The importance of grain size in crystalline materials

1. AGH
University of Science and Technology
Introduction to Materials Science
Nicola Ergo
THE IMPORTANCE
OF GRAIN SIZE
FROM COARSE-GRAIN TO ULTRAFINE GRAIN MATERIALS
Author: Nicola Ergo

2. PLAN
 INTRODUCTION
• WHAT ARE NANOMATERIALS?
• THE IMPORTANCE OF THE GRAIN SIZE
 MECHANICAL PROPERTIES
 GRAIN SIZE
 PRODUCTION METHODS
 PROPERTIES AFTER SPD PROCESSING
 SUMMARY OF PSD
 APPLICATION
 GLOSSARY

3. INTRODUCTION - WHAT ARE NANOMATERIALS?
Nanomaterials are defined as materials in which on of the dimensions (x, y, or z) is in
the range (length scale) of 1 – 100 nanometers (nm=m-9).
• Nanoparticles are objects with all three external dimensions (x, y, and z) at the nanoscale
(1 to 100 nm).
• Nanofibers (or nanowires) are objects with two external dimensions at the nanoscale.
• Nanosheets (or nanofilms) are objects with one external dimension at the nanoscale.

4. INTRODUCTION - THE IMPORTANCE OF THE GRAIN SIZE
The grain size is the major microstructural parameter in dictating the properties of a
polycrystalline material.
The significance of decreasing grain size in order to improve the mechanical properties of a
material is apparent in the production of ultrafine grain materials (UFG) which have one
dimension in the order of 100-1000 nm. UFG materials are further deformed to produce
nanomaterials.
In order to improve mechanical properties, the grain structure of the material is systematically
altered.
This includes:
• increasing the number of dislocations and grain boundaries;
• varying orientation of the grains and associated grain boundaries.
This is done through a process of Severe Plastic Deformation (SPD).

5. INTRODUCTION - THE IMPORTANCE OF THE GRAIN SIZE
Fig. 1 - Differences in grain size between conventional material and nanomaterial.
 Nanocrystalline grain boundaries store interstitial defects, then fire them back into the
matrix to annihilate passing vacancies, destroying both defects and healing the material.
 In conventional materials, interstitials diffuse to the surface, leaving internal voids and
causing the swell.

6. MECHANICAL PROPERTIES
 HIGH STRENGTH TO WEIGHT RATIO
 HIGH DUCTILITY
 CREEP BEHAVIOUR
 HIGH PURITY AND HOMOGENEITY
 HIGH FRACTURE TOUGHNESS
 HIGH DURABILITY
 FATIGUE RESISTANT – cycling loading
 INCREASED TENSILE STRENGTH – high dislocation density
 HIGH THERMAL STABILITY
 CORROSION RESISTANCE

7. MECHANICAL PROPERTIES
 HIGH STRENGTH TO WEIGHT RATIO
By improving the strength quality of the materials, less of the material needs to be used in
order for it to withstand specific loading.
 HIGH DUCTILITY
High ductility is a sought after property as this prevents fast fracture of the material and grain
boundaries slide under conditions of superplastic flow, this combined with limited
intragranular slip prevents the development of internal cavities. (at high temperatures)
 CREEP BEHAVIOUR
Creep behaviour is the way in which the materials reacts to prolonged exposure to applied
stress and usually at higher temperature than room temperature. Creep deformation depends
on grain boundary diffusion described by Nabarro-Herring and Coble theory, so that smaller
are the grains, more are the grain boundaries, less is the creep resistance. The creep
resistance can be improved by post machining, thus improving the properties of the original
coarse-grained material.

8. MECHANICAL PROPERTIES
 HIGH PURITY AND HOMOGENEITY
High purity is associated with homogeneity. The material has the same properties throughout
the sample as the grain sizes are significantly small and do not allow for many impurities and
irregularities. As the grain size decreases, the homogeneity of the sample increases.
 HIGH FRACTURE TOUGHNESS
Fracture Toughness is defined as the property which describes the ability of a material
containing a crack to resist fracture, and is one of the most important properties of any
material for many design applications. The decrease in the grain size results in an increase in
the amount of grain boundaries within the material. Grain boundaries and dislocations resist
crack growth. Fracture toughness is directly related to durability.
 HIGH DURABILITY
Durability is the ability of the material to resist fracture and wear under the present of
monotonic and cyclic loading and stress. This follows onto fatigue resistance.
 FATIGUE RESISTANT
Fatigue is the wear of a material due to repeated exposure to variations in imposed stress
such as cyclic loading.

9. MECHANICAL PROPERTIES
 INCREASED TENSILE STRENGTH
Tensile strength is the ability of the material to withstand fracture and damage under an
applied tensile force. This is due to the increased presence of dislocations and grain
boundaries which prevent the movement of dislocations thus preventing plastic deformation.
 HIGH THERMAL STABILITY
Thermal stability is directly related to creep behaviour. Thermal stability is the ability of a
material to maintain its mechanical properties at varying temperatures. Materials operating at
low temperatures have a tendency to fast fracture as they lose their ductility, whereas
materials operating at high temperatures lose their electro-mechanical properties and
experience changes in strength of the material.
 CORROSION RESISTANCE
Corrosion is a surface phenomenon in which a metal forms an oxidation layer which alters its
mechanical properties. Corrosion occurs when there is a high presence of surface defects. The
large amount of grain boundaries in UFG materials which intersect with the surface layer of
the material should result in a decreased in the corrosion resistance of the materials, however
these defects are infinitesimally small. Corrosion resistance can be improved with the correct
surface post-machining.

10. GRAIN SIZE
The precise significance of the grain size is dependent upon two relationships that are
applicable at either low or high operating temperature, respectively.
 At low operating temperature, the strength generally follow the Hall-Petch relationship:
where σy is the yield stress, σo is the lattice friction
stress, ky is a constant of yielding, and d is the
grain size.
,
Thus, the strength of the material increases
when the grain size is reduced.

11. GRAIN SIZE
The precise significance of the grain size is dependent upon two relationships that are
applicable at either low or high operating temperature, respectively.
 At high temperatures and under conditions of constant stress or load, the steady-state
strain rate, , is given by a relationship of the form:
where D is the appropriate diffusion coefficient, T is the absolute temperature, G is the
shear modulus, b is the Burger’s vector, d is the grain size, k is Boltzmann’s constant, σ is the
applied stress, p and n are exponents of the inverse of grain size and stress, and A is a
dimensionless constant.
Thus, grain refinement provides an opportunity for achieving superplastic elongations at
elevated temperatures provided the small grains have reasonable thermal stability.
,

12. PRODUCTION METHODS
Metals having grain sizes smaller than 1μm (1000nm) may be
produced in two fundamentally different ways:
 Bottom-up approach:
Bottom up approach refers to the build up of a material from
the bottom: atom by atom, molecule by molecule or cluster by
cluster.
• Deposition techniques
• Nanoscale building blocks
 Top-down approach:
Top down approach refers to slicing or successive cutting of a
bulk material to get nano sized particle.
• Severe plastic deformation (SPD)

13. PRODUCTION METHODS – SEVERE PLASTIC DEFORMATION (SPD)
Equal Channel Angular Pressing (ECAP) High Pressure Torsion (HPT)
Accumulative Roll Bonding
Multi-axial Forging
Twist Extrusion

14. PRODUCTION METHODS - ECAP
Equal-channel angular pressing (ECAP) makes use of a
die containing a channel bent through a sharp angle
near the centre of the die.
• A sample billet is fed through the channel using a
plunger which has pressure P applied to it.
• The cross sectional dimensions remain unchanged
throughout the process.
• The process is repeated in order to decrease the
grain size.
The grain size and orientation is dependent on the
angle between the two parts of the channel, φ, and
the angle at the arc of curvature, Ψ. The angle at the
arc of curvature becomes more important if it is
below 90°.
The purpose is to introduce a high dislocation density without any change in the
cross-sectional dimensions.
Fig. 2 – The principle of ECAP including an X, Y,
and Z coordinate system.

15. PRODUCTION METHODS – ECAP: φ=90°, Ψ=20°, RT
• The grain colours denote the orientation of
the individual grains.
• Black lines denote low-angle boundaries
where the misorientations are between 2°
and 15°.
• Red lines denote high-angle boundaries
where the misorientations are >15°.
Fig. 3 - Microstructures in high purity Al in (a) and (b)–(g) after
processing by ECAP.
60μm 10μm 10μm
10μm 10μm 2μm
After the first pass there is an array of
elongated subgrains but thereafter the
microstructure gradually evolves into
arrays of reasonably equiaxed grains
separated by boundaries having high-
angles of misorientations.
It is also possible to notice that since the
lattice structure of adjacent grains differs
in orientation, it requires more energy for
a dislocation to change directions and
move into the adjacent grain.

16. PRODUCTION METHODS - HPT
High pressure torsion occurs when a thin sample disk is
placed between two anvils, subjected to a pressure P
and then torsionally strained through rotation of either
the lower or upper anvil.
 Constrained HPT: sample placed in cavity in lower
anvil preventing lateral flow.
 Unconstrained HPT: anvils are flat and material
flows outward during processing.
 Quasi-constrained HPT: sample disk contained in
depressions on both upper and lower anvils allowing
for limited outward lateral flow during processing.
Fig. 4 – The principle of HPT.

17. PRODUCTION METHODS - HPT
Thus, the two parameters, i.e. a number of turns applied to the disk, N, and a magnitude of
the imposed pressure, P, are important in the HPT process.
• Applied pressure reduces diffusion rate and facilitates grain refinement and hardening.
• Imposed Von Mises Strain Ɛeq:
where N is the number of turns of torsional straining, r is the distance measured from the
centre of the disk, and h is the initial height or thickness of the sample.
Thus, the strain varies across the disk with its maximum value at the outer edge and a
value of 0 at the centre where r=0.
,

18. PRODUCTION METHODS – HPT: 6.0GPa, RT
Fig. 5 – Microstructures in a Cu–0.1% Zr alloy after processing by HPT
through (a) 1 turn and (b) 5 turns.
2μm 2μm
2μm 2μm
It is apparent in Fig. 5(a) that there is an
inhomogeneous microstructure after
processing through one turn with average
grain sizes measured as ~ 580 nm in the
central region and ~ 410 nm near the edge.
After five turns the microstructure is more
equiaxed and the grain size is ~ 500 nm in
the center and ~ 410 nm at the edge.
This suggests the microstructure
remains reasonably constant at
the edge but there is continuous
grain refinement in the central
region.
Thus, with more turns it’s
possible to achieve an
homogeneous condition.
(a) (b)

19. PROPERTIES AFTER SPD PROCESSING
HIGH STRENGTH
For all alloys, the proof stress increases
sharply in the first pass but thereafter there
is only a minor additional increase up to a
maximum of 8 passes.
Fig. 6 - The increase in proof stress with increasing numbers
of ECAP passes for a range of commercial aluminum alloys.

20. PROPERTIES AFTER SPD PROCESSING
SUPERPLASTIC PROPERTIES
A second important property is the ability to achieve superplastic properties when testing in
tension at elevated temperatures.
These properties can be achieved only when the grain size remains ultrafine at the high
temperatures which are needed for diffusion-controlled superplastic flow.
Fig. 7 - Exceptional superplasticity in an extruded ZK60 magnesium
alloy processed by ECAP for 2 passes and then tested in tension at
473 K: the elongation of 3050% is the highest elongation recorded to
date in any magnesium-based alloy processed under any conditions.

21. SUMMARY OF SPD
Using severe plastic deformation it’s possible to achieve:
 significant grain refinement of coarse-grained materials;
 arrays of equiaxed grains having sizes within the submicrometer range;
 grains separated by boundaries having high angles of misorientation;
 reasonable levels of homogeneity;
in order to have high strength materials at room temperature and superplastic
properties at high temperatures.

22. APPLICATIONS
Nanomaterials are used in specialist applications due to the high production and processing
costs. Applications such as:
 biomedical use in cranial drill bits and precision cutting tools;
 aerospace and aeronautics are also popular fields of use;
 materials which can cope with extreme environmental conditions such as the corrosive
properties of sea water and large imposed frictional forces experienced by aeroplanes and
spaceships;
 electronics such as nano-chips and nanotechnology;
 high performance sport equipment.

23. APPLICATIONS
This diagram demonstrates that these UFG materials will probably find major applications
under extreme environmental conditions and where the required properties are unusually
severe.
Fig. 8 - The innovation potential as a function of material
strength showing the use of strong materials in extreme
environmental conditions.

24. REFERENCES
 Extreme grain refinement by severe plastic deformation: A wealth of challenging science –
Y. Estrin, A. Vinogradov
 Advances in ultrafine-grained materials – Yi Huang, Terence G. Langdon

25. THANK YOU
FOR THE ATTENTION

26. GLOSSARY
Microstructural parameter: a physical and measurable factor of the microstructure of the
material defining and affecting a set of conditions.
Mechanical properties: a property that involves a relationship between stress and strain or
a reaction to an applied force. They refer to how materials deform (elongate, compress, twist)
or break as a function of applied load, time, temperature, and other conditions.
Systematically altered: to change the microstructure in order to achieve a particular set of
results.
Fast fracture: a phenomenon in which a flaw (such as a crack) in a material expands quickly,
and leads to catastrophic failure of the material.
Superplastic flow: a state in which solid crystalline material is deformed well beyond its usual
breaking point, usually over about 200% during tensile deformation.
Intragranular slip: movement of grains in relation to one another (movement by slipping).
Coarse-grained material: a material made up of relatively large parts or particles (large
grains).

27. GLOSSARY
Monotonic loading: imposed stress having the property either of never increasing or of never
decreasing as the values of the independent variable.
Cyclic loading: frequently encountered in rotating machinery where a bending moment is
applied to a rotating part.
Infinitesimally small: indefinitely or exceedingly small.
Yield stress: it is defined in engineering and materials science as the stress at which a material
begins to deform plastically.
Fig. 1 - Stress and strain diagram.
1.True Elastic Limit
2.Proportionality Limit
3.Elastic Limit or Yield Strength
4.Offset Yield Strength

28. GLOSSARY
Steady-state: condition which does not change over time.
Deposition techniques: are special bottom up processes used to produce nano or ultrafine
grain materials exploiting chemical or physical reactions.
Billet: cylindrical sample.