Processing and mechanical properties of pure mg and in situ aln reinforced mg 5al composite 6

Investigation of time dependent deformation behaviors by creep test


133
Chapter 6
Investigation of time dependent deformation behaviors by creep test

6.1 Introduction
More than one creep mechanism frequently operates at the same time and the main
creep deformation mechanisms can be categorized as follows [1]:
(a) Dislocation glide - involves dislocations moving along slip planes and
overcoming barriers by thermal activation. This mechanism occurs at high
stress,

/G >10
-2
where G is shear modulus.
(b) Dislocation creep - involves the movement of dislocations which overcome
barriers by thermally assisted mechanisms involving the diffusion of vacancies
or interstitials. It occurs for 10
-4
<

/G >10
-2
.
(c) Diffusion creep - involves the flow of vacancies and interstitials through a
crystal under the influence of applied stress. It occurs for

/G <10
-4

. This
category includes Nabarro-Herring and Coble creep.
(d) Grain boundary sliding - involves the sliding of grains past each other.

From the tensile results and microstructural observation, time dependent deformation
behavior was observed to dominate at the grain size of 33 nm. A thermal activation
process is believed to play a significant role in the present nc composite material
through tensile tests at different strain rates. From the deformation parameters and
microstructural studies, the thermally activated process is inferred to be dependent on
grain boundary diffusion. Due to large volume fraction of grain boundaries which
facilitate higher diffusivity with shorter path for diffusion, unusually high ductility
Investigation of time dependent deformation behaviors by creep test


134
with softening behaviors at room temperature was observed in nc Mg composites.
Since creep deformation involves time dependent mechanisms, diffusion and GBS,
creep tests at various temperatures were performed to further investigate the probable
mechanism in this composite material.

6.2 Experimental
Creep test was performed on the 40h-MMed Mg-5Al-1AlN cylindrical tensile
specimens with a gauge diameter of 5mm and a gauge length of 25 mm at 273, 298
and 323K according to ASTM E139 standard. Detailed test procedures have been
described in Chapter 5. Creep tests were conducted at various constant stress levels of
40, 60, 80, 100, 120 and 130 MPa with dwelling time of 2 hours.

6.3 Results and discussion
6.3.1 Creep behaviors

Table 6.1 Creep strain rate (s
-1
) at various applied stresses and temperatures

Applied stress Temperature
(MPa) 273K 298K 323K
40 2.53x10
-07
2.68 x10
-07
3.07 x10
-07

60 3.47 x10
-07
3.49 x10
-07
3.54 x10
-07

80 3.75 x10
-07
5.42 x10
-07
6.10 x10
-07

100 3.81 x10
-07
9.69 x10

-07
1.35 x10
-06

120 6.90 x10
-07
8.52 x10
-06
1.92 x10
-05

130 1.05 x10
-06
3.14 x10
-05



The steady state creep rates are taken from the gradients of the creep strain versus time
curve as shown in Fig. 5.9(a). The creep rates were found to be in the range between
10
-7
and 10
-5
s
-1
as shown in table 1.

Investigation of time dependent deformation behaviors by creep test

135
273K

(MPa)
30 100 150
1E-4
1E-7
1E-6
1E-5
.

(s
-1
)

(a)

298 K

(MPa)
30 100 150
1E-4
1E-7
1E-6
1E-5
.

(s
-1

)

(b)



(MPa)
30 100 150
1E-4
1E-7
1E-6
1E-5
.

(s
-1
)
323 K

(c)
Figure 6.1 ln


versus ln

at different temperatures: (a) 273K, (b) 298K and (c) 323K.

Investigation of time dependent deformation behaviors by creep test

136
The creep in the composite shows a steady state behavior [2], which may be described
by Norton’s law [3, 4].
n
B




(6.1)

The relationship between the double logarithmic coordinates of


and

is shown in
Fig. 6.1. The relationship between stress and creep strain rate is not linear at different
temperatures. Two outstanding features of the influence of particles have been reported
[5]:
i. A linear relationship between


and

is lost and appears to be replaced by a
relationship of the form





-

0
where

0
is a threshold stress below which
creep does not occur and the effective applied stress (

e
) is defined as

e =


-

0
.

0
appears to increase linearly with the volume fraction of second phase [6, 7].
ii. In many cases, creep rate progressively decreases with strain, which appears to
be associated with particle collection on boundaries parallel to the tensile stress
axis [8,9].

The power-law relation for steady state creep,



=B

n
exp (-Q/RT) [4], can be rewritten
to incorporate

0
as [3]

n
B
/1
0




(6.2)

By substituting suitable values of n in equation 6.2, a linear plot of

versus
n/1


is
used to obtain

0
from the best linear regression line at different temperatures. The

threshold stress is found to be in the range of 52.5 to 54 MPa at different temperatures
from the various best linear fits at
n=2 as shown in Fig. 6.2.


Investigation of time dependent deformation behaviors by creep test


137
.

1/2
0
2E-4
1.2E-3
1E-3
8E-4
6E-4
4E-4
040
20
8060 140120
100


(MPa)



= Pa

n = 2

(a)

.

1/2
0
5.0E-4
3.0E-3
2.5E-3
2.0E-3
1.5E-3
1.0E-3
04020 8060 140120
100


(MPa)



=

Pa
n = 2

(b)

.


1/2
0
1E-3
6E-3
5E-3
4E-5
3E-3
2E-3
040
20
8060 140120
100


(MPa)



= 52.5

Pa
n = 2

(c)

Figure 6.2 Linear plots of

versus
n/1



at (a) 273K, (b) 298K and (c) 323K.


Investigation of time dependent deformation behaviors by creep test


138
The existence of the threshold stress may imply that the grain boundaries do not act as
perfect sources and sinks of vacancies [10-
13]. The rate of diffusion at grain boundaries is
expected to be different due to the imperfect emission and absorption of atoms (or
vacancies) at grain boundaries. From Arrhenius plot of ln[


/(

-

0
)
2
] versus 1/T with
stress exponent n = 2, the activation energy Q could be determined to be about 61 kJmol
-1

as shown in Fig. 6.3. This value is about 66% of the activation energy for grain boundary
diffusion of pure Mg where Q
gb(Mg)

= 92 kJmol
-1

[14].

Q=61 kJ mol
-1
1/Tx10
-3
(K
-1
)
3.0 3.73.1 3.3
3.2
3.4 3.63.5
.
ln[




)
2
]
273K
323 K
298 K
-16
-26
-24

-22
-18
-20
-12
-14

Figure 6.3
Arrhenius plot of ln[


/(

-

0
)
2
] versus 1/T.

As in the present study, low activation energy of 0.5
Q
gb
in Mg + 30 vol.% Y
2
O
3
[15],
0.7
Q
gb

in nano Ni-P alloy [16] and 0.5-0.6 Q
gb
for Al with Al
2
O
3
oxide particles [17]
has been reported in the literature. As in the present experiments, the low activation
energy for diffusion indicates the domination of diffusionally accommodated sliding
process or ‘‘interfacial creep’’ [18]. The measured activation energy is expected to
represent that for interfacial diffusion. Under diffusion control, the measured activation
energy simply represents that for atomic diffusion along the interface, which has a high
diffusivity path. Therefore, when vacancies are in plentiful supply, interface diffusion
Investigation of time dependent deformation behaviors by creep test


139
control is likely to result in low activation energy, rather than the high activation
energy values typically observed under interface reaction control [18].

Many material systems including dispersion strengthened metals (e.g. [6,10,12,19]),
eutectic alloys [20] and discontinuously reinforced metal-matrix composites [21-25]
display an indirect evidence of diffusionally accommodated sliding at phase
boundaries and interfaces during creep/superplastic deformation. Interface sliding
controlled creep usually displays a temperature dependent threshold stress [12], a
stress exponent (n) ranging from 1 to 2 [12, 20] and an activation energy which is
typically higher than that for matrix volume diffusion (
Q
vol
) e.g. Refs [12, 19, 24]), but

sometimes lower than
Q
vol
[20].

When the boundary (or interface) has an abundant population of mobile grain
boundary dislocations (GBDs) which allow the boundary to act as a perfect source and
sink for vacancies [12], GBS may be represented by a continuum model of diffusional
creep (e.g. Ref. [26]). The kinetics of boundary/interface sliding is believed to become
“interface reaction controlled” when the density or the mobility of dislocation sources
in the boundary is limited [12]. The interaction of highly mobile GBDs or interface
dislocations (IDs) with interfacial dispersoids or asperities, which exert a drag on
mobile GBDs/IDs, results in a threshold stress for creep. When the mobility of
GBDs/IDs is restricted, interface reaction control may result in high activation energy
Q
i
[12]. The mechanism based on interface reaction control [12] is able to account for
the temperature-dependent threshold stress and an activation energy value that is
significantly different from that for matrix self diffusion during diffusional creep.

Investigation of time dependent deformation behaviors by creep test


140
6.3.2 Comparison with existing models
The theoretical predictions of creep due to diffusional transport of matter via the lattice
(Nabarro-Herring creep) or via the grain boundaries (Coble creep) have preceded
experimental verification. Nabarro-Herring (NH) creep is accomplished solely by
diffusional mass transport. NH creep dominates creep behavior at much lower stress
levels and higher temperatures where dislocation glide is not important. NH creep rate

(
NH


) can be expressed as [27]















kTd
D
A
el
NHNH


2


(6.3)

where
A
NH
is a constant, D
l
the lattice diffusion coefficient, d the grain size,

e
the
effective applied stress,  the atomic volume, k Boltzmann constant and T the absolute
temperature.

Coble creep is closely related to NH creep in the fact that Coble creep is driven by the
same vacancy concentration gradient. However, mass transport in Coble creep occurs by
diffusion along grain boundaries in a polycrystal or along the surface of a single crystal.
Coble [
28] derived an expression for grain boundary diffusional creep rate (
C


) as
follows:

kTd
D
kTd
D
A

gbe
e
gb
CC
33
148























(6.4)

where







RT
Q
DD
gb
gb
exp
0

(6.5)

Investigation of time dependent deformation behaviors by creep test


141
and A
C
is a constant, D
gb
the grain boundary diffusion coefficient,

the grain boundary
thickness, D

0
a pre-exponential constant, Q
gb
the activation energy for grain boundary
diffusion and R the gas constant.

From equations 6.3 and 6.4, it can be seen that Coble creep is more sensitive to grain size
than NH creep. During polycrystalline diffusional creep, additional mass transfer must
occur at grain boundaries to prevent the formation of internal voids or cracks. This results
in GBS and the diffusional creep rate must be balanced exactly by the GBS rate if internal
voids are not to form.

In the case where co-existence of more than one mechanism in the composite is possible
during creep deformation, the deformation may be accommodated in the grain boundaries
with many small GBS events controlled by grain boundary diffusion. The rate of
deformation for GBS may be given as [
29]:

23
5
102















Gd
b
kT
GbD
e
gb




(6.6)

where G is the shear modulus, b the Burgers vector and the other symbols have their
usual meaning defined previously.

Using the parameters for Mg in Table 6.2, a theoretical value of D
gb
is predicted to be
3.7410
-28
m
2
s
-1
. However, Q

gb
value in Table 6.2 is for coarse grain Mg and it is not
suitable to use this value for the present nanocrystalline Mg. Using the value of
activation energy estimated from the experimental results (Fig. 6.3), i.e. 61 kJ mol
-1
,
D
gb
is calculated to be 1.0210
-22
m
2
s
-1
which is about 6 orders of magnitude faster
Investigation of time dependent deformation behaviors by creep test


142
than that of D
gb
for coarse grain counterpart. As mentioned in Section 2.4, it has been
reported in literature that diffusivities in nc materials are several orders higher than
those in coarse-grained polycrystals.

Table 6.2 Parameters used for calculations [14]

Parameter Symbol unit
atomic volume


2.33x10
-28
m
3

Burgers vector
b
3.21x10
-10
m
grain boundary thickness

(~3b)
9.63x10
-10
m
Boltzmann constant
k
1.38x10
-23
JK
-1

activation energy for grain boundary diffusion
Q
gb

92 kJmol
-1

activation energy for lattice diffusion
Q
l

134 kJmol
-1

gas constant
R
8.3145 Jmol
-1
K
-1

pre-exponential constant
D
0

5.0x10
-12
m
3
s
-1

shear modulus
G
16.7 GPa

As shown in Fig. 6.4, the actual creep strain rate is one to two orders of magnitude

higher than the theoretical values predicted by Coble’s model of grain boundary
diffusion controlled creep model (
equation 6.4) and GBS model (equation 6.6). Similar
results were reported for the creep behavior of nanostructured Mg alloys [30] and
nanocrystalline Cu, Pd, and Al-Zr [31]. The existing Coble creep and GBS
mechanisms are unsuccessful in describing the creep behavior of the present nano
composite material exhibiting one to two orders of magnitude difference in creep strain
rate between experimental results and the theoretical prediction.

The Coble creep due to stress-directed diffusional transport of matter involves two
consecutive processes:
(i)
emission and/or absorption of vacancies by grain boundaries and
(ii)
diffusion of emitted vacancies via the grain boundaries.
Investigation of time dependent deformation behaviors by creep test


143
The creep is then diffusion controlled only if the grain boundaries act as perfect
sources and sinks for vacancies. In the present materials, besides reinforcement AlN
particulates, significant increase in defects such as dispersion of second phase
constituents or oxide particles and excess free volumes has been inherited from
processing history. In fact, some of these particles and nanovoids are located at the
grain boundaries and the latter cannot serve as perfect sources and sinks. In such case,
although creep results from diffusional transport of matters, it is controlled by the
processes at the grain boundaries (interface-controlled diffusional creep).




(MPa)
4
10
100
.

(s
-1
)
Coble creep (equation 6.4) Present study
Grain boundary sliding model (equation 6.6)
1E-3
1E-10
1E-8
1E-7
1E-6
1E-4
1E-5
1E-9

Figure 6.4 Comparison of theoretical predictions and experimental results.

In diffusional creep, energy dissipation occurs in the following three irreversible
processes [32]:
(i)
diffusional transport of atoms,
(ii)
grain-boundary sliding and
(iii)
interfacial reaction for the sink and the creation of vacancies in grain

boundaries.
Energy dissipated in both the grain-boundary sliding and interfacial reaction is
negligibly small for conventional grain sizes since grain boundaries will act as perfect
Investigation of time dependent deformation behaviors by creep test


144
sinks and sources of vacancies [32]. Therefore, the rate of total energy dissipated as
heat can be equated to that of energy dissipated in the diffusional process. In such case,
the strain rate caused by grain-boundary diffusional creep is given by the well known
equation of Coble creep, provided that the energy stored as grain-boundary energy can
be neglected. In the present study where the grain size is very small, the increase in
grain boundary energy cannot be neglected whereas the energy dissipated in processes
(ii) and (iii) can be neglected [33]. Therefore, the conventional equation of Coble creep
alone cannot be sufficient to represent the nc materials, since the effect of increase in
grain boundary area becomes significant with decreasing grain size to nanoscale.

Positron annihilation spectroscopy has proven the existence of nanovoids in grain
boundaries of nc materials [
34,35]. The excess free volume which might have formed
at the grain boundary during sintering especially for materials consolidated from
powders has been suggested to be the origin of nano-voids. The enhanced diffusivity
and low activation energy for grain boundary diffusion may be understood in terms of
free volume in the cores of the grain boundaries of nc materials [
36-38].

An essential change in the grain boundary state in metals is caused by diffusion fluxes
of impurity atoms from external sources. It has been reported that the effect of
diffusion induced loss of strength by creep at lower temperature is due to much higher
value of diffusion coefficients of impurities in nanostructures [39]. Creep kinetics can

also be changed by the dispersion of particles at the grain boundaries since grain
boundaries are no longer assumed as perfect sources and sinks for vacancies [10]. For
optimum smaller particles at a given volume fraction, the contribution to the strength
Investigation of time dependent deformation behaviors by creep test


145
expected from the reinforcement is fully relaxed due to enhanced interfacial diffusion
along the matrix and reinforcement interface [40-42].

The matrix/inclusion relaxation processes of sliding and diffusion must occur in a
composite in order for the steady state creep rate to be non-zero [43]. The stress
concentrations at the particles can be relaxed by the massive diffusion flow at smaller
grain sizes even though there are particles residing at the grain boundaries. Therefore,
the stress concentration is suppressed for continuous sliding to take place, avoiding
cavity formation as seen in Fig. 6.5. Instead of the particles at the grain boundaries
impeding GBS leading to stress concentration, they facilitate to enhance sliding and
hence show a much higher creep strain rate practically.

Grain 1
Grain 2
Grain 3


Figure 6.5 Schematic illustration of particles located at the grain boundaries.

Deformation in the aggregate of the grains cannot occur by diffusion alone. Lifshitz
[44] and Stevens [45] pointed out that GBS is necessary in creep deformation in order
for the relative motion of individual grains to accommodate the macroscopic
deformation. There are two possible sliding modes during the creep deformation of

MMC: (a) grain boundary sliding and (b) interfacial sliding between matrix and
Investigation of time dependent deformation behaviors by creep test


146
particle. GBS is not affected by the presence of reinforcement, when the rate of
interfacial sliding is larger than that of GBS under the same stress condition. In such
case, the deformation mechanism of MMC is the same as that for unreinforced metals.
Stress concentrations at triple points of grain boundaries will be relaxed by diffusional
flow in a solid state. On the other hand, when the rate of interfacial sliding is lower
than that of GBS under the same stress condition, stress concentrations are developed
around the reinforcements. In such a case, cavities are formed by the presence of
reinforcements and large elongation cannot be attained.




(MPa)
4
10
100
.

c(c)

(s
-1
)
1E-2
1E-14

1E-12
1E-10
1E-8
1E-4
1E-6
273K 323 K298 K
Present study

Figure 6.6 The variation in the critical strain with effective applied stress for 40h-
MMed composite samples.

Stowell [46] formulated an equation to gauge the possibility of cavity nucleation using
critical strain rate
)(cc


below which cavity nucleation is highly improbable and this
critical strain rate is given by

kT
D
cdd
gb
p
e
cc



2

)(
5.11 



(6.7)

Investigation of time dependent deformation behaviors by creep test


147
where c is the fraction of the total strain carried by GBS, d the grain size, d
p
the
particle diameter and T the absolute temperature (Room temperature 298K). The
critical strain rates are plotted as a function of effective applied stress at room
temperature as illustrated in Fig. 6.6, where d, d
p
and c are taken to be 33 nm, 274 nm
and 0.6 [47] respectively. As shown in Fig. 6.6, the critical strain rates at various
temperatures are well below the strain rate from experimental results indicating the
highly possible cavity nucleation during creep deformation of the present material.

When GBS is not sufficiently accommodated by diffusional flow or dislocation
movement, stress concentrations cause excessive cavity formation, thereby large
elongations are not attained. A special accommodation process is required to attain
large elongations when the sliding process is not sufficiently accommodated by
diffusional flow. The Needleman-Rice parameter  may be used to determine the
critical particle size below which the reinforcement particles are not likely to nucleate
cavities, and above which cavities develop due to stress concentrations [48,49]

3/1













kT
D
gb

(6.8)

where
 is the atomic volume,

the grain boundary width,

the applied stress, D
gb

the grain boundary diffusion coefficient,

k Boltzmann’s constant, T the absolute
temperature and


the creep strain rate.

The average particle size of AlN reinforcement estimated from FE-SEM micrograph
using Scion Image for Windows software is 274 nm which is much larger than the
critical particle size of ~1 Å calculated from equation 6.8. It is suggested that stress
Investigation of time dependent deformation behaviors by creep test


148
concentrations could be developed around the AlN particles when diffusional assisted
flow operates as an accommodation process. In such a case, superplastic-like large
elongation is unlikely to be attained in the present Mg composite samples as verified
by the highest attainable tensile elongation of only 35
1%.

Except for 1 wt% of AlN reinforcement, additional ~0.11% of second phase particles
(MgAl
2
O
4
, MgO, etc.) of size between 4 and 10 nm is expected in the sample as
reported by Chua et al. [30]. It is well accepted that the reinforcement/matrix interfaces
are preferential sites for cavity nucleation as a result of high stress concentration. The
particles themselves cannot accommodate sliding strain by slip. Therefore, in order to
attain large elongations in a solid state, the stress concentrations on the particles at the
grain boundaries must be relaxed by diffusional flow. Assuming that the sliding

displacements are too large to be accommodated elastically and that the sliding is
accommodated by diffusional flow in a solid state, the local shear stress around the
reinforcements caused by sliding can be given by [26]

)/51(6.1
2
3
lpgbl
p
i
DdDD
dkTd







(6.9)

where

is the space between particles and the other symbols have their usual meaning
defined previously. The space between particles can be given by [50]

f
p
V
d

2
3
2



(6.10)

where V
f
is the volume fraction of the particle. Therefore, the local tensile stress caused
by sliding at the interfaces, σ
i
(=3

i
[14]) can be given in the form [51]:
Investigation of time dependent deformation behaviors by creep test


149
)/51(
92.0
lpgbl
fp
i
DdDD
dVkTd








(6.11)

Assuming σ
i
in equation 6.11 is equal to σ
e
in equation 6.6 that causes plastic flow in
the composite sample, critical strain rate for accommodation helper mechanism,
1c


,
below which no stress concentrations around reinforcements at the grain boundaries
develop, can be derived as [52]:
gbfp
pgbl
c
DVd
dDD
bkT
dG 11
)/5(
1
1091.5
22

4
6
1






































(6.12)

The critical strain rates calculated from equation 6.12 are 7.89x10
-12
s
-1
, 7.23 x10
-12
s
-1

and 6.67 x10
-12
s
-1
at 0°C, 25°C and 50°C respectively, which are much lower than the
experimental results (creep strain rates) tabulated in Table 6.1. When
1c





, no stress
concentrations are caused around reinforcements and the deformation mechanism is
the same as that for unreinforced metals. On the other hand, when
1c



 as in the
present case, a special accommodation process by the accommodation helper such as a
liquid phase or diffusional flow is required to relax the stress concentration around the
particles [51].

If the reinforcement particles are located in the interior of the grains, they would hinder
the movement of dislocations from one side of the grain to the other side and thus
affect the plastic deformation. Mishra et al. [53] proposed the critical strain rate below
which overall GBS would not be influenced parametrically, assuming that the stress
concentrations can be relaxed by diffusional flow around the particles. The critical
strain rate,
2c


, is given by:
Investigation of time dependent deformation behaviors by creep test


150






















2
2
2
3
)6/5(
)/2(21)1(
9
p
lf
c
d

DV
kT
Gvv





(6.13)

where

is the Poisson’s ratio.

It is well accepted that when the shear modulus of the particle exceeds that of the
matrix, a dislocation is repelled from a particle. The stress state of the material
becomes different from the unrelaxed state owing to the occurrence of diffusional
relaxation process. The relaxation of dislocation-particle repulsion via diffusion in the
matrix and at the particle–matrix interface has been verified by Srolovitz
et al. [54,55].
Taking the difference in elastic constants between the matrix and the particle into
consideration, Onaka
et al. [56] derived the relaxation time as given by



)1(
)21(2)1(
16
1

2






vGG
vGvG
D
kTd
t
l
p

(6.14)

where G
*
is the shear modulus (210 GPa for AlN)

and

*
the Poisson’s ratio of the
reinforcement (0.287 for AlN). On the other hand, the strain rate from GBS is given by
[57]:

dt
a

3




(6.15)

where a is the unit of sliding (=b) and t the period of the time over which sliding
occurs. By combining equations (6.14) and (6.15), the critical strain rate for the
relaxation at the intragranular particle,
3c


, can be defined as:

Investigation of time dependent deformation behaviors by creep test


151

)21(2)1(
)1(1
24.9
2
3



























vGvG
vGG
D
dd
b
kT
l
p
c




(6.16)

From equation 6.16, the respective critical strain rates of 2.55x10
-10
s
-1
, 2.34 x10
-10
s
-1

and 2.15x10
-10
s
-1
at 0, 25 and 50°C respectively are much lower than the experimental
results listed in Table 6.1. When
3c




, the intragranular particles are in the fully
relaxed state, and thus the particles do not affect the accommodation process.
Intragranular particles would not influence the deformation behavior, if there is enough
time for relaxation by lattice diffusion. However, when the time for relaxation is not
sufficient as in the present study, that is,

3c



 , dislocations are suggested to be piled
up at the particles since the gliding dislocations cannot bypass the particles. Besides
the low volume fraction of second phase constituents, since the Mg grain size is in
nanoscale and thus less likely for the reinforcement and in-situ formed particles to
exist in the interior of the Mg grain, this effect should be negligible in the present
material.

An appropriate grain size distribution could also impart both high strength and
ductility [58,59]. It can also result from stress-assisted grain growth developed in-situ
during constant stress testing [60]. Nc materials are composed of small grains that
possess large driving force for grain growth, and the applied stress during plastic flow
can also be very high. From the practical point of view, particle (10-274 nm range in
AlN particulates) and grain size (20-70 nm range in 40h-MMed composite sample)
distributions exist and entail significant volume fractions of grains much larger than
the average grain size to display dominant deformation mechanisms such as diffusional
creep or GBS.
Investigation of time dependent deformation behaviors by creep test


152
As shown in Fig. 4.15 (c), no clear evidence of lattice dislocations or dislocation
interactions with particles could be observed in the interior of the grains and grain
elongation after tensile deformation. Similar finding has been reported by Chua et al. [30]
in both tensile and constant stress-creep deformed nc Mg alloy. From Fig. 6.4, Coble creep
is closer to the experimental result at lower stress level. However, at high stress level,
creep rates from GBS model and Coble creep are comparable. The higher slope of creep

rate curve in GBS model indicates that creep rate from the GBS model may be closer to
experimentally observed value when the stress level is increased. The creep deformation
parameters (stress exponent n=2 and activation energy Q for creep process of about 61
kJmol
-1
) and microstructural observation indicate that GBS accommodated with grain
boundary diffusion is the highly possible dominant deformation mechanism in the present
nc Mg composite. In addition, the simultaneous operation of Coble creep is evident
especially at the lower stress levels.

6.4 Conclusions

Low temperature creep tests at 0, 25 and 50˚C (<0.35T
m
where T
m
is melting
temperature) were carried out to further investigate the time dependent deformation
behaviors of the nc Mg composite. The present nc composite displays an activation
energy of
61 kJmol
-1
which is close to the value for grain boundary diffusion in Mg and
a stress exponent of 2 in power-law relation for steady state creep. These experimental
results imply that the current creep behavior cannot be described by Coble creep (grain
boundary diffusion creep) alone. Reinforcement particles, impurity and excess free
volume of processing defects may alter the nature of diffusivity in the grain boundary
region. Although deformation parameters favor GBS accommodated with grain
boundary diffusion, the co-existence of Coble creep is evident in the present nc Mg
composite deformation.

Investigation of time dependent deformation behaviors by creep test


153
6.5 References

1. GE Dieter, Mechanical Metallurgy SI Metric Edition, Page 445. McGraw-Hill,
Singapore. 1988.
2. R W Bailey, The utilization of creep test data in engineering design, Proc
IMechE 131 (1953) 131-349.
3. S
Hwang, C Nishimura, PG McCormick, Scripta Mater 44 (2001) 1507-1511.
4. SB Singh, Eur J Mech A Solids 27 (2008) 680-690.
5. B Burton, Mater Sci Eng 11 (1973) 337-343.
6. FK Sautter, ES Chen. In: Oxide dispersion strengthening, ed. by GS Ansell, TD
Cooper, FV Lenel, Vol 47, pp. 495-508. Gordon and Breach, New York. 1968.
7. B Burton, Metal Sci J 5 (1971) 11-15.
8. JE Harris, RB Jones, GW Greenwood, MJ Ward, J Aust Inst Met 14 (1969) 154.
9. RL Squires, RT Weiner, M Phillips, J Nucl Mater 8 (1963) 77-80.
10. MF Ashby, Scripta Metall 3
(1969) 837-842.
11. GW Greenwood, Scripta Metall 4 (1970) 171-174.

12. E Arzt, MF Ashby, RA Verrall,
Acta Metall 31 (1983) 1977-1989.
13. H Gleiter, Acta Mater 27 (1979) 187-192.
14. HJ Frost, MF Ashby, Deformation-mechanism maps: the plasticity and creep of
metals and ceramics, pp. 43-52. Oxford, New York, Pergamon Press. 1982.

15. BQ Han, DC Dunand, Mat Sci Eng A 300 (2001) 235-244.

16. J Deng, D Wang, QP Kong, JP Shui, Scripta Metall Mater 32 (1995) 349-352.
17. C Schuh, BQ Han, DC Dunand, Metall Mater Trans A 31 (2000) 2647-2657.
18. JV Funn, I Dutta, Acta Mater. 47 (1999) 149-164.
19. RG Stang, CR Barret, Scripta Metall 7 (1973) 233-236.
20. M Ignat, R Bonnet, Acta Metall 31 (1983) 1991-2001.
21. J Rosler, G Bao, AG Evans, Acta Metall Mater 39 (1991) 2733-2738.
22. J Rosler, JJ Valencia, CG Levi, AG Evans, R Mehrabian. In: Intermetallic
Matrix Composites, Vol. 194, ed. by DL Anton, PL Martin, DB Miracle, R.
McMeeking, pp. 241-248. Mater Res Soc Symp Proc, Pittsburgh, PA. 1990.
23. RS Mishra, AK Mukherjee, Scripta Metall Mater 25 (1991) 271-275.
24. RS Mishra, TR Bieler, AK Mukherjee, Acta Metall Mater 45 (1997) 561-568.
25. PBR Nimmagadda, P Sofronis, Acta Mater 44 (1996) 2711-2716.
26. R Raj and MF Ashby, Metall Trans 2 (1971) 1113-1127.
27. C Herring, J Appl Phys 21 (1950) 437-445.
28. RL Coble, J Appl Phys, 34 (1963) 1679-1682.
29. H Luthy, RA White, OD Sherby, Mater Sci Eng 39 (1979) 211-216.
30. BW Chua, L Lu, MO Lai, Mater Res Bulletin 41 (2006) 2102-2110.
31.
PG Sanders, M Rittner, E Kiedaisch, JR Weertman, H Kung, YC Lu, Nanostruct
Mater 9 (1997) 433-440.
32.
MF Ashby, RA Verrall, Acta Metall 21 (1973) 149-163.
33. Y. Ogino, Scripta Mater 43 (2000) 149-153.
34. HE
Schaefer, R Wurschum, T Gessmann, G Stockl, P Scharwaechter, W Frank, RZ
Valiev, HJ Fecht, C Moelle, Nanostruct Mater 6 (1995) 869-872.
35. SV Petegem, FD Torre, D Segers, HV Swygenhoven, Scripta Mater 48 (2003) 17-
22.
36. PP Chattopadhyay, SK Pabi, I Manna, Mater Chem Phys 68 (2001) 80-84.
37. H Gleiter, Phys Stat Sol B 172 (1992) 41-51.

38. HE Schaeffer, R Wurschum, R Birringer, H Gleiter, Phys Rev B 38 (1988) 9545-
9554.
Investigation of time dependent deformation behaviors by creep test


154
39. YR Kolobov, GP Grabovetskaya, IV Ratochka,, KV Ivanov, Nanostruct Mater 12
(1999) 1127-1130.
40. E Arzt, J Rösler, Acta Metall 36 (1988) 1053-1060.
41. J Rösler, G Bao, AG Evans, Acta Mater 39 (1991) 2733-2738.
42. E Arzt, G Dehm, P Gumbsch, O Kraft, D Weiss, Prog Mater Sci 46 (2001) 283-307.
43.
T Mori, Y Nakasone, M Taya, K Wakashima, Phil Mag Lett 75 (1997) 359-366.
44. IM Lifshitz, Soviet Phys JETP 17 (1963) 909-920.
45. RN Stevens, Phil Mag 23 (1971) 265-284.
46. MJ Stowell, Superplastic Forming of Structural Alloys. pp.
321. Warrendale,
Pennsylvania, Metallurgical Society of AIME. 1982.

47. D Lee, Acta Metall 17 (1969) 1057-1069.
48. A Needleman, JR Rice, Acta Metall 28 (1980) 1315-1332.
49. AK Chokshi, AK Mukherjee, Acta Metall 37 (1989) 3007-3017.
50.
G Le Roy, JD Embury, G. Edwards, M.F. Ashby, Acta Metall 29 (1981) 1509-
1522.
51. M Mabuchi, K Higashi, Acta Mater 47 (1999) 1915-1922.
52. M Mabuchi, K Higashi, Mat Trans 40 (1999) 787-793.
53. RS Mishra, TR Bieler, AK Mukherjee, Acta Mater 43 (1995) 877-891.
54. DJ Srolovitz, RA Petkovik-Luton, MJ Luton, Phil Mag A 48 (1983) 795-809.
55. DJ Srolovitz, MJ Luton, R Petkovik-Luton, DM Barnett, WD Nix, Acta metall

32 (1984) 1079-1088.
56. S Onaka, S Miura, M Kato, Mech Mater 8 (1990) 285-292.
57. TG Langdon. Acta Metall Mater 42 (1994) 2437-2443.
58. X Zhang, H Wang, RO Scattergood, J Narayan, CC Koch, AV Sergueeva et al.,
Acta Mater 50 (2002) 4823–4830.
59. YM Wang, E Ma, Acta Mater 52 (2004) 1699–1709.
60. DS Gianola, S Van Petegem, M Legros, S Brandstetter, H Van Swygenhoven,
KJ Hemker, Acta Mater 54 (2006) 2253–2263.
61. RC Giekins, Mat Sci Eng 2 (1967) 181-192.