Chapter_1_-_Introduction.pdf

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Fracture and Fatigue of MaterialsME5513

2007/08 Semester I

Zeng Kaiyang

Department of Mechanical Engineering

Blk EA 07-36

E-mail: [email protected]

Tel: x 6627


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EXAMINATION

Continuous Assessment (CA): 30% (15% on Fracture and15% on Fatigue)

Final exam: 70% (35% on Fracture and 35% on Fatigue)

Understanding of fundamental concepts of fracture and fatigueApplications of fundamental concepts of fracture and fatigueExample and Case studies


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MAIN REFERENCE BOOKS

N.E.Dowling, Mechanical Behavior of Materials, 3rd Edition,

Pearson International Edition, 2007.

D. Broek,The Practical Use of Fracture Mechanics, Kluwer

Academic Publishers, Dordrecht, 1988.

D. Broek: Elementary Engineering Fracture Mechanics, 4th

revised edition, MartinusNijhoff Publishers, Dordrecht, 1986.

R. W. Hertzberg, Deformation and Fracture Mechanics ofEngineering Materials, 4th Edition, John Wiley & Sons, NewYork, 1996.

T.L.Anderson, Fracture Mechanics Fundamentals andApplications, 2nd Editon, CRS Press, Boca Raton, 1994.


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CHAPTER 1 A GENERAL

INTRODUCTION


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Fracture of a material

Over-load fractureFracture due to

cracking

Failure CriteriaFailure Criteria:Max. Normal Stress Criteria;Max. Shear Stress Criteria;

von MisesCriteria(Yield strength)

Fracture Mechanics:Fracture Mechanics:Theory

ExperimentsMaterial Properties

(Fracture toughness)


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OVERLOAD


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EXAMPLES OF FRACTURE #3

The Koror-BabeldaobBridge (Palau)collapsed suddenly in1996 after it had stood

for 20 years. Thisoccurred shortly after areplacement of itspavement.

Before the bridge collapses

After the bridge collapses

Brittle fracture of the 584-ft-long Tank Barge I.O.S.

3301 in 1972, in which the1-yr-old vessel suddenlybroken almost completelyin half while in port with

calm seas.

Hartford Civic CenterArena roof collapses(Connecticut) in Jan.

1978 due to some designerrors and constructionerrors reduced the loadthat the roof could safely

carry.

Source: Internet


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Shown on the left is a Fire Department aerialladder failure. Structural failure of a ladderis not at all an uncommon event. Failure canresult, for example, from poor design, use ofinferior material or fabrication methods, orfrom a phenomenon called fatigue. Fatigueis a failure mode which occurs in structural

materials and is driven by repeat loading.

Right image is a ScanningAcoustic Microscopy (SCA)image showing delamination (redregions) in a micro-electronicspackage.

Source: Internet


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Shown of the left are the

common cases of the bonefracture, it is said that almosteveryone will have at leastonce bone fracture in his/herlife

Right image is an X-ray imageof fractured bone when thepatient is examined in hospital

Source: Internet


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CRACK AND STRENGTH

It is now understood that flaws and stress concentrations (andto a certain extent internal stresses) were responsible for thefailure of materials or structures.

D.Broek: Elementary Engineering Fracture Mechanics, 4th Edition, Page 6, Figure 1.1


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FRACTURE MECHANICS

After World War II the use of high strength materialshas increased considerably. These materials are often

selected to realize weight savings. The high strength materials have a low crack resistance(fracture toughness): the residual strength under the

presence of cracks is low. When only small cracksexist, structures designed in high strength materials mayfail at stresses below the highest service stress they

were designed for. The occurrence of low stress fracture in high strengthmaterials induced the development ofFractureFracture

Mechanics.Mechanics.


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FRACTURE MECHANICS

Fracture MechanicsFracture Mechanicscan deliver the methodology tocompensate the inadequacies of conventional designconcepts. The conventional design criteria are based ontensile strength, yielding strength and buckling stress.

These criteria are adequate for many engineeringstructures, but they are insufficient when there is thelikelihood of cracks.

After approximately three decades of development,Fracture MechanicsFracture Mechanicshave become a useful tool indesign with high strength materials.


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FRACTURE MECHANICS

Fracture MechanicsFracture Mechanicsshould be able to answer thefollowing questions:

What is the residual strength as a function of crack size? What size of crack can be tolerated at the expected service load;

i.e. what is the critical crack size?

How long does it take for a crack to grow from a certain initialsize to the critical size?

What size of pre-existing flaw can be permitted at the momentthe structure starts its service life?

How often should the structure be inspected for cracks?

Fracture MechanicsFracture Mechanicsprovides satisfactory answers tosome of these questions and useful answers to the others.


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DEFINITION OF FRACTURE

Fracture is the propagation of a crack across a loadedsection.

Thematerial property that characterizes fractureresistance is itstoughness. Note that strength is not amaterial property.

Toughness is related to the energy per unit crackadvance.

Fromlinear elastic fracture mechanics, the units oftoughness areMPam.

Just as for yield strength, toughness scales with elastic

modulus.

THE BROAD FIELD OF


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THE BROAD FIELD OF

FRACTURE MECHANICS

Applied mechanics provide the crack tip stress fields as well as the elastic andplastic deformations of the material in the vicinity of the crack. The predictionsmade about fracture strength can be checked experimentally.

Materials science concerns itself with the fracture processes on the scale of atomsand dislocations to that of impurities and grains. From a comprehension of theseprocesses the criteria which govern growth and fracture should be obtainable.


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CASE STUDY #1Problems with wind loading The Tay Bridge Disaster

The disaster is one of the most famousbridgefailures and to date it is still the worst structuralengineering failure in the British Isles.

Source: Internet

http://en.wikipedia.org/wiki/Tay_Rail_Bridge

http://taybridgedisaster.co.uk/


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The bridge was significantlyunder- designed for the windloading

The train is also contribute tothe loading to the bridge inadditional to the wind

Source: Internet


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Material Embrittlement


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Material Embrittlement The termembrittlementembrittlement is used to describe a variety of phenomena causing

mechanical performance degradation as a result of a stressed materials exposure toa hostile environment.

There are many types of embrittlement: such as stress-corrosion cracking; hydrogenembrittlement; impurity-atom embrittlement; radiation damage etc; metals,ceramics, glasses, and polymers are all shown embrittlementone way or another.

CASE STUDY #6


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CASE STUDY #6Problems with loads and design Comet Aircraft Crashes

In the early 1950s, the Comet

aircraft was the first jet transportintroduced into commercialpassenger service.

Not long after coming into service,two planes underwent explosive

decompressions of then fuselage onclimbing to cruise altitude, whichresulted in the loss of the planes aswell as the lives of all aboard.

Intensive investigation revealedthat these crashes were due to

fatigue cracking of the fuselageat regions of high stress adjacentto corners of more-or-less square

(rather than round windows).http://en.wikipedia.org/wiki/De_Havilland_Comet


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The fatigue loading was due to the

pressurization anddepressurization of the cabin,which occurred in each takeoff and

landing cycle.The presence of fatigue crackingwas confirmed through study of

the fracture surfaces of criticalparts of the wreckages.

As understanding by the Comet

crashes, fatigue must be animportant consideration in thedesign of aircraft.

A.J .McEvily: Metal Failures, Page 7, Figure 1-2.

D.R.H.J ones, Engineering Materials 3, Page 131-142.


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Fracture is more important than strength from an engineering

point of view! When we build something, we want it to resist theloads that we put on it and not break. Of course, objects cancome apart in way that is not necessarily disastrous just through

regular wear and tear. By fracture, we generally mean unanticipated (worse,

unpredictable) breakage. Metallurgists are fond of quoting the

Liberty ship experience because of its historical significance. As an example of a ceramic system, think of the inconvenience

and pain of cracking or breaking a tooth (never mind a bone).

RELEVANCE OF STUDY FRACTURE


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CONCEPTS OF FRACTURE


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CONCEPTS OF FRACTURE

MECHANICSFrom investigating fallen structures, engineers found that mostfailure began withcracks. Which may be caused by:

material defects (dislocation, impurities...); discontinuities in assembly and/or design (sharp corners,

grooves, nicks, voids...); harsh environments (thermal stress, corrosion...); and

damages in service (impact, fatigue, unexpected loads...).

Most microscopic cracks are arrested inside the material but it

takes one run-away crack to destroy the whole structure.

To analyze the relationship among stresses, cracks, and fracture

toughness, Fracture Mechanics was introduced.

THE FRACTURE MECHANICS


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APPROACH TO DESIGN

The strength of materials approach traditional approach tostructural design and material selection

Applied Stress Yield or tensilestrength

The fracture mechanical approach has three important variables

Applied Stress

Fracture ToughnessCrack Size

Fracture mechanics quantifies the critical combinations of thesethree variables.


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FRACTURE MODE


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Mode IMode I denotes a symmetric opening, the relative displacements betweencorresponding pairs being normal to the fracture surface.

Mode IIMode II denotes antisymmetricseparation through relative tangentialdisplacement, normal to the crack front.

Mode IIIMode III denotes antisymmetricseparation through relative tangentialdisplacement, parallel to the crack front.

Crack growth usually takes place inCrack growth usually takes place inModel IModel I or close to it.or close to it.

Mode I


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MECHANISMS OF FRACTURE


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MECHANISMS OF FRACTURE

AND CRACK GROWTH By itself, crack seldom leads to fracture.

When a crack due to fatigue or stress corrosion hasdeveloped to a certain size, final fracture will takeplace by cleavage or by ductile fracture.

Two principle fracture mechanisms are cleavagefracture and ductile fracture

Main cracking mechanisms are fatigue, stresscorrosion, creep, hydrogen induced cracking, liquidmetal induced cracking

CRACK AND STRENGTH


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It is now understood that flaws and stress concentrations (andto a certain extent internal stresses) were responsible for thefailure of materials or structures.

D.Broek: Elementary Engineering Fracture Mechanics, 4th Edition, Page 6, Figure 1.1

SHEAR STRENGTH OF PERFECT

AND REAL CRYSTALS


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AND REAL CRYSTALS

R.W.Hertzberg, Deformation and Fracture Mechanics of Engineering Materials, Page 44, Table 2.1

STRENGTH OF PERFECT AND


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REAL CRYSTALS

It is therefore necessary to explain not the great strength ofsolids, but their weakness.

Materials possess low fracture strength relative to theirtheoretical capacity because most materials deform plastically atmuch lower stress levels and eventually fail by an accumulation

of this irreversible damage.Components and structures are not perfect. They contain manymaterial defects(such as pores, slag particles, inclusions, and

brittle particles), manufacturing flaws(such as scratches,gouges, weld torch arc strikes, weld undercutting, and machiningmarks), and design defects (such as excessive stress

concentrations resulting from inadequate fillet radii anddiscontinuous changes in section size).

GRIFFITH & GLASS FIBRES


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GRIFFITH & GLASS FIBRES

A.A. Griffith is considered to have made the first substantialscientific contribution to the understanding of brittle fracture(1920).

He measured the breaking strength of glass fibresof varyingthicknesses and found that their strength varied in inverseproportion to their diameter, see Fig. from Greens book (nextslide).

He then showed that Inglissequation for the stress(concentration) at the root of an elliptical crack could be appliedto the problem to rationalize the results.

That is, by assuming that the largest flaw was of order of thefibrediameter, he could demonstrate that his results wereconsistent with Inglisstheory.

GLASS FIBRES STRENGTH


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Strength of glass fibers, as determined by Griffith. Notethe inverse relationship between size and strength.

D. Green, Mechanical Behavior of Ceramic Materials, Figure 8.2

MICROSTRUCTURE EFFECT ON


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FRACTURE

Whether or not a material fractures on loading depends on acompetition between flow and fracture. If flow is easy then

fracture will only occur when necking (localization) happens. Ifflow is difficult then fracture will relieve the loading instead.

Microstructure: weakly bonded second phase particles tend topromote fracture by acting as initiation sites for cracks.

Fine grain size tends to inhibit fracture by providing a highdensity of crack arrest/deflection points. Also, even if a graincracks, then the stress concentration at the end of the crackdecreases with decreasing crack size (= grain size).

TEMPERATURE EFFECT


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TEMPERATURE EFFECT

Temperature: temperature affects plasticity in many materials.Higher temperatures promote deformation whereas low

temperatures promote fracture. In many materials, a ductile-to-brittle transition can be detected as you lower thetemperature.

This also illustrates the essential aspect of competition

between fracture and plastic flow. If dislocation slip is easy,then even a artificially made crack will blunt by plastic flow atits tip.

TOUGHNESS-TEMPERATURE


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TRANSITIONS

A.H.Cottrell: The Mechanical Properties of Matter, Page 358

DUCTILE-BRITTLE TRANSITION

TEMPERATURE (DBTT)


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TEMPERATURE (DBTT)

The DBTT is the temperatureat which a material changes

from ductile to brittle fracture.

The fracture toughness offerritic steels can changedrastically over a smalltemperature.

The brittleness of the steel atlow temperature has beenidentified as one of the factorscontributing to the sink of

TitanicTitanic

ENVIRONMENT AND LOADING


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Environments will affect the fracture behavior of the materials,such as hydrogen embrittlementin steels or welding, stress-corrosion cracking etc.

Ammonia is notorious as a promoter ofcorrosion fatigue, e.g.cracking in brass, similarly chloride ions (salt) in iron alloys(even stainless steel!). Example:http://en.wikipedia.org/wiki/Corrosion_fatigue

Type of loading: multiaxial stresses involving tension promotefracture whereas stresses involving compression promote

deformation, especially if deviatoricstresses are maximized.

Monotonic loading is generally less severe than cyclic loading.

Specimen design is also critical notches promote fracture overdeformation.

STRESS CONCENTRATION


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Now we need to take stress concentration into account at thetip of a crack.

We employ a formula by Inglisfor an elliptical crack oflengthaand thicknessb:

maximum/applied = 1 + 2a/b

The sharper thecrack, the greaterthe stressconcentration at the

crack tip,maximum.

2a

2b

R.W.Hertzberg, Deformation and Fracture

Mechanics of Engineering Materials, Page 240,Figure 7.5

STRESS CONCENTRATION

FACTORS


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FACTORS

(a) Axial loading of notched bar(b) Axial loading of bar with fillet

R.W.Hertzberg, Deformation and Fracture Mechanics of Engineering Materials, Page 241, Figure 7.6

ENGINEERING SERVICE

FAILURE


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FAILURE

Above-Fracture surfaces of aluminum testspecimens revealing flat and slant-typefailure. Toughness level increases with

increasing relative amount of slant fracture

Below-Chevron markings curve infrom the two surfaces and point backto the crack origin.

Engineering service failurescan generate large areas of

fracture surface.

R.W.Hertzberg, Deformation and Fracture Mechanics of Engineering Materials, Page 248, Figure 7.11, and Page249, Figure 7.12

MICROSCOPIC FRACTURE

MECHANISMS METALS


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MECHANISMS - METALS

Above-Metallographic section revealingtranscrystallinecrack propagation at (A)and intercrystallinecrack growth at (B)

Using light optical

microscope, it is possible toobtain importantinformation about the

fracture path, for example,to determine whether thefailure was oftranscrystallineorintercrystalline.



MECHANISMS METALS


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MECHANISMS - METALS

Left- Microvoidcoalescenceunder tensile loading, whichleads to equiaxeddimplemorphology; (a) TEM iamgeand (b) SEM image

An important fracture mechanisms, common to most materials regardless offundamental differences in crystal structure and alloy composition, ismicroviodcoalescence.

Amorphous polymers also experience failure by this mechanism.

It is believed that stress-induced fracture of brittle particles, particle-matrixinterface failure, and perhaps, complex dislocation interactionslead to theformation of microcracksor pores within the stressed component.



MECHANISMS - METALS


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MECHANISMS METALS

Above-Microvoidcoalescence under shearloading, which leads to elongated dimplemorphology; (a) TEM image; and (b) SEM

iamge

At increasing stress levels, thevoids grow and finally coalesceinto a broad crack front. When

this growing flaw reachescritical dimensions, total failureof the component results.

When failure is influenced byshear stresses, the voids thatnucleate in the manner citedbefore grow and subsequently

coalesce alone planes ofmaximum shear stress.

Consequently, these voids tends to be elongated and result in the formation ofparabolic depressions on the fracture surface



MECHANISMS - METALS


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MECHANISMS - METALS

These diagrams illustrate the effect ofthree stress states on microvoid

morphology:

(a) tensile stresses produce equiaxedmicrovoids;

(b) pure shear stresses generate microviodselongated in the shearing direction(voids point in opposite directions on thetwo fracture surfaces);

(c) tearing associated with nonuniformstress (combined tension and bending) ,which produces elongated dimples onboth fracture surfaces that point back to

crack origin.R.W.Hertzberg, Deformation and Fracture Mechanics ofEngineering Materials, Page 254, Figure 7.18.

CRACK AND MICROSTRUCTURE

Cleavage fractureisusually


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Cleavage fracture is usually

associated with little plasticdeformation, it is called brittlefracture

Ductile fracture is usually

associated with plasticdeformation

Intergranularfracture requiresoperation of some

form of either one

INTERGRANULAR AND

TRANSGRANULAR FRACTURES


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TRANSGRANULAR FRACTURES

K.Zengand D.J .Rowcliffe, J . Mater. Res., Vol. 9, No. 7, 1994, Page 1693-1700

Intergranular fracture in Al2O3ceramics

Transgranular dominated fracturein Al2O3ceramics


MECHANISMS - METALS


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MECHANISMS METALSLeft-Cleavage fracture in alow carbon steel. Note parallelplateau and ledge morphologyand river patterns reflecting

crack propagation along manyparallel cleavage planes; (a)TEM, (b) SEM

Right-Cleavage facets revealfine-scale height elevationscaused by localized

deflection of the cleavagecrack along twin matrixinterfaces; (a) TEM (b) SEM.

R.W.Hertzberg, Deformation and Fracture Mechanics of Engineering Materials, Page 255, Figure 7.19 and Page256, Figure 7.20.


MECHANISMS - METALS


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The process of cleavage involves transcrystallinefracture along specificcrystallographic planes and is usually associated with low-energy fracture.

This mechanism is observed in BCC, HCP, and ionic and covalently bonded

crystals, but occurs in FCC metals only when they are subjected to severeenvironmental conditions.

Cleavage facets are typically flat, although they may reflect a paralleledplateau and ledge morphology.

Often these cleavage steps appear as river patterns wherein fine steps areseen to merge progressively into larger ones.

It is generally believed that the flowof the river pattern is in the direction

of microscopic crack propagation.

The sudden appearance of the river pattern was probably brought on by themovement of a cleavage crack across a high-angle grain boundary, where the

splintering of the crack plane represents an accommodation process as theadvancing crack reoriented in search of cleavage planes in the new grain.

FRACTURE MECHANISMS -

POLYMERS


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Deformation in many amorphous polymers involves the formation of thincrazes that contain interconnected microvoidsand polymer fibrils extended inthe craze thickness direction.

Subsequent fracture then occurs usually in two stages, typified by eithermirrorlike(smooth and highly reflective) or misty macroscopic fracture surfaceappearance.

Crazes in polyphenyleneoxide revealinginterconnected microvoidsand aligned fibrils

Above-Model of crack advance inassociation with craze matter. Region A:crack advance by void formation throughcraze mid-plane. Region B: crack advancealong alternate craze-matrix interfaces toform patch or mackerel patterns. Region C:crack advance through craze bundles to formhackle bands

R.W.Hertzberg, Deformation and Fracture Mechanics ofEngineering Materials, Page 257, Figure 7.22,

FRACTURE MECHANISMS

CRYSTALLINE POLYMERS


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Left-Fracture associated withspherulitesin crystallinepolymers (c) Fast runningcrack fracture surface in

polypropylene revealing thefour crack paths. (d)Interspherulitic fracture inpolypropylene associated

with slow crack velocity.

The fracture surface appearance of the semicrystallinepolymers depends on thecrack path with respect to underlying microstructural features. For example, acrack may choose an interspheruliticcrack path or pass through the spherulitealong a tangential or radial direction.

It should be noted that fractographicevidence for transspheruliticorinterspherulitic failure may be obscured by extensive prior deformation of thepolymer, which distorts beyond recognition characteristic details of theunderlying microstructure.

R.W.Hertzberg, Deformation and Fracture Mechanics of Engineering Materials, Page 262, Figure 7.27.

FRACTURE SURFACES OF

CERAMICS


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C CSLeft-Fracture surface appearance in glassyceramic revealing mirror, mist, and hackleregions. (a) Plate glass fracture surface,Tensile fracture stress = 28.3 MPa, Crack

origin is at upper-right. (b) Schematicdiagram showing different fracture regionsand approximate textural detail (source offailure, smooth mirror region, Mist region,and Hackle region).

The fracture surfaces of brittle solids often reveal severalcharacteristic regions as shown in the left. Surrounding thecrack origin is a mirror region associated with a highly

reflective fracture surface. This smooth area is bordered bya misty region that contains small radial ridgesassociated with numerous microcracks.

The mist region in turn is surrounded by an area that is rougher in appearance

and contains larger secondary cracks. Depending on the size of the sample, thishackle region may be bounded by macroscopic crack branching.

R.W.Hertzberg, Deformation andFracture Mechanics of EngineeringMaterials, Page 263, Figure 7.28.


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End of Chapter 1: Introduction toEnd of Chapter 1: Introduction to

Fracture of MaterialsFracture of Materials

Chapter_1_-_Introduction.pdf

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