Mechanical Properties of Nano Materials

7/30/2019 Mechanical Properties of Nano Materials

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Submitted By:

Ankit Verma

B.Tech 3rd YearMechanical & Industrial Engg. DepttIIT Roorkee


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One of the very basic results of the physics andchemistry of solids is the insight that most propertiesof solids depend on the microstructure, i.e. thechemical composition, the arrangement of the

atoms (the atomic structure) and the size of a solidin one, two or three dimensions.


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The important aspects related to structure are: Atomic defects, dislocations and strains Grain boundaries and interfaces

Porosity Connectivity and percolation Short range order

The most well-known example of the correlationbetween the atomic structure and the properties of abulk material is probably the spectacular variation in thehardness of carbon when it transforms fromdiamond to graphite


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Properties Changes

Density

The strength depends on

orelative density and decreased with increasingporosity

Fracture Strength


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Figure 1 Shows a comparison

of strength and fracturetoughness of alumina basednanocomposites at roomtemperature as a function ofSiC content as reported byseveral groups.


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Strengthening Mechanism

The evidence is that Al2O3/SiC nanocompositesshow an explicit increase in strengthaccompanied by a modest increase in toughness.

Furthermore, grain boundaries are strengthened

in nanocomposites as manifested by the trans-crystalline fracture mode as well as by theincreased resistance to wear and creep.


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Figure 2 shows strength and fracturetoughness for various Si3N4/SiCnanocomposites as a function of SiCvolume fraction.


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Critical Flaw size reduction1) Zener grain size boundary pinning

The effect of grain boundary pinning by small inclusionsis described by Smith after a semi quantitative approachby Zener:

whereR is the average matrix grain boundary radius of curvature,

depending on the radius (r) andthe volume fraction (Vf) of sphericalinclusions. Equation is often given in the form

D r/ Vf

WhereD is the average matrix grain diameter


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In Fig. 3 the Zener model is comparedwith experimental data where MatrixSizeR is plotted as a function of 1/Vf


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Reduction in processing flaw size

Increased strength of the nanocomposites is areduction in the size of processing flaws

In Al2O3/SiC nano-composite powder mixtures,hard SiC agglomerates. The latter commonly

cause large processing flaws such as voids inalumina ceramics.


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Crack Healing Cracks in nanocomposites can heal during

annealing

Alumina and Al2O3/SiC nanocomposites areindented with a Vickers piramid to generateradial cracks

After annealing at 1300 C inAr for 2 h the

material behave completely differently. Whereascracks in alumina grow, cracks in nanocomposites close, thus explaining the strengthincrease of annealing nanocomposites.


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Crack Deflection The interactions of a crack frontwith second-

phase inclusions, such as spherical particles in

nanocomposites, depend on the differences inthe thermo elastic properties of the matrixand inclusions.

The toughening of the composite is a result ofdiminishing the stress intensity directly at the tip ofthe deflected crack.

Niihara has proposed a toughening effect due tocrack deflection caused by compressive residualstresses around the SiC particles.


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Toughening

R-curves

Concerning R curve effects one has todistinguish between mechanisms acting on thecrack wedge behind the crack tip andmechanism acting directly at or in front of the

crack tip. In nanocomposites any toughening effects actingon the crack wedge behind the crack tip areunlikely because of the lack of bridging elements


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Fig. 4 Schematically dependence of the

toughness as a function of crack lengthby assuming a step and a flat rise forshort crack lengths.

By assuming thesame initial flaw sizes

and plateau toughnessvalues, a higher

strength can beachieved for a sharplyrising R-curve.


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Grain boundary StrengtheningMechanism

Conceivable reasons for the grain boundarystrengthening are:

(1) Deflection of a crack running along a grainboundary at an SiC particle into the grain

(2) Strengthening of the grain boundaries due tolocal internal stresses


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Thermal expansion mismatch The thermal expansion misfit stress, T, inside a single

spherical inclusion in infinitematrix can be described bythe following expression after Selsing:

Where E and v are Youngs modulus and Poissons ratio ofthe matrix (m) and the particles (p).

The tangential, T, and the radial, T, stress distributions

in the matrix around the particle are given by:

where r denotes the radius of the inclusion and x is the

radial distance from the inclusion surface.


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Average Internal Stress

The average residual micro stresses inside thematrix and the particles, m and p, are given

by the following expressions:

Where


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BCs

For Vf=0, above eqn provides the same value forthe stresses inside the particles as the Selsing

model.

Another boundary condition is given bymechanical equilibrium with

m(1Vf)+p Vf

=0.


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Local Stress Distribution


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Summary


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Metastable Phase Diagram


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Another situation arises if

the material in the massivestate does not showpolymorphism (see fig. 5).For example, if the -

phase is stable over theWhole range oftemperature in massivebodies, decreasing thesample dimensions

may give rise to theformation of the -phase.


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Hall Petch Effects Pile-up of dislocations against grain boundaries, which results in adependence of the hardening increment on the square root of the grainsizeD:

Where kHPis a constant. This is the classicalHall-Petch effect.

Limits to Hall-Petch behavior: Dislocation curvatureVs. Grain size

A clear limit for the occurrence of dislocation plasticity ina poly-crystal is given by the condition that at least onedislocation loop must fit into average grain


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Where Td: line tension , D: Grain size

Characteristic length (d) is a function of the size parameter (D). The resultingstrength increment is given by:

The dislocation density scales inversely with grain sizeD, the obstacle

spacing is L~1/p~D, which yields:

reduces correctly to Hall-Petch behavior forD >>r0

The characteristic length, i.e. the loop diameter, must now be comparedwith the grain sizeD as the relevant size parameter:

or (2)

(1)


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contains a lower (r0) and an upper (r1) cut-off distance for the stress field of

the dislocation

One possible explanation for such a softening effect comes from areconsideration of the line tension Td in equation (2). the more refinedexpression

Because of the viscous behavior of amorphous materials(which can be considered the limiting case for grain refinement) thegrain size strengthening effect will have to be reversed oncethe grain sizeD starts to approach the grain-boundary thickness b.


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Grain size strengthening, as explained by pile-ups of dislocation loops against grainboundaries(a). this mechanism must break down when the diameter d of the smallest loop nolonger fits into a grain of size D(b). The limiting condition is shown as the heavy line in(c) where the shear strength isplotted schematically as a function of

grain size D


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The relation between yield stress and grain size is described mathematically by

the Hall-Petch equation:

where y is the yield stress, o is a materials constant for the starting stress

for dislocation movement (or the resistance of the lattice to dislocation motion),

ky is the strengthening coefficient (a constant unique to each material), and d

is the average grain diameter.
http://en.wikipedia.org/wiki/File:HallPetchLimit.png


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Hall-Petch Strengthening is limited by the size of

dislocations. Once the grain size reaches about

10 nanometres (3.9107 in), grain boundaries start to

slide.
http://en.wikipedia.org/wiki/File:HallPetchLimit.pnghttp://en.wikipedia.org/wiki/File:HallPetchLimit.png


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Inverse Hall-Petch behavior in nanocrystalline Cu (H-H0) denotes the

hardness increment,D the grain size): the classical behavior breaks down at agrain size of about 50 nm, in agreement with an estimate based on the loopdiameter Replotted after Chokshi et al. [23].


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Mechanical Properties of Nano Materials

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