Processing and mechanical properties of pure mg and in situ aln reinforced mg 5al composite 2

Literature Review

8
Chapter 2
Literature Review

2.1 Strengthening of crystalline materials

By restricting dislocation motion, crystalline solids can be strengthened. Other
dislocations, internal boundaries (such as grain, subgrain, or cell boundaries), solute
atoms and second-phase particles are commonly employed as obstacles to the motion
of dislocations.

Additional dislocations generated during plastic deformation give rise to work or
strain hardening. Material strength increases owing to the decrease in dislocation
mobility concurrent with an increase in dislocation population. Strain hardening is
caused by dislocations interacting with each other and with barriers which impede their
motion through the crystal lattice. Dislocation multiplication can arise from
condensation of vacancies, by regeneration under applied stress from existing
dislocation by Frank-Read mechanism or multiple cross-slip mechanism or by
emission of dislocations from a high-angle grain boundary. Generally, the rate of strain
hardening is lower for hcp metal than for cubic metal.

Solid solution impurity atoms are generally considered weak hardener whereas
second-phase particles sometimes provide exceptional strengthening. Solute atoms
have more influence on the frictional resistance to dislocation motion than on the static
locking of dislocations. Generally, the strength of such precipitation or dispersion
hardened alloys are limited by the fineness of the particle dispersion in the matrix.
Most high-strength alloys are hardened by more than one mechanisms and the total
Literature Review

9
hardening can be approximated as the sum of the strength contributions resulting from
the separate hardening mechanisms such as work hardening, solid solution
strengthening, precipitation strengthening, grain and subgrain strengthening,
dislocation strengthening, load transfer between matrix and reinforcement in metal
matrix composites (MMCs).

It is common to strengthen an alloy by dispersion hardening in which small second
phase particles such as oxides, carbides, nitrides, borides, etc. are introduced into a
ductile matrix. These finely dispersed second phase particles are more effective in
resistance to recrystallization and grain growth than those in precipitation-hardening
system. Second phase particles act in two distinct ways to retard the motion of
dislocations: particles either may be cut by the dislocations or the particles resist
cutting and the dislocations are forced to bypass them. The degree of strengthening
resulting from second phase particles depends on the distribution of particles in the
ductile matrix. In addition to shape, the second-phase dispersion can be described by
specifying the interrelated factors such as volume fraction, average particle diameter,
and mean interparticle spacing.

A moving dislocation is unable to penetrate a grain boundary and hence grain
boundary is a particularly effective strengthening agent. High density of grain
boundary can be obtained by reducing the grain size to usually 5 µm or less. When the
grain size is reduced to nanometre range, nc materials exhibit a variety of properties
that are different and often considerably improved in comparison with those of
conventional coarse grain polycrystalline materials. Therefore, grain refinement is one
of the most effective strengthening methods in polycrystalline materials.
Literature Review

10
The well-known effect of mean grain size on low-temperature mechanical properties is

described by the Hall-Patch (H-P) empirical relationship: [1,2]

2/1
 dk
HPiy

or
2/1
0

 dkHH
HP

(2.1)

where

y
is the yield strength,

i
the lattice frictional stress, d the grain size, H the
hardness and k
HP
a constant often referred to as the Hall-Petch slope and is material
dependent. This equation is based on the concept that grain boundaries act as barriers
to dislocation motion. It is assumed that a dislocation source at the centre of a grain d
sends out dislocations to pile-up at the grain boundary. The stress at the tip of this pile-
up must exceed some critical shear stress to continue slip past the grain-boundary
barrier thus initiating slip in the next grain as illustrated in Fig. 2.1.


grain 1
grain 2
S
1
S
2



Figure 2.1 Schematic illustration of a pile-up formed in grain 1 under an applied
resolved shear stress

. S
2
is a source in grain 2. The trace of the preferred slip plane in
each grain is marked by a dashed line.

At a critical stress the yielding process rapidly spreads across the specimen. As the
grain size reduces, the increase in grain boundaries constitutes more pile-ups to act as
barriers to dislocation motion causing higher stress concentrations in the neighbouring
grains resulting in increase in yield stress. The mechanical behavior of a
Literature Review

11
polycrystalline pure solid varies with grain size and can be schematically summarized
in Fig. 2.2 [3]. The figure is divided into four regions.

Region I (d>1 μm), where materials have been widely studied, is characterized by a

relatively strong work hardening (caused by dislocation interactions), relatively low
strength, and high ductility. Plasticity is controlled primarily by dislocation motion
within the grains. Material strength in this region follows the classical H–P
relationship, namely, yield strength increases with decreasing grain size. Tensile
failure initiates at macroscopic necking and the fracture mode is intragranular.

Grain size
~1

m

~10-20 nm
I
II
III
IV

Figure 2.2 Yield strength as a function of grain size. According to Hall–Petch
relationship, properties are classified into four regions.

In Region II (1 μm>d>20 nm), the H–P relationship still prevails and the strength of a
material continues to increase as a result of reducing grain size. However, both the
strain hardening rate and the tensile ductility decrease. There is also a gradual
transition of fracture mode from intragranular to intergranular. Another important
observation was that shear deformation becomes localized [4].

Literature Review

12
As the grain size further reduces, one enters into Region III—a region where only

limited reliable experimental data are available [5]. However, recent computer
simulations indicate that materials in this region are characterized by an inverse H–P
relationship, i.e. strength decreases as grain size decreases [6]. Materials exhibit
negligible strain hardening in this region. Plasticity occurs primarily within the grain
boundary region in which sliding of atomic planes is the dominant mode.

Region IV (marked by an arrow) corresponds to amorphous materials (also known as
metallic glasses), which have been extensively explored in recent years [7] and [8].
Experimental results showed that a metallic glass in compression [8] exhibits no strain
hardening and behaves like a perfectly plastic material. In tension, on the other hand,
the material is highly elastic and essentially brittle [7]. The fracture of metallic glasses
occurs by highly localized shear banding. The mechanical characteristics in the four
regions can be conveniently summarized in Table 2.1.

Table 2.1 Mechanical characteristics in different grain size regions [3]
Reg. Grain
size

Strength Ductility Strain
hardening
Fracture Dislocation
activity

Grain-
boundary
activity


I
>1 μm Low High Strong Transgranular,

ductile fracture

High Negligible
II
<1 μm,
>20 nm

Decreases
with grain
size

Moderate Low Transition from
transgranular to
intergranular

Moderate Moderate
III
<20 nm Increases
with grain
size

Low Negligible Sliding of
atomic planes in
grain boundaries

Negligible Dominant
IV 0
High ~0 None Fracture by
localized shear
band formation

None Practically
100%



Literature Review

13
2.2 Nanocrystalline materials
Nc materials (characterized by extremely high volume fraction of grain boundary
phase) represent a new generation of advanced materials exhibiting unique properties
due to the size and interface effects [9-18]. Nc materials are single-phase or multi-
phase materials, the crystal size of which is of the order of a few (typically 1-100)
nanometers in at least one dimension. Because of the extremely small size of the
grains, a large fraction of the atoms in these materials is located in the grain boundaries
(Fig. 2.3) and thus the material exhibits enhanced combinations of physical,
mechanical, and magnetic properties compared to materials with a more conventional
grain size, i.e., >1 μm. These include increased strength/hardness, enhanced
diffusivity, improved ductility/toughness, reduced density, reduced elastic modulus,
higher electrical resistivity, increased specific heat, higher thermal expansion
coefficient in comparison with conventional coarse grain materials. All of these
properties are being extensively investigated to explore possible applications.



Figure 2.3 Schematic arrangement of atoms in an equiaxed nc metal distinguishing
atoms associated with the individual grains (

) and those constituting grain boundary

network () [19].

One of the specific features of deformation processes in nc materials manifests itself in
deviation from the well-known classical Hall-Petch relationship which well behaves
Literature Review

14
for grains larger than about a micron. Most of the investigators try to explain such
unique behaviour based on the effect of large volume fraction of grain boundary and
structural defects induced during material processing. From investigation of nc iron
materials using Mössbauer spectroscopy, nc materials consist of two components of
comparable volume fractions: a crystalline component and an interfacial component
formed by atoms located either in the crystals or in the interfacial regions between
them [20]. Within the large volume fraction of grain boundaries and interfaces, highly
disordered lower atomic density state with vacancy-size free volume is verified with
positron lifetime spectroscopy [21]. Significantly larger component of grain boundary
relative to coarse-grained counterparts suggests the unique mechanical properties
different from coarse-grain polycrystalline materials. Different from coarse grained
structure, at the smallest grain sizes, new phenomena have to be used to explain the
controlling deformation behaviour. It has been suggested that such phenomena may
involve GBS and/or grain rotation accompanied by short-range diffusion assisted
healing events [22].

The properties of nc materials are sensitive to their processing history which influences
the types of microstructures and the processing flaws such as contaminants, porosity,
etc. depending on the processing techniques. Such structural defects generated during
processing play an important role to alter the properties of bulk nc materials.

2.3 Mechanical behaviours of nanocrystalline materials
For understanding of the mechanical properties of nanophase materials in general, a

quantitative framework as shown in Fig. 2.4 is useful. It appears that with decreasing
grain sizes into nanophase regime, the frequency of dislocation activity decreases and
Literature Review

15
that of GBS increases. Which of these effects dominates depends upon the grain size
regime, the specific type of material and most importantly, the nature of its interatomic
bonding.

frequency (arbitrary units)
metals
Grain boundary
sliding
Dislocation
activity
ceramicsintermetallics
decreasing grain size (arbitrary units)

Figure 2.4 Schematic framework for grain size dependence of dislocation activity and
GBS contributions to the deformation behavior of various classes of nanophase
materials. The nature of its interatomic bonding determines the appropriate location for
a particular material [17].

2.3.1 Hardness/Strength and ductility
Most experimental results on the mechanical behaviour of nanophase metals are from
measurement of hardness, which is like strength typically derived from the difficulty in
creating dislocations and the impedance of their motion by the development of barriers
[23]. It has long been observed experimentally in conventional metallic materials that
hardness/strength varies with the grain size through the empirical Hall-Petch relation
(equation 2.1). Hardness typically increases with decreasing grain size and pure nc

metal can be 2 to 7 times harder than large-grain metal (>1 m).

Literature Review

16
In nanograin-size regime, conventional Hall-Petch hardening from the introduction of
increasing number of grain boundaries as barriers against dislocation motion seems to
play an insignificant role. The paucity of mobile dislocations in nanophase grains has
been well documented experimentally [24] and is simply a result of the long known
and well understood image forces that act on dislocations near surfaces and hence in
confined media [25]. The difficulty in creating new dislocations within the spatial
confinements of ultra fine crystallites has also long been evident [26, 27] from earlier
research on single crystal whiskers and wear debris. Since the minimum stresses
required to activate common dislocation sources (such as Frank-Read source) are
inversely proportional to the distance between dislocation pinning points, these
stresses will increase dramatically with decreasing grain sizes into the nanophase
regime owing to the limitation of the maximum distance between such pinning points.
Thus, it appears that the increasing hardness and strength observed in pure nanophase
metals with decreasing grain size is simply a result of diminishing dislocation activity.
While it is clear that the hardness of pure metals increases as their grain sizes are
reduced into the nano size regime, the full extent to which this hardening occurs is not
clear.

Elastic modulus changes can be expected as materials enter the nanophase regime. The
apparent elastic moduli measured to date on nanophase materials [23, 28] have
decreased in value relative to those in their coarse-grained counterparts, probably
because of porosity and flaws resulting from processing [29]. Both grain boundaries
and triple junctions have some contribution to the decrease in the Young’s modulus
due to the increased volume in the interfacial region. However, the steep increase in
Literature Review

17
the triple junction volume fraction largely accounts for the sharp drop in the Young’s
modulus at the smallest grain size [30].

Ductility of nc materials is sensitive to flaws and porosity, surface finish and method
of testing (e.g. tension or compression test). The limited ductility of nc materials is
attributed to difficulties associated with the generation, movement and multiplication
of dislocations inside the nanograins and/or the presence of significant flaw
populations [23, 31, 32]. Since nc materials are very hard (and strong), it is doubtful
whether the formability can be substantially improved (at least in tension), especially
in non-cubic intermetallic compounds. However, room temperature or low
homologous temperature superplasticity in nc materials has been reported by many
investigators [30, 33-36]. Mohamed et al. [36] summarized the experimental results for
both creep and superplasticity in nc materials as shown in Table 2.2.

Recently, high tensile ductility of 45% at room temperature with softening behaviour
indicating inverse Hall-Petch relationship has been reported in bulk nanostructured
Mg-5wt.% Al alloy synthesized via MA with a grain size of ~45 nm [37]. This
enhancement of superplastic behaviour was attributed to enhanced grain boundary
diffusional creep providing the plasticity at ambient or low homologous temperatures.
In other words, Coble creep may be enhanced when the grain size is reduced to
nanoscale region.

It has been reported that as grain size decreases, superplasticity occurs at lower
temperature and higher strain rate. PM alloys containing reinforcement and MMCs
often exhibit high-strain-rate superplasticity (HSRS). This will result in economically
Literature Review

18

Table 2.2 Summary of studies on creep and superplasticity in nanocrystalline materials

Investigators Materials
Processing


Grain size (nm) T (K) n Q (kJ/mol) e
f
Test mode Refs.
Nieman et al. (1990) Pd ICG 7-10 RT - - - tension [29]
Nieman et al. (1991) Cu, Pd ICG 50 RT - - - tension [38]
Sanders et al. (1997) Cu, Pd, Al-Zr ICG 10-55 0.24-0.64 T
m
- - - tension [39]
Hahn and Averback (1991) TiO
2
ICG 40 873-1073 3 - - compression [40]
Cui and Hahn (1992) TiO
2
ICG 40 973-1073 - - - bending [41]
Wang et al. (1994) abd Deng et al. (1995) Ni-P AC 28 543-573 1.2 68.5 - tension [42], [43]
Wang et al. (1994) abd Deng et al. (1995) Ni-P AC
257 573-648 2.5 106 - tension [42], [43]
Xiao and Kong (1997) Fe-B-Si AC
27 733-763 1.2 144 - tension [44]
Xiao and Kong (1997) Fe-B-Si AC 250 733-673 2.0 193 - tension [44]
Wang et al. (1997) Ni ED 6-40 RT 1.2-5 - - tension [45]
Taketani et al. (1994) Al-Ni-Mn-Zr HPGA 80 873 2 - - tension [46]
Mishra et al. (1997) Zn-22Al TS 37 393 3 - - tension [47]
Mishra et al. (1997) Pb-62Sn TS 32 RT 2 - 300% tension [47]

Mishra et al. (1998) Ni
3
Al TS 50 923-998 - - 560% tension [48]
Mishra et al. (1996) Ti-Al-Cr BM 25-50 1023-1223 6 - - compression [49]
Valiev et al. (1998) Ni
3
Al TS 70 923 - - tension [50]
Rittner et al. (1997) Al-Zr IGC 10-100+ RT - - 300% tension [51]
Mcfadden et al. (1999) Ni ED 20 553-693 1-12% tension [33]
Mcfadden et al. (1999) 1420-Al Severe deformation 100 523-623 >200% tension [33]
Mcfadden et al. (1999) Ni
3
Al Severe deformation 50 923-998 350% tension [33]

IGC: inert gas condensation, HPGA: high pressure gas atomization, AC: amorphous crystallization, BM: ball milling, TS: torsion straining and ED: electrodeposition.
e
f
: Elongation to failure.
T
m
: melting temperature.
Literature Review

19
viable, near-net-shape forming techniques under the typical forming rate of
commercial hot working. Therefore, the superplastic deformation mechanisms of these
materials are now under serious consideration. High strain rate (10
0
-10
2

s
-1
)
superplasticity was reported in powder metallurgy Mg composite with grain size 0.3 to
1.7 m by Nieh [52] and Watanabe [53]. From the literature, it is noted that GBS
dominates in the deformation of fine grain size Mg composites.

The constitutive equation to describe superplasticity in metallic materials is generally
expressed as [54,55]

D
d
b
EkT
Gb
A
pn





















0




(2.2)

where


is the strain rate, A a constant, σ the applied stress, σ
0
the threshold stress, E
the Young’s modulus,
G the shear modulus, k the Boltzmann's constant, n the stress
exponent (=1/
m; m is the strain rate sensitivity exponent), d the grain size, b the
Burgers vector,
p the grain size exponent, T the absolute temperature and D the
diffusion coefficient.

To date, several flow mechanisms have been proposed to account for HSRS and
several constitutive equations were also developed to describe the superplastic flow in

PM alloys and MMCs. These are summarized in Table 2.3. All equations predict
n=2,
indicating that slip accommodated GBS is the dominant deformation process [56].
However, it is pointed out that every equation has its own grain size exponent and rate-
controlling diffusion process, depending on the micromechanism concomitant with
GBS. These uncertainties are the result of the fact that the effect of reinforcement on
superplastic behavior has not been fully understood.
Literature Review

20
Table 2.3 Summary of the proposed constitutive equations of superplasticity in powder
metallurgy alloy and metal matrix composites [53]

Constitutive Equation Mechanism Remarks Ref.
L
D
d
b
GkT
Gb
A























1
2
2
0





Pile-up dislocations disappeared by
the climb through the distance of
subgrain size
[57]
i
D
p
dd

b
GkT
Gb
A






















2
2
0





Interfacial diffusion between the
matrix and reinforcement at the
grain boundary is rate-controlling
[55]
gb
D
d
b
G
l
kT
Gb
A
3
2
)
0
)(1(



























Similar to conventional super-
plasticity; consistent results were
obtained when the occurrence of
load transfer from the matrix to the
reinforcement is considered
>0 when
T<Ti,
 = 0 when
T

Ti
[58]
L

D
q
bd
b
GkT
Gb
A





























2
2
2
)
0
(






Dislocations are piled up at the
intragranular particle

[59]

1
, Subgrain size; d
p
, size of reinforcement; T
i
, incipient melting temperature;

l

, load transfer
coefficient;

2
, interparticle spacing; q, reinforcement-spacing exponent (0.5~1); D
L
, lattice diffusion
coefficient; D
i
, interfacial diffusion coefficient; D
gb
, grain boundary diffusion coefficient.

2.3.2 Inverse Hall-Petch relationship or Failure of dislocation strengthening
mechanism
The H-P relation predicts that strength or hardness increases with decreasing grain
size. Recently several studies on nc materials have not only reported observations of a
normal H-P relation but also an inverse H-P relation, that is, hardness increases with
increasing grain size [23,60-64]. Obviously, the equation has limitations because the
strength cannot increase indefinitely with decreasing grain size. Any relaxation process
at grain boundaries associated with an extremely fine grain size could lead to a
decrease in strength and this could result in an inverse relationship below some critical
grain size. Strengthening mechanism in H-P relation is based on dislocation pile-ups at
physical obstacles such as grain boundaries. As the grain size in a polycrystalline
material decreases, there arrives a point at which each individual grain will no longer
be able to support more than one dislocation; at this point, the H-P relation will no
longer hold. From another point of view, when the grain size approaches zero, the
Literature Review

21

material essentially becomes amorphous. Grain boundary strengthening effect will
then disappear.

l

app

app


Figure 2.5 Dislocation pile-up at grain boundaries. The equilibrium distance between
the two dislocations is determined by the externally applied stress [65].

The repulsive force,
f, per unit length between two edge dislocations as shown in Fig.
2.5, in a pile-up is estimated as:

l
Gb
f
1
)1(2
2





(2.3)

where G is the shear modulus, b the Burgers vector, v the Poisson's ratio, and l the
distance between the two dislocations. (A similar relation holds if the critical
deformation event is bowed out of a grain boundary dislocation of length equal to l.)
These two dislocations will move to their equilibrium positions when the repulsive
force between them is cancelled out by the externally applied force

app
b, where

app
is
the applied stress.
Assuming

app
~(

app
/2), it is readily shown that the equilibrium distance, l
c
, between
the two edge dislocations is
Literature Review

22

)1()1( 




MGbGb
l
c

(2.4)

where

=M

, the uniaxial tensile stress is related to the critical resolved shear stress by
Taylor factor with M~6.5 for polycrystalline Mg [66]. In principle, when the grain
size, d, is smaller than l
c
, there will be no dislocation pile-ups, and the H-P relation will
break down.

A number of investigators have suggested that the inverse Hall-Petch relation may be
attributed to the increased grain-boundary activity due to GBS and/or diffusional mass
transfer via grain-boundary diffusion [67-69]. For example, Masumura et al. [70]
suggested that strength softening with decreasing grain size is due to the competition
between the conventional dislocation motion and grain-boundary diffusion via Coble
creep, which is assumed to be responsible for the room-temperature plastic
deformation of nc materials. However, it is not clear that Coble creep [71], which
successfully describes the creep mechanism of coarse-grained polycrystals, can be
extended to nc materials with grain sizes of several nanometers. Moreover,
experimental data indicate a mild grain-size dependence of yield strength in the
strength-softening region [60], in contrast to very strong grain-size dependence, as
required by Coble creep.

Dynamic in-situ deformation studies have been performed in TEM using a straining
stage to provide direct evidence of deformation mechanisms in nc materials [72-76].
However, it is questionable that deformation processes in a thin, electron-transparent
foil can represent those in the bulk material. Mechanical thinning during TEM sample
preparation followed by ion thinning or twin jet polishing, thinning the foil to
Literature Review

23
perforation in most cases, will inevitably result in some relaxation of a previously
deformed microstructure.

2.3.3 Creep
The extensive intercrystalline region composed of gain boundaries and triple junctions
is expected to have profound effect on the bulk mechanical behaviours of nanophase
materials. Since creep is primarily controlled by diffusion, it is expected to occur
readily in nanophase which has short diffusion distance. For a number of nanophase
intermetallics investigated thus far, the mechanical response in the larger end of the
nanophase grain size regime seems rather similar to that for the pure metals. However,
a number of these typically harder and more strongly bound materials exhibit a clear
transition from hardening behaviour to softening behaviour with decreasing grain sizes
or, in some cases, only softening. The softening behaviour or increased ductility
appears to be related to an increase in GBS with decreasing grain size as evidenced by
stress-strain [77] and creep [78] measurements, although direct metallographic
observation of GBS are still lacking in these materials.

It has been suggested [28] that nc materials exhibit nine orders of magnitude
enhancement of the creep rate compared to their microcrystalline counterparts, which
are commonly found in most engineering applications. Sandars et al. [39] reported that
the measured creep rates of nc Cu, Pd and Al-Zr made by inert gas condensation and
compaction were two to four orders of magnitude smaller than the values predicted by

the equation for Coble creep. At moderate temperatures, the creep rates were
comparable or lower than the corresponding coarse-grain rate. Controversially, creep
rates of nano-grained (~28 nm) Ni-P alloy and (27 nm) Fe-B-Si alloy are larger than
Literature Review

24
those of corresponding coarse-grained (~250 nm) samples at the same condition [43,
44].

Superplasticity is generally associated with fine grains [79]. The estimations made by
Valiev et al. [80] showed that decrease in grain size to nanoscale region resulted in
lowering the optimal temperature and increasing the strain rate of superplasticity.
However, the experimental results with respect to the effect of grain size on the creep
rate of polycrystalline materials, as well as the deviation from the Hall-Petch relation
due to creep mechanisms, appear to be inconsistent with each other as well as with
theories. Hahn and Averback [81] studied the creep behaviours of nc (15-40 nm) TiO
2

at temperatures between 600 and 800°C. They reported that the compressive creep
deformation demonstrated an interface reaction controlled mechanism and a weaker
dependence on grain size. The study of the creep of nc (28 nm) Ni
80
P
20
at temperatures
ranging from 270-320°C [42] also suggested that the governing factor of creep
deformation under the experimental condition was grain (and/or phase) boundary
diffusion. Superplastic behaviour of Al alloys with grain size in the sub-micrometer
region indicated that the grain boundaries in ultrafine-grained materials are in a non-
equilibrium condition in comparison to grain boundaries in conventional coarse-

grained ones [80, 82]. However, study on the creep properties of nc pure metals, Pd
and Cu, carried out by Nieman et al. [38] led to a conclusion that creep was not
enhanced in the ultrafine-grained materials at room temperature.

2.4 Role of grain boundary activities in nanocrystalline materials
A nanocrystalline material can be viewed as a composite consisting of a crystalline
component and an intercrystalline component, including grain boundaries, triple lines
Literature Review

25
and quadruple nodes [83]. The volume fractions of these components are illustrated in
Fig. 2.6. It is logical to conclude that the grain boundary deformation process plays a
crucial role in nc materials since the volume fraction of the interfacial component
becomes comparable to the volume fraction of the crystals in nc materials. Diffusion in
nc materials is expected to be comparable or even higher than the rapid short-circuit
diffusion along grain boundaries. Because of the small size of the crystals, the
interfaces may form an extremely dense network of paths for fast diffusion in the nc
materials. It has been found that the high diffusivity results not only from high volume
fraction of the grain boundary phase in such materials but also mostly from residual
porosity, impurity segregation and other factors related to the processing routine of nc
materials [84-86].

Volume Fraction
100010010
Grain Size (nm)
0.6
0.8
0.4
0.2
1.0

0.0
1
Crystalline
Triple line
Grain boundary
Quadruple node
Intercrystalline

Figure 2.6 Plot of volume fractions of crystalline and intercrystalline components
versus grain size. (The grain boundary thickness is assumed to be 1 nm.) [45]

Horváth et al. reported the diffusion coefficients at 353K and 393K to be 2x10
-18
m
2
/s
and 1.7x10
-17
m
2
/s, respectively, which are about 16 or 14 orders of magnitude larger
than bulk self-diffusion and about 3 orders of magnitude larger than the grain-
boundary self-diffusion in copper [87]. They concluded that the vacancy-type defects
Literature Review

26
may give rise to the different contributions to the diffusivity in nc materials.
Investigation from Schumacher et al. [88] revealed that the diffusivity of silver in nc
copper is 2-4 orders of magnitude faster than the diffusion of silver in grain boundaries
of copper bicrystals.

Palumbo et al. [89] reported that the diffusivity of triple lines in nc (17 nm) pure nickel
electrodeposits was three times greater than that of grain boundaries. The higher
diffusivity along triple lines underscores the importance of triple junction defects to the
bulk properties of nc materials [90], which has been taken into account in the analysis
of creep data.

Nabarro–Herring creep [91,92] and Coble creep [71] are well-established models to
account for the diffusional flow creep mechanisms at low stress and fine grain sizes. In
Nabarro–Herring creep, vacancies diffuse through the grain volume and the creep rate
is given by:





















Gd
b
kT
GbD
A
l
NHNH


2


(2.5)

where
A
NH
is a constant, D
l
the lattice diffusivity, G the shear modulus, b the Burgers
vector,
k Boltzmann's constant, T the absolute temperature, d the grain size and σ the
applied stress. On the other hand, the diffusion of vacancies occurs along the grain
boundaries in Coble creep and the creep rate is given by:























Gd
b
kT
GbD
A
gb
CC


3


(2.6)

where
A
C
is a constant (~66) and D
gb
the grain boundary diffusion coefficient.
Literature Review

27
Since the Nabarro–Herring and Coble processes represent two independent
mechanisms, the faster process controls the creep behavior. From equations 2.5 and
2.6, it can be derived a criteria (equation 2.7) that Coble creep should predominate
over Nabarro–Herring creep.

















NH
C
l
gb
A
A
D
D
d
b

(2.7)

Low homologous temperatures and very small normalized grain sizes favor to satisfy
the criteria given by equation 2.7. On this basis, Coble creep (diffusional creep along
grain boundaries) becomes dominant in nanostructured materials with ultra-fine grain
size and the large volume fraction of intergrain areas or grain boundaries when these
materials are subjected to creep deformation at low temperatures. An enhancement in
the creep rate of nc materials by a factor of 10
9
over the microcrystalline materials is
achievable due to the inverse cubic dependence of


on d in equation 2.6 [29].

In nc materials, triple junction creep is also a possibility. While the activation energy
for triple junction diffusion is not available, it is reasonable to anticipate that it would
have a lower value than the grain boundary diffusion energy due to a larger degree of
disorder of atomic arrangement in triple junction areas. However, according to a model

proposed by Suryanarayana et al. [93], when the grain size is about 30 nm the volume
fraction of triple junctions is less than 1% while the fraction of grain boundaries is
about 10% by assuming grain boundary thickness of 1 nm. Based on this information,
the triple junction process is likely to be important when the grain size is less than 10
nm [90].

Literature Review

28
2.5 Texture and mechanical property relationship for hexagonal materials
The deformation texture of hexagonal Mg develops in accordance with the relative
contribution mainly from three distinct slip systems and one twinning system: basal
{0001} <
0211
>, Prismatic {
0110
} <
0211
>, Pyramidal {
1110
} <
0211
>, { 2211 }
<
3211
> and twinning {
2110
} <
1110
> (Fig. 2.7).

Basal



Prismatic



Pyramidal



Twinning

Figure 2.7 Main deformation mechanisms in magnesium crystal.

A large difference in critical resolved shear stress (CRSS) between basal and non-basal
slip gives rise to the severe anisotropic mechanical properties [94]. As a result, their
mechanical properties are significantly influenced by texture in addition to grain size
[95-98]. Directionality or anisotropy of physical, chemical and mechanical properties
)0001(
]0121[
)0110(
)1110(

)2110(

]0121[

]0121[
]0111[
Literature Review

29
will result wherever texture exists in polycrystalline materials. Therefore, the optimum
conditions for texture strengthening can be determined with knowledge of active
deformation modes.

RD
TD
RD
TD

(a) (b)

Figure 2.8 (a) Simulated rolling texture in HCP metals with c/a ratio approximately
equal to 1.633 [100], (b) experimental (0001) and (
0110 ) pole figures for Mg showing
fibre texture [101].

Mg with c/a ratio of 1.624 approximately equal to the ideal c/a ratio of 1.633 tends to
form fibre texture as shown in Fig. 2.8. In extruded magnesium alloys, a strong fibre
texture with the basal plane parallel to the extrusion direction confers high tensile
strength along the extrusion direction due to inhibition of basal slip system even
though low in compressive strength [98]. Mukai et al. [99] reported that equal channel-
angular-extruded (ECAE) and annealed AZ31 Mg alloy exhibited lower yield stress
and tensile elongation-to-failure of two times higher compared to the conventionally

extruded alloy with similar grain size. This is due to the distribution of basal plane
along the extrusion direction in the directly extruded alloy and similar distribution in
both extrusion direction and perpendicular to the extrusion direction in
ECAE/annealed sample.

It has been reported that when the composite is deformed in the extrusion direction, the
addition of ceramic particles induces a decrease in the {
0110 } fiber texture which
Literature Review

30
results in decrease in the yield stress and in the tension/compression asymmetry [102,
103]. At room temperature, the yield stress of Mg-Y
2
O
3
composites produced by
powder metallurgy depends strongly on the intensity of the {
0110
} fiber texture
which decreases with yttria volume fraction [103]. At low temperature (below 300°C),
substantial influence of texture on mechanical properties is observed in extruded Mg
[104, 105] exhibiting higher yield stress of unreinforced extruded Mg with respect to
Mg-Y
2
O
3
[106]. As the testing temperature increases, the activation of non-basal slip
system would result in the disappearance of the texture contribution to the material
strengthening and the composite would present higher mechanical strength compared

with the unreinforced magnesium.

It is generally accepted that grain refinement enhances the GBS mechanism and GBS
progressively removes the texture. It is also known that texture weakens under
superplastic deformation. The texture effect is connected with changes in the grain
boundary structure and Kaibyshev [107] claimed that high angle misorientations
enhance GBS. However, there are controversial reports claiming that texture has a
negligible effect on GBS (or superplasticity) [108,109]. Wide range of reports on grain
size (up to nanometer range) and texture (for micrometer range) dependence of
mechanical properties in Mg can be found in literature. However, the influence of
texture on the mechanical properties of nanograined Mg has not been clarified so far.

2.6 Processing of bulk nanocrystalline materials via mechanical milling/alloying
Nc materials have been synthesized by a number of techniques starting from vapour
phase (e.g., inert gas condensation, sputtering, plasma processing, physical/chemical
vapour deposition), liquid phase (e.g., electrodeposition, rapid solidification), and solid
Literature Review

31
state (e.g., MA/MM, sliding wear, spark erosion) [110]. The advantage of using MM
for the synthesis of nc materials lies in its ability to produce bulk quantities of
materials in the solid state at room temperature using simple equipment.

Besides grain size, chemical composition, and structure, additional parameters such as
the structure and the thickness of the boundary regions are equally important
parameters that control the mechanical properties of a nanostructured material such as
strength and ductility. Nc Ni with the same composition and the same grain size of
about 10 nm exhibited low ductility (<3%) when it was prepared by powder
consolidation whereas Ni prepared by electrodeposition exhibited high ductility
(>100%) [9]. In this case, depending on the processing history, the difference in

ductility behavior seems to reflect the difference in the energy stored in the interfacial
regions of both grades of Ni. Different processing procedures may lead to significant
differences in the initial microstructures of a particular nc material that in turn may
influence the trend of experimental data.


Figure 2.9 Schematic drawing of ball-powder-ball collision.

MA/MM is usually carried out in high-energy mills such as vibratory mills (Spex 8000
mixer/mill), planetary mills (Fritsch and Retsch mills), and attritor mills (Szegvari
attritor) [110]. The kinetics of alloying and other phase transformations induced during
Literature Review

32
MA/MM depend on the energy transferred to the powder from the balls during milling
(Fig. 2.9). This process is governed by many parameters such as the type of mill,
milling speed, type, size and size distribution of the balls, ball/powder weight ratio,
extent of filling of the vial, dry or wet milling, temperature of milling, atmosphere in
the mill and finally, the duration of milling. The kinetic energy of the balls changes
with speed of milling and mass of balls [111-114].

The higher the ball-to-powder ratio, the shorter the required milling time due to the
increase in the number of collision per unit time. Higher collision frequency leads to
the increase in milling temperature, which in turn favours the diffusivity and defect
concentration thus influencing the phase transformation induced by milling. However,
high energy and high frequency collision of balls can introduce contamination from
milling tools. Ball-to-powder weight ratio is normally in the rage of 10:1 and 20:1
[115, 116] and a ratio of about 20:1 is often used particularly for planetary ball mills
[112].

One of the sources of contamination is process control agent (PCA) which is added to
minimise excessive cold welding. However, the PCAs are usually added in very small
quantities (about 1 to 3 wt %) and are not a cause for much concern. Though finer
particle size can be obtained with higher content of PCA, excessive PCA may lead to
inhibition of cold welding and hence prevents the formation of new materials [112].
Furthermore, the addition of PCA results in appreciable pick-up of carbon, oxygen or
nitrogen in the final powder.