Fracture and Fatigue
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Transcript of Fracture and Fatigue
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1Fracture and fatigueKey point:
Preexisting surface flaws and preexisting internal cracks play a central role in the failure of materials.
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?
ISSUES TO ADDRESS...
Fracture mechanisms
Ductile fracture Occurs with plastic deformation and with high energy
absorption before fracture
Brittle fracture Little or no plastic deformation with low energy
absorption Catastrophic
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2An oil tanker that fractured in a brittle manner by crack propagation around its girth
Ductile vs Brittle Failure
Very Ductile Moderately Ductile BrittleFracture behavior
Large Moderate%AR or %EL Small
Classification:
Ductile fracture is usually desirable! Ductile: warning before fracture Brittle: no warning
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3 Ductile failure:--one piece--large deformation
Figures from V.J. Colangelo and F.A. Heiser, Analysis of Metallurgical Failures(2nd ed.), Fig. 4.1(a) and (b), p. 66 John Wiley and Sons, Inc., 1987. Used with permission.
Example: Failure of a Pipe
Brittle failure:--many pieces--small deformation
Evolution to failure:
Resultingfracturesurfaces(steel)
50 mm
particlesserve as voidnucleationsites.
50 mm
From V.J. Colangelo and F.A. Heiser, Analysis of Metallurgical Failures (2nd ed.), Fig. 11.28, p. 294, John Wiley and Sons, Inc., 1987. (Orig. source: P. Thornton, J. Mater. Sci., Vol. 6, 1971, pp. 347-56.)
100 mmFracture surface of tire cord wire loaded in tension. Courtesy of F. Roehrig, CC Technologies, Dublin, OH. Used with permission.
Moderately Ductile Failure
neckings
void nucleation
void growth and linkage
shearing at surface fracture
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4Ductile vs. Brittle Failure
Adapted from Fig. 8.3, Callister 7e.
cup-and-cone fracture brittle fracture
Fractured aluminium alloy I, with a dimpled texture Fractured aluminium alloy II, with a typical cleavage texture
Fractured tensile test bars
Cup and cone
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5Scanning electron micrographs (a) spherical dimples characteristic of ductile fracture, (b) parabolic-shaped dimples characteristic of ductile fracture.
Brittle Failure
Arrows indicate origin of crack
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6Transgranular fracture Intergranular fracture
Brittle Failure
Flaws are Stress Concentrators or stress raisers
Results from crack propagation Griffith Crack
where rt = radius of curvature of the crack tipso = applied stresssm = stress at crack tip
Kt : stress concentration factor
ot
/
tom K
as=
r
s=s
21
2
rt
Principles of fracture mechanics
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7Concentration of Stress at Crack Tip
Adapted from Fig. 8.8(b), Callister 7e.
Engineering Fracture Design
r/hsharper fillet radius
increasing w/h
0 0.5 1.01.0
1.5
2.0
2.5
Stress Conc. Factor, K ts
maxs
o=
Avoid sharp corners!s
Adapted from Fig. 8.2W(c), Callister 6e.(Fig. 8.2W(c) is from G.H. Neugebauer, Prod. Eng.(NY), Vol. 14, pp. 82-87 1943.)
r , fillet
radius
w
h
o
smax
ot
/
tom K
as=
r
s=s
21
2
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8Crack Propagation
Cracks propagate due to sharpness of crack tip A plastic material deforms at the tip, blunting the crack.
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
plasticbittle
Deformed region
When Does a Crack Propagate?
Critical stress for crack propagates in a brittle material
where E = modulus of elasticity gs = specific surface energy a = one half length of internal crack Kc = sc/s0
For ductile => replace gs by gs + gpwhere gp is plastic deformation energy
212 /sc a
E
pg
=si.e., sm > sc
or Kt > Kc
Example problem 8.1, p217
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9Fracture toughness
KC: fracture toughnessthe critical (c) value of the stress intensity factor at a crack tip necessary to produce failure
KC = Ysc ( a)1/2
1. Y: geometry factor, on the order of 12. sc the overall applied stress at failure3. a: the length of a surface crack (one-half the
length of an internal crack)4. Unit of KIC: MPa m1/2
p
a
a
Critical stress for crack propagation (sc) and crack length (a)
The three modes of crack surface displacement
(a) mode I, opening or tensile modeplane strain fracture toughness
(b) mode II, sliding mode(c) mode III, tearing mode
KIC = Ysc ( a)1/2p
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10
Room-temperature mechanical properties for selected engineering materials
Fracture ToughnessGraphite/ Ceramics/ Semicond
Metals/ Alloys
Composites/ fibersPolymers
5
KIc
(MPa
m
0.5 )
1
Mg alloysAl alloys
Ti alloysSteels
Si crystalGlass -sodaConcrete
Si carbide
PC
Glass 6
0.5
0.7
2
43
10
20
30
Diamond
PVCPP
Polyester
PS
PET
C-C(|| fibers) 1
0.6
67
40506070
100
Al oxideSi nitride
C/C( fibers) 1
Al/Al oxide(sf) 2
Al oxid/SiC(w) 3Al oxid/ZrO 2(p)4Si nitr/SiC(w) 5
Glass/SiC(w) 6
Y2O3/ZrO 2(p)4
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11
Crack growth condition:
Largest, most stressed cracks grow first!
Design Against Crack Growth
K Kc = aY ps
--Result 1: Max. flaw sizedictates design stress.
max
cdesign
aYKp
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12
Loading Rate Increased loading rate...
-- increases sy and TS-- decreases %EL
Why? An increased rategives less time for dislocations to move past obstacles.
s
e
sy
sy
TS
TS
largere
smallere
Charpy test of impact energy
1. A notched specimen stress concentrating
2. Loading applied rapidly3. impact energy - the energy
necessary to fracture the test specimen
The swinging pendulumThe intial height hThe final height h
Impact fracture testing
Izod test
Charpy test
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13
1040 carbon steel: Fe-0.4C-0.75 MnJ: joule. 1J = 1N m
Cu: fcc, ductileMg alloy: hcp, relatively brittle
Toughness = , the area under the s - ecurve esd
Fracture
Unit of toughness: N/m2Or (N/m2) (mm / mm) = N m / (mm)3
Toughness: the energy necessary to fracture per unit volume of material
Toughness obtained in a tensile test
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14
Temperature dependence of the Charpy V-notch inpact energy and shear fracture for an A283 steel.
Schematic curves for the three general types of impact energy-versus-temperature behavior
More DuctileBrittle
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15
Ductile-to-Brittle Transtion Temperature (DBTT)
1. in bcc alloys2. an abrupt drop in ductility and toughness as the temperature is lowered
Plain-carbon steels with various carbon levels
Fe-Mn-0.05C alloys with various manganese levels
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!
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16
Fatique
Fatique = failure under cyclic stress failure after N cycles load < T.S
Fatique-testing apparatusfor making rotating-bending tests
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17
Stress varies with time.-- key parameters are S, sm, and frequency
smax
smin
s
time
smS
Key points: Fatigue...--can cause part failure, even though smax < sc.--causes ~ 90% of mechanical engineering failures.
Random stress cycle.
S = stress amplitude, sm= mean stress,sm = (smax + smin)/2S = (smax smin)/2Load ratio R = smin/smax
Typical fatique curve (S-N curve)
or fatigue strength
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18
Fatigue limit, Sfat:--no fatigue if S < Sfat
Fatigue Design Parameters
Sfat
case for steel (typ.)
N = Cycles to failure103 105 107 109
unsafe
safe
S = stress amplitude
Sometimes, thefatigue limit is zero! (a
material does not display a fatique limit)
Adapted from Fig. 8.19(b), Callister 7e.
case for Al (typ.)
N = Cycles to failure103 105 107 109
unsafe
safe
S = stress amplitude
Fatique S-N probability of failure curves for a 7075-T6 Al alloy
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19
Crack grows incrementallytyp. 1 to 6
( ) a~ sDincrease in crack length per loading cycle
Failed rotating shaft--crack grew even though
Kmax < Kc--crack grows faster as
Ds increases crack gets longer loading freq. increases.
crack origin
Fatigue Mechanism
( )mKdNda
D=
Texture of the fatigue fracture surface clamshell or beachmark texture
Intrusions and extrusions. SEM.
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20
Transmission electron fractograph showing fatique striations in aluminumEach striationis thougth to represent the advance distance of a crack front during a single load cycle, striation width deponds on and incearses with increasing stress range.
Improving Fatigue Life
2. Impose a compressive surface stress (to suppress surface cracks from growing)
--Method 1: shot peening
put surface
into compression
shot--Method 2: carburizing
C-rich gas
3. Remove stress concentrators.bad
bad
better
better
1. Decrease the mean stress level
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21
Engineering materials don't reach theoretical strength. Flaws produce stress concentrations that cause
premature failure.
Sharp corners produce large stress concentrationsand premature failure.
Failure type depends on T and stress:- for noncyclic s and T < 0.4Tm, failure stress decreases with:
- increased maximum flaw size,- decreased T,- increased rate of loading.
- for cyclic s:- cycles to fail decreases as Ds increases.
- for higher T (T > 0.4Tm):- time to fail decreases as s or T increases.
SUMMARY
Homework 8.6 and 8.12, p246