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

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 conventiona

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

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

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

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

to dislocation motion It is assumed that a dislocation source at the centre of a grain d

sends out dislocations to 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

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

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

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]

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]

Grain-I >1 μm Low High Strong Transgranular,

ductile fracture High Negligible

Moderate Moderate

III <20 nm Increases

with grain size

Low Negligible Sliding of

atomic planes in grain boundaries

Negligible Dominant

localized shear band formation

None Practically

100%

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

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

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

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)

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

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

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

 IGC: inert gas condensation, HPGA: high pressure gas atomization, AC: amorphous crystallization, BM: ball milling, TS: torsion straining and ED: electrodeposition

ef : Elongation to failure

Tm : melting temperature.

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 (100-102 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 E

kT

Gb A

p n

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 G

[57]

i D p dd

b G

[55]

gb D d

b G

l kT

Gb

A

3 2 ) 0 )(

b d

b G

 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

material essentially becomes amorphous Grain boundary strengthening effect will then disappear

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

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

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

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) TiO2

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) Ni80P20 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

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]

10

G rain 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 m2/s and 1.7x10-17 m2/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

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

b kT

Gb D

NH NH



where ANH is a constant, Dl 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:

b kT

Gb D

C C

