View
111
Download
8
Category
Preview:
DESCRIPTION
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?. - PowerPoint PPT Presentation
Citation preview
MATERIALS SCIENCE
Week 5Fracture, Toughness, Fatigue, and Creep
2
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 loadingfrom waves.
Computer chip-cyclicthermal loading.
Hip implant-cyclicloading from walking.
Mechanical Failure
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.
4
Fracture mechanisms
Ductile fracture Occurs with plastic deformation
• Brittle fracture
– Little or no plastic deformation
– Catastrophic
5
Ductile vs Brittle Failure
Very Ductile
ModeratelyDuctile BrittleFracture
behavior:
Large Moderate%AR or %EL Small
• Ductile fracture is usually desirable!
• Classification:
Ductile: warning before
fracture
Brittle: No
warning
6
• Ductile failure:
--one/two piece(s) --large deformation
Example: Failure of a Pipe
• Brittle failure:
--many pieces --small deformation
7
• Evolution to failure:
• Resulting fracture surfaces
(steel)
50 mm
particlesserve as voidnucleationsites.
50 mm
100 mm
Moderately Ductile Failure
necking
void nucleation
void growth and linkage
shearing at surface fracture
8
Ductile vs. Brittle Failure
cup-and-cone fracture brittle fracture
Transgranular vs Intergranular Fracture
Transgranular Fracture
Intergranular Fracture
10
• Intergranular
(between grains)• Transgranular
(within grains)
Al Oxide(ceramic)
316 S. Steel (metal)
304 S. Steel (metal)
Polypropylene(polymer)
3 mm
4 mm160 mm
1 mm
Brittle Fracture Surfaces
11
• Stress-strain behavior (Room T):
Ideal vs Real Materials
TS << TSengineeringmaterials
perfectmaterials
E/10
E/100
0.1
perfect mat’l-no flaws
carefully produced glass fiber
typical ceramic typical strengthened metaltypical polymer
• 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!
12
Flaws are Stress Concentrators!
Results from crack propagationGriffith Crack
where t = radius of curvature
o = applied stress
m = stress at crack tip
Kt = Stress concentration factor
ot
/
tom K
a
21
2
t
13
Concentration of Stress at Crack Tip
14
Engineering Fracture Design
r/h
sharper fillet radius
increasing w/h
0 0.5 1.01.0
1.5
2.0
2.5
Stress Conc. Factor, K tmax
o=
• Avoid sharp corners!
r ,
fillet
radius
w
h
o
max
15
Crack Propagation
Cracks propagate due to sharpness of crack tip A plastic material deforms at the tip, “blunting” the
crack. deformed region
brittle
Energy balance on the crackElastic 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
plastic
16
When Does a Crack Propagate?
Crack propagates if above critical stress
where 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
212
/
sc a
E
i.e., m > c
ot
/
tom K
a
21
2
17
• Crack growth condition:
• Largest, most stressed cracks grow first!
Fracture Toughness: Design Against Crack Growth
K ≥ Kc = aY
--Result 1: Max. flaw size dictates design stress.
max
cdesign
aY
K
amax
no fracture
fracture
--Result 2: Design stress dictates max. flaw size.
2
1
design
cmax Y
Ka
amax
no fracture
fracture
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
19
Fracture ToughnessGraphite/ Ceramics/ Semicond
Metals/ Alloys
Composites/ fibers
Polymers
5
KIc
(MP
a ·
m0
.5)
1
Mg alloys
Al alloys
Ti alloys
Steels
Si crystalGlass -soda
Concrete
Si carbide
PC
Glass 6
0.5
0.7
2
4
3
10
20
30
<100>
<111>
Diamond
PVC
PP
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) 3
Al oxid/ZrO 2(p)4Si nitr/SiC(w) 5
Glass/SiC(w) 6
Y2O3/ZrO 2(p)4
Kc = aY
20
• Two designs to consider...Design A --largest flaw is 9 mm --failure stress = 112 MPa
Design B --use same material --largest flaw is 4 mm --failure stress = ?
• Key point: Y and Kc are the same in both designs.
Answer: MPa 168)( B c• Reducing flaw size pays off!
• Material has Kc = 26 MPa-m0.5
Design Example: Aircraft Wing
• Use...max
cc
aY
K
c amax A
c amax B
9 mm112 MPa 4 mm --Result:
21
Loading Rate
• Increased loading rate...
-- increases y and TS -- decreases %EL
• Why? An increased rate gives less time for dislocations to move past obstacles and form into a crack.
y
y
TS
TS
larger
smaller
22
Impact Testing
final height initial height
• Impact loading:
-- severe testing case -- makes material more brittle -- decreases toughness
(Charpy)
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 V-notch 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
1. 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
29
• Increasing temperature...
--increases %EL and Kc
• Ductile-to-Brittle Transition Temperature (DBTT)...
Effect of Temperature on Toughness
BCC metals (e.g., iron at T < 914°C)
Imp
act
Ene
rgy
Temperature
High strength materials (y > E/150)
polymers
More Ductile Brittle
Ductile-to-brittle transition temperature
FCC metals (e.g., Cu, Ni)
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
34
• Crack grows incrementally
typ. 1 to 6
a~
increase in crack length per loading cycle
• Failed rotating shaft
--crack grew even though
Kmax < Kc
--crack grows faster as • increases • crack gets longer • loading freq. increases.
crack origin
Fatigue Mechanism
mKdN
da
35
Improving Fatigue Life
1. Impose a compressive surface stress (to suppress surface cracks from growing)
N = Cycles to failure
moderate tensile mLarger tensile m
S = stress amplitude
near zero or compressive mIncreasing
m
--Method 1: shot peening
put surface
into compression
shot--Method 2: carburizing
C-rich gas
2. Remove stress concentrators.
bad
bad
better
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 steadyIn 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
39
• Occurs at elevated temperature, T > 0.4 Tm
Creep
elastic
primarysecondary
tertiary
40
• Strain rate is constant at a given T,
stress exponent (material parameter)
strain rateactivation energy for creep(material parameter)
applied stressmaterial const.
• Strain rate increases for higher T,
10
20
40
100
200
10-2 10-1 1Steady state creep rate (%/1000hr)
s
Stress (MPa)
427°C
538°C
649°C
RT
QK cn
s exp2
Secondary Creep
41
Creep Failure• Estimate rupture time
S-590 Iron, T = 800°C, = 20 ksi• Failure:
along grain boundaries.
time to failure (rupture)
function ofapplied stress
temperature
L)t(T r log20
appliedstress
g.b. cavities
• Time to rupture, trL)t(T r log20
1073K
Ans: tr = 233 hr
24x103 K-log hrL(103K-log hr)
Str
ess,
ksi
100
10
112 20 24 2816
data for S-590 Iron
20
Numerical Problems
Problems 8.1 – 8.10; 8.14 – 8.23; and 8.27
Recommended