Microstructure-Properties: I Fracture Toughness - Materials Science ...

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Microstructure-Properties: I
Fracture Toughness: how to
maximize it through
microstructure control
27-301
Lecture 6C
Fall, 2007
Prof. A. D. Rollett
Processing
Performance
Microstructure Properties

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Happy Guy Fawkes Day (Nov. 5th)!
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Objective
• The objective of this lecture is to show you how to
exploit microstructure in order to maximize
toughness, especially in brittle materials.
• Part of the motivation for this lecture is to prepare
the class for a Lab on the sensitivity of mechanical
properties to microstructure.
• Note that the equations used are not derived -
rather the emphasis is on basic principles and a
broad range of methods for toughening.

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Applications?
Why do we care about toughness?
• Steels are used to build pressure vessels for
nuclear reactors. The irradiation that these
vessels experience, however, lowers the
toughness of the steels. This must be allowed for
in the design and operation of the reactors.
http://ecow.engr.wisc.edu/cgi-bin/get/neep/541/allentodd/notes/
Courtney
(Ch. 13)

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Applications: ceramic gas turbines
• The thermal efficiency of a gas turbine engine is directly related to its operating
temperature. Conventional gas turbines use Ni-based alloys whose operating
temperature is limited by their melting point (although clever design of thermal
barrier coatings and cooling has dramatically raised their capabilities).
Ceramic (oxide) components have much higher melting/softening points but
their intrinsic toughness is far too low. Therefore the toughening of structural
ceramics is essential if these systems are to succeed. The silicon nitridebased
part shown (left) has machined strengths of up to 960 MPa and asprocessed
strengths of up to 706 MPa.
www1.eere.energy.gov/vehiclesandfuels/pdfs/success/advanced_gas_turbine.pdf
www.p2pays.org/ref%5C08/07468.pdf -

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Key Points
• Maximizing fracture resistance requires maximizing work done
in breaking a material.
• Minimize defect content, especially voids, cracks in brittle
materials.
• Increasing toughness generally requires adding additional
structural components to a material, either at the microscopic
scale or by making a composite.
• If appropriate (in relation to the way in which a material is
loaded), laminate the material i.e. put in crack deflecting
planes.
• If appropriate (in relation to the way in which a material is
loaded), include stiff fibers in the material to give load transfer
and fiber pull-out.
• Design the composite to have inclusions that deflect the crack
path.
• Design the composite to include particles that transform (or
crack) and thus require work to be done for crack propagation
to take place.

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Strength versus toughness
• If you imagine testing the (tensile) strength of a
material that you could make arbitrarily tough or
brittle, how would its measured strength vary?
Breaking Strength
?
Toughness

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Strategies for toughness and
microstructure
• Yield strength depends on the obstacles to
dislocation motion.
• Toughness is more complex: there is no
direct equivalent to obstacles to dislocation
motion.
• Instead, we must look for ways to (a)
eliminate or minimize cracks; (b) ways to
maximize the energy cost of propagating a
crack.

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(a) Minimize/eliminate
Minimize/ eliminate cracks
• How do we eliminate cracks?
• First, consider the sources of cracks:
- in metals, voids from solidification are deleterious
(especially in fatigue), so minimizing gas content
during solidification helps (Metals Processing!).
- rough surfaces (e.g. from machining) can be
made smooth.
- also in metals, large, poorly bonded (to the
matrix) second phase particles are deleterious,
e.g. oxide particles. Therefore removal of
interstitials (O, N, C, S) from steel melts (or Fe &
Si from Al) is important because they tend to react
with the base metal to form brittle inclusions (as in,
e.g. clean steel technology).

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(a) Minimize/eliminate Minimize/eliminate
cracks
• How do we minimize cracks?
Grain Structure:
- there are various mechanisms that lead to cracks at grain
boundaries, or at triple junctions between boundaries.
Therefore - in some materials - making the grain size as small
as possible is important because it determines the maximum
crack size. Crack size matters because of stress
concentration at the crack tip: longer cracks mean higher
stress concentrations.
- how to minimize grain size? Either by thermomechanical
processing (maximum strain + minimum recrystallization
temperature) or by starting with small powders and
consolidating to 100% density.

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Distributions
• Remembering that it is the largest crack that limits
breaking strength, it is not the average crack length
that matters but rather the maximum crack size that
we should care about.
• For materials in which the grain size determines the
typical crack size, experience shows that the grain
size distribution is approximately constant. The
maximum grain size observed is a small multiple of
the average - about 2.5 times.
• Also important in distributions is the spatial
distribution of particles (that can generate cracks);
cracks at, or near the surface are more deleterious
than cracks in the interior.

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Spatial Distributions
• Anisotropic spatial distributions are most commonly
encountered in thermomechanically processed
metals. They occur, for example, in silicon nitride
processed (tape casting + sintering) to promote
directional growth of beta-Si 3 N 4 for high thermal
conductivity heat sink materials.
• The sensitivity of toughness to the direction in
which the testing is performed has led to a special
jargon for specimen orientation.

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Specimen Orientation Code
• The first letter denotes the loading direction; the
second letter denotes the direction in which crack
propagation occurs.
[Hertzberg]

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Mechanical Fibering
• Any second phase particles present from solidification tend to
be elongated and dispersed in sheets parallel to the rolling
plane; called “stringers”.
• Toughness in the S-L or S-T orientations is typically much
lower than for the L-T or L-S orientations because the crack
plane is parallel to the planes on which the particles lie close
to one another.
[Hertzberg]
Lowest
toughness

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Inclusion effects
• Graph plots variation
in strength with (plane
strain) toughness with
varying sulfur contents
in 0.45C-Ni-Cr-Mo
steels.
• Increasing levels of S
lead to lower
toughness at the same
strength level.
• This occurs because
the sulfur is present as
sulfide inclusions in
the steel.
• “Clean steel”
technologies have
reduced this problem
in recent years. [Dieter]

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[Hertzberg]
Laminate Composites
• The weakness of such layers of inclusions, which provide planes on
which crack nucleation is relatively easy, can however be exploited.
• By providing planes of low crack resistance perpendicular to the
anticipated crack propagation direction, a crack can be deflected,
thereby reducing the load at the crack tip.
• In designing a laminate composite, it is important to balance the
fracture toughness (brittleness) against the interfacial weakness.
The more brittle the matrix (layers), the weaker the interfaces
between the layers need to be. Example: Wood, Mollusc shells

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Effect of lamination on the DBTT
• The effect of orienting the laminations of a
composite in the crack arrestor configuration is to
dramatically lower the transition temperature.
• This is actually an example of crack deflection.
[Hertzberg, after Embury]

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Explanation of Lamination
This crack propagation
direction follows the
inclusion+grain shape
(less toughness)
This crack propagation
direction leads to
delamination and crack
blunting (more
toughness)

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Energy absorption: 1
• How do we increase the amount of energy consumed in
propagating a crack?
- One method, already discussed, is to maximize the amount
of plastic work. This requires the yield strength to be
minimized so as to maximize the size of the plastic zone.
- For very tough materials, however, it turns out that the same
parameters that control ductility also affect toughness. Lower
densities of second phase particle increase toughness.
Second phase particles well bonded to the matrix increase
toughness. Small differences in thermal expansion coefficient
help (Why?).
• Read papers by Prof. Warren Garrison’s group.

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Energy absorption: 2
• Other methods of toughening materials are generally called
extrinsic. There are three general classes of approach:
1) Crack deflection (and meandering)
2) Zone shielding
3) Contact shielding
• The term “shielding” means that the crack tip is shielded from
some part of the applied stress.
• Up to this point, the discussion has been mostly about metalbased
materials which are intrinsically tough to being with
(except at low temperatures). Extrinsic toughening methods
are mostly concerned with ceramics in which the intrinsic
toughness is low.

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Energy absorption: 3
• Sub-divisions of extrinsic toughening methods:
1) Crack deflection (and meandering)
2) Zone shielding
- 2A Transformation Toughening
- 2B Microcrack toughening
- 2C Void formation
3) Contact shielding
- 3A Wedging/ crack bridging
- 3B Ligament/fiber bridging
- 3C Crack sliding, interference
- 3D Plasticity induced crack closure

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1 Crack deflection
• If particles of a second phase are present, large differences in
elastic modulus can either attract or repel the crack.
• Some authors (e.g. Green) distinguish between crack bowing
and crack deflection. Technically, the former is toughening
from deflection in the plane of the crack and the latter is
deflection out of the plane of the crack.
• In either case, the net result is that the crack tip no longer
sees as large a stress as it would if the crack were straight,
and in the plane.
• Crack deflection can be caused by particles that are more
resistant to cracking, or have different elastic stiffness (higher
or lower modulus).
• Laminate composites also achieve crack deflection, as
previously discussed.

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1. Crack
deflection:
examples
[Green]

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Zone Shielding: 2A transformation toughening
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• Various mechanisms exist for shielding crack tips from some
of the applied (and concentrated) stress.
• The best known mechanism is transformation toughening.
• This applies to both metals (stainless steels, Hadfield steels)
and ceramics (zirconia additions).
• The principle on which the toughening is based is that of
including a phase that is metastable at the service
temperature and which will transform when loaded (but not
otherwise).
• The transformation always has a volume change associated
with the change in crystal structure, which can be written as a
strain. The product of stress and strain is then the work done
or expended during the (stress-induced) transformation.

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2A Transformation toughening:
transformation strain
• The large volume change on transformation is
equivalent to a significant transformation strain which
is the key to the success of the method. Recall that
our basic measure of fracture resistance is the work
done, ∫ σdε, in breaking the material.
• The volume change (dε) is ~ 4%, accompanied by a
shear strain of ~ 7%. Since the transformation has a
particular habit plane (i.e. a crystallographic plane in
each phase in common), two twin-related variants
occur in each particle so that the shear strains are
(approximately) canceled out. This leaves only the
4% dilatational (volume) strain that contributes to the
work done.

2A Transformation toughening: phase
2A
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Transformation toughening: phase
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change in zirconia
• The classic example of transformation toughening is the
addition of a few (volume) % of ZrO 2 to oxides and other brittle
ceramics.
• The high temperature form of zirconia is a tetragonal form (t-
ZrO 2 ) which has a significantly larger atomic volume than the
low temperature, monoclinic form (m-ZrO 2 ).
• In order to reduce the driving force for the tetragonal
monoclinic transformation (i.e. lower the transformation
temperature), some “stabilizer” is added. Typical are ceria
(Ce 2 O 3 ) and yttria (Y 2 O 3 ).
• The subtle point about this approach is that some “trick” is
needed in order to keep the zirconia from transforming once
the material is cooled to room temperature, i.e. to maintain it
in a metastable, untransformed state.

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2A Transformation toughening:
critical size of zirconia particles
• An important consequence of the volume change on
transformation is that it leads to an elastic driving force that
opposes the transformation for particles embedded in a matrix
of a different material.
• Therefore we take advantage of having the zirconia
embedded as small particles in the matrix of the ceramic to be
toughened.
• The particles must be small enough for the elastic energy term
to be effective. The upper limit for retention of the high
temperature (tetragonal) phase is ~ 0.5 µm.
[Green]

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2A Transformation toughening:
transformation →→ work
• Consider the effect of the tensile stress in the vicinity of the
crack tip: the stress removes the constraint on each particle,
allowing it to transform. The transformed particle was
metastable, thermodynamically, and so remains in the low T,
monoclinic form after the crack has gone by.
• The stress acting to cause the transformation strain performs
work and so energy is consumed in the phase transformation.
This energy (work done) adds to the surface energy required
to create crack length.
• Additional toughening arises from the particles causing crack
deflection.

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2A Transformation toughening:
the process zone
• The region in which transformation occurs becomes
the crack wake as the crack propagates. The
region around the crack tip is known as the process
zone because this is where the toughening process
is operative.
Process zone width
Crack propagation direction
[Green]

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2A Transformation toughening:
microstructure
• Microstructural evidence for
the transformation is
obtainable through x-ray
diffraction and Raman
spectroscopy (the two different
forms of zirconia have quite
different infra-red spectra).
• (a) lenticular particles of MgOstabilized
ZrO 2 (untransformed)
in cubic ZrO 2 .
(b) transformed particles of
ZrO 2 around a crack (dashed
line).
[Chiang]

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2A Transformation toughening:
limits on toughening
• As the particle size is
increased, so the particles
become less and less
stable; the transformation
becomes easier and more
effective at toughening the
material. If the particles
become too large, however,
the toughening is lost
because the particles are no
longer stabilized in their
high temperature form.
• Effect of test temperature?
• Effect of stabilizing additions
to the ZrO2 ?
[Green]

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2A Transformation toughening:
quantitative approach
• It is not possible to lay out the details of how to
describe transformation toughening in a fully
quantitative fashion here.
• An equation that describes the toughening effect is as
follows, where K is the increment in toughness (units of
stress intensity, MPa√m):
∆K = C E V trans ε trans √h / (1-ν)
C is a constant (of order 1), E = elastic modulus,
V trans = volume fraction transformed,
ε trans = transformation strain (dilatation, i.e. bulk
expansion), h is the width of the process zone, and ν is
Poisson’s ratio.
• What controls the width of the process zone?

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2B Microcracking
• Less effective than transformation toughening is
microcracking in the process zone.
• Microstructural elements are included that crack
over limited distances and only at the elevated
(tensile) stresses present in the crack tip.
[Green]

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2B Microcracking
• The principle of Micro-cracking as a toughening mechanism is that one
designs the material so that additional (micro-)cracking occurs in the vicinity
of the crack tip as it advances, thereby increasing the crack area created
(per unit advance of crack), thereby increasing the toughness (resistance to
crack propagation).
• This is most effective in two-phase ceramics in which the 2 phases have
different CTEs. As the material cools after sintering (or other high
temperature processing), one phase is in tension (and the other in
compression, to balance). The phase under residual tensile stress will
crack more easily than the other one under additional tensile load, e.g. near
a crack tip.
• Now we have to consider what can happen in the material. If the residual
stress is too high, then the phase in tension will crack during cooling. If it is
entirely (micro-)cracked, then no further cracking can occur at a crack tip (to
absorb energy) and the toughening effect is lost. What controls this,
however, is the grain size: smaller grain sizes are more resistant to
cracking. To find the critical grain size, d c , we use the Griffith equation, with
K co as the fracture toughness and σ R as the residual stress, substituting
grain size for crack size:
d c = ( K co / σ R ) 2
• The process zone size, r c , then depends on the ratio of the actual grain
size, d, to the critical grain size:
• The graph, from Courtney, shows how one needs to be within a certain
rather narrow range of grain size in order to have a finite process zone size
and therefore effective toughening. Grain sizes larger than the critical grain
size simply result in spontaneous cracking. Too small grain sizes (

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2B Microcracking: Microcracking:
particles
• Microcracking depends on second phase particles that can crack
easily.
• The cracking tendency depends on particle size: if they are too small,
then the stress intensity does not reach their critical K (typically, 1µm),
based on the Griffith equation.
• (Tensile) residual stresses aid cracking, so differences in thermal
expansion (with the matrix) are important.
• An equation that describes the toughening effect is as follows, where
K is again the increment in toughness (units of stress intensity):
∆K = C E ε crack √h / (1-ν)
C is a constant (of order 1), E = modulus, ε crack = cracking strain
(dilatation) h is the width of the process zone, and ν is Poisson’s ratio.
The cracking strain is approximately the strain associated with the
difference in CTE: ε crack ≈ ∆α ∆T.
• Note the strong similarity to the equation that describes
transformation toughening! The only difference is the physical
meaning of the strain term.

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2C Void formation
• Void formation in a process zone can have a similar
effect to micro-cracking. In materials such as high
strength steels, e.g. 4340, the source of the voiding
is ductile tearing on a small scale as the crack
opens.
• The spatial organization of the voids is important.
Random distributions are better than either clusters
or sheets. Carbide particles in steels, or dispersoid
particles in aluminum alloys (e.g. Al 3 Fe) are typical
nucleation sites for voids. Sheet-like sets of voids
can arise from carbide particles that have grown on
martensite or bainite laths during tempering of
martensitic microstructures.

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3A Crack wedging/ bridging
• Wherever the crack results in interlocking grain
shapes exerting force across the crack, stress
(intensity) at the crack tip is reduced.
[Chiang]
Crack
opening

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3B Fiber/ligament bridging (Composites)
• Anything that results in a load bearing link across the crack (behind
the tip) decreases the stress (intensity) at the crack tip.
• Either rigid (elastic) fibers (ceramic matrix composites) or plastic
particles (ductile metal particles in an elastic matrix) are effective.
• In order to estimate the increase in toughness, one can calculate a
work associated with crack advance and then estimate with
∆K = √(EG).
[Chiang]

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3B Fiber/ligament bridging
• Scanning electron micrographs of a SiC whisker
bridging at various stages of crack opening. From
left to right, the stress intensity is increasing.
[Green]

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3B Fiber/ligament bridging
strain dependence
• The balance
between fiber
strength, matrix
strength and the
fiber/matrix
interface is critical.
• In general, a
relatively weak
fiber/matrix
interface
promotes
toughness.
• Why? [Green]

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3D Plasticity induced crack closure
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• Plasticity induced crack closure is
another way of stating the effect of
plastic deformation around the crack tip.
• Very tough materials exhibit an
interesting behavior in Charpy impacts.
For high ductilities, the specimen can
deform without fully breaking, with
consequent enormous energies
absorbed.

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References
• D.J. Green (1998). An Introduction to the Mechanical
Properties of Ceramics, Cambridge Univ. Press, NY.
• Materials Principles & Practice, Butterworth
Heinemann, Edited by C. Newey & G. Weaver.
• G.E. Dieter, Mechanical Metallurgy, McGrawHill, 3rd
Ed.
• Courtney, T. H. (2000). Mechanical Behavior of
Materials. Boston, McGraw-Hill.
• R.W. Hertzberg (1976), Deformation and Fracture
Mechanics of Engineering Materials, Wiley.
• N.E. Dowling (1998), Mechanical Behavior of
Materials, Prentice Hall.
• A.H. Cottrell (1964), The Mechanical Properties of
Matter, Wiley, NY.

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Lab 2: points of interest
• Consider the following items in the (second) Lab.
• Relate the fracture morphology of wood to what we discussed
in this lecture concerning laminated composites.
• Can you detect changes in fracture morphology as a function of
test temperature (steels)? Can you relate the fracture surface
features to the measured grain size? What about the spacing
of the pearlite colonies (depending on the microstructure)?
• Can you detect changes in fracture morphology as a function of
microstructural change? For example, in the normalized
(pearlitic) condition, can you detect the lamellae at the fracture
surface? Do you think that there is any interaction between the
fracture process and the lamellar structure?
• For the quench+tempered condition, can you relate the particle
(carbide) spacing to features on the fracture surface?
• For the martensitic condition, can you estimate the energy that
should be absorbed if it goes only towards creating crack
surface? How does this number compare with a reasonable
surface energy for iron?