19 charpy (1)
TRANSCRIPT
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ASE324L: Aerospace Materials Laboratory
Lecture 19-20: Fracture Energy and Charpy Impact Test
Rui Huang
Dept of Aerospace Engineering and Engineering Mechanics
The University of Texas at Austin
Fall 2012
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Fracture toughness test
Quantitative measurements of fracture toughness
Quasi-static loading (displacement control)
Room temperature Uniaxial tensile stress (mode I)
How about failure under dynamic loading, low temperatures,and triaxial stresses?
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Charpy impact test
Qualitative measurement offracture energy Different temperatures
High strain rate
Triaxial stress at the notch
Anvil
Starts at h1
Stops at h2
Loss in potential energy goes to:
Surface energy
Plastic dissipation
Kinetic energy
h2
h1
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Ductile-to-brittle transition
The measured impact
energy decreases with
decreasing temperature.
For steels, the impact
energy drops remarkably
over a narrow temperature
range, indicating a ductile-
to-brittle transitionphenomenon.
brittle
ductile
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Transition temperature Temperature at specific
impact energy (e.g., 15 ft-lbor 20 J).
Temperature correspondingto some given fracturesurface character (e.g., 50%
shear fracture).
No unified criterion!
Used to qualitatively rank
the materials (simple butdirty test)
Design philosophy: the service temperature should be greater
than the transition temperature.
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Energy dissipation
Energy loss of the pendulum goes to:
Surface energy (cleavage)
Plastic deformation (shear) Kinetic energy
Embrittlement: plastic deformation issuppressed at low temperature, high
strain rate, and triaxial stress state at the
notch.
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Specimen thickness effects
The transition temperature increases with increasing specimen thickness.
Plane-stress/plane-strain transition.
Laboratory results may not be directly used for design components!
To overcome this difficulty, use dynamic tear (DT) test and drop-weight teartest (DWTT).
Sample thickness
Transition
temperature
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Energy approach in fracture mechanics
Elastic deformation: strain energy (recoverable)
Plastic deformation: energy dissipation
Crack opening: surface energy
Energy release rate vs fracture resistance:
fracture releases elastic strain energy but
dissipates energy by cleavage (bond breaking)and plastic deformation
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Linear elastic strain energy
The bar acts like an elastic spring, storing and releasing
energy upon loading and unloading.
P
LEA
EALPPWU
2221
22
====
P
Strain energy density:
22
22 E
EAL
Uu ===
Static load, no dynamic or inertia effects.
Work done by the load equals the strain
energy stored in the bar (energy
conservation).
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Plastic energy dissipation
Plastic deformation dissipates energy, i.e., the energy that
is not recovered due to permanent deformation.
P
P
PE UUPdWU +===
0
PU EU
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Energy Release Rate
Reference state: VE
U2
2
0
= Opening a crack: ta
EUE
22
2~
Fixed grips during crack opening: no work done to the specimen.
Crack relaxes elastic energy, but increases surface energy andplastic energy dissipation.
Energy release rate: reduction of elastic
energy per unit area of crack growth
E
ag
A
UG E
2=
=
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Fracture condition
For the crack to grow: G
2g
Eaa c
=> or
ga
Ec
2
=>
Driving force: reduction of elastic energy (Energy release rate G)
Resistance: energy dissipation per unit area of crack growth
(including surface energy and plastic energy): .
is considered to be a material property, also called toughness, or
critical energy release rate.
E
agG
2=
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Effect of plastic deformation
For brittle materials (such as glass or ceramics), plastic
deformation is negligible, thus 2.
For ductile materials (e.g., steels), plastic energy
dissipation dominates. Plane strain vs plane stress
Typical values of : Glass: ~ 1-10 J/m2
Epoxy: ~ 30 J/m2
Aluminum: ~ 8-30 kJ/m2
Steels: ~ 100 kJ/m2
pu+= 2
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Griffiths experiment: a revisit
a
Kcf
=
2a
cKK=aK =
EaG
2
= =Ga
Ef
=
Both fracture criteria give the same dependence of the critical stress
on the crack length.
E
KG
2
=E
Kc2
=Irwins relation:
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Example: double cantilever beam (DCB)
P
Pc
2H
Deflection of a cantilever beam of length c:EI
Pc
3
3
=
Elastic strain energy in DCB:EI
cPPU32
1232
==
Energy release rate:23
22
4
23 12
4
3
BEH
cP
c
EH
A
UG =
=
=
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DCB: stability of crack growth
P
Pc
2H23
22
4
2312
4
3
BEH
cP
c
EHG =
=
G
c0
c1 c2
1
2 > 1
Displacement control:
stable growthG
c0
P1P2 > P1
c1
Load
control:
unstable
growth
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Measure compliance to determine G
PAC
=)(Determine compliance from load-displacement curve
Elastic strain energy:)(22
1 2
ACPU
==
a
C
b
P
A
C
CA
UG
=
=
=
22
2
2
2Energy release rate:
P
a1
a3
a2C
aa
P, W
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Environmentally assisted crack growth
Corrosion pit Pre existing
cracks, damage
Solventpenetration
Grain
boundaries Intergranular
fracture
a
WSolvent
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Stress corrosion mechanism
Stress: open cracks to allow environmental molecules(e.g., H2O) to attack the atomic bonds at the crack tip.
Corrosion: chemical reaction to reduce the bondstrength
With the help of the environment, crack grows
slowly under static loading even though K < Kc(subcritical cracking).
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Characterizing environmentally assisted
crack growth
)(Kfdt
da=
dt
da
log
Klog
f(K) is determined experimentally for a
specific material in a specific environment.
a
P W a
t
a0
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7075-T6 aluminum in 3.5% NaCl
Artificial sea waterenvironment
Effect of
temperatureDiffusion
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Crack growth regions
Region I: diffusion controls;very sensitive to K, moderately
sensitive to environment.
Region II: chemical reactioncontrols; insensitive to K, but
sensitive to environment.
Region III: fast fracture;insensitive to environment.
dt
dalog
Klog
I
II
III
ThresholdKth Toughness Kc
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Infinite life
Region 1
Region II
Region III
Idealized response & properties
pth
KKK
dt
dalog
Klog
III
III
Kth Kc
pa
n
1
pK
th
KK ac>> a0>ath
0/ 2 / 2 1 / 2 1
0
2 1 1
( 2)
pa
I n n n n nap
dat
AK A n a a
= =
nAKdtda =
p CK K K