1 27-301 Microstructure-Properties Fracture Toughness: maximize via microstructure Profs. A. D....

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127-301

Microstructure-PropertiesFracture Toughness:

maximize via microstructure Profs. A. D. Rollett, M. De Graef

MicrostructurePropertiesProcessing Performance

Last modified: 3rd Dec. ‘15


2 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.• For the wood experiments, see if you can identify a point group that applies to the symmetry of the

properties.• Compare wood to man-made composites: is it more or less complicated than, say, carbon

reinforced plastics?• For the steel Lab, try using the Thermocalc results to define which second phases (mainly carbides)

you expect to observe in your heat treated samples.• 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?

• The fracture surfaces of the steel often show features that resemble delamination: what causes this, and why would you not see them under brittle fracture conditions? Can you relate them to the banding that you sometimes see in metallography?


3 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 explain the science that supports and informs the second 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.


4 Questions & Answers1.Describe 3 ways in which microstructure can be used to

maximize fracture toughness. Lamination, crack bridging and transformation toughening.

2.Explain what is meant by the “weakest link principle” in connection with brittle materials. In a brittle materials it is the largest flaw (aka weakest link) that will open and cause the material to fail.

3.Explain the terminology used to orient toughness tests. See the notes. Which orientations will show high toughness and which low values? For example, weak planes oriented perpendicular to a crack will divert the crack and give higher toughness. How does this relate to laminated composites? See above.

4.Discuss the effect of impurities in steels, for example, on the trade-off between strength and toughness. Impurities (e.g. O, N, C, S) in any metal typically have low solubility and are thus present as ceramic particles. These particles act as nucleation points for cracks and voids, which lower toughness (for a given strength).

5.Describe the various extrinsic toughening methods for brittle materials and the pros and cons of each one. See the notes for these details.

6.Describe how transformation toughening works. Briefly, metastable particles transform only when a high tensile stress near a crack tip is applied to them; the transformation strain results in extra energy required to advance a crack. What is the point of adding dopants to ZrO2 in order to control transformation temperatures? This controls the degree of metastability. Why is there a critical size for the particles of ZrO2? Because the particles only retain their high temperature, metastable state by being containing in the matrix.

7.How is micro-cracking similar to transformation toughening, and how does it differ? Similar in that work is done to crack a particle which contributes to toughness; obviously differs in the mechanism.

8.How can we estimate the contribution to (or increase in) toughness from transformation toughening or microcracking? See notes for an equation involving the process zone height.

9.How do fibers toughen ceramic matrix composites? By crack bridging, i.e. the fibers carry load across a crack. Why is it helpful to toughness if the fibers are not perfectly bonded to the matrix? Because work has to be done to pull the fibers out of their matrix.


5 Applications? Why do we care about toughness?Courtney (Ch. 13)

http://ecow.engr.wisc.edu/cgi-bin/get/neep/541/allentodd/notes/

• Steels are used to build pressure vessels for nuclear reactors. The irradiation that these vessels experience, however, lowers the toughness of the steels and raises the DBTT (see figures below for Charpy impact energy versus test temperature). This must be allowed for in the design and operation of the reactors.

• This, and related issues, is discussed in the course on Materials for Nuclear Energy Systems, 27-725.

Examinable


6 Applications: ceramic gas turbinesThe 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 nitride-based part shown (left) has machined strengths of up to 960 MPa and as-processed strengths of up to 706 MPa.

www.p2pays.org/ref%5C08/07468.pdf -www1.eere.energy.gov/vehiclesandfuels/pdfs/success/advanced_gas_turbine.pdf


7 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.

Examinable


8 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?

Toughness

Breaking Strength?


9Strategies 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.


10 (a) Minimize or 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).

Examinable


11 (a) Minimize or eliminate cracks• How do we minimize cracks, either number (density) or their effect?

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.

Examinable


12 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 (and approximately log-normal). 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.

• In brittle materials in particular, it is the largest flaw that determines the (breaking) strength. Therefore we refer to the weakest link principle. This in turn means that we must consider extremes values in the distribution of flaws.

• A useful source of information on extreme values is the on-line NIST Handbook: http://www.itl.nist.gov/div898/handbook/prc/section1/prc16.htm. Also search with key words “extreme values strength materials”.

http://www.itl.nist.gov/div898/handbook/prc/section1/prc16.htm

http://www.itl.nist.gov/div898/handbook/prc/section1/prc16.htm


13 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-Si3N4 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.


14Specimen Orientation Code

[Hertzberg]

• The first letter denotes the loading direction; the second letter denotes the direction in which crack propagation occurs. This is an example of bi-axial alignment which just means that two directions have some particular alignment, not just one.

Examinable


15 Mechanical Fibering

[Hertzberg]

Lowesttoughness

• Any second phase particles present from solidification tend to be elongated and dispersed in sheets parallel to the rolling plane; called “stringers”. Such stringers are commonly found in (older) aerospace aluminum alloys.

• 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.

• Charpy tests on steels (Lab 2, for example) often show delaminations for L-S or T-S oriented tests.

Examinable


16 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 for steel making have reduced this problem in recent years.

[Dieter]

Examinable


17 Laminate Composites

[Hertzberg]

• 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 and increasing the work that must be done in order to advance 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

SiC-fiber reinforced Cu.Web: femas-ca.eu,via images.google

Examinable


18 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]


19 Explanation of LaminationThis crack propagation

direction leads to delamination and crack blunting (more toughness)

This crack propagation direction follows the inclusion+grain shape (less toughness)

[Hertzberg]

Examinable


20 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.

Examinable


21 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 shielding3) 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 metal-based 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.

Examinable


22 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

Examinable


23 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.


24

1. Crack deflection:examples[Green]


25Zone Shielding: 2A transformation toughening• 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.

Examinable


26 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, ∫ d, in breaking the material.

• The volume change (d) 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.

Examinable


27 2A Transformation toughening: phase change in zirconia• The classic example of transformation toughening is the addition of a few (volume) % of ZrO2 to oxides and other brittle ceramics.

• The highest temperature form of zirconia is cubic (c-ZrO2) with an intermediate tetragonal form (t-ZrO2). Both of these have significantly larger atomic volumes than the low temperature, monoclinic form (m-ZrO2), and the cubic has a larger volume than the tetragonal form.

• 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 (Ce2O3) and yttria (Y2O3).

• 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.

• The following slides show phase relationships for ZrO2 with CaO, and ZrO2 with Y2O3.

Examinable


28 ZrO2 and CaZrO2• In pure ZrO2 there is a large

volume change for the tetragonal to monoclinic transition upon cooling, starting at about 1150 °C.

• This leads to cracking throughout a ZrO2 component and thus total mechanical failure.

• This is avoided by doping with Calcia from 3-7 % to form cubic and monoclinic (and no tetragonal about 1000 °C).

• Below this T diffusion is too slow to form enough monoclinic to generate the unwanted cracks.

• “Partially Stabilized Zirconia”

Slide courtesy Dr. Alpay, Univ. Connecticut: http://www.ims.uconn.edu/~alpay/Group_Page/Courses/MMAT%20244/Lecture%2005.ppt


29 Yttria Stabilized Zirconia• The monoclinic transition

can be suppressed even further by stabilizing zirconia with yttria from 3-8 %.

• Retains cubic and tetragonal phases (avoiding monoclinic) down to roughly 700 °C.

• Yttria, partially, and cubic stablized zirconia (CZ) are commercially useful.

Slide courtesy Dr. Alpay, Univ. Connecticut: http://www.ims.uconn.edu/~alpay/Group_Page/Courses/MMAT%20244/Lecture%2005.ppt

Examinable


30 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.

• The size effect is, however, quite subtle. If we were to consider only the elastic energy from the volume change then this would be proportional to the (volumetric) driving force for the phase change. In fact, however, there is a shear strain associated with the phase transformation that is larger than the dilatational strain. This shear strain is accommodated by having multiple shear variants, whose average shear strain is close to zero, leaving only the volume change. These variants have interfaces (boundaries) between them, which requires the creation of surface area in the transformation. Therefore there is, in fact, a balance between the release of volumetric driving force (offset by the dilatational strain energy) and the creation of internal interfaces between martensite variants.

• 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 in particle size for retention of the high temperature (tetragonal) phase is ~ 0.5 µm.

[Green]

Examinable


31 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.

Examinable

http://www.vertebr.ae/Blog/wp-content/uploads/2010/02/zirconia-transformation-toughening-in-ceramics.gif


32 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.

[Green]Crack propagation direction

Process zone width

Examinable


33 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 MgO-stabilized ZrO2 (untransformed) in cubic ZrO2.(b) transformed particles of ZrO2 around a crack (dashed line).

[Chiang]


34 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]

Examinable


35 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 Vtrans etrans √h / (1-n)C is a constant (of order 1), E = elastic modulus, Vtrans = volume fraction transformed, etrans = transformation strain (dilatation, i.e. bulk expansion), h is the width of the process zone, and n is Poisson’s ratio.

• What controls the width of the process zone?

Examinable


36 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]

Examinable


37 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, dc, we use the Griffith equation, with Kco as the fracture toughness and R as the residual stress, substituting grain size for crack size: dc = ( Kco / R )2

• The process zone size, rc, 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 (< 0.6 dc) mean no micro-cracking at the crack tip.

[Courtney]


38 2B Microcracking: particles• Microcracking depends on second phase particles that can crack easily.• The cracking tendency depends on particle size (typically, 1µm): if they are too small, then the stress

intensity does not reach their critical Kc, based on the Griffith equation.• (Tensile) residual stresses aid cracking, so differences in thermal expansion (with the matrix) are

important. Recall that the thermal expansion, as a (stress-free) strain, is equal to the Coefficient of Thermal Expansion (CTE or a) multiplied by the change in temperature (∆T), ethermal = a ∆T. Where a volumetric strain is important, V0+∆V = (l0 + ∆l)3 = { l0 (1+ethermal) }3 = l0

3 (1+3e+3e2+e3) V0 (1+3ethermal) ; ∆V/V = 3ethermal

• An equation that describes the toughening effect is as follows, where ∆K is again the increment in toughness (units of stress intensity):

∆K = C Vf E ecrack √h / (1-n)C is a constant (of order 1), E = modulus, ecrack = cracking strain (dilatation),h is the width of the process zone, and n is Poisson’s ratio. The cracking strain is approximately 3*strain associated with the difference in CTE:

ecrack 3∆ ∆T.• Note the strong similarity to the equation that describes transformation toughening! The only difference

is the physical meaning of the strain term. If the volume fraction, Vf, is not given, one can assume =1, if there are nearly equal fractions of the two phases so that most grains crack.

• See the next slide for an explanation of how the cracking strain is equivalent to an eigenstrain.

Examinable

39

expanding region

isolate region

expansion

eigenstrains

surface traction

non-expanding matrix

place back into matrix

eigenstresses

Thermoelastic Stress

J. D. Eshelby, Proceedings of the Royal Society of London A, vol. 252, pp. 561-569, 1959

Slide courtesy of B. Anglin &

S. Donegan


40 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. Al3Fe) 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.


413A 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]Crackopening


42 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]


433B 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]


443B Fiber/ligament bridgingstrain 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]


453D Plasticity induced crack closure• 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.


46 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 (1986), 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.• Y.-T. Chiang, D.P. Birnie III, W.D. Kingery, Physical Ceramics (1997), Wiley,

New York, ISBN 0-471-59873-9.• A.H. Cottrell (1964), The Mechanical Properties of Matter, Wiley, NY.• For gas turbine engines, ASME runs a yearly conference called ASME

Turbo Expo, which has sessions that discuss materials issues.

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