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27-‐301 Microstructure-‐Proper-es

Fracture Toughness: maximize via microstructure

Profs. A. D. RolleB, M. De Graef

Microstructure Properties

Processing Performance

Last modi.ied: 3rd Dec. ‘15

Please acknowledge Carnegie Mellon if you make public use of these slides

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 idenPfy a point group that applies to the symmetry of

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

reinforced plasPcs? •  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 funcPon 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 funcPon of microstructural change? For example, in the normalized (pearliPc) condiPon, can you detect the lamellae at the fracture surface? Do you think that there is any interacPon between the fracture process and the lamellar structure?

•  For the quench+tempered condiPon, can you relate the parPcle (carbide) spacing to features on the fracture surface?

•  For the martensiPc condiPon, can you esPmate the energy that should be absorbed if it goes only towards creaPng crack surface? How does this number compare with a reasonable surface energy for iron?

•  The fracture surfaces of the steel oXen show features that resemble delaminaPon: what causes this, and why would you not see them under briBle fracture condiPons? Can you relate them to the banding that you somePmes see in metallography?


3

Objective •  The objecPve of this lecture is to show you how to

exploit microstructure in order to maximize toughness, especially in briBle materials.

•  Part of the moPvaPon for this lecture is to explain the science that supports and informs the second Lab on the sensiPvity of mechanical properPes to microstructure.

•  Note that the equaPons used are not derived -‐ rather the emphasis is on basic principles and a broad range of methods for toughening.


Questions & Answers 1. Describe 3 ways in which microstructure can be used to maximize fracture toughness. LaminaPon, crack bridging and transformaPon toughening.

2. Explain what is meant by the “weakest link principle” in connecPon with briBle materials. In a briBle 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 orientaPons 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 impuriPes in steels, for example, on the trade-‐off between strength and toughness. ImpuriPes (e.g. O, N, C, S) in any metal typically have low solubility and are thus present as ceramic parPcles. These parPcles act as nucleaPon points for cracks and voids, which lower toughness (for a given strength).

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

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

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

8. How can we esPmate the contribuPon to (or increase in) toughness from transformaPon toughening or microcracking? See notes for an equaPon 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.

4


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 irradiaPon 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 operaPon 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 turbines The thermal efficiency of a gas turbine engine is directly related to its operaPng temperature. ConvenPonal gas turbines use Ni-‐based alloys whose operaPng temperature is limited by their melPng point (although clever design of thermal barrier coa2ngs and cooling has dramaPcally raised their capabiliPes). Ceramic (oxide) components have much higher melPng/soXening points but their intrinsic toughness is far too low. Therefore the toughening of structural ceramics is essenPal if these systems are to succeed. The silicon nitride-‐based part shown (leX) 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 briBle materials. •  Increasing toughness generally requires adding addiPonal structural

components to a material, either at the microscopic scale or by making a composite.

•  If appropriate (in relaPon to the way in which a material is loaded), laminate the material i.e. put in crack deflecPng planes.

•  If appropriate (in relaPon to the way in which a material is loaded), include sPff 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 parPcles that transform (or crack) and

thus require work to be done for crack propagaPon to take place.

Examinable


8

Strength versus toughness •  If you imagine tesPng the (tensile) strength of a material

that you could make arbitrarily tough or briBle, how would its measured strength vary?

Toughness

Breaking Strength

?


9 Strategies for toughness and microstructure

•  Yield strength depends on the obstacles to dislocaPon moPon.

•  Toughness is more complex: there is no direct equivalent to obstacles to dislocaPon moPon.

•  Instead, we must look for ways to (a) eliminate or minimize cracks; (b) ways to maximize the energy cost of propagaPng a crack.


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(a) Minimize or eliminate cracks •  How do we eliminate cracks? •  First, consider the sources of cracks:

-‐ in metals, voids from solidificaPon are deleterious (especially in faPgue), so minimizing gas content during solidificaPon helps (Metals Processing!). -‐ rough surfaces (e.g. from machining) can be made smooth. -‐ also in metals, large, poorly bonded (to the matrix) second phase parPcles are deleterious, e.g. oxide parPcles. Therefore removal of intersPPals (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 briBle 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 juncPons 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 maBers because of stress concentraPon at the crack Pp: longer cracks mean higher stress concentraPons. -‐ how to minimize grain size? Either by thermomechanical processing (maximum strain + minimum recrystallizaPon temperature) or by starPng with small powders and consolidaPng 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 maBers 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 distribu2on is approximately constant (and approximately log-‐normal). The maximum grain size observed is a small mulPple of the average -‐ about 2.5 Pmes.

•  Also important in distribuPons is the spa2al distribu2on of parPcles (that can generate cracks); cracks at, or near the surface are more deleterious than cracks in the interior.

•  In briBle materials in parPcular, 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 distribu2on of flaws.

•  A useful source of informaPon on extreme values is the on-‐line NIST Handbook: hBp://www.itl.nist.gov/div898/handbook/prc/secPon1/prc16.htm. Also search with key words “extreme values strength materials”.


13

Spatial Distributions •  Anisotropic spaPal distribuPons are most commonly

encountered in thermomechanically processed metals. They occur, for example, in silicon nitride processed (tape casPng + sintering) to promote direcPonal growth of beta-‐Si3N4 for high thermal conducPvity heat sink materials.

•  The sensiPvity of toughness to the direcPon in which the tesPng is performed has led to a special jargon for specimen orientaPon.


14

Specimen Orientation Code

[Hertzberg]

•  The first leBer denotes the loading direcPon; the second leBer denotes the direcPon in which crack propagaPon occurs. This is an example of bi-‐axial alignment which just means that two direcPons have some parPcular alignment, not just one.

Examinable


15

Mechanical Fibering

[Hertzberg]

Lowest�toughness

•  Any second phase parPcles present from solidificaPon 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 orientaPons is typically much lower than for the L-‐T or L-‐S orientaPons because the crack plane is parallel to the planes on which the parPcles lie close to one another.

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

Examinable


16

Inclusion effects

•  Graph plots variaPon 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 nucleaPon is relaPvely easy, can however be exploited.

•  By providing planes of low crack resistance perpendicular to the anPcipated crack propagaPon direcPon, a crack can be deflected, thereby reducing the load at the crack Pp and increasing the work that must be done in order to advance the crack Pp.

•  In designing a laminate composite, it is important to balance the fracture toughness (briBleness) against the interfacial weakness. The more briBle the matrix (layers), the weaker the interfaces between the layers need to be. Example: Wood, Mollusc shells

SiC-‐Yiber reinforced Cu. Web: femas-‐ca.eu,�via images.google

Examinable


18

Effect of lamination on the DBTT •  The effect of orienPng the laminaPons of a composite in

the crack arrestor configuraPon is to dramaPcally lower the transiPon temperature.

•  This is actually an example of crack deflec2on.

[Hertzberg, after Embury]


19

Explanation of Lamination This crack propagaPon

direcPon leads to delaminaPon and crack blunPng (more toughness)

This crack propagaPon direcPon follows the inclusion+grain shape (less toughness)

[Hertzberg]

Examinable


20

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

propagaPng a crack? -‐ One method, already discussed, is to maximize the amount of plasPc work. This requires the yield strength to be minimized so as to maximize the size of the plasPc zone. -‐ For very tough materials, however, it turns out that the same parameters that control ducPlity also affect toughness. Lower densiPes of second phase parPcle increase toughness. Second phase parPcles 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 deflecPon (and meandering) 2) Zone shielding 3) Contact shielding

•  The term “shielding” means that the crack Pp 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 deflecPon (and meandering)

2) Zone shielding

-‐ 2A TransformaPon Toughening -‐ 2B Microcrack toughening -‐ 2C Void formaPon

3) Contact shielding -‐ 3A Wedging/ crack bridging -‐ 3B Ligament/fiber bridging -‐ 3C Crack sliding, interference -‐ 3D PlasPcity induced crack closure

Examinable


23

1 Crack de.lection •  If parPcles of a second phase are present, large differences in

elasPc modulus can either aBract or repel the crack. •  Some authors (e.g. Green) disPnguish between crack bowing and

crack deflec2on. Technically, the former is toughening from deflecPon in the plane of the crack and the laBer is deflecPon out of the plane of the crack.

•  In either case, the net result is that the crack Pp no longer sees as large a stress as it would if the crack were straight, and in the plane.

•  Crack deflecPon can be caused by parPcles that are more resistant to cracking, or have different elasPc sPffness (higher or lower modulus).

•  Laminate composites also achieve crack deflecPon, as previously discussed.


24

1. Crack de.lection:�examples

[Green]


25

Zone Shielding: 2A transformation toughening

•  Various mechanisms exist for shielding crack Pps from some of the applied (and concentrated) stress.

•  The best known mechanism is transforma2on toughening. •  This applies to both metals (stainless steels, Hadfield steels) and

ceramics (zirconia addiPons). •  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 transformaPon always has a volume change associated with the change in crystal structure, which can be wriBen as a strain. The product of stress and strain is then the work done or expended during the (stress-‐induced) transformaPon.

Examinable


26 2A Transformation toughening: transformation strain

•  The large volume change on transformaPon is equivalent to a significant transforma2on 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 transformaPon has a parPcular habit plane (i.e. a crystallographic plane in each phase in common), two twin-‐related variants occur in each parPcle so that the shear strains are (approximately) canceled out. This leaves only the 4 % dilataPonal (volume) strain that contributes to the work done.

Examinable


27

2A Transformation toughening: �phase change in zirconia

•  The classic example of transformaPon toughening is the addiPon of a few (volume) % of ZrO2 to oxides and other briBle 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 transformaPon (i.e. lower the transformaPon temperature), some “stabilizer” is added. Typical are ceria (Ce2O3) and yBria (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 relaPonships for ZrO2 with CaO, and ZrO2 with Y2O3.

Examinable


ZrO2 and CaZrO2 •  In pure ZrO2 there is a large

volume change for the tetragonal to monoclinic transiPon upon cooling, starPng 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. •  “ParPally Stabilized Zirconia”

28

Slide courtesy Dr. Alpay, Univ. Connecticut: http://www.ims.uconn.edu/~alpay/Group_Page/Courses/MMAT%20244/Lecture%2005.ppt Please acknowledge Carnegie Mellon if you make public use of these slides

Yttria Stabilized Zirconia

•  The monoclinic transiPon can be suppressed even further by stabilizing zirconia with yBria from 3-‐8 %.

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

•  YBria, parPally, and cubic stablized zirconia (CZ) are commercially useful.

29

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 transformaPon is that it leads to an elasPc driving force that opposes the transformaPon for parPcles embedded in a matrix of a different material.

•  The size effect is, however, quite subtle. If we were to consider only the elasPc energy from the volume change then this would be proporPonal to the (volumetric) driving force for the phase change. In fact, however, there is a shear strain associated with the phase transformaPon that is larger than the dilataPonal strain. This shear strain is accommodated by having mulPple 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 creaPon of surface area in the transformaPon. Therefore there is, in fact, a balance between the release of volumetric driving force (offset by the dilataPonal strain energy) and the creaPon of internal interfaces between martensite variants.

•  Therefore we take advantage of having the zirconia embedded as small parPcles in the matrix of the ceramic to be toughened.

•  The parPcles must be small enough for the elasPc energy term to be effecPve. The upper limit in parPcle size for reten2on 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 Pp: the stress removes the constraint on each parPcle, allowing it to transform. The transformed parPcle was metastable, thermodynamically, and so remains in the low T, monoclinic form aXer the crack has gone by.

•  The stress acPng to cause the transformaPon strain performs work and so energy is consumed in the phase transformaPon. This energy (work done) adds to the surface energy required to create crack length.

•  AddiPonal toughening arises from the parPcles causing crack deflecPon.

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 transformaPon occurs becomes the crack wake as the crack propagates. The region around the crack Pp is known as the process zone because this is where the toughening process is operaPve.

[Green] Crack propaga2on direc2on

Process zone width

Examinable


33 2A Transformation toughening: �microstructure

•  Microstructural evidence for the transformaPon is obtainable through x-‐ray diffracPon and Raman spectroscopy (the two different forms of zirconia have quite different infra-‐red spectra).

•  (a) lenPcular parPcles of MgO-‐stabilized ZrO2 (untransformed) in cubic ZrO2. (b) transformed parPcles of ZrO2 around a crack (dashed line).

[Chiang]


34 2A Transformation �toughening: limits on toughening

•  As the parPcle size is increased, so the parPcles become less and less stable; the transformaPon becomes easier and more effecPve at toughening the material. If the parPcles become too large, however, the toughening is lost because the parPcles are no longer stabilized in their high temperature form.

•  Effect of test temperature? •  Effect of stabilizing addiPons to

the ZrO2?

[Green]

Examinable


35 2A Transformation �toughening: quantitative approach

•  It is not possible to lay out the details of how to describe transformaPon toughening in a fully quanPtaPve fashion here.

•  An equaPon 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 εtrans √h / (1-‐ν) C is a constant (of order 1), E = elasPc modulus, Vtrans = volume fracPon transformed, εtrans = transformaPon strain (dilataPon, i.e. bulk expansion), h is the width of the process zone, and ν is Poisson’s raPo.

•  What controls the width of the process zone?

Examinable


36

2B Microcracking •  Less effecPve than transforma2on 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 Pp.

[Green]

Examinable


37

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

the material so that addiPonal (micro-‐)cracking occurs in the vicinity of the crack Pp as it advances, thereby increasing the crack area created (per unit advance of crack), thereby increasing the toughness (resistance to crack propagaPon).

•  This is most effecPve in two-‐phase ceramics in which the 2 phases have different CTEs. As the material cools aXer 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 addiPonal tensile load, e.g. near a crack Pp.

•  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 enPrely (micro-‐)cracked, then no further cracking can occur at a crack Pp (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 criPcal grain size, dc, we use the Griffith equaPon, with Kco as the fracture toughness and σR as the residual stress, subsPtuPng grain size for crack size: dc = ( Kco / σR )2

•  The process zone size, rc, then depends on the raPo of the actual grain size, d, to the criPcal 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 effecPve toughening. Grain sizes larger than the criPcal grain size simply result in spontaneous cracking. Too small grain sizes (< 0.6 dc) mean no micro-‐cracking at the crack Pp.

€

rcd≈

0.232

1− ddc

$

% &

'

( )

2

[Courtney]


38

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

intensity does not reach their criPcal Kc, based on the Griffith equaPon. •  (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 α) mulPplied by the change in temperature (∆T), εthermal = α ∆T. Where a volumetric strain is important, V0+∆V = (l0 + ∆l)3 = { l0 (1+εthermal) }3 = l03 (1+3ε+3ε2+ε3) ≈ V0

(1+3εthermal) ; ∆V/V = 3εthermal •  An equaPon that describes the toughening effect is as follows, where ∆K is again the increment in

toughness (units of stress intensity): ∆K = C Vf E εcrack √h / (1-‐ν) C is a constant (of order 1), E = modulus, εcrack = cracking strain (dilataPon), h is the width of the process zone, and ν is Poisson’s raPo. The cracking strain is approximately 3*strain associated with the difference in CTE: εcrack ≈ 3∆α ∆T.

•  Note the strong similarity to the equaPon that describes transformaPon toughening! The only difference is the physical meaning of the strain term. If the volume fracPon, Vf, is not given, one can assume =1, if there are nearly equal fracPons of the two phases so that most grains crack.

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

Examinable


expanding region

isolate region

expansion

eigenstrains

surface tracPon

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

39

Slide courtesy of B. Anglin &

S. Donegan

40

2C Void formation •  Void formaPon 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 ducPle tearing on a small scale as the crack opens.

•  The spaPal organizaPon of the voids is important. Random distribuPons are beBer than either clusters or sheets. Carbide parPcles in steels, or dispersoid parPcles in aluminum alloys (e.g. Al3Fe) are typical nucleaPon sites for voids. Sheet-‐like sets of voids can arise from carbide parPcles that have grown on martensite or bainite laths during tempering of martensiPc microstructures.


41 3A Crack wedging/ bridging •  Wherever the crack results in interlocking grain shapes

exerPng force across the crack, stress (intensity) at the crack Pp is reduced.

[Chiang]

Crack�opening


42

3B Fiber/ligament bridging (Composites) •  Anything that results in a load bearing link across the crack (behind the Pp)

decreases the stress (intensity) at the crack Pp. •  Either rigid (elasPc) fibers (ceramic matrix composites) or plasPc parPcles

(ducPle metal parPcles in an elasPc matrix) are effecPve. •  In order to esPmate the increase in toughness, one can calculate a work

associated with crack advance and then esPmate with ∆K = √(EG).

[Chiang]


43

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

at various stages of crack opening. From leX to right, the stress intensity is increasing.

[Green]


44 3B Fiber/ligament bridging�strain dependence

•  The balance between fiber strength, matrix strength and the fiber/matrix interface is criPcal.

•  In general, a relaPvely weak fiber/matrix interface promotes toughness.

•  Why? [Green]


45

3D Plasticity induced crack closure •  PlasPcity induced crack closure is another way of staPng the effect of plasPc deformaPon around the crack Pp.

•  Very tough materials exhibit an interesPng behavior in Charpy impacts. For high ducPliPes, the specimen can deform without fully breaking, with consequent enormous energies absorbed.


46

References •  D.J. Green (1998). An IntroducPon to the Mechanical ProperPes of

Ceramics, Cambridge Univ. Press, NY. •  Materials Principles & PracPce, BuBerworth 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), DeformaPon and Fracture Mechanics of

Engineering Materials, Wiley. •  N.E. Dowling (1998), Mechanical Behavior of Materials, PrenPce Hall. •  Y.-‐T. Chiang, D.P. Birnie III, W.D. Kingery, Physical Ceramics (1997), Wiley,

New York, ISBN 0-‐471-‐59873-‐9. •  A.H. CoBrell (1964), The Mechanical ProperPes of MaBer, 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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