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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