chapter 8: failure analysis and prevention issues to address

경상대학교 Ceramic Design Lab.


ISSUES TO ADDRESS... • How do flaws in a material initiate failure? • How is fracture resistance quantified; how do different material classes compare? • How do we estimate the stress to fracture? • How do loading rate, loading history, and temperature affect the failure stress?

Ship-cyclic loading from waves.

Computer chip-cyclic thermal loading.

Hip implant-cyclic loading from walking.

Chapter 8: Failure Analysis and Prevention


Preventing Failure

In service, under loading (mechanical, thermal) • How to assure performance, safety and durability?

– Avoid excess deformation that may deteriorate the functionality

– Avoid cracking that may propagate to complete fracture

• The study of deformation and fracture in materials the response of materials to mechanical loads or

deformation.


Deformation and Failure

• Deformation – Time independent

• Elastic • Plastic

– Time dependent • Creep

• Fracture – Static loading

• Brittle: rapid run of cracks through a stressed material • Ductile • Environmental (combination of stress and chemical effects)

– High-strength steel may crack in the presence of hydrogen gas – Creep rupture (creep deformation proceeding to the point of

separation) – Fatigue/cycling loading

• High cycle/low cycle • Fatigue crack growth • Corrosion fatigue


Types of Failure • Fracture

– Cracking to the extent that component to be separated into pieces – Steps in fracture:

• crack formation • crack propagation

• Depending on the ability of material to undergo plastic deformation before the

fracture two fracture modes can be defined - ductile or brittle – Ductile fracture - most metals (not too cold):

• Extensive plastic deformation ahead of crack • Crack is “stable”: resists further extension unless applied stress is

increased

– Brittle fracture - ceramics, ice, cold metals: • Relatively little plastic deformation • Crack is “unstable”: propagates rapidly without increase in applied

stress


Crack formation mechanisms Metals typically form cracks by the accumulation of dislocations at a crack nucleation site (grain boundaries, precipitate interface, free surface, etc.) Ceramics, semiconductors, some plastics (hard and brittle, eg., thermosetting plastics) and intermetallic compounds form cracks by planar defects (grain boundaries, two-phase interfaces, etc.) Soft plastics crack by the sliding of the long polymer chairs across each other by breaking the Van der Wall bonds.

Fracture of Materials


Impact Testing

final height initial height

• Impact loading: -- severe testing case -- makes material more brittle -- decreases toughness

(Charpy)

(Izod)


Figure 8.2 Impact energy for a ductile fcc alloy (copper C23000–061, “red brass”) is generally high over a wide temperature range. Conversely, the impact energy for a brittle hcp alloy (magnesium AM100A) is generally low over the same range. (From Metals Handbook, 9th ed., Vol. 2, American Society for Metals, Metals Park, OH, 1979.)


Impact Tests: Test conditions • The impact data are sensitive to test conditions. Increasingly sharp

notches can give lower impact-energy values due to the stress concentration effect at the notch tip

• The FCC alloys→ generally ductile fracture mode

• The HCP alloys→ generally brittle fracture mode

• Temperature is important

• The BCC alloys→ brittle modes at relatively low temperatures

and ductile mode at relatively high temperature


• Increasing temperature... --increases %EL and Kc

• Ductile-to-Brittle Transition Temperature (DBTT)...

Temperature

BCC metals (e.g., iron at T < 914°C)

Impa

ct E

nerg

y

Temperature

High strength materials ( σ y > E/150)

polymers More Ductile Brittle

Ductile-to-brittle transition temperature

FCC metals (e.g., Cu, Ni)


• Pre-WWII: The Titanic • WWII: Liberty ships

• Problem: Used a type of steel with a DBTT ~ Room temp.

Reprinted w/ permission from R.W. Hertzberg, "Deformation and Fracture Mechanics of Engineering Materials", (4th ed.) Fig. 7.1(a), p. 262, John Wiley and Sons, Inc., 1996. (Orig. source: Dr. Robert D. Ballard, The Discovery of the Titanic.)

Reprinted w/ permission from R.W. Hertzberg, "Deformation and Fracture Mechanics of Engineering Materials", (4th ed.) Fig. 7.1(b), p. 262, John Wiley and Sons, Inc., 1996. (Orig. source: Earl R. Parker, "Behavior of Engineering Structures", Nat. Acad. Sci., Nat. Res. Council, John Wiley and Sons, Inc., NY, 1957.)

Design Strategy: Stay Above The DBTT!


Figure 8.3 Variation in ductile-to-brittle transition temperature with alloy composition. (a) Charpy V-notch impact energy with temperature for plain-carbon steels with various carbon levels (in weight percent). (b) Charpy V-notch impact energy with temperature for Fe–Mn–0.05C alloys with various manganese levels (in weight percent). (From Metals Handbook, 9th ed., Vol. 1, American Society for Metals, Metals Park, OH, 1978.)


Transition Temperatures • As temperature decreases a ductile material can become

brittle - ductile-to-brittle transition – The transition temperature is the temp at which a

material changes from ductile-to-brittle behavior

• Alloying usually increases the ductile-to-brittle transition temperature. FCC metals remain ductile down to very low temperatures. For ceramics, this type of transition occurs at much higher temperatures than for metals.


• BCC metals have transition temperatures • FCC metals do not • Can use FCC metals at low temperatures (eg

Austenitic Stainless Steel)


Fracture mechanisms • Ductile fracture

– Occurs with plastic deformation • Brittle fracture

– Little or no plastic deformation – Catastrophic


Ductile vs Brittle Failure

Very Ductile

Moderately Ductile Brittle Fracture

behavior:

Large Moderate %AR or %EL Small

• Ductile fracture is usually desirable!

• Classification:

Ductile: warning before

fracture

Brittle: No

warning


• Ductile failure: --one piece --large deformation

Example: Failure of a Pipe

• Brittle failure: --many pieces --small deformation


• Evolution to failure:

• Resulting fracture surfaces (steel)

50 mm

particles serve as void nucleation sites.

50 mm

From V.J. Colangelo and F.A. Heiser, Analysis of Metallurgical Failures (2nd ed.), Fig. 11.28, p. 29, John Wiley and Sons, Inc., 1987. (Orig. source: P. Thornton, J. Mater. Sci., Vol. 6, 1971, pp. 347-56.)

100 mm Fracture surface of tire cord wire loaded in tension. Courtesy of F. Roehrig, CC Technologies, Dublin, OH. Used with permission.

Moderately Ductile Failure

necking σ

void nucleation

void growth and linkage

shearing at surface fracture


Ductile vs. Brittle Failure

cup-and-cone fracture brittle fracture


Fig. Photograph of fracture surfaces of A36 steel Charpy V-notch specimens tested at indicated temperatures(oC)


Brittle Failure Arrows indicate pt at which failure originated


• Intergranular (between grains)

• Intragranular (within grains)

Al Oxide (ceramic)

316 S. Steel (metal)

.)

304 S. Steel (metal)

Polypropylene (polymer)

3 mm

4 mm 160 mm

1 mm

Brittle Fracture Surfaces


Fig. 입내파괴와 입계파괴에서의 균열전파의 개략적 단면도


Microstructure of Fracture in Metals Most often ductile fracture occurs in a transgranular manner, which means through the grains rather than only along grain boundaries. Brittle fracture is typically intergranular or along the grain boundaries, which is enhanced when impurities collect and weaken the grain boundaries. In a simple tensile test, ductile fracture begins by the nucleation, growth and coalescence of microvoids at the center of a sample (in the necked region). The stress causes separation of the grain boundaries or the interfaces between the metal and small impurity particles (inclusions or precipitates). As the local stresses increase, the micro-voids grow and coalesce into larger cavities. Eventually the metal-to-metal contact is too small to support the load and fracture occurs.


• Stress-strain behavior (Room T):

Ideal vs Real Materials

TS << TS engineering materials

perfect materials

σ

ε

E/10

E/100

0.1

perfect mat’l-no flaws

carefully produced glass fiber

typical ceramic typical strengthened metal typical polymer

• DaVinci (500 yrs ago!) observed... -- the longer the wire, the smaller the load for failure. • Reasons: -- flaws cause premature failure. -- Larger samples contain more flaws!

경상대학교 Ceramic Design Lab. 27

Fracture Mechanics:

The general analysis of the failure of structural materials with preexisting flaws

→ The main outcome of the analysis is fracture toughness


Fracture Mechanics

• Fracture strength of a brittle solid is related to the cohesive forces between atoms.

• • One can estimate that the theoretical cohesive strength of a

brittle material should be ~ E/10. But experimental fracture strength is normally E/100 - E/10,000.

• This much lower fracture strength is explained by the effect of stress concentration at microscopic flaws.

• The applied stress is amplified at the tips of micro-cracks, voids, notches, surface scratches, corners, etc. that are called stress raisers. The magnitude of this amplification depends on micro-crack orientations, geometry and dimensions.


Fracture Mechanics

• Cracks or crack-like flaws (surface scratches, voids in welds, delaminations, foreign substances in cast materials…) exist frequently – Commercial aircraft – Ship structures – Bridges – Pressure vessels and piping

• Fracture mechanics: a methodology to aid in selecting

materials and designing components to minimize the possibility of fracture where cracks are difficult to avoid


Flaws are Stress Concentrators! Results from crack propagation • Griffith Crack

where ρt = radius of curvature

σo = applied stress σm = stress at crack tip

ot

/

tom Ka

σ=

ρ

σ=σ21

2

ρt


Concentration of Stress at Crack Tip


Engineering Fracture Design

r/h

sharper fillet radius

increasing w/h

0 0.5 1.0 1.0

1.5

2.0

2.5

Stress Conc. Factor, K t σ max

σ o =

• Avoid sharp corners! σ

r , fillet

radius

w

h

o

σ max


Crack Propagation Cracks propagate due to sharpness of crack tip • A plastic material deforms at the tip, “blunting” the

crack. deformed

region brittle

Energy balance on the crack • Elastic strain energy-

• energy stored in material as it is elastically deformed • this energy is released when the crack propagates • creation of new surfaces requires energy

plastic


When Does a Crack Propagate? Crack propagates if above critical stress

where – E = modulus of elasticity – γs = specific surface energy – a = one half length of internal crack – Kc = σc/σ0

For ductile => replace γs by γs + γp

where γp is plastic deformation energy

212 /s

c aE

πγ

=σi.e., σm > σc

or Kt > Kc


Fracture Toughness

Based on data in Table B5, Callister 7e. Composite reinforcement geometry is: f = fibers; sf = short fibers; w = whiskers; p = particles. Addition data as noted (vol. fraction of reinforcement): 1. (55vol%) ASM Handbook, Vol. 21, ASM Int., Materials Park, OH (2001) p. 606. 2. (55 vol%) Courtesy J. Cornie, MMC, Inc., Waltham, MA. 3. (30 vol%) P.F. Becher et al., Fracture Mechanics of Ceramics, Vol. 7, Plenum Press (1986). pp. 61-73. 4. Courtesy CoorsTek, Golden, CO. 5. (30 vol%) S.T. Buljan et al., "Development of Ceramic Matrix Composites for Application in Technology for Advanced Engines Program", ORNL/Sub/85-22011/2, ORNL, 1992. 6. (20vol%) F.D. Gace et al., Ceram. Eng. Sci. Proc., Vol. 7 (1986) pp. 978-82.

Graphite/ Ceramics/ Semicond

Metals/ Alloys

Composites/ fibers Polymers

5

K Ic

(MPa

· m

0.5 )

1

Mg alloys Al alloys

Ti alloys Steels

Si crystal Glass - soda Concrete

Si carbide

PC

Glass 6

0.5

0.7

2

4 3

10

2 0

3 0

<100> <111>

Diamond

PVC PP

Polyester

PS

PET

C-C (|| fibers) 1

0.6

6 7

4 0 5 0 6 0 7 0

100

Al oxide Si nitride

C/C ( fibers) 1

Al/Al oxide(sf) 2

Al oxid/SiC(w) 3

Al oxid/ZrO 2 (p) 4 Si nitr/SiC(w) 5

Glass/SiC(w) 6

Y 2 O 3 /ZrO 2 (p) 4


FIGURE 8.6 A design plot of stress versus flaw size for a pressure-vessel material in which general yielding occurs for flaw sizes less than a critical size, acritical, but catastrophic fast fracture occurs for flaws larger than acritical.


• Crack growth condition:

• Largest, most stressed cracks grow first!

Design Against Crack Growth

K ≥ Kc = aY πσ

--Result 1: Max. flaw size dictates design stress.

max

cdesign aY

Kπ

<σ

σ

amax no fracture

fracture

--Result 2: Design stress dictates max. flaw size.

21

σπ<

design

cmax Y

Ka

amax

σ no fracture

fracture


• Two designs to consider... Design A --largest flaw is 9 mm --failure stress = 112 MPa

Design B --use same material --largest flaw is 4 mm --failure stress = ?

• Key point: Y and Kc are the same in both designs.

Answer: MPa 168)( B =σc• Reducing flaw size pays off!

• Material has Kc = 26 MPa-m0.5

Design Example: Aircraft Wing

• Use... max

cc aY

Kπ

=σ

σc amax( )A = σc amax( )B9 mm 112 MPa 4 mm

--Result:


Loading Rate

• Increased loading rate... -- increases σy and TS -- decreases %EL

• Why? An increased rate gives less time for dislocations to move past obstacles.

σ

ε

σy

σy

TS

TS

larger ε

smaller ε


Figure 8.7 Two mechanisms for improving fracture toughness of ceramics by crack arrest. (a) Transformation toughening of partially stabilized zirconia involves the stress-induced transformation of tetragonal grains to the monoclinic structure, which has a larger specific volume. The result is a local volume expansion at the crack tip, squeezing the crack shut and producing a residual compressive stress. (b) Microcracks produced during fabrication of the ceramic can blunt the advancing crack tip.


Fatigue • Fatigue = failure under cyclic stress.

• Stress varies with time. -- key parameters are S, σm, and frequency

σ max

σ min

σ

time

σ m S

• Key points: Fatigue... --can cause part failure, even though σmax < σc. --causes ~ 90% of mechanical engineering failures.

tension on bottom

compression on top

counter motor

flex coupling

specimen

bearing bearing


FIGURE 8.10 Typical fatigue curve. (Note that a log scale is required for the horizontal axis.)


• Fatigue limit, Sfat: --no fatigue if S < Sfat

Fatigue Design Parameters

Sfat

case for steel (typ.)

N = Cycles to failure 10 3 10 5 10 7 10 9

unsafe

safe

S = stress amplitude

• Sometimes, the fatigue limit is zero! case for

Al (typ.)

N = Cycles to failure 10 3 10 5 10 7 10 9

unsafe

safe



Stages of Fatigue Failure

There are typically three stages to fatigue failure. First a small crack is initiated or nucleates at the surface and can include scratches, pits, sharp corners due to poor design or manufacture, inclusions, grain boundaries or dislocation concentrations. Second the crack gradually propagates as the load continues to cycle. Third a sudden fracture of the material occurs when the remaining cross-section of the material is too small to support the applied load. At a local size scale the stress intensity exceeds the yield strength.

For fatigue to occur at least part of the stress in the material has to be tensile.

Fatigue is most common in metals and plastics, whereas ceramics fail catastrophically without fatigue because of their low fracture toughness.


Fatigue crack initiation

Figure 8.11 An illustration of how repeated stress applications can generate localized plastic deformation at the alloy surface leading eventually to sharp discontinuities.


• Crack grows incrementally typ. 1 to 6

( ) a~ σ∆

increase in crack length per loading cycle • Failed rotating shaft --crack grew even though Kmax < Kc --crack grows faster as • ∆σ increases • crack gets longer • loading freq. increases.

crack origin

Fatigue Mechanism

( )mda A KdN

= ∆


Figure 8.14 Characteristic fatigue fracture surface. (a) Photograph of an aircraft throttle-control spring 1-1/2× that broke in fatigue after 274 h of service. The alloy is 17–7PH stainless steel. (b) Optical micrograph (10×) of the fracture origin (arrow) and the adjacent smooth region containing a concentric line pattern as a record of cyclic crack growth (an extension of the surface discontinuity shown in Figure 8.11). The granular region identifies the rapid crack propagation at the time of failure. (c) Scanning electron micrograph (60×), showing a closeup of the fracture origin (arrow) and adjacent “clamshell” pattern. (From Metals Handbook, 8th ed., Vol. 9: Fractography and Atlas of Fractographs, American Society for Metals, Metals Park, OH, 1974.)


Figure 8.12 Illustration of crack growth with number of stress cycles, N, at two different stress levels. Note that, at a given stress level, the crack growth rate, dɑ/dN, increases with increasing crack length, and, for a given crack length such as ɑ1, the rate of crack growth is significantly increased with increasing magnitude of stress.


Figure 8.13 Illustration of the logarithmic relationship between crack growth rate, da/dN, and the stress intensity factor range, ΔK. Region I corresponds to nonpropagating fatigue cracks. Region II corresponds to a linear relationship between log dɑ/dN and log ΔK. Region III represents unstable crack growth prior to catastrophic failure.


FIGURE 8.15 Comparison of fatigue curves for (a) ferrous and (b) nonferrous alloys. The ferrous alloy is a ductile iron. The nonferrous alloy is C11000 copper wire. The nonferrous data do not show a distinct endurance limit, but the failure stress at N = 108 cycles is a comparable parameter. (After Metals Handbook, 9th ed., Vols. 1 and 2, American Society for Metals, Metals Park, OH, 1978, 1979.)


Figure 8.16 Plot of data from Table 8.4 showing how fatigue strength is generally one-fourth to one-half of the tensile strength.


Figure 8.17 Fatigue strength is increased by prior mechanical deformation or reduction of structural discontinuities.

FIGURE 8.18 The drop in strength of glasses with duration of load (and without cyclic-load applications) is termed static fatigue.


Improving Fatigue Life 1. Impose a compressive surface stress (to suppress surface cracks from growing)

N = Cycles to failure

moderate tensile σ m Larger tensile σ m


near zero or compressive σ m Increasing

σm

--Method 1: shot peening

put surface

into compression

shot --Method 2: carburizing C-rich gas

2. Remove stress concentrators.

bad

bad

better

better


Fatigue • Repeated, also called cyclic loads resulting in cyclic stresses can

lead to microscopic physical damage.

• Accumulation of this microscopic damage with continued cycling is possible until it develops into a macroscopic crack such as cracks that may lead to failure

• Fatigue: Damage progression to failure due to repeated or cyclic loading at amplitudes considerably lower than tensile or yield strengths of material under a static load

• Estimated to causes 90 % of all failures of metallic structures (bridges, aircraft, machine components, etc.)

• Fatigue failure is brittle-like (relatively little plastic deformation) - even in normally ductile materials. Thus sudden and catastrophic!


Static Fatigue

Figure 8.18 The drop in strength of glasses with duration of load (and without cyclic-load applications) is termed static fatigue. (From W. D. Kingery, Introduction to Ceramics, John Wiley & Sons, Inc., New York, 1960.)


Figure 8.20 Comparison of (a) cyclic fatigue in metals and (b) static fatigue in ceramics.

Figure 8.19 The role of H2O in static fatigue depends on its reaction with the silicate network. One H2O molecule and one –Si– O–Si– segment generate two Si–OH units, which is equivalent to a break in the network.


Figure 8.21 Fatigue behavior for an acetal polymer at various temperatures. (From Design Handbook for Du Pont Engineering Plastics, used by permission.)


Figure 8.22 A schematic of x-radiography.

Nondestructive Testing (NDT)

0xI I e µ−=


The ultrasonic principle is based on the face that solid materials are good conductors of sound waves.

Ultrasonic (ultrasound) : 주파수를 기준으로 음파보다 높은 주파수의

음파를 초음파 'Ultrasonic' or 'Ultrasound'라 함.

100 101 102 103 104 105 106 107 108

진동

음파

AE(음향방출)

초음파

(Hz)

1, 2.25 , 5(4) , 10 , 15 (MHz)

초음파(Ultrasonic)란?


감쇠 (attenuation) : 초음파가 재질을 통해

진행할 때 일어나는 에너지 손실

산란(scattering)과 흡수(absorption)

가 주 원인으로 작용.

분해능 (resolution) : 근접한 두개의 결함을 감지 할 수 있는 능력.

고 주파수 사용 시 분해능이 좋아짐.

전파력 : 고 주파수를 사용할 경우 전파력이 낮아짐.

파장 (⋋) 감쇠 전파력 분해능

High frequency ↓ 검출거리(↓) ↑ ↓ ↑ (작은결함검출)

Low frequency ↑ 검출거리(↑) ↓ ↑ ↓ (작은결함불리)

초음파 기본이론

http://id.mind.net/%7Ezona/mstm/physics/waves/partsOfAWave/waveParts.htm%23frequency




소리

진동발생 20KHZ 이상이면 초음파 전기

기계

초음파장비에서는 Probe에서

전기적 진동을 기계적 진동으로 변환시켜 준다

초 음 파 = 소리 = 진동 = 주파수 (Hz)

압전효과 [수신] 역압전효과[송신]

Figure 8.23 A schematic of a pulse echo ultrasonic test.


1. 장점

-균열 등 면상결함의 검출능력이 RT보다 탁월하다.

☞고장력강 등 강한 재료일수록 균열에 민감하고,균열에의한 감도저하가 현저하다.

-투과능력이 탁월하다.

-내부결함의 위치,크기,방향을 어느 정도 정확히 측정할 수있다.

-검사결과를 브라운관을 통해 즉시 알 수 있다.

-검사자 또는 주변인에 대해 장해가 없다.

-이동성이 양호하다.

-결함종류의 식별이 극히 곤란하다.

☞결함의 발생위치와 각종 주사방법을 이용한 경우의 에코높이 및 그 형태의 변화와 경험(절단시험이나 가우징에의한 결함의 확인)의 축적에 의해 결함종류의 식별이 가능한 경우도 적지않지만,그것으로도 식별확률은 불충분하다.

-수동검사 시 검사자의 경험을 필요로 한다.

-시험체의 표면 거칠기,형상,두께,내부조직상태에 따라서 검사가 불가능한 경우도 있다.

-결함과 초음파빔의 방향에 따른 영향이 크다.

-초음파의 효과적 전달을 위해 접촉매질이 필요하다.

2. 단점

초음파 시험의 장단점


A wide spectrum of failure

• Ductile fracture • Brittle fracture • Fatigue failure • Corrosion-fatigue failure • Stress corrosion cracking • Wear failure • Liquid-erosion failure • Liquid-metal embrittlement • Hydrogen embrittlement • Creep and stress-rupture failures • Complex failures


• Engineering materials don't reach theoretical strength. • Flaws produce stress concentrations that cause premature failure.

• Sharp corners produce large stress concentrations and premature failure. • Failure type depends on T and stress:

- for noncyclic σ and T < 0.4Tm, failure stress decreases with: - increased maximum flaw size, - decreased T, - increased rate of loading. - for cyclic σ: - cycles to fail decreases as ∆σ increases. - for higher T (T > 0.4Tm): - time to fail decreases as σ or T increases.

SUMMARY

chapter 8: failure analysis and prevention issues to address

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