Microstructure-Properties: I Fracture Toughness: how …pajarito.materials.cmu.edu/rollett/27301/L6C_fract... ·  · 2007-11-05Microstructure-Properties: I Fracture Toughness: how

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Microstructure-Properties: IMicrostructure-Properties: IFracture Toughness: how toFracture Toughness: how to

maximize it throughmaximize it throughmicrostructure controlmicrostructure control

27-301Lecture 6CFall, 2007

Prof. A. D. Rollett

Microstructure Properties

Processing Performance

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Happy Guy Happy Guy Fawkes Fawkes Day (Nov. 5th)!Day (Nov. 5th)!

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ObjectiveObjective• The objective of this lecture is to show you how to

exploit microstructure in order to maximizetoughness, especially in brittle materials.

• Part of the motivation for this lecture is to preparethe class for a Lab on the sensitivity of mechanicalproperties to microstructure.

• Note that the equations used are not derived -rather the emphasis is on basic principles and abroad range of methods for toughening.

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Applications?Applications?Why do we care about toughness?Why do we care about toughness?• Steels are used to build pressure vessels for

nuclear reactors. The irradiation that thesevessels experience, however, lowers thetoughness of the steels. This must be allowed forin the design and operation of the reactors.

Courtney (Ch. 13)

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

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Applications: ceramic gas turbinesApplications: 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 operatingtemperature is limited by their melting point (although clever design of thermalbarrier coatings and cooling has dramatically raised their capabilities).Ceramic (oxide) components have much higher melting/softening points buttheir intrinsic toughness is far too low. Therefore the toughening of structuralceramics 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

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Key PointsKey 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 microscopicscale or by making a composite.

• If appropriate (in relation to the way in which a material isloaded), laminate the material i.e. put in crack deflectingplanes.

• If appropriate (in relation to the way in which a material isloaded), include stiff fibers in the material to give load transferand fiber pull-out.

• Design the composite to have inclusions that deflect the crackpath.

• Design the composite to include particles that transform (orcrack) and thus require work to be done for crack propagationto take place.

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Strength versus toughnessStrength versus toughness• If you imagine testing the (tensile) strength of a

material that you could make arbitrarily tough orbrittle, how would its measured strength vary?

Toughness

Breaking Strength

?

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Strategies for toughness andStrategies for toughness andmicrostructuremicrostructure

• Yield strength depends on the obstacles todislocation motion.

• Toughness is more complex: there is nodirect equivalent to obstacles to dislocationmotion.

• Instead, we must look for ways to (a)eliminate or minimize cracks; (b) ways tomaximize the energy cost of propagating acrack.

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(a) Minimize/(a) Minimize/eliminateeliminate cracks 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 contentduring solidification helps (Metals Processing!).- rough surfaces (e.g. from machining) can bemade smooth.- also in metals, large, poorly bonded (to thematrix) second phase particles are deleterious,e.g. oxide particles. Therefore removal ofinterstitials (O, N, C, S) from steel melts (or Fe &Si from Al) is important because they tend to reactwith the base metal to form brittle inclusions (as in,e.g. clean steel technology).

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(a) (a) MinimizeMinimize/eliminate cracks/eliminate cracks• How do we minimize cracks?

Grain Structure:- there are various mechanisms that lead to cracks at grainboundaries, or at triple junctions between boundaries.Therefore - in some materials - making the grain size as smallas possible is important because it determines the maximumcrack size. Crack size matters because of stressconcentration at the crack tip: longer cracks mean higherstress concentrations.- how to minimize grain size? Either by thermomechanicalprocessing (maximum strain + minimum recrystallizationtemperature) or by starting with small powders andconsolidating to 100% density.

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DistributionsDistributions• Remembering that it is the largest crack that limits

breaking strength, it is not the average crack lengththat matters but rather the maximum crack size thatwe should care about.

• For materials in which the grain size determines thetypical crack size, experience shows that the grainsize distribution is approximately constant. Themaximum grain size observed is a small multiple ofthe average - about 2.5 times.

• Also important in distributions is the spatialdistribution of particles (that can generate cracks);cracks at, or near the surface are more deleteriousthan cracks in the interior.

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Spatial DistributionsSpatial Distributions• Anisotropic spatial distributions are most commonly

encountered in thermomechanically processedmetals. They occur, for example, in silicon nitrideprocessed (tape casting + sintering) to promotedirectional growth of beta-Si3N4 for high thermalconductivity heat sink materials.

• The sensitivity of toughness to the direction inwhich the testing is performed has led to a specialjargon for specimen orientation.

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Specimen Orientation CodeSpecimen Orientation Code• The first letter denotes the loading direction; the

second letter denotes the direction in which crackpropagation occurs.

[Hertzberg]

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Mechanical Mechanical FiberingFibering

[Hertzberg]

Lowesttoughness

• Any second phase particles present from solidification tend tobe elongated and dispersed in sheets parallel to the rollingplane; called “stringers”.

• Toughness in the S-L or S-T orientations is typically muchlower than for the L-T or L-S orientations because the crackplane is parallel to the planes on which the particles lie closeto one another.

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Inclusion effectsInclusion effects• Graph plots variation

in strength with (planestrain) toughness withvarying sulfur contentsin 0.45C-Ni-Cr-Mosteels.

• Increasing levels of Slead to lowertoughness at the samestrength level.

• This occurs becausethe sulfur is present assulfide inclusions inthe steel.

• “Clean steel”technologies havereduced this problemin recent years. [Dieter]

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Laminate CompositesLaminate Composites

[Hertzberg]

• The weakness of such layers of inclusions, which provide planes onwhich crack nucleation is relatively easy, can however be exploited.

• By providing planes of low crack resistance perpendicular to theanticipated 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 thefracture toughness (brittleness) against the interfacial weakness.The more brittle the matrix (layers), the weaker the interfacesbetween the layers need to be. Example: Wood, Mollusc shells

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Effect of lamination on the DBTTEffect of lamination on the DBTT• The effect of orienting the laminations of a

composite in the crack arrestor configuration is todramatically lower the transition temperature.

• This is actually an example of crack deflection.

[Hertzberg, after Embury]

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Explanation of LaminationExplanation of LaminationThis crack propagation

direction leads todelamination and crackblunting (moretoughness)

This crack propagationdirection follows theinclusion+grain shape(less toughness)

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Energy absorption: 1Energy absorption: 1• How do we increase the amount of energy consumed in

propagating a crack?- One method, already discussed, is to maximize the amountof plastic work. This requires the yield strength to beminimized so as to maximize the size of the plastic zone.- For very tough materials, however, it turns out that the sameparameters that control ductility also affect toughness. Lowerdensities of second phase particle increase toughness.Second phase particles well bonded to the matrix increasetoughness. Small differences in thermal expansion coefficienthelp (Why?).

• Read papers by Prof. Warren Garrison’s group.

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Energy absorption: 2Energy 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 fromsome 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 methodsare mostly concerned with ceramics in which the intrinsictoughness is low.

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Energy absorption: 3Energy 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 deflection1 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 tougheningfrom deflection in the plane of the crack and the latter isdeflection out of the plane of the crack.

• In either case, the net result is that the crack tip no longersees 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 moreresistant to cracking, or have different elastic stiffness (higheror lower modulus).

• Laminate composites also achieve crack deflection, aspreviously discussed.

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1. Crack1. Crackdeflection:deflection:examplesexamples

[Green]

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Zone Shielding: 2A transformation tougheningZone Shielding: 2A transformation toughening

• Various mechanisms exist for shielding crack tips from someof 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 servicetemperature and which will transform when loaded (but nototherwise).

• The transformation always has a volume change associatedwith the change in crystal structure, which can be written as astrain. The product of stress and strain is then the work doneor expended during the (stress-induced) transformation.

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2A Transformation toughening:2A Transformation toughening:transformation straintransformation strain

• The large volume change on transformation isequivalent to a significant transformation strain whichis the key to the success of the method. Recall thatour basic measure of fracture resistance is the workdone, ∫ σdε, in breaking the material.

• The volume change (dε) is ~ 4%, accompanied by ashear strain of ~ 7%. Since the transformation has aparticular habit plane (i.e. a crystallographic plane ineach phase in common), two twin-related variantsoccur in each particle so that the shear strains are(approximately) canceled out. This leaves only the4% dilatational (volume) strain that contributes to thework done.

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2A Transformation toughening: phase2A Transformation toughening: phasechange in zirconiachange in zirconia

• The classic example of transformation toughening is theaddition of a few (volume) % of ZrO2 to oxides and other brittleceramics.

• The high temperature form of zirconia is a tetragonal form (t-ZrO2) which has a significantly larger atomic volume than thelow temperature, monoclinic form (m-ZrO2).

• In order to reduce the driving force for the tetragonal monoclinic transformation (i.e. lower the transformationtemperature), some “stabilizer” is added. Typical are ceria(Ce2O3) and yttria (Y2O3).

• The subtle point about this approach is that some “trick” isneeded in order to keep the zirconia from transforming oncethe material is cooled to room temperature, i.e. to maintain itin a metastable, untransformed state.

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2A Transformation toughening:2A Transformation toughening:critical size of zirconia particlescritical size of zirconia particles

• An important consequence of the volume change ontransformation is that it leads to an elastic driving force thatopposes the transformation for particles embedded in a matrixof a different material.

• Therefore we take advantage of having the zirconiaembedded as small particles in the matrix of the ceramic to betoughened.

• The particles must be small enough for the elastic energy termto be effective. The upper limit for retention of the hightemperature (tetragonal) phase is ~ 0.5 µm.

[Green]

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2A Transformation toughening:2A Transformation toughening:transformation transformation →→ work work

• Consider the effect of the tensile stress in the vicinity of thecrack tip: the stress removes the constraint on each particle,allowing it to transform. The transformed particle wasmetastable, thermodynamically, and so remains in the low T,monoclinic form after the crack has gone by.

• The stress acting to cause the transformation strain performswork and so energy is consumed in the phase transformation.This energy (work done) adds to the surface energy requiredto create crack length.

• Additional toughening arises from the particles causing crackdeflection.

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2A Transformation toughening:2A Transformation toughening:the process zonethe process zone

• The region in which transformation occurs becomesthe crack wake as the crack propagates. Theregion around the crack tip is known as the processzone because this is where the toughening processis operative.

[Green]Crack propagation direction

Process zone width

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2A Transformation toughening:2A Transformation toughening:microstructuremicrostructure

• Microstructural evidence forthe transformation isobtainable through x-raydiffraction and Ramanspectroscopy (the two differentforms of zirconia have quitedifferent infra-red spectra).

• (a) lenticular particles of MgO-stabilized ZrO2 (untransformed)in cubic ZrO2.(b) transformed particles ofZrO2 around a crack (dashedline).

[Chiang]

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2A Transformation toughening:2A Transformation toughening:limits on tougheninglimits on toughening

• As the particle size isincreased, so the particlesbecome less and lessstable; the transformationbecomes easier and moreeffective at toughening thematerial. If the particlesbecome too large, however,the toughening is lostbecause the particles are nolonger stabilized in theirhigh temperature form.

• Effect of test temperature?• Effect of stabilizing additions

to the ZrO2? [Green]

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2A Transformation toughening:2A Transformation toughening:quantitative approachquantitative approach

• It is not possible to lay out the details of how todescribe transformation toughening in a fullyquantitative fashion here.

• An equation that describes the toughening effect is asfollows, where K is the increment in toughness (units ofstress intensity, MPa√m):

∆K = C E Vtrans εtrans √h / (1-ν)

C is a constant (of order 1), E = elastic modulus,Vtrans = volume fraction transformed,εtrans = transformation strain (dilatation, i.e. bulkexpansion), h is the width of the process zone, and ν isPoisson’s ratio.

• What controls the width of the process zone?

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2B 2B MicrocrackingMicrocracking• 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 2B MicrocrackingMicrocracking• The principle of Micro-cracking as a toughening mechanism is that one

designs the material so that additional (micro-)cracking occurs in the vicinityof the crack tip as it advances, thereby increasing the crack area created(per unit advance of crack), thereby increasing the toughness (resistance tocrack propagation).

• This is most effective in two-phase ceramics in which the 2 phases havedifferent CTEs. As the material cools after sintering (or other hightemperature processing), one phase is in tension (and the other incompression, to balance). The phase under residual tensile stress willcrack more easily than the other one under additional tensile load, e.g. neara crack tip.

• Now we have to consider what can happen in the material. If the residualstress is too high, then the phase in tension will crack during cooling. If it isentirely (micro-)cracked, then no further cracking can occur at a crack tip (toabsorb energy) and the toughening effect is lost. What controls this,however, is the grain size: smaller grain sizes are more resistant tocracking. To find the critical grain size, dc, we use the Griffith equation, withKco as the fracture toughness and σR as the residual stress, substitutinggrain size for crack size: dc = ( Kco / σR )2

• The process zone size, rc, then depends on the ratio of the actual grainsize, d, to the critical grain size:

• The graph, from Courtney, shows how one needs to be within a certainrather narrow range of grain size in order to have a finite process zone sizeand therefore effective toughening. Grain sizes larger than the critical grainsize simply result in spontaneous cracking. Too small grain sizes (<0.6 dc)mean no micro-cracking at the crack tip.

!

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2B 2B MicrocrackingMicrocracking: particles: 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 thermalexpansion (with the matrix) are important.

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

∆K = C E εcrack √h / (1-ν)

C is a constant (of order 1), E = modulus, εcrack = 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 thedifference in CTE: εcrack ≈ ∆α ∆T.

• Note the strong similarity to the equation that describestransformation toughening! The only difference is the physicalmeaning of the strain term.

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2C Void formation2C Void formation• Void formation in a process zone can have a similar

effect to micro-cracking. In materials such as highstrength steels, e.g. 4340, the source of the voidingis ductile tearing on a small scale as the crackopens.

• The spatial organization of the voids is important.Random distributions are better than either clustersor sheets. Carbide particles in steels, or dispersoidparticles in aluminum alloys (e.g. Al3Fe) are typicalnucleation sites for voids. Sheet-like sets of voidscan arise from carbide particles that have grown onmartensite or bainite laths during tempering ofmartensitic microstructures.

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3A Crack wedging/ bridging3A 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

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3B Fiber/ligament bridging (Composites)3B Fiber/ligament bridging (Composites)

• Anything that results in a load bearing link across the crack (behindthe tip) decreases the stress (intensity) at the crack tip.

• Either rigid (elastic) fibers (ceramic matrix composites) or plasticparticles (ductile metal particles in an elastic matrix) are effective.

• In order to estimate the increase in toughness, one can calculate awork associated with crack advance and then estimate with∆K = √(EG).

[Chiang]

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3B Fiber/ligament bridging3B Fiber/ligament bridging• Scanning electron micrographs of a SiC whisker

bridging at various stages of crack opening. Fromleft to right, the stress intensity is increasing.

[Green]

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3B Fiber/ligament bridging3B Fiber/ligament bridgingstrain dependencestrain dependence

• The balancebetween fiberstrength, matrixstrength and thefiber/matrixinterface is critical.

• In general, arelatively weakfiber/matrixinterfacepromotestoughness.

• Why? [Green]

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3D Plasticity induced crack closure3D Plasticity induced crack closure

• Plasticity induced crack closure isanother way of stating the effect ofplastic deformation around the crack tip.

• Very tough materials exhibit aninteresting behavior in Charpy impacts.For high ductilities, the specimen candeform without fully breaking, withconsequent enormous energiesabsorbed.

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ReferencesReferences• D.J. Green (1998). An Introduction to the Mechanical

Properties of Ceramics, Cambridge Univ. Press, NY.

• Materials Principles & Practice, ButterworthHeinemann, Edited by C. Newey & G. Weaver.

• G.E. Dieter, Mechanical Metallurgy, McGrawHill, 3rdEd.

• Courtney, T. H. (2000). Mechanical Behavior ofMaterials. Boston, McGraw-Hill.

• R.W. Hertzberg (1976), Deformation and FractureMechanics of Engineering Materials, Wiley.

• N.E. Dowling (1998), Mechanical Behavior ofMaterials, Prentice Hall.

• A.H. Cottrell (1964), The Mechanical Properties ofMatter, Wiley, NY.

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Lab 2: points of interestLab 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 surfacefeatures to the measured grain size? What about the spacingof the pearlite colonies (depending on the microstructure)?

• Can you detect changes in fracture morphology as a function ofmicrostructural change? For example, in the normalized(pearlitic) condition, can you detect the lamellae at the fracturesurface? Do you think that there is any interaction between thefracture 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 thatshould be absorbed if it goes only towards creating cracksurface? How does this number compare with a reasonablesurface energy for iron?