4102- Chap 3 FM Design.pdf
Transcript of 4102- Chap 3 FM Design.pdf
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FATIGUE & FRACTURE
MAAE 4102
ro essor . e
Department of Mechanical & AerospaceEngineering
ell
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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
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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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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
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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
12 Ni maragingsteel - Fig 5.12
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
.
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
12 Ni maragingsteel - Fig 5.12
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
.
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
12 Ni maragingsteel - Fig 5.12
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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Exam le of K Test
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A517 Steel
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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
12 Ni maragingsteel - Fig 5.12
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
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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
Department of Mechanical & Aerospace Engineering
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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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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. . .
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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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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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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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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
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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
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