Loading Rate
• Increased loading rate...
--increases σy and TS
--decreases %EL
• Why? An increased rate
gives less time for disl. to
move past obstacles.
• Impact loading:
σ
σy
TS
larger ε
TS
σy
smaller ε
ε
sample
(Charpy)
--severe testing case
--more brittle
--smaller toughness
Adapted from Fig. 8.11(a) and
(b), Callister 6e. (Fig. 8.11(b)
is adapted from H.W. Hayden,
W.G. Moffatt, and J. Wulff, The
Structure and Properties of
Materials, Vol. III, Mechanical
Behavior, John Wiley and
Sons, Inc. (1965) p. 13.)
final height
initial height
Temperature
• Increasing temperature...
--increases %EL and Kc
Impact Energy
• Ductile-to-brittle transition temperature (DBTT)...
, Ni)
u
C
,
.
g
.
e
(
ls
FCC meta
BCC metals (e.g., iron at T < 914C)
polymers
Brittle
More Ductile
High strength materials (σy>E/150)
Temperature
Ductile-to-brittle
transition temperature
Adapted from C. Barrett, W. Nix,
and A.Tetelman, The Principles
of Engineering Materials, Fig. 6-21,
p. 220, Prentice-Hall, 1973.
Electronically reproduced by
permission of Pearson Education,
Inc., Upper Saddle River, New
Jersey.
Ductile to Brittle Transition (Steels)
DBTT and Fracture Nature
Mid-carbon steel
DBTT (carbon content in steel)
Design Strategy: Stay Above the DBTT!
• Pre-WWII: The Titanic
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.)
• WWII: Liberty ships
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.)
• Problem: Used steel with a DBTT ~ room temp.
Fatigue
• Fatigue = failure under cyclic stress.
specimen
bearing
compression on top
bearing
counter
motor
flex coupling
tension on bottom
• Stress varies with time.
--key parameters are S and σm
σmax
σm
σ
Adapted from Fig. 8.16,
Callister 6e. (Fig. 8.16
is from Materials
Science in Engineering,
4/E by Carl. A. Keyser,
Pearson Education,
Inc., Upper Saddle
River, NJ.)
S
σmin
• Key points: Fatigue...
--can cause part failure, even though σmax < σc.
--causes ~ 90% of mechanical engineering failures.
time
Fatigue Design Parameters
• Fatigue limit, Sfat:
S = stress amplitude
--no fatigue if S < Sfat
unsafe
Sfat
103
• Sometimes, the
fatigue limit is zero!
safe
Adapted from Fig.
8.17(a), Callister 6e.
105
107
109
N = Cycles to failure
S = stress amplitude
unsafe
safe
103
case for
steel (typ.)
105
107
109
N = Cycles to failure
case for
Al (typ.)
Adapted from Fig.
8.17(b), Callister 6e.
Fatigue S-N with Probability
S-N Curve with Probability for Failure (Al 7075 Alloy)
Fatigue Mechanism
• Crack grows incrementally
( )
typ. 1 to 6
m
da
= ∆K
dN
~ ∆σ
( )a
increase in crack length per loading cycle
crack origin
• Failed rotating shaft
--crack grew even though
Kmax < Kc
--crack grows faster if
• ∆σ increases
• crack gets longer
• loading freq. increases.
Adapted from
Fig. 8.19, Callister
6e. (Fig. 8.19 is
from D.J. Wulpi,
Understanding How
Components Fail,
American Society for
Metals, Materials
Park, OH, 1985.)
Common Fatigue Fracture Surface
Fatigue Crack
Fast Fracture
Fatigue Striations in Al
Each striation
One loading cycle
Crack extension
Improving Fatigue Life
1. Impose a compressive
surface stress
S = stress amplitude
Adapted from
Fig. 8.22, Callister 6e.
(to suppress surface
cracks from growing)
near zero or compressive σm
moderate tensile σm
larger tensile σm
N = Cycles to failure
--Method 1: shot peening
--Method 2: carburizing
shot
put
surface
into
compression
2. Remove stress
concentrators.
bad
C-rich gas
better
Adapted from
Fig. 8.23, Callister 6e.
bad
better
Creep
• Occurs at elevated temperature, T > 0.4 Tmelt
• Deformation changes with time.
σ,ε
strain, ε
σ
INCREASING T
0
tertiary
t
primary
secondary
elastic
0
T < 0.4 Tm
time
Adapted from
Figs. 8.26 and 8.27,
Callister 6e.
Secondary Creep
• Most of component life spent here.
• Strain rate is constant at a given T, σ
--strain hardening is balanced by recovery
stress exponent (material parameter)
⎛ Q ⎞
.
n
εs = K 2 σ exp ⎜ − c ⎟
⎝ RT ⎠
strain rate
material const.
• Strain rate
increases
for larger T, σ
activation energy for creep
(material parameter)
applied stress
200
100
40
20
10
Stress (MPa)
427C
538C
649C
Adapted from
Fig. 8.29, Callister 6e.
(Fig. 8.29 is from
Metals Handbook:
Properties and
Selection: Stainless
Steels, Tool Materials,
and Special Purpose
Metals, Vol. 3, 9th ed.,
D. Benjamin (Senior
Ed.), American
Society for Metals,
1980, p. 131.)
1
10-2
10-1
Steady state creep rate εs (%/1000hr)
Creep Failure
• Failure:
• Estimate rupture time
along grain boundaries.
S 590 Iron, T = 800C, σ = 20 ksi
g.b. cavities
applied
stress
From V.J. Colangelo and F.A. Heiser, Analysis of
Metallurgical Failures (2nd ed.), Fig. 4.32, p. 87,
John Wiley and Sons, Inc., 1987. (Orig. source:
Pergamon Press, Inc.)
• Time to rupture, tr
T(20 + log t r ) = L
temperature
function of
applied stress
time to failure (rupture)
Stress, ksi
100
20
10
data for
S-590 Iron
1
12 16 20 24 28
L(103K-log hr)
Adapted from
Fig. 8.45, Callister 6e.
(Fig. 8.45 is from F.R.
Larson and J. Miller,
Trans. ASME, 74, 765
(1952).)
24x103 K-log hr
T(20 + log t r ) = L
1073K
Ans: tr = 233hr
Summary
• Engineering materials don't reach theoretical strength.
• Flaws produce stress concentrations that cause
premature failure.
• Sharp corners produce large stress concentrations
and premature failure.
• Failure type depends on T and stress:
-for noncyclic σ and T < 0.4Tm, failure stress decreases with:
increased maximum flaw size,
decreased T,
increased rate of loading.
-for cyclic σ:
cycles to fail decreases as ∆σ increases.
-for higher T (T > 0.4Tm):
time to fail decreases as σ or T increases.
Chapters 15
Mechanical Behavior of Polymers
ISSUES TO ADDRESS...
• What are the basic microstructural features?
• How do these features dictate room T tensile
response?
• Hardening, anisotropy, and annealing in polymers.
• How does elevated temperature mechanical
response compare to ceramics and metals?
Polmer Microstructure - Review
• Polymer = many mers
mer
H H H H H H
C C C C C C
H H H H H H
Polyethylene (PE)
mer
H H H H H H
C C C C C C
H CH3 H CH3 H CH3
mer
H H H H H H
C C C C C C
H Cl H Cl H Cl
Polyvinyl chloride (PVC)
Polypropylene (PP)
Adapted from Fig. 14.2, Callister 6e.
• Covalent chain configurations and strength:
secondary
bonding
Linear
Branched
Cross-Linked
Direction of increasing strength
Network
Adapted from Fig. 14.7, Callister 6e.
Molecular Weight & Crystallinity
• Molecular weight, Mw: Mass of a mole of chains.
smaller Mw
larger Mw
• Tensile strength (TS):
--often increases with Mw.
--Why? Longer chains are entangled (anchored) better.
• % Crystallinity: % of material that is crystalline.
--TS and E often increase
with % crystallinity.
crystalline
--Annealing causes
region
crystalline regions
amorphous
to grow. % crystallinity
region
increases.
Adapted from Fig. 14.11, Callister 6e.
(Fig. 14.11 is from H.W. Hayden, W.G. Moffatt,
and J. Wulff, The Structure and Properties of
Materials, Vol. III, Mechanical Behavior, John
Wiley and Sons, Inc., 1965.)
Polymer Stress-Strain Behavior
A - Brittle
B - Plastic
C – Highly Elastic (Elastomer)
Plastic Polymer Strength Definitions
Tensile Response: Brittle & Plastic
Near Failure
σ(MPa)
brittle failure
x
60
40
Initial
20
0
0
onset of
necking
near
failure
plastic failure
x
unload/reload
2
4
aligned,networked
case
crosslinked
case
6
8
ε
crystalline
regions
slide
semicrystalline
case
amorphous
regions
elongate
crystalline
regions align
Stress-strain curves adapted from Fig. 15.1, Callister 6e. Inset figures along plastic response curve
(purple) adapted from Fig. 15.12, Callister 6e. (Fig. 15.12 is from J.M. Schultz, Polymer Materials
Science, Prentice-Hall, Inc., 1974, pp. 500-501.)
Example:
Temperature-Dependence of Mechanical Properties
PMMA Stress-Strain (T)
Significant plastic deformation at high T
Brittle behavior at low T
Pre-Deformation by Drawing
• Drawing...
--stretches the polymer prior to use
--aligns chains to the stretching direction
• Results of drawing:
--increases the elastic modulus (E) in the
stretching dir.
--increases the tensile strength (TS) in the
stretching dir.
Adapted from Fig. 15.12,
Callister 6e. (Fig. 15.12 is from
--decreases ductility (%EL)
J.M. Schultz, Polymer
Materials
Science, Prentice• Annealing after drawing...
Hall, Inc., 1974, pp. 500-501.)
--decreases alignment
--reverses effects of drawing.
• Compare to cold working in metals!
Tensile Response: Elastomer Case
σ(MPa)
60 xbrittle failure
plastic failure
40
x
20
0
0
initial: amorphous chains are
kinked, heavily cross-linked.
Stress-strain curves
adapted from Fig.
15.1, Callister 6e.
Inset figures along
elastomer curve
(green) adapted from
Fig. 15.14, Callister
6e. (Fig. 15.14 is from
Z.D. Jastrzebski, The
x
elastomer
2
4
6
ε
8
final: chains
are straight,
still
cross-linked
Nature and Properties
of Engineering
Materials, 3rd ed.,
John Wiley and Sons,
1987.)
Deformation
is reversible!
• Compare to responses of other polymers:
--brittle response (aligned, cross linked & networked case)
--plastic response (semi-crystalline case)
Thermoplastics vs. Thermosets
• Thermoplastics:
--little cross linking
--ductile
--soften w/heating
--polyethylene (#2)
polypropylene (#5)
polycarbonate
polystyrene (#6)
T
mobile
liquid
viscous
liquid
crystalline
solid
Callister,
rubber
Fig. 16.9
tough
plastic
Tm
Tg
partially
crystalline
solid
Molecular weight
• Thermosets:
Adapted from Fig. 15.18, Callister 6e. (Fig. 15.18 is from F.W.
Billmeyer, Jr., Textbook of Polymer Science, 3rd ed., John Wiley
and Sons, Inc., 1984.)
--large cross linking
(10 to 50% of mers)
--hard and brittle
--do NOT soften w/heating
--vulcanized rubber, epoxies,
polyester resin, phenolic resin