4102- Chap 3 FM Design.pdf

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FATIGUE & FRACTURE

MAAE 4102

ro essor . e

Department of Mechanical & AerospaceEngineering

ell

Chapter 3 - Fracture Mechanics inDesign

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Department of Mechanical & Aerospace Engineering

ap er


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aC K K I IC

Design of large complex structures using fracture mechanicsusually means that an attempt is made to minimize fabricationdiscontinuities which are initiation sites for failures caused

y r tt e racture, at gue, stress corros on crac ng etc.

To use fracture mechanics in design the basic equation

is required.

Therefore the material toughness K IC must be known.This material property is measured by laboratory testing.


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Consider the stress equation in the y direction

and for

r

K

s

I y

0

21

0

2cos2

StressPlaneK

r ys

I y

2

2

1

Irwin suggested that for PlaneStrain the yield stress in tensionis increased by a factor of 3

StrainPlaneK

r ys

I y

2

61


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IC

crack extension occurs.

Temperature

IC epen s on:

Strain rateCorrosive environment

cons ra n .

ASTM S ec. E399-83


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C IC aC K PropertyMaterial

E-399-83 is very restrictive with respect to specimen sizerequirements in order to obtain elastic plane strain behaviour

This limits the K IC approach to: Brittle materials

Low testing temp belowservice tempVery high strain rates

field elasticanIn

yr

2sin2sin12cos2


7

ys y


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2

1 I K

ICI K K yinstabilitAt

2

ys y

21

sizezone plasticLimiting

ys

IC y

K r

This is under PLANE STRESSUnder PLANE STAIN conditions

2

( 6

ys IC

StrainPlane yr


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1. Determine specimen

2. Select specimen1. Three point bend specimen

. 3. Arc shaped specimen4. Disc shaped specimen


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Disc S ecimen

C Specimen


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3. Fati ue crack the

specimen K f < 0.6 K Q


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.

1. Loading2. Test record

.


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5. P - Analysis

. s a s Q


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5. P - Analysis

. s a s Q


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7. Calculate K Q for a bend specimen

2

92

72

52

32

1

23 7.386.378.216.49.2 w

awa

wa

wa

wa

BW

S PK

QQ

8. Check the ASTM restrict ions on a, B and W

len thcrack5.2

2

IC K a

hicknessSpecimen t 5.2

2

IC

ys

K B

idthSpecimen w 0.5

2 IC

ys

K W


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ys


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9. Then K = K

10. KQ can be calculated for each

aS PQ W BW 2

3Q

W a f

BW Q

21QK SpecimenTensionCompact


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Exam le of K Test


High Strength Aluminum


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BK IC 2 5

2

.

es pec menDimensions

n mumRequired B

Material and Fig F YS(ksi)

FT

(ksi)B(in

a(in)

W(in)

P5(lb)

Pmax(lb)

PQ(lb)

K Q(ksi %in)

K IC(ksi %in

YS

7001-T75very high

strength Al -

70.6 80.5 1.37 1.08 2.00 3,140 3,150 3,150 19.9 19.8Valid

0.2

Fig 5.11

18 Ni maragingsteel - Fig 5.10

190.0 196.0 1.24 0.95 3.50 22,950 22,950 22,950 113.0 113.0Valid

0.88


183.0 191.0 1.00 0.46 3.00 55,000 80,150 55,000 143.0 Invalid 3.2

A517 steelFig 5.13

110.0 121.0 2.00 2.60 6.00 47,800 66,000 47,800 150.0 Invalid 2.5


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18 Ni maraging Steel


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BK IC 2 5

2

.


n mumRequired B


FT

(ksi)B(in

a(in)

W(in)

P5(lb)

Pmax(lb)

PQ(lb)

K Q(ksi %in)

K IC(ksi %in

YS

7001-T75very high

strength Al -

70.6 80.5 1.37 1.08 2.00 3,140 3,150 3,150 19.9 19.8Valid

0.2

Fig 5.11


190.0 196.0 1.24 0.95 3.50 22,950 22,950 22,950 113.0 113.0Valid

0.88


183.0 191.0 1.00 0.46 3.00 55,000 80,150 55,000 143.0 Invalid 3.2

A517 steelFig 5.13

110.0 121.0 2.00 2.60 6.00 47,800 66,000 47,800 150.0 Invalid 2.5


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BK IC 2 5

2

.


n mumRequired B


FT

(ksi)B(in

a(in)

W(in)

P5(lb)

Pmax(lb)

PQ(lb)

K Q(ksi %in)

K IC(ksi %in

YS

7001-T75very high

strength Al -

70.6 80.5 1.37 1.08 2.00 3,140 3,150 3,150 19.9 19.8Valid

0.2

Fig 5.11


190.0 196.0 1.24 0.95 3.50 22,950 22,950 22,950 113.0 113.0Valid

0.88


183.0 191.0 1.00 0.46 3.00 55,000 80,150 55,000 143.0 Invalid 3.2

A517 steelFig 5.13

110.0 121.0 2.00 2.60 6.00 47,800 66,000 47,800 150.0 Invalid 2.5

Chapter 3 - Fracture Mechanics inDesign 23


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Exam le of K Test


A517 Steel



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BK IC 2 5

2

.


n mumRequired B


FT

(ksi)B(in

a(in)

W(in)

P5(lb)

Pmax(lb)

PQ(lb)

K Q(ksi %in)

K IC(ksi %in

YS

7001-T75very high

strength Al -

70.6 80.5 1.37 1.08 2.00 3,140 3,150 3,150 19.9 19.8Valid

0.2

Fig 5.11


190.0 196.0 1.24 0.95 3.50 22,950 22,950 22,950 113.0 113.0Valid

0.88


183.0 191.0 1.00 0.46 3.00 55,000 80,150 55,000 143.0 Invalid 3.2

A517 steelFig 5.13

110.0 121.0 2.00 2.60 6.00 47,800 66,000 47,800 150.0 Invalid 2.5



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Constraint Temperature



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Loading Rate



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Goal: To provide safe, fracture resistant structures

Traditional Approach

MaterialDesign stress level

Codes

Involves:Detailing members so that design stress is exceeded

Assumes:Perfect fabrication no flaws



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Fracture Mechanics A roach

Selection of Material given

Discontinuities exist from:Fabrication

Cyclic loadingress corros on crac ng

Some level of notch toughness is desirable

Fracture Mechanics makes this method more quantitative



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We must accept that flaws exist :

We will confine ourselves to LEFM to:Design fracture resistant structures to prevent bri ttle fractureFortunately most materials behave in non plane strain at service

HOWEVERWhen designs become more complex

g s reng or c sec ons are use n p ace o r ve esectionsFabrication and construction become more complexLoading levels increase

The probability of britt le fracture in large complex structuresincrease



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aC K C IC

2

sizeflawCritical

factor geometrycrackC

C a IC c

IC

Select probable flaw type.

Determine the stress vs flaw size curve



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factor safetyaincludeTo

2

IC Design I K

To minimize the possibility of

3 primary factorsMaterial toughnessNormal stress

Flaw size in structu re(inspection

Other factors such as

Loading rateResidual stress

These only effect the primary


ac ors


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sizecrackCritical

2

indexanasthischooseCanYS

IC c

K a

How high must this be to ensureSatisfactory performance

Type of structureFre uenc of ins ection

Choice depends on:Consequences of failureRedundancy of load paths

Access for inspectionQuality of inspectionDesi n for ins ection

Probability of overloadFabrication costsMaterial costs



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Critical Crack Size as a Function of


Yield Strength and Toughnesscrack icknessThrou h th

Critical Flaw Size, 2a (in.)

(actual design stress level, ksi,is shown in parenthesis)

ss AssumedICK

platewideain design a

(ksi) K IcIc Values(ksi %%in.) = 100% ysys = 75% ysys = 50% ysys = 25% ysys

260 80 0.06(260) 0.11(195) 0.24(130) 0.96(65)

220 110 0.16(220) 0.28(165) 0.64(110) 2.55(55)

(ksi %%in.)

80

2

1

design

IC K a

180 140 0.39(180) 0.68(135) 1.54(90) 6.16(45)

180 220 0.95(180) 1.69(135) 3.80(90) 15.22(45)

140 260 2.20(140) 3.90(105) 8.78(70) 35.13(35)

2

22

design

IC K a

110 170 1.52(110) 2.70(82.5) 6.08(55) 24.33(27.5)

80 200 3.98(80) 7.07(60) 15.92(40) 63.66(20)

40 100 3.98(40 7.07(30) 15.92(20) 63.66(10)



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K

Brittle Fracture



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-


Construction of a 3 ft. diameter pressure vesselOperating pressure 2000 psi.Material

Fracture toughness 60 ksi inYield strength 85 ksi at the operating temp

Wall thickness 0.75 in.

Design requirement Leak before breakPeriodic inspection The technique can reliably detect acrack with a surface length of > 0.5 in.Will the vessel leak before burst when the surface lengtho e crac s sma er an s s zeWhat is the largest crack which can develop and sti llmaintain the leak before burst criterion?



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f h i l &


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-


in.0.75aof crackafor

criteria burst beforeleakFor

K K IC

75.00.48

12.1Q

a

K IC

982.1

.

Q

Q

40.0

found becantlength thasurfacethe

.an.org.es ngY

a

Therefore a surface crack of length1.875 in.

875.12938.04.02

75.0

cand c

c

c r sma er w ensure a e vesse wLeak before break.

Also the vessel will not fail catastrophically


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. . .

D t t f M h i l &


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In 1974 water leaked from the primary transpor t system into thegas annulusThe Zircaloy-2 tubes were removed and it was found that the


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ea was n e area o e ro e o n


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Department of Mechanical &


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The stainless steel end fitting was

in the area of high residual stress

Hydrogen, normally in the pressuretubes had migrated to the area ofhi h residual stress and a smallcrack initiatedPropagation was by fracture of thehydrides which are brittle whencoldOnce initiated the crack proceed togrow through the wall thickness byrepeated formation and fracture ofthe hydrides when the system was

When the system was hot thehydrogen was in solution and crackgrowth did no proceed


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The cause of the rolling problem was

into the tapered section of the end fitting

The residual stress reached levels of 700MPa

MPaFuel channel safety was not significantlyeffected because of the leak-before-breakcriterionCracks were about 15-20 mm (0.6-0.8in.) in surface length and were confined toa very small regionThe crack len ths were si nificantl less

than the critical crack length of about 3 in.The leak-before-break criterion was welldemonstrated


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-

p Aerospace Engineering

Tube diameter of 100 mmOperating pressure 11.3 MPa.Material - Zr-2-2.5Nb

Fracture toughness 60 MPa mYield strength 433 MPa at the operating temp of 280 oC

Wall thickness 4 mm.Design requirement Leak before breakInclude a safety factor of 3What is the critical crack len th CCL


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-

p Aerospace Engineering

433.55 MPam MPaK Y IC

.4

.502

3.11

mmt

mmr MPa p

12.11

K

in tension plateaincrackThumbnail

I

a

tr thinisVessel

aand condependsand factorshapetheisQ

33.0141

ratioStress

1414

.

StressHoop

MPat


48

Y



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-

Aerospace Engineering

K K IC mm.4aof crackafor

criteria burst beforeleakFor

Q

aK

IC

004.014155

12.1

Q

Q

936.0

.3

a 08.0

found becanlengthsurfacethe

.an.org.es ngY

Therefore a surface crack of length 50 mm.

mmceimc

c

c

502..05.02

208.0

004.0r sma er w ensure a e vesse w

Leak before break.The CCL is ~ 50 mm


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J.M. Barsom and S.T. Rolfe, Fatigue & Fracture Control in Structures,Prentice Hall, 1987.

P.A. Ross-Ross, The Investigation into the Cracking of Pressure Tubes inPickering Units 3 and4, From Steam to Space, CSME 1996.

Standard Method for Plane-Strain Fracture Toughness of MetallicMaterials. ASTM Specification E-399-83

Chapter 3- Fracture Mechanics inDesign

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4102- Chap 3 FM Design.pdf

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