Week 5
Fracture, Toughness, Fatigue,
and Creep
MATERIALS SCIENCE
Mechanical Failure
ISSUES TO ADDRESS...
• 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?
Ship-cyclic loading
from waves.
Computer chip-cyclic
thermal loading.
2
Hip implant-cyclic
loading from walking.
What is a Fracture?
 Fracture is the separation of a body into two or
more pieces in response to an imposed stress that is
static and at temperatures that are low relative to the
melting temperature of the material.
 The applied stress may be tensile, compressive,
shear, or torsional
 Any fracture process involves two steps—crack
formation and propagation—in response to an
imposed stress.
Fracture mechanisms
4
 Ductile fracture
 Occurs with plastic deformation
• Brittle fracture
– Little or no plastic deformation
– Catastrophic
Ductile vs Brittle Failure
• Classification:
5
Fracture
behavior:
%AR or %EL
• Ductile
fracture is usually
desirable!
Very
Ductile
Large
Ductile:
warning before
fracture
Moderately
Ductile
Brittle
Moderate
Small
Brittle:
No
warning
Example: Failure of a Pipe
• Ductile failure:
--one/two piece(s)
--large deformation
• Brittle failure:
--many pieces
--small deformation
6
Moderately Ductile Failure
• Evolution to failure:
necking
s
• Resulting
fracture
surfaces
void
nucleation
void growth
and linkage
shearing
at surface
50
50mm
mm
(steel)
100 mm
particles
serve as void
nucleation
sites.
7
fracture
Ductile vs. Brittle Failure
8
cup-and-cone fracture
brittle fracture
Transgranular vs Intergranular Fracture
Transgranular
Fracture
Intergranular Fracture
Brittle Fracture Surfaces
• Transgranular
• Intergranular
(between grains)
(within grains)
304 S. Steel
(metal)
316 S. Steel
(metal)
160 mm
4 mm
Polypropylene
(polymer)
1 mm
10
Al Oxide
(ceramic)
3 mm
Ideal vs Real Materials
• Stress-strain behavior (Room T):
E/10
s perfect mat’l-no flaws
TS
carefully produced glass fiber
E/100
typical ceramic
typical strengthened metal
typical polymer
0.1
e
• DaVinci (500 yrs ago!) observed...
-- the longer the wire, the
smaller the load for failure.
• Reasons:
-- flaws cause premature failure.
-- Larger samples contain more flaws!
11
<< TS
engineering
materials
perfect
materials
Flaws are Stress Concentrators!
12
Results from crack propagation
 Griffith Crack
a
s m  2so 
 t
t
1/ 2



 K t so
where
t = radius of curvature
so = applied stress
sm = stress at crack tip
Kt = Stress concentration factor
Concentration of Stress at Crack Tip
13
Engineering Fracture Design
• Avoid sharp corners! 14
so
smax
Stress Conc. Factor, K t =
so
w
smax
r,
fillet
2.5
h
2.0
increasing
w/h
radius
1.5
1.0
0
0.5
sharper fillet radius
1.0
r/h
Crack Propagation
15
Cracks propagate due to sharpness of crack tip
 A plastic material deforms at the tip, “blunting” the crack.
deformed
plastic region
brittle
Energy balance on the crack
 Elastic strain energyenergy stored in material as it is elastically deformed
 this energy is released when the crack propagates
 creation of new surfaces requires energy

When Does a Crack Propagate?
16
Crack propagates if above critical stress
i.e., sm > sc
where



1/ 2
 2E s 
sc  

 a 
a
s m  2so 
 t
E = modulus of elasticity
s = specific surface energy (J/m2)
a = one half length of internal crack
For ductile => replace s by s + p
where p is plastic deformation energy
1/ 2



 K t so
Fracture Toughness: Design Against
Crack Growth
• Crack growth condition:
K ≥ Kc
=
Ys a
• Largest, most stressed cracks grow first!
--Result 2: Design stress
--Result 1: Max. flaw size
dictates max. flaw size.
dictates design stress.
sdesign
Kc

Y amax
amax
amax
s
fracture
no
fracture
1  K c

  Ysdesign




fracture
no
fracture
amax
17
s
2
Fracture Toughness
 For relatively thin specimens, the value of Kc will
depend on specimen thickness. However, when
specimen thickness is much greater than the crack
dimensions, Kc becomes independent of thickness.
 The Kc value for this thick-specimen situation is
known as the plane strain fracture toughness
KIC
Fracture Toughness
Metals/
Alloys
Graphite/
Ceramics/
Semicond
Composites/
Polymers 19
fibers
100
K Ic (MPa · m0.5 )
70
60
50
40
30
C-C(|| fibers) 1
Steels
Ti alloys
Al alloys
Mg alloys
20
Al/Al oxide(sf) 2
Y2 O 3 /ZrO 2 (p) 4
C/C( fibers) 1
Al oxid/SiC(w) 3
Si nitr/SiC(w) 5
Al oxid/ZrO 2 (p) 4
Glass/SiC(w) 6
10
7
6
5
4
Diamond
Si carbide
Al oxide
Si nitride
PET
PP
3
PVC
2
1
0.7
0.6
0.5
PC
<100>
Si crystal
<111>
Glass -soda
Concrete
PS
Polyester
Glass 6
Kc
= Ys a
Design Example: Aircraft Wing
• Material has Kc = 26 MPa-m0.5
• Two designs to consider...
Design A
--use same material
--largest flaw is 4 mm
--failure stress = ?
--largest flaw is 9 mm
--failure stress = 112 MPa
• Use...
sc 
Design B
Kc
Y amax
• Key point: Y and Kc are the same in both designs.
--Result:
112 MPa
sc
9 mm
amax
A  sc
amax
B
Answer: (sc )B  168 MPa
• Reducing flaw size pays off!

4 mm
20
Loading Rate
21
• Increased loading rate...
-- increases sy and TS
-- decreases %EL
s
sy
TS
• Why?
An increased rate
gives less time for
dislocations to move past
obstacles and form into a crack.
e
larger
TS
e
smaller
sy
e
Impact Testing
22
• Impact loading:
(Charpy)
-- severe testing case
-- makes material more brittle
-- decreases toughness
final height
initial height
Impact Tests
 A material may have a high tensile strength and yet




be unsuitable for shock loading conditions
Impact testing is testing an object's ability to resist
high-rate loading.
An impact test is a test for determining the energy
absorbed in fracturing a test piece at high velocity
Types of Impact Tests -> Izod test and Charpy
Impact test
In these tests a load swings from a given height to
strike the specimen, and the energy dissipated in the
fracture is measured
A. Izod Test
 The Izod test is most commonly
used to evaluate the relative
toughness or impact toughness of
materials
 Izod test sample usually have a Vnotch cut into them
 Metallic samples tend to be square
in cross section, while polymeric
test specimens are often
rectangular
Izod Test - Method
 It involves striking a suitable test
piece with a striker, mounted at
the end of a pendulum
 The test piece is clamped
vertically with the notch facing
the striker.
 The striker swings downwards
impacting the test piece at the
bottom of its swing.
Determination of Izod Impact Energy
 At the point of impact, the striker has a
known amount of kinetic energy.
 The impact energy is calculated based
on the height to which the striker
would have risen, if no test specimen
was in place, and this compared to the
height to which the striker actually
rises.
 Tough materials absorb a lot of energy,
whilst brittle materials tend to absorb
very little energy prior to fracture
B. Charpy Test
 Charpy test specimens normally measure 55 x 10 x 10mm
and have a notch machined across one of the larger faces
 The Charpy test involves striking a suitable test piece with a
striker, mounted at the end of a pendulum.
 The test piece is fixed in place at both ends and the striker
impacts the test piece immediately behind a machined
notch.
Factors Affecting Impact Energy
For a given material the impact energy will be seen
to decrease if the yield strength is increased
2. The notch serves as a stress concentration zone
and some materials are more sensitive towards
notches than others
3. Most of the impact energy is absorbed by means of
plastic deformation during the yielding. Therefore,
factors that affect the yield behavior (and hence
ductility) of the material such as temperature
and strain rate will affect the impact energy
1.
Effect of Temperature on Toughness
• Increasing temperature...
--increases %EL and Kc
• Ductile-to-Brittle Transition Temperature (DBTT)...
Impact Energy
FCC metals (e.g., Cu, Ni)
BCC metals (e.g., iron at T < 914°C)
polymers
Brittle
More Ductile
High strength materials ( s y > E/150)
Temperature
Ductile-to-brittle
transition temperature
29
Fatigue Test
 Fatigue is concerned with the premature fracture of
metals under repeatedly applied low stresses
 A specified mean load (which may be zero) and an
alternating load are applied to a specimen and the
number of cycles required to produce failure (fatigue life)
is recorded.
 Generally, the test is repeated with identical specimens
and various fluctuating loads.
 Data from fatigue testing often are presented in an S-N
diagram which is a plot of the number of cycles
required to cause failure in a specimen against the
amplitude of the cyclical stress developed
Fatigue Testing Equipment
Fatigue Loading
Fatigue Test - S-N Curve
 This S–N diagram
indicates that some
metals can withstand
indefinitely the
application of a large
number of stress
reversals, provided the
applied stress is below a
limiting stress known as
the endurance limit
Fatigue Mechanism
• Crack grows incrementally
da
m
 K 
dN
typ. 1 to 6
~ s a
• Failed rotating shaft
increase in crack length per loading cycle
crack origin
--crack grew even though
Kmax < Kc
--crack grows faster as
• s increases
• crack gets longer
• loading freq. increases.
34
Improving Fatigue Life
35
1. Impose a compressive
surface stress
(to suppress surface
cracks from growing)
S = stress amplitude
Increasing
sm
near zero or compressive sm
moderate tensile sm
Larger tensile sm
N = Cycles to failure
--Method 1: shot peening
--Method 2: carburizing
shot
put
surface
into
compression
2. Remove stress
concentrators.
C-rich gas
bad
better
bad
better
4. Creep Test
 Creep is defined as plastic (or
irrevresible) flow under constant stress
 Creep is high temperature progressive
deformation at constant stress
 A creep test involves a tensile
specimen under a constant load
maintained at a constant temperature.
 At relatively high temperatures creep
appears to occur at all stress levels, but
the creep rate increases with increasing
stress at a given temperature.
Creep Test
 Creep occurs in three stages:
Primary, or Stage I; Secondary, or
Stage II, and Tertiary, or Stage III
Creep Test
 Stage I occurs at the beginning of the tests, and creep
is mostly transient, not at a steady rate.
 In Stage II, the rate of creep becomes roughly steady
 In Stage III, the creep rate begins to accelerate as the
cross sectional area of the specimen decreases due to
necking decreases the effective area of the specimen
Creep
• Occurs at elevated temperature, T > 0.4 Tm
tertiary
primary
secondary
elastic
39
Secondary Creep
• Strain rate is constant at a given T, s
stress exponent (material parameter)
Qc 

e s  K 2s exp 

 RT 
n
strain rate
material const.
• Strain rate
increases
for higher T, s
activation energy for creep
(material parameter)
applied stress
200
100
Stress (MPa)
427°C
538 °C
40
20
649 °C
10
10 -2
10 -1
1
Steady state creep rate es (%/1000hr)
40
Creep Failure
• Failure:
along grain boundaries.
•41Estimate rupture time
S-590 Iron, T = 800°C, s = 20 ksi
g.b. cavities
applied
stress
20
10
Stress, ksi
100
data for
S-590 Iron
• Time to rupture, tr
T ( 20  logtr )  L
function of
applied stress
time to failure (rupture)
temperature
1
12 16 20 24 28
L(10 3 K-log hr)
24x103 K-log hr
T ( 20  logtr )  L
1073K
Ans: tr = 233 hr
Numerical Problems
 Problems 8.1 – 8.10; 8.14 – 8.23; and 8.27