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

Effects of strain rate on tensile properties

108
Chapter 5
Effects of strain rate on tensile properties

5.1 Introduction
The strength and ductility of nc metals are dependent upon strain rate and temperature.
The strain-rate sensitivity index, m, where


T
m
,
ln/ln







, in a
m



type
relationship is one of the key engineering parameters that reflects the deformation
behaviors of metals. A highly strain rate sensitive material is expected to resist
localized deformation and hence may be ductile, and in the extreme case of very high

rate sensitivity, be superplastic.

Very low work hardening rates are observed with an increase in the strain rate
sensitivity in Mg when the grain size is reduced to nanometric scale [1]. Recent
experiments on face-centered cubic (fcc) and hexagonal close packed (hcp) nc metals
have reported a more than 10-fold increase in strain-rate sensitivity in contrast to their
conventional coarse-grained counterparts [2,3].
In most practical applications, m is
very small and in certain cases it may even be negligible from engineering point of
view. Superplastic deformation shows large m values and approaches even the value of
1.0 which corresponds to viscoplasticity. Low m-value in the low strain rate range is
often observed in superplastic materials. It has been reported that such values are
associated with the existence of a threshold stress [4]. At high strain rates of over 1 ×
10
−2
s
−1
, the m-value is reduced to a small value where dislocation processes dominate
deformation [5, 6].

Effects of strain rate on tensile properties

109
The overall strain-rate dependence of a material is influenced by dislocation activity,
GB diffusion, and lattice diffusion [7-11]. Generally the contribution of lattice
diffusion is negligible at room temperature. Several authors [12- 16] have reported that
the highly localized dislocation activity (e.g. dislocation nucleation and/or dislocation
de-pinning) at the GBs leads to an enhanced strain-rate sensitivity for nc metals.

Besides enhanced strain-rate dependence in nc materials, a more pronounced

temperature dependence arises from the thermally activated deformation mechanisms
controlling the plastic flow. Deformation at temperature below room temperature
exhibited a rapid increase in YS in nc Ni and Cu, [17]. The origin of the strong
temperature dependence, as well as for the rate sensitivity, has been linked to the small
activation volume of dislocation mobility observed in strain rate change tests [13-
15,17]. The activation volume, in turn, is a signature
of the underlying deformation
processes
[15].

For deformation mechanism, although superplastic deformation is believed to be
achieved by GBS in combination with dislocation glide, the former mechanism, being
strongly dependent on diffusion, naturally leads to a high amount of strain-rate
sensitivity [18]. Conrad and Jung [19,20] proposed a GBS mechanism to explain the
grain size dependence of the plastic deformation kinetics of Cu and Ag in the grain
size range of 10
−2
μm < d < 1 μm. In addition, GBS has been reported as deformation
mechanism of nc metallic materials experimentally by mechanical testing and
theoretically by simulation models [21-26]. However, Jain and Christman [27]
suggested that nc Fe alloy deformed by the ‘core-mantle’ GBS mechanism, whilst
Malow et al. [28] obtained strain rate sensitivity values corresponding to typical
Effects of strain rate on tensile properties

110
deformation by dislocation. For better understanding of deformation mechanisms of nc
Mg-5Al-1AlN composite, several deformation parameters such as strain rate
sensitivities, activation volume and activation energy have been estimated
experimentally in the present study.

5.2 Experimental
7mm diameter extruded Mg-5Al-1AlN composite rods were machined to produce the
cylindrical tensile samples with a gauge diameter of 5mm and a gauge length of 25
mm according to ASTM E8M-96 standard. Uniaxial tensile test was conducted using
an automated Instron 8501 servo hydraulic testing machine at controlled strain rates of
3.33x10
-3
s
-1
, 3.33x10
-4
s
-1
and 3.33x10
-5
s
-1
as shown in Fig. 5.1(a). At least three
samples were tested for reproducibility and conformity to the tensile test standard. For
the purpose of comparison, pure Mg samples were synthesized with same processing
parameters and tested under the same conditions as the composite samples.




(a) (b)
Figure 5.1 Experimental set-up in (a) Instron 8501 for tensile test and (b) Instron 8871
with environmental chamber for creep test.

Instron 8874 axial-torsional servohydraulic test system with environmental chamber

was employed to conduct constant stress test on the tensile samples at 0, 25 (room
Extensometer
Creep sample
attached with
external
thermocouple
Effects of strain rate on tensile properties

111
temperature) and 50°C according to the ASTM E139 as shown in Fig. 5.1(b). The test
system is equipped with 25 kN load cell with
0.005% accuracy, position control with
accuracy of ±0.5% of transducer full travel,
and strain controller with accuracy of
0.005% of transducer capacity or 0.25% of readingtransducer accuracy. Liquid
nitrogen was introduced into the chamber for low temperature (0°C) testing. Type T
external thermocouple attached to the sample was used to monitor its temperature. The
working temperature was well controlled within ±1°C. After holding at the test
temperature for at least 20 minutes and the sample was mechanically loaded to the
target stress level. At a stress of 120 MPa, the sample was held for two hours. Creep
strains in the elastic region of 0.002 strain and in tertiary creep region are truncated for
the analysis. Fractured surfaces of the tensile samples were examined under a Hitachi
S4100 field emission scanning electron microscope (FESEM) at 20 kV.

5.3 Results and discussion
5.3.1 Effects of stain rate at room temperature on composite samples
True stress-true strain curves of the composite samples for each milling duration tested
at different strain rates of 3.33x10
-3
s

-1
, 3.33x10
-4
s
-1
and 3.33x10
-5
s
-1
are shown in Fig.
5.2 and the detailed results are given in Table 5.1.

Compared to unmilled samples, milling enhanced YS (true stress at 0.2% true strain,
yield stress) with the exception of 40h-MMed samples with lower YS at strain rates of
3.33x10
-4
s
-1
and 3.33x10
-5
s
-1
. 0h-MMed samples were quite insensitive to strain rate.
Generally, at higher strain rate, enhanced YS with lower ductility is observed. In terms
of ductility, the 40h-MMed samples showed an exceptional case of producing similar
ductility of 35
1% elongation at all strain rates. Except for the 10h-MMed samples, all
as-milled samples showed strain softening behaviors.
Effects of strain rate on tensile properties

112
True strain
True stress (MPa)
0
200
100
500
400
300
700
600
00.30.1 0.2 0.4 0.5
3.33x10
-5
s
-1
3.33x10
-3
s
-1
3.33x10
-4
s
-1
0 h

True strain
True stress (MPa)
0
200

100
500
400
300
700
600
00.30.1 0.2 0.4 0.5
10 h
3.33x10
-5
s
-1
3.33x10
-4
s
-1
3.33x10
-3
s
-1

(a) (b)
True strain
True stress (MPa)
0
200
100
500
400
300

700
600
00.30.1 0.2 0.4 0.5
3.33x10
-5
s
-1
3.33x10
-3
s
-1
3.33x10
-4
s
-1
20 h

True strain
True stress (MPa)
0
200
100
500
400
300
700
600
00.30.1 0.2 0.4 0.5
3.33x10
-3

s
-1
3.33x10
-4
s
-1
30 h
3.33x10
-5
s
-1

(c) (d)
True strain
True stress (MPa)
0
200
100
500
400
300
700
600
00.30.1 0.2 0.4 0.5
3.33x10
-5
s
-1
3.33x10
-3

s
-1
3.33x10
-4
s
-1
40 h



(e)
Figure 5.2 Strain rate effects on composite samples milled for durations of (a) 0h, (b)
10h, (c) 20h, (d) 30h and (e) 40h.

Very distinct variation in YS and ductility with respect to strain rate was manifested in
the samples MMed for 20h and 30h. Table 5.1 indicates that the highest loading rate
caused an increase of about 50% in YS in 30h- and 40h-MMed samples compared to
the lowest loading rate.



Effects of strain rate on tensile properties

113
Table 5.1 Yield strength and % elongation of composite samples milled for different
milling durations at different strain rates

3.33x10
-5
s

-1
3.33x10
-4
s
-1
3.33x10
-3
s
-1
Milling
duration
(h)
YS
(MPa)
Elong-
ation (%)
YS
(MPa)
Elong-
ation (%)
YS
(MPa)
Elong-
ation (%)
0 212 15 219 12 228 8
10 431 8 465 5 515 6
20 417 19 505 9 558 5
30 232 41 334 28 347 14
40 176 36 205 34 262 34

At the lowest strain rate of 3.33x10
-5
s
-1
, the YS of 0h-MMed sample was comparable
to that of 30h-MMed sample and higher than that of 40h-MMed sample. However, in
terms of ductility, the 30h- and 40h-MMed samples achieved 187% and 140% higher
respectively compared to the 0h-MMed samples. This indicates the strain rate, in other
words, time dependence nature of strength in nanostructured Mg composite materials.
This phenomenon is one of the unique properties of nanostructured materials and it has
been reported by previous studies [29]. This phenomenon indicates the involvement of
a dynamic process in terms of material transport operating in the course of loading the
sample [21].

Strain rate sensitivity is gauged by the strain rate sensitivity index m which is obtained
from the slope of the ln(σ) versus ln(


) graph (Fig. 5.3a). Strain rate sensitivity of
metal is quite low (<0.1) at room temperature but it increases with temperature up to
the range 0.1≤m≤0.2 which is common in hot working conditions [30]. For the present
materials, the strain rate sensitivity index increases significantly with milling time
from 0.0153 at 0h up to 0.0881 at 30h but it decreases slightly to 0.0873 for the 40h-
MMed sample (Fig. 5.3b). The high value of m might imply the deviation of room
temperature deformation behavior from the coarse-grained counterparts.

Effects of strain rate on tensile properties

114
ln (


)
-4-11
-9
-10 -7
-8 -5
-6
6.4
5.0
6.0
5.6
5.4
5.2
5.8
6.2
ln ()
m
0
=0.0153
m
10
=0.0386
m
20
=0.0635
m
30
=0.0881
m
40

=0.0873

Milling duration (h)
04010 3020
0.10
0.04
0.02
0.00
0.08
0.06
Strain rate sensitivity (m)

(a) (b)
Figure 5.3 (a) ln(

) versus ln(


) graph and (b) strain rate sensitivity of the composite
samples for different milling durations.

Ductility in terms of percentage elongation at strain rates as a function of milling
duration are illustrated in Fig. 5.4. Generally, gradual increase in ductility was
observed with decreasing strain rate for all milling durations and increasing milling
duration at all strain rates. It is quite interesting that the loading curves for 0h-MMed
samples at all strain rates are almost identical and the slight increase in ductility with
decreasing strain rate. It is noticed that ductility of 10h-MMed samples is not
significantly influenced by strain rate as compared to other as-milled samples showing
6, 5 and 8% at 3.33x10
-3

s
-1
, 3.33x10
-4
s
-1
and 3.33x10
-5
s
-1
strain rates respectively.
Another noticeable property is the strain softening of samples after 20h of MM.

Elongation (%)
Milling duration (h)
04010 3020
5
45
20
10
0
25
15
35
40
30
3.33x10
-5
s
-1

3.33x10
-3
s
-1
3.33x10
-4
s
-1


Figure 5.4 Ductility (% elongation) of composite samples for different milling
durations at different strain rates.
Effects of strain rate on tensile properties

115
5.3.2 Effects of stain rate at room temperature on pure Mg samples
True stress-true strain curves of pure Mg samples after each milling duration tested at
different strain rates of 3.33x10
-3
s
-1
, 3.33x10
-4
s
-1
and 3.33x10
-5
s
-1
are shown in Fig.

5.5 and the detailed results are given in Table 5.2.

True stress (MPa)
0
200
100
300
400
0 h
True strain
00.40.1 0.2 0.3
3.33x10
-3
s
-1
3.33x10
-5
s
-1
3.33x10
-4
s
-1

True stress (MPa)
0
200
100
300
400

10 h
True strain
00.40.1 0.2 0.3
3.33x10
-3
s
-1
3.33x10
-5
s
-1
3.33x10
-4
s
-1

(a) (b)
True stress (MPa)
0
200
100
300
400
20 h
True strain
00.40.1 0.2 0.3
3.33x10
-3
s
-1

3.33x10
-5
s
-1
3.33x10
-4
s
-1

True stress (MPa)
0
200
100
300
400
30 h
True strain
00.40.1 0.2 0.3
3.33x10
-3
s
-1
3.33x10
-5
s
-1
3.33x10
-4
s
-1

(c) (d)
True stress (MPa)
0
200
100
300
400
40 h
True strain
00.40.1 0.2 0.3
3.33x10
-3
s
-1
3.33x10
-5
s
-1
3.33x10
-4
s
-1



(e)
Figure 5.5 Strain rate effects on pure Mg milled for the durations of (a) 0h, (b) 10h,
(c) 20h, (d) 30h and (e) 40h.

Effects of strain rate on tensile properties

116
Table 5.2 Yield strength and % elongation of pure Mg milled for different milling
durations at different strain rates

3.33x10
-5
s
-1
3.33x10
-4
s
-1
3.33x10
-3
s
-1
Milling
duration
(h)
YS
(MPa)
Elong-
ation (%)
YS
(MPa)

Elong-
ation (%)
YS
(MPa)
Elong-
ation (%)
0 129 10 122 10 138 8
10 283 14 311 8 328 6
20 180 39 256 10 313 5
30 208 26 216 18 268 10
40 170 38 210 33 277 12

From Fig. 5.5 and Table 5.2, as in the composite samples, 0h-MMed samples show
similar ductility of 8-10% and yield stress ranging from 122 to 138 MPa indicating
insignificant dependence of strain rate. Coarse grained unmilled samples deformed in
work hardening behavior show increased resistance to dislocation motion. Very
different stress-strain behaviors can be seen in the as-milled samples compared to the
blended samples which display strain rate dependence phenomenon. The samples show
relatively low yield stress and high ductility at lower strain rate whereas high yield
stress but low ductility are observed at higher strain rate. Strain softening is evident in
all as-milled samples at all strain rates although it is not obvious in 10h-MMed
samples.

It is evident that the yield stress and ductility are strain rate dependent. For example,
for the 40h-MMed samples, the highest strain rate of 3.33x10
-3
s
-1
produced the highest
yield stress of 277 MPa with lowest ductility of 12%. However, the lowest strain rate

of 3.33x10
-5
s
-1
displayed the lowest yield stress of 170 MPa with a high ductility of
38%.



Effects of strain rate on tensile properties

117
ln (

)
-4-11
-9
-10 -7
-8 -5
-6
6.0
4.6
5.6
5.2
5.0
4.8
5.4
5.8
ln ()
m

10
=0.0316
m
0
=0.0142
m
20
=0.1184
m
30
=0.0579
m
40
=0.1062

(a)
M illing duration (h)
04010 3020
Strain rate sensitivity (m)
0.10
0.04
0.02
0.00
0.08
0.06
0.12

(b)
Figure 5.6 (a) ln(


) versus ln(


) graph and (b) strain rate sensitivity of pure Mg
samples for different milling durations.

From Fig. 5.6, strain rate sensitivity increased with milling time. The 20h-MMed Mg
sample shows the highest strain rate sensitivity of m=0.1184 with extensive ductility of
39% followed by 40h-MMed sample with m=0.1062. From Fig. 5.7, enhanced
ductility is observed with decreasing strain rate and increasing milling duration.
However, no significant increase in ductility with milling duration at the highest strain
rate is detected.

Elongation (%)
Milling duration (h)
04010 3020
5
45
20
10
0
25
15
35
40
30
3.33x10
-5
s
-1

3.33x10
-3
s
-1
3.33x10
-4
s
-1

Figure 5.7 Ductility (% elongation) of pure Mg samples for different milling durations
at different strain rates.

Both composite and pure Mg samples show time dependent deformation behavior at
room temperature. Addition of Al for solid solution strengthening and the
reinforcement of AlN particles for dispersion strengthening show enhancement in YS
Effects of strain rate on tensile properties

118
but does not alter the deformation behavior. In nanocrystalline region, intragranular
dislocation activity is expected to be rather limited so that conventional strain
hardening may also be limited. Although there is evidence that nc materials have
higher strain rate sensitivity than those of the coarse-grained counterparts, the values of
m are still low (<0.1) to sustain large ductility.

Conventional physical models for crystal plasticity and traditional approaches of solids
mechanics should be revised and modified to include size effects due to the presence
of a high density of grain and phase boundaries in the nanostructured materials.
Interfaces and their junctions present obstacles to the deformation process and
contribute to the strengthening of the material. Plastic deformation in nanophase
materials can take place mainly at interfaces which are softer than the bulk crystal.

Therefore, it is clear that the interaction of individual defects with interfaces and
junctions of interfaces should be considered as main event which is responsible for the
mechanical properties of nanoscaled materials [31].

This explains why during tensile testing, when the strain rate is faster than the rate of
diffusion in the MMed pure Mg and composite, the sample does not yield until when
the yield stress is high enough for grain boundary diffusion to be activated. On the
other hand, a low strain rate provides adequate time for the movement of atoms so that
the yield stress to activate the grain boundary process becomes lower. In a stress
activated process, diffusion is essential for the continual operation of the sliding
process. Since diffusivity of grain boundaries is a few tenth order of magnitude higher
than that of volume diffusion, it is possible for nc materials to deform by GBS
accompanied with diffusional process at room temperature.
Effects of strain rate on tensile properties

119
5.3.3 Deformation parameters
Orowan equation depicted in equation 5.1 can be written with orientation factor M and
shear strain rate


as in equation 5.2 [32].




b



(5.1)




















kT
VF
M
lb
kT
G


expexp

0
0


(5.2)

where

is the dislocation density, b the Burgers vector,

the dislocation velocity,

0

the frequency of vibration of the dislocation,

l the distance between dislocation
barriers,

F the change in Helmholtz free energy required to overcome obstacle
without aid from external stress,


the applied resolved shear stress and V

the
effective activation volume.

The activation barrier can be lowered by mechanical workdone



V

where the
activation volume V


represents the average volume of dislocation structure involved in
the deformation process. For thermally activated plastic flow, the apparent activation
volume V
a
is given by [33]


























lnln
TMkTkV
BBa

(5.3)

where k
B
is the Boltzmann’s constant (1.3087x10
-23
JK
-1
), T the absolute temperature,


the applied shear stress and


the tensile strain rate.

The activation volume in m
3
is usually expressed in terms of b

3
where b=3.21x10
-10
m
for Mg [34]. Fig. 5.8 shows the apparent activation volume V
a
of the samples with
respect to milling duration. V
a
of composite sample decreases sharply from 241b
3
to
Effects of strain rate on tensile properties

120
44b
3
after 10h milling. An unusually small V
a
of 26b
3
, 27b
3
and 41b
3
are observed in
the 20, 30 and 40h-MMed sample respectively. For pure Mg samples, no drastic drop
occurs but gradual decrease in V
a
is observed as shown in Fig. 5.8. The present

findings agree with the fact that for truly nc metals, the activation volumes are in the
range of 3b
3
to 100b
3
investigated by Asarro and Suresh [15] and Wang et al. [35].

M illing duration (h)
04010 3020
Activation volume (b
3
)
300
0
50
200
100
250
150
MgMg-5Al-1AlN

Figure 5.8 Apparent activation volume of composite and pure Mg samples at different
milling durations.

The thermal activation energy Q for the 40h-MMed sample can be determined using
the Arrhenius relationship as in equation 5.4.











)/1(
)/ln(
0
T
RQ



(5.4)

where


is the actual strain rate and
0


the normalized strain rate which is defined as
1s
-1
for mathematical reasons to make the argument of the natural logarithm
)/ln(
0





“dimensionless”.

The steady strain rate is obtained from the gradient of the creep curves of strain versus
time at the various test temperatures at constant applied stress of 120MPa as shown in
Fig. 5.9(a). The apparent activation energy value is found to be about 50 kJmol
-1
(Fig.
Effects of strain rate on tensile properties

121
5.9b) which is lower but closer to the activation energy (92 kJ mol
-1
) for grain
boundary diffusion in Mg. It indicates that the thermal activation process is favorable
during plastic deformation.

Time (s)
0
40002000 80006000
Strain (

0.05
0.04
0.03
0.00
0.02
0.01

0.06
50°C
At constant stress 120 MPa
25°C
0°C

1/Tx10
-3
(K
-1
)
-6
-8
-4
-16
-14
-10
-12
3.0 3.73.1 3.33.2 3.4 3.63.5
.
ln(

)
Q=50 kJ mol
-1

(a) (b)
Figure 5.9 (a) Strain with respect to time at constant stress for various temperatures
and (b) Arrhenius plot of
ln(



) versus (1/T) for activation energy in the 40h-MMed
composite sample.

5.3.4 Fractography
Samples fractured at room temperature generally exhibited mixed mode fracture of
quasi cleavage with dimple-like ductile fracture. Numerous micro cracks and matrix
fracture were observed on macroscopically rough and predominantly transgranular
fracture surface of the 0h-MMed sample as shown in Fig. 5.10(a). Straight and sharply
defined slip lines which might represent basal slip were also observed.

Multitudinous micro voids, dimples and localized brittle features were observed on the
fracture surfaces of the as-milled sample (Figs. 5.10b and 5.10c). Microvoid
coalescence is generally the predominant fracture mode in particulate reinforced
MMCs [36]. The localized brittle region reminiscent of locally brittle failure may be
attributed to the presence of reinforcement AlN particles and second phase particles. In
the 10h- and 20h-MMed samples, several micro cracks on the uneven fractured surface
T (K)


(s
-1
)
273 6.90x10
-7

298 8.52x10
-6
323 1.92x10

-5
Effects of strain rate on tensile properties

122
were observed whereas the 30h- and 40h-MMed samples produced flat fracture surface
with multitudinous micro voids (Figs. 5.10d and 5.10e). The most ductile 40h-MMed
sample shows typical ductile failure exhibiting necking and fracture surface with
dimples and micro voids.


(a)

(b)

(c)

(d)

(e)

Figure 5.10 Representative fracture surfaces of (a) 0h-, (b) 10h-, (c) 20h-, (d) 30h- and
(e) 40h-MMed composite samples after tensile deformation at 3.33x10
-4
s
-1
.


Effects of strain rate on tensile properties

123
5.3.5 Kinetics of deformation
The energy that has to be provided for dislocations to overcome the short-range or long-
range barriers they encounter during slip determines the dependence of the flow stress on
temperature and applied strain rate [
37]. If the energy barrier is sufficiently small, thermal
vibration of the crystal atoms can assist the dislocations to overcome obstacles at lower
applied stress than that required at 0K. An increase in temperature or a reduction in
applied strain rate will reduce the flow stress under such condition.

x
x
1
x
2
K
K
max


bl
Thermal
Mechanical


Figure 5.11 Profile of resistance force K versus distance x for barriers opposing
dislocation motion.

Consider a dislocation gliding in the x direction under an applied resolved shear stress




and encounters obstacles, each of which produces a resistance force K as shown in Fig.
5.11. For the dislocation to overcome the barrier, the line must move from x
1
to x
2
and the
required Helmholtz free energy change,

F, which is the isothermal energy change
equivalent to the area under the K versus x curve between x
1
and x
2
is given as



2
1
x
x
KdxF
(5.5)

Part of the energy can be provided in the form of mechanical work


V


done by the
applied shear stress and the remaining part of the energy can be supplemented by the
thermal contribution which is the Gibbs free energy change between the two states
x
1

Effects of strain rate on tensile properties

124
and x
2
at the same temperature and applied stress given as

G=

F-


V

. Generally, the
dislocation motion is hindered by short-range barriers, which can be overcome by thermal
activation and long-range forces which produce barrier too large for thermal activation to
be significant. Thus, the flow stress consists of thermal component


and the athermal
component


G

which is almost independent of temperature apart from the small variation
of shear modulus G with temperature as in equation 5.6.

G




(5.6)

In particular, an increase in temperature or a decrease in applied strain rate provides an
increase in the probability of thermal activation and therefore results in a reduction in
flow stress.

The low strain rate sensitivity m~0.015 in the coarse grained sample suggests that the
flow stress is mainly from athermal stress contribution

G
with minimal contribution
from thermal contribution


at room temperature. The grain boundaries being the
regions of considerable atomic misfit act as strong barriers to dislocation motion. The
additional dislocation density due to the presence of grain boundaries, which cause
dislocation pile-ups, increases the athermal component

G

of the flow stress. According
to the dislocation density model, the contribution to athermal stress from the
boundaries acting as a source of dislocation during deformation is given as [38],

2
1

MGb
G



(5.7)

where
M is the average Taylor factor ~6.4 for random textureless polycrystalline Mg
[39],
b the magnitude of the Burgers vector and

a constant given as 0.35 for Mg
[40].
Effects of strain rate on tensile properties

125
Despite the presence of Mg
17
Al
12
precipitates and the nanosized AlN particles, their
contribution to


G
is neglected due to their low volume fraction. Grain refinement
present with higher volume of grain boundaries in the 10h-MMed sample, where
significant increase in applied stress is observed in tensile deformation. The low strain
rate sensitivity of m~0.039 indicates the insignificant thermal component of stress
contribution in the 10h-MMed sample. The increase in dislocation density


is
inversely related to grain size d during deformation (equation 5.8) and the athermal
component of the yield stress

G
can be expressed similar to the Hall-Petch relation as
in equation 5.9.

d
1



(5.8)
2
1
dK
HPG



(5.9)

where
K
HP
is the Hall-Petch coefficient.

The average spacing of the barriers along the dislocation lines decreases with the
increase in dislocation density when the deformation proceeds. Consequently, with
reference to equation 5.10, the decrease in the spacing of the barriers
l

results in
lowering activation volume
V


which is evident in Fig. 5.8.


 lbV
(5.10)

where
 is the width of the short-range barrier.


It is clear in Fig. 5.8 that the values of the apparent activation volume of composite
samples decreased with milling time: from 241
b

3
for as-blended sample to 44b
3
, 26b
3
,
27
b
3
and 41b
3
after 10, 20, 30 and 40h MM respectively. From Fig. 5.3, the strain rate
sensitivity increased with milling time showing 0.0153, 0.0386, 0.0635, 0.0881 and
Effects of strain rate on tensile properties

126
0.0873 for 0, 10, 20, 30 and 40h-MMed composite samples respectively. Significant
increase in strain rate sensitivity accompanied with decrease in activation volume for
the samples milled for longer durations strongly suggests the onset of a thermal
activation process.

Strain softening becomes significant for the samples after longer milling hours. The
detachment of dislocation from the particles due to thermal activation is considered
one of the possible reasons for the phenomenon of softening in these mechanically
milled materials [41-44]. Han et al. [45] and Longo et al. [46] reported that the
annihilation of accumulated dislocations in the vicinity of the particles under high
applied stress could result in softening. Softening could also be due to a low energy
dislocation structure reorganization or transformation, as typical for directional strain
softening [47]. Alternatively, reduction in frictional stress of Hall-Petch strengthening
as in dislocation unlocking from impurity or alloying atmosphere, or breaking of

barriers in grain or dislocation structure could also cause the softening [48]. These
mechanisms may be applicable for the 20h-MMed samples in which some dislocation
activities may still be operative to some extent.

The applicability of dislocation detachment, annihilation, rearrangement mechanisms
in references [41-48] is doubtful for 30 and 40h-MMed composite samples which are
in nanostructure with low volume fraction of particles and highly possible absence of
lattice dislocations. The contribution of dislocations to plastic deformation in
nanocrystalline materials and even their presence in this class of material are still
subjects of debate [49]. The problem of stability of dislocations in small particles and
nonocrystals has been addressed in references 50 and 51. It was suggested that
Effects of strain rate on tensile properties

127
dislocations are seldom seen inside the grains, particularly when the grain size in the
lower range of the nanometer scale [52] and even those that are seen have some special
sessile (immovable) configurations. It has been suggested that the existence of image
forces in finite atomic ensembles tend to pull the mobile dislocations out of the grains.
Therefore, the contribution to plasticity in nc materials from mobile dislocations is not
possible unless they can be readily created, e.g. Frank-Read source. However, as the
force required for the creation of a dislocation is inversely proportional to the distance
between the pinning points, the operation of the Frank-Read source becomes
increasingly difficult with decreasing grain size [53].

At some critical grain size in nanophase regime, breakdown of lattice dislocation
multiplication and generation can lead to the suppression of thermally activated
dislocation process in the sample. The following findings indicate the dominant role of
grain boundary in deformation of 40h-MMed composite samples such as thermally
activated unpinning of boundaries due to enhanced diffusivity in grain boundaries [54]
and diffusional flow [55]:

i.
The apparent activation energy of 50 kJ mol
-1
in the 40-MMed composite
sample is close to the activation energy of 92 kJ mol
-1
for grain boundary
diffusion in Mg
ii.
Unusually small activation volume of 41 b
3
in the 40-MMed composite
sample

A value of
m greater than 0.3 is usually referred to as the superplastic behavior in the
materials [56]. GBS is the predominant deformation mechanism that could explain the
elongations of hundreds of percent that are commonly seen in materials undergoing
Effects of strain rate on tensile properties

128
superplastic deformation. Only under hot work conditions, most metals possess quite
low strain rate sensitivity of 0.1 to 0.2 [33]. Compared to most metallic materials,
m
value of 0.09 in the 40h-MMed composite sample at room temperature is quite high.
Although the room temperature deformation of the present material does not infer full
superplastic behavior, it exhibits a considerably high elongation of 35
1% at strain rate
between 3.33x10
-5

s
-1
and 3.33x10
-3
s
-1
with absence of work hardening. Based on the
results and the analysis so far, the time (rate) dependent phenomena at room
temperature in this sample could be the mixture of two major deformation mechanisms:
i. grain boundary process such as sliding and rotation that can be accounted
for the high ductility and
ii.
simultaneous grain boundary diffusion that preserves material continuity
and continue sliding.

It has been shown by researchers including Zelin et al. [57-61] that, at the microscale,
GBS actually occurs in groups in a process known as cooperative grain boundary
sliding (CGBS). As such, the deformation of the 40h-MMed composite samples can be
envisioned: (1) local grain rotation and sliding accommodated by dislocation motion
and/or diffusional processes to align the grain boundaries into stringers (the boundaries
of long-range shear) in accordance with applied stress, (2) once aligned, large groups
of grains will slide cooperatively until an unfavorably oriented grain/grain boundary
stops the event. This process repeats itself throughout the material in different areas as
changing local stress states altering the planes of long-range shear throughout the
material [62].

Effects of strain rate on tensile properties

129
GBS must accompany diffusional creep [63] and Gifkins [64] proposed the

accompanying mechanism as either lattice or grain boundary diffusion. This
mechanical response can be handled phenomenologically through the use of the
Mukherjee-Bird-Dorn equation [65]:

np
gb
Gd
b
kT
GbAD

















(5.11)
and








RT
Q
DD
gb
exp
0

(5.12)

where


is the shear creep rate, A a constant, D
gb
gain boundary diffusion coefficient,
T the absolute temperature, p the grain size sensitivity, n the stress exponent and D
0

the pre-exponential for boundary diffusion.

This constitutive equation depicted in equation 5.11 is the best to date to represent the
deformation mechanism of GBS assisted diffusion (e.g. references 21 and 66). From
equation 5.11, it is evident that forming (strain) rates can be increased by decreasing
the grain size at constant temperature. In addition, at constant strain rate, the decrease

in grain size from micrometer to nanometer scale can lead to a lowering of the
superplastic forming temperature.

Creep test will be carried out in the next chapter to verify the possibility of grain
boundary deformation with grain boundary diffusion controlled process in nc Mg
composite.



Effects of strain rate on tensile properties

130
5.4 Conclusions
The present experimental results have clearly shown the time dependence of the
mechanical properties of bulk nanostructured Mg composite and superplastic-like
behaviors in these composites even at room temperature. Although there are limited
data available on the deformation behavior of these composites, some generalizations
may be made regarding the deformation mechanisms based on the present study. It is
possible that a grain size distribution is present in the MMed samples. For the larger
grain size of about 17 µm to 116 nm, dislocation activity such as gliding and twining
may still be dominant at room temperature especially for the larger grain size. As grain
size decreases to perhaps less than 100 nm such as in the samples that have been
mechanically milled for 30 and 40 hours with grain size mostly in the nanoscale range,
dislocation activity like gliding apparently decreases or may even have disappeared.
Creation of new dislocations is difficult as the grain size reaches the lower end of the
nanoscale. Thus, at the smallest grain size range, some new mechanisms controlling
deformation behavior may play a more prominent role.

From the deformation parameters and microstructural evidence, the thermally activated
process is more favorable to be grain boundary process dominant rather than thermally

activated lattice dislocation process. This is supported by the activation energy for the
thermal activation process in the nanostructured Mg composite, which is close to the
activation energy for grain boundary diffusion in Mg. Phenomena such as absence of
dislocations in the grains, softening behaviors and high ductility in the nanostructured
composite at room temperature are suggested to be due to GBS assisted by enhanced
grain boundary diffusivity.

Effects of strain rate on tensile properties

131
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