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8/12/2019 MT-201B Fractrure Fatigue and Creep
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Mechanical Failure
• How do flaws in a material initiate failure?
• How is fracture resistance quantified; how do different
• How do we estimate the stress to fracture?
• How do loading rate, loading history, and temperature
affect the failure stress?
Cyclic loading
from waves: Ship
Cyclic thermal loading:
Computer chip
Cyclic loading due to
walking: Hip implant.
Callister’s Materials Science andEngineering, Adapted Version.
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Fracture mechanisms
• Ductile fracture
– Occurs with plastic deformation
•
– Little or no plastic deformation
– a as rop c
2
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Ductile vs Brittle Failure
Very ModeratelyFracture• Classification:
uc e uc ebehavior:
Adapted from Fig. 8.1,
.
Large Moderate% AR or %EL Small• Ductile
fracture is usually
Ductile:
warning before
fracture
Brittle:
No
warnin
3
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Exam le: Failure of a Pi e
• Ductile failure:--one piece
--large deformation
• Brittle failure:--man ieces
--small deformation
4V.J. Colangelo and F.A. Heiser, Analysis
of Metallurgical Failures (2nd ed.),
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Moderatel Ductile Failure• Evolution to failure:
neckingvoid void growth shearing
fracture
σ
• Resulting 50 mm50 mm
surfaces
steel
particles
serve as voidFrom V.J. Colangelo and F.A. Heiser,
Analysis of Metallurgical Failures (2nd
100 mm
Fracture surface of tire cord wire
loaded in tension. Courtesy of F.
5
nucleation
sites.
. , . . , . ,
Sons, Inc., 1987. (Orig. source: P.
Thornton, J. Mater. Sci., Vol. 6, 1971, pp.
347-56.)
, , ,
OH. Used with permission.
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Ductile vs. Brittle Failure
cup-and-cone fracture brittle fracture
6
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Brittle Failure
failure
7
From Fig. 11.5(a)Callister’s Materials Science and Engineering, Adapted Version.
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Brittle Fracture Surfaces• Inter granular (between grains)
• Intragranular (within grains)
. ee
(metal)
304 S. Steel
(metal))
Al OxidePolypropylene
4mm
ceram cpo ymer .
81mm(Orig. source: K. Friedrick, Fracture 1977, Vol.
3, ICF4, Waterloo, CA, 1977, p. 1119.)
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Stress-Strain Curves
Brittle solids:
Ceramics andDuctile materials:
Metals and Polymers (above
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Ductile and brittle fracture
--fracture in Alfracture in Al
••CeramicsCeramics alonalon withwith somesome ol mersol mers andand metalsmetals(steels(steels atat lowlow temperature)temperature) showshow littlelittle ductilityductility– – failurefailureinin anan unun predictablepredictable brittlebrittle manner manner under under tensiletensile
loadingloading
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Fracture and Flow
propagation of crack: dislocation motion:
lastic flow
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Why metals are tough?
When stress ahead of a crack tip exceeds the metal’s yield
-
blunts the crack tip, and leads to toughness.
σ
y e strengt
x
app e
crack
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Why ceramics are brittle??
Ionic bonding (dislocation movement restricted only to specificplanes due to charge neutrality conditions)
Covalent bonding (high energy required to distort highly
directional bonds)
Dislocation core width is narrower than that in metals
-
Less than five independent and active slip systems
(failure of Von Mises criterion!)
Difficult for a ceramic grain to change its shape by
rotation : strain incompatibilities at grain boundaries
lead to high localised stresses and brittle fracture!!
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Ideal vs Real Materials
• Stress-strain behavior (Room T):
TS << TSengineering
materials
perfect
materials
σE/10 perfect mat’l-no flaws
carefull roduced lass fiber
E/100
typical ceramic typical strengthened metal
ε0.1
• Reprinted w/...-- the longer the wire, the
smaller the load for failure.
permission from R.W.
Hertzberg,
"Deformation and
Fracture Mechanics
of En ineerin
• Reasons:
-- flaws cause premature failure.
--
Materials", (4th ed.)
Fig. 7.4. John Wiley
and Sons, Inc., 1996.
15
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Flaws are Stress Concentrators!
Results from crack propagation
• Griffith Crack
/ 21
ot
t
om Ka
σ=⎟⎟⎜⎜ ρσ=σ 2
where
ρt = radius of curvature
σo = applied stressσm = stress at crack tip
16
From Fig. 11.8(a)
Callister’s Materials Science and Engineering, Adapted Version.
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Concentration of Stress at Crack Ti
17
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En ineerin Fracture Desi n
• Avoid sharp corners!
Stress Conc. Factor, K tmax
σo
=
w.
r , h
max
increasing w/h2.0filletradius
1.5 Adapted from Fig.
8.2W(c), Callister 6e.
(Fig. 8.2W(c) is from G.H.
r /h0 0.5 1.0
1.0, . .
(NY), Vol. 14, pp. 82-87
1943.)
18
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Crack Pro a ation
Cracks propagate due to sharpness of crack tip
• A plastic material deforms at the tip, “blunting” the
crack.deformed
region
• Elastic strain energy-
• ener stored in material as it is elasticall deformed
• this energy is released when the crack propagates
• creation of new surfaces requires energy
19
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Griffith Theory of Brittle Fractureσ Energy criterion
•Increase in surface ener associated
with crack : Us = 4cγs
2c
energy: Uel = σ 2π c2 /2E
σ
Overall system energy U= Us- Uel
For the spontaneous crack extension above a critical crack length22
⎞⎛ cd dU π σ
2=
⎠⎝ −=
E dcdc s
2/1
⎠⎝ = c
s
f π σ
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When Does a Crack Pro a ate?
Crack propagates if above critical stress
2/1
2 ⎞⎛ E sγ i.e., σm > σc
⎠⎝ cc
π or Kt > Kc
– E = modulus of elasticity
– =s
– c = one half length of internal crack
– Kc = σc/σ0
For ductile => replace γs by γs + γp
21
whereγp
is plastic deformation energy
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Crack opening in different mode of loading geometries
Cracks in engineering components loaded in one of three ways (or a
combination of all three):
Mode I is the most dan erous since the K-factor is much
mode I mode II mode III
larger in mode-I than in other modes of crack opening as
the tensile stress tries to open up the crack more severely.
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Measurement of K
Long crack fracture toughness measurement :
SENB
Short crack fracture toughness measurement :
Indentation tests
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Single Edge Notched Beam test (SENB)
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Indentation Microfracture method
KIc
= 0.016 (E/H)1/2P/c3/2 (Anstis’s formula)
. . ,(K
Ic) can be computed from the expression given by Niihara et al.:
( K ϕ /H a1/2)*(H/Eϕ)2/5 = 0.035(l/a)-1/2ϕ ϕ
Where ϕ = 3 and l= Plamqvist crack length =c-a
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Indentation Microfracture method
For median cracks (c/a ≥2.5), the corresponding expression is
ϕ ϕ -Icϕ ϕ = .
Shett at el.163 modified the e uation of Niihara et al.
KIc = 0.025(E/H)0.4
(HW)1/2
where W= P/4a (P the indentation load, 2a the Vickers diagonal).
I d i h i B di
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Indentation strength in Bending
K = η(E/H)1/8(σP1/3)3/4
Chantikul’s formula
where η= 0.59
and σ the failure
.
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Fracture Tou hnessGraphite/Ceramics/Semicond
Metals/ Alloys
Composites/fibers
Polymers
100
Ti alloys
Steels- ers
40
506070
Based on data in Table B5,Callister’s Materials Science and
Engineering, Adapted Version. 0 . 5 ) Mg alloys
20
30
Al/Al oxide(sf) 2
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.,
a ·10
Diamond7
C/C( fibers) 1 Al oxid/SiC(w) 3
Al oxid/ZrO 2(p)4
Si nitr/SiC(w) 5
Y2O3/ZrO 2(p)4
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
5
I c ( M
car e
4
3PVC
PP
PET Al oxideSi nitride
Glass/SiC(w)
. . - .
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.
PC2
29
6. (20vol%) F.D. Gace et al., Ceram. Eng. Sci.
Proc., Vol. 7 (1986) pp. 978-82.Si crystal
Glass -sodaConcrete
Glass
0.50.7
<111>
Polyester
PS
0.6
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Desi n A ainst Crack Growth
• Crack growth condition:
• Largest, most stressed cracks grow first!
c = aπσ
--Result 1: Max. flaw size
dictates design stress.
--Result 2: Design stress
dictates max. flaw size.
cdesign
aYKπ
<σ
2
1⎟⎟ ⎞⎜⎜⎛
σπ<
desi n
cmax
YKa
σ amax
no
fracture
no
fracture
30
max
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Desi n Exam le: Aircraft Win
• Material has Kc = 26 MPa-m0.5
...
Design A
--largest flaw is 9 mm
Design B
--use same material--failure stress = 112 MPa --largest flaw is 4 mm
--failure stress = ?
• Use...cK
=σ
• Key point: Y and Kc are the same in both designs.max
aY π
σ a = σ a
9 mm112 MPa 4 mm-- esu :
Answer: MPa168)( B =σc
A B
31
• Reducing flaw size pays off!
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Loadin Rate
• Increased loadin rate... • Wh ? An increased rate
-- increases σy and TS
-- decreases %EL
gives less time for
dislocations to move pasto s ac es.
σ
σy larger
TSsmaller
ε
ε
σy
32
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Im act Testin
• Impact loading: (Charpy)
-- makes material more brittle
-- decreases toughness
Adapted from Fig. 11.12(b),
Callister’s Materials Science and
Engineering, Adapted Version.
(Fig. 11.12(b) is adapted fromH.W. Hayden, W.G. Moffatt, and
J. Wulff, The Structure and
Pro erties of Materials, Vol. III,
Mechanical Behavior , John Wiley
and Sons, Inc. (1965) p. 13.)
final height initial height
33
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Tem erature
• Increasing temperature...--increases %EL and K
• Ductile-to-Brittle Transition Temperature (DBTT)...
° y
FCC metals (e.g., Cu, Ni)
. .,
t E n e
r
polymers
More DuctileBrittle
I m p a
High strength materials (σy > E/150)
Temperature
Ductile-to-brittle
. .Callister’s Materials Science
and Engineering,
Adapted Version.
34
rans on empera ure
D i St t
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Design Strategy:
• re- : e an c • : er y s ps
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,
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,The Discovery of the Titanic.) "Behavior of Engineering Structures", Nat. Acad. Sci.,
Nat. Res. Council, John Wiley and Sons, Inc., NY,
1957.)
35
.
F ti
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Fatigue
• Fatigue = failure under cyclic stress.Ex: Rotating shafts, connecting rods, aircraft wings and leaf
spr ngs e c. . . ,
Callister’s Materials
Science and Engineering,
Adapted Version.
compression on top
motor
specimen
g. . s rom
Materials Science in
Engineering, 4/E by Carl.
A. Keyser, Pearson
Education, Inc., U ertension on bottom
flex coupling
ear ng ear ng
• tress var es w t t me.-- key parameters are S, σm, and σmax
σmS
Saddle River, NJ.)
σmin time
• Key points: Fatigue...--can cause part failure, even though σmax < σc.
-- ~
36
.
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Fati ue
• Fatigue = failure under cyclic stress.
. . ,
Callister’s Materials
Science and Engineering,
Adapted Version.
compression on top
counter motor
specimen
bearing bearingg. . s rom
Materials Science in
Engineering, 4/E by Carl.
A. Keyser, Pearson
Education, Inc., U er
tension on bottom
flex coupling
• tress var es w t t me.-- key parameters are S, σm, and σmax
σmS
Saddle River, NJ.)
σmin time
• Key points: Fatigue...--can cause part failure, even though σmax < σc.
-- ~
37
.
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Fati ue Desi n Parameters
• Fatigue limit, Sfat: case forS = stress amplitude
-- fat
Sfat
s ee yp.unsa e
From Fig. 11.19(a),
Callister’s MSE
Adapted Version.10
310
510
710
9
• Sometimes, theS = stress am litude
Al (typ.)unsafe
From Fig. 11.19(b),
Callister’s MSE
Adapted Version.
safe
38N = Cycles to failure
10 10 10 10
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Fati ue Mechanism
• Crack grows incrementally
.
a~ σΔ
( )mK
dN
daΔ=
increase in crack length per loading cycle
crack ori in• a e ro a ng s a
--crack grew even though
--crack grows faster as• σ increases From Fig. 11.21,
’• crac ge s onger
• loading freq. increases.
Science and
Engineering, Adapted
Version.
(Fig. 11.21 is from D.J.
39
u p , n ers an ng
How Components Fail,
American Society forMetals, Materials Park,
OH, 1985.)
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Im rovin Fati ue Life
1. Impose a compressive S = stress amplitudeFrom Fig. 11.24,
Callister’s Materials
Science and
(to suppress surface
cracks from growing) moderate tensile σm
near zero or compressive σmIncreasing
σm
ng neer ng, ap e
Version.
N = Cycles to failure
-- e o : s o peen ng
putsurface
shot
-- e o : car ur z ng
C-rich gas
intocompression
2. Remove stress
concentrators. From Fig. 11.25,
bad better
40
a s er s a er a s
Science and
Engineering, AdaptedVersion.
bad better
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Cree
Sample deformation at a constant stress (σ) vs. time
σ
,
0 t
s g emp. e orma on . m; (Tm is MP in K)
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Cree
• Occurs at elevated temperature, T > 0.4 Tm
tertiary
elastic
secondary
rom gs. . ,
Callister’s Materials
Science and Engineering, Adapted Version.
C
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Creep
Primary Creep: slope (creep rate) decreases with time.Secondary Creep: steady-state i.e., constant slope.
, . . .
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Secondar Cree
• Strain rate is constant at a given T, σ-- strain hardening is balanced by recovery
stress exponent (material parameter)
strain rateactivation energy for creep(material parameter)⎟ ⎠⎜⎝ −σ=ε RT
QK
cn
s exp2&
applied stressmaterial const.
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• ,
100
427°C
538°C
20
40
649°C
10-2 10-1 1Steady state creep rate (%/1000hr)
From Fig. 11.31, Callister’s Materials Science and Engineering, Adapted Version.
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C F il
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Cree Failure• Failure:
along grain boundaries.
g.b. cavities
stress
From V.J. Colangelo and F.A. Heiser, Analysis ofMetallurgical Failures (2nd ed.), Fig. 4.32, p. 87, John
Wiley and Sons, Inc., 1987. (Orig. source: Pergamon
LtT =+ lo20
• Time to rupture, tr
Press, Inc.)
function of
a lied stresstemperature
time to failure (rupture)
C F il
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Cree Failure
• Estimate rupture timeS-590 Iron, T = 800°C, σ = 20 ksi
From Fig. 11.32,
Callister’s Materials
Science and
En ineerin Ada ted i
100
Version.
(Fig. 11.32 is from F.R.
Larson and J. Miller, t r e s s ,
k s
10
20
. , ,
(1952).)
112 20 24 2816
data for
S-590 Iron
LtT =+ lo20
24x103 K-log hr L(103K-log hr)
1073K
ns: tr = r
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Dr. Anandh, IITK
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Dr. Anandh, IITK
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Dr. Anandh, IITK
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Dr. Anandh, IITK
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• Engineering materials don't reach theoretical strength.
• Flaws produce stress concentrations that cause
premature failure.
• arp corners pro uce arge s ress concen ra ons
and premature failure.
•
- for noncyclic σ and T < 0.4Tm, failure stress decreases with:
- increased maximum flaw size
- decreased T,
- increased rate of loading.
-- cycles to fail decreases as Δσ increases.
- for higher T (T > 0.4Tm):
- time to fail decreases as σ or T increases.