accumulate near triple
junctions under action of mechanical load (c)
dislocation with Burgers vector b0 moves and
comes into reaction with two dislocations (with
Burgers vectors b1 and b2), resulting in
formation of grain boundary dislocation with
Burgers vector b3
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Deformation in nanocrystalline materials
Grain boundary sliding
In nanocrystalline materials with their
high-density ensembles of triple junctions, the
critical shear stress needed for GB dislocations
to overcome triple junctions specifies the
contribution of GB sliding to the yield stress.
With the transformation of GB dislocations (Fig.
6) treated as a basic elementary act of plastic
deformation at its initial stage in as-prepared
nanocrystalline solids, the yield stress is given
as follows tk1k2/d where k1 and k2 are
constants. Grain size d occurs in such equation
as a length scale characterising elastic
interaction between GB dislocations located near
different triple junctions (Fig. 6b and c)
separated by d from each other.
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Deformation in nanocrystalline materials
Grain boundary sliding
Such equation quantitatively characterises GB
sliding as a deformation mode (being in
competition with other deformation modes) and
gives a t(d) dependence which is in rather good
agreement with the corresponding experimental
data on mechanical characteristics of as-prepared
nanocrystalline NiAl materials synthesised by the
ball milling technique (Fig. 5). Heat treatment
of nanocrystalline materials gives rise to
annihilation of GB dislocations and thereby
suppresses GB sliding, in which case diffusional
deformation mechanisms compete with conventional
dislocation slip in heat-treated nanocrystalline
materials. The yield stress dependence on grain
size d in heat-treated nanocrystalline NiAl
materials has been calculated, taking into
account competition between the conventional
dislocation slip and Coble creep (treated as
alternative to GB sliding). The theoretical
dependence is in a good agreement with the
corresponding experimental data (Fig. 5).
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Deformation in nanocrystalline materials
Grain boundary sliding
Superplasticity
We will consider the role of GB sliding in
superplasticity exhibited by some nanocrystalline
solids at relatively high strain rates and low
temperatures. It is characterised by very high
flow stresses and strengthening which are the
specific features of superplastic nanocrystalline
materials, their deformation behaviour differing
from that of conventional microcrystalline
materials exhibiting superplasticity. The
dominant mode of superplasticity in
nanocrystalline materials is viewed to be GB
sliding, in which case the unusual strengthening
should be related to the specific features of GB
sliding in nanocrystalline materials. A
theoretical model has been suggested describing
the strengthening in nanocrystalline materials
exhibiting superplasticity as the phenomenon
caused by transformations of GB dislocations
carriers of GB sliding at triple junctions of
GBs.
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Deformation in nanocrystalline materials
Grain boundary sliding
Shear bands
Now let us discuss the experimentally observed
phenomenon of plastic flow localisation in
nanocrystalline materials. In general, plastic
deformation in nanocrystalline materials can be
spatially homogeneous or localised in narrow
shear bands. The model of Hahn and colleagues
describes plastic flow localisation as the
phenomenon occurring owing to a local migration
of GBs that accompanies GB sliding. More
precisely, the local migration of GBs is
considered to provide the formation of a
tentatively planar ensemble of the GBs (Fig. 8)
along which an intensive plastic shear occurs via
the correlated GB sliding processes. Triple
junctions do not play the role of geometric
obstacles at planar GBs along which GB sliding is
thereby enhanced. These macroscopic planar GB
structures are associated with shear bands where
high (super)plastic deformation is localised,
resulting in a large macroscopic deformation of a
nanocrystalline sample.
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Deformation in nanocrystalline materials
Grain boundary sliding
Shear bands
Fig.8 Plastic flow localisation (a) local
migration of grain boundaries gives rise to (b)
formation of local zone where grain boundaries
are parallel to each other and intensive plastic
shear occurs.
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Deformation in nanocrystalline materials
Grain boundary sliding
Shear bands
Results of computer simulations of plastic
deformation processes in model nanocrystalline
metals support the idea of the essential
contribution of GB sliding to these processes.
The competition between lattice dislocation
motion and GB sliding has been revealed. For
small grain sizes (tentatively lt10 nm), all
deformation is accommodated in GBs and occurs, in
particular, through atomic jumps that can be
treated as elementary acts of GB sliding and
accommodating diffusion. At higher grain sizes,
intragrain deformation is observed which occurs
via the motion of partial dislocations in grain
interiors, in which case these dislocations are
emitted and absorbed in the opposite GBs. Thus,
results of computer modelling indicate in favour
of the competition between conventional
intragrain sliding via lattice dislocation motion
and GB sliding in nanocrystalline materials. In
doing so, the role of GB sliding increases with
reduction in grain size.
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Deformation in nanocrystalline materials
Interaction between deformation modes
Nanocrystalline materials are aggregates of
nano-sized grains in which different deformation
mechanisms can strongly influence each other.
That is, there is a kind of effective interaction
between deformation modes in nanocrystalline
materials, which definitely should be taken into
consideration. In particular, it is of crucial
importance in high-strain-rate superplasticity of
nanocrystalline materials, which, according to
experimental data, involves GB sliding, grain
rotations and lattice dislocation slip as the key
deformation modes strongly influencing each
other. In this context, a new approach in the
theory of plastic deformation processes has
recently been developed which takes into
consideration the combined action of interacting
deformation modes that enhance each other.
Interaction between deformation modes is
sensitive to characteristics of GB structures,
triple junction geometry and GB defects, and not
only to grain size distribution.
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Deformation in nanocrystalline materials
Interaction between deformation modes
Therefore, this approach is potentially able to
explain effectively preparationstructurepropert
ies relationships that are responsible for the
new macroscale phenomena (iii) and (iv). An
example of interacting deformation modes is the
GB sliding enhanced owing to lattice dislocation
slip. Lattice dislocations moving in grain
interiors come to GBs where they split into GB
dislocations that carry intensive GB sliding.
This kind of interaction between deformation
modes is well known in the theory of
superplasticity of conventional microcrystalline
materials and definitely plays a significant role
in nanocrystalline materials with grain sizes
ranging from 30 to 100 nm, in which lattice
dislocation slip is intensive. In nanocrystalline
materials characterized by a high volume fraction
of the GB phase, GBs not only absorb but also
intensively emit lattice dislocations. This
phenomenon has been observed in direct
experiments.
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Deformation in nanocrystalline materials
Interaction between deformation modes
Another case of interacting deformation modes is
the crossover from GB sliding to rotational
deformation in nanocrystalline materials. Triple
junctions of GBs, where GB planes change their
orientations, serve as obstacles for the GB
dislocations that carry GB sliding. Under these
circumstances, GB dislocations stopped at a
triple junction are capable of being split into
climbing GB dislocations (Fig. 12). When this
process repeatedly occurs at a triple junction,
it results in the formation of two walls of
dislocations climbing along the grain GBs beside
the triple junction (Fig. 12). The climbing
dislocation walls cause crystal lattice rotation
in the grain interior, in which case the
repeatedly occurring splitting of gliding GB
dislocations at the triple junction provides the
crossover from GB sliding to rotational
deformation mode.
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Deformation in nanocrystalline materials
Interaction between deformation modes
48
Deformation in nanocrystalline materials
Conclusions
Theoretical models of plastic flow and diffusion
modes in nanocrystalline materials have been
reviewed with special attention paid to
explanation of experimentally detected features
in these materials. In general, there are three
key theoretical approaches to a description of
the unusual deformation behaviour of
nanocrystalline materials. The first approach
treats nanocrystalline materials as composites
with GBs and grain interiors playing the role of
constituent phases. In the framework of this
approach, the yield stress is given by the
so-called rule-of-mixture (conventionally used in
the theory of composites) as a weighted sum of
the yield stresses that characterise the GB phase
and grain interiors.
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Deformation in nanocrystalline materials
Conclusions
The second approach focuses on competition
between physical mechanisms of plastic
deformation in nanocrystalline materials and its
dependence on grain size d and its distribution.
This approach attributes the abnormal HallPetch
relationship to either essential modification of
conventional lattice dislocation slip or
transition to another deformation mechanism
(associated with the active role of GBs) in
plastically deformed nanocrystalline materials
owing to nanoscale effects and the existence of
high-density ensembles of GBs.
50
Deformation in nanocrystalline materials
Conclusions
The third approach describes different
deformation mechanisms as interacting in
nanocrystalline solids with emphasis on
characteristics of GB structures, triple junction
geometry and defects. This approach is promising
in the explanation of high-strain-rate
superplasticity of nanocrystalline materials,
which involves several deformation modes. Also,
the deformation induced enhancement of
diffusivity in nanocrystalline materials is worth
considering on account of the unusual mechanical
properties of these materials and materials with
bimodal (nano- and micro-grained) structure.
51
Deformation in nanocrystalline materials
Conclusions
Different theoretical models give different
explanations of the deformation behaviour of
nanocrystalline materials, in which case most of
them well account for the corresponding
experimental data. However, it is extremely
difficult to experimentally identify the
deformation mechanism(s) in nanocrystalline
materials owing to their very complicated
nanoscale structure and the transformations
occurring at various length scales during plastic
deformation. In addition, the deformation
mechanisms may be different in different
nanocrystalline materials or even in the same
material under different conditions of loading or
at different stages of deformation. Under these
circumstances, further theoretical and
experimental investigations in this area are
highly desired to improve understanding of the
fundamentals of the excellent deformation
behaviour of nanocrystalline materials and
development of advanced technologies exploiting
their unique mechanical and diffusional
properties.