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

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 typi

(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

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

The creep in the composite shows a steady state behavior [2], which may be described

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

from the various best linear fits at n=2 as shown in Fig 6.2

02E-4

1.2E-31E-38E-46E-44E-4

3.0E-32.5E-32.0E-31.5E-31.0E-3

6E-35E-34E-53E-32E-3

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]

-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 0.5Q gb in Mg + 30 vol.% Y2O3 [15],

0.7Q gb in nano Ni-P alloy [16] and 0.5-0.6 Q gb for Al with Al2O3 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

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

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 ( ) can be expressed as [27] NH

D

NH NH



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 ( ) as Cfollows:

kT d

D kT

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]:

2 3 5

102

b kT

Gb

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

m2 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

m2 s-1 which is about 6 orders of magnitude faster

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]

grain boundary thickness  (~3b) 9.63x10-10 m

activation energy for grain boundary diffusion Q gb 92 kJmol-1

activation energy for lattice diffusion Q l 134 kJmol-1

pre-exponential constant D 0 5.0x10-12 m3s-1

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

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)

1E-10

1E-81E-71E-6

1E-41E-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

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

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

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

1E-141E-121E-101E-8

1E-41E-6

273K 298 K 323 K Present study

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

40h-Stowell [46] formulated an equation to gauge the possibility of cavity nucleation using critical strain rate  below which cavity nucleation is highly improbable and this c (c)critical strain rate is given by

kT

D cdd

gb

p

e c



