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Loading Rate
• Increased loading rate...--increases σy and TS--decreases %EL
• Why? An increased rategives less time for disl. tomove past obstacles.
initial heightfinal height
sample
σ
ε
σy
σy
TS
TSlarger ε
smaller ε
(Charpy)• Impact loading:--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.)
Temperature
• Increasing temperature...--increases %EL and Kc
• Ductile-to-brittle transition temperature (DBTT)...
BCC metals (e.g., iron at T < 914C)
Imp
ac
t E
ne
rgy
Temperature
FCC metals (e.g., Cu, Ni)
High strength materials (σy>E/150)
polymers
More Ductile Brittle
Ductile-to-brittle transition temperature
Adapted from C. Barrett, W. Nix,and A.Tetelman, The Principlesof Engineering Materials, Fig. 6-21, p. 220, Prentice-Hall, 1973.Electronically reproduced by permission of Pearson Education, Inc., Upper Saddle River, NewJersey.
Ductile to Brittle Transition (Steels)
DBTT (carbon content in steel)DBTT and Fracture NatureMid-carbon steel
Design Strategy: Stay Above the DBTT!
• Pre-WWII: 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.)
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.)
• Problem: Used steel with a DBTT ~ room temp.
Fatigue
• Fatigue = failure under cyclic stress.
tension on bottom
compression on top
countermotor
flex coupling
bearing bearing
specimen
• Stress varies with time.--key parameters are S and σm
σmax
σmin
σ
time
σmS
• Key points: Fatigue...--can cause part failure, even though σmax < σc.--causes ~ 90% of mechanical engineering failures.
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.)
Fatigue Design Parameters
• Fatigue limit, Sfat:--no fatigue if S < Sfat
• Sometimes, thefatigue limit is zero!
Sfat
case for steel (typ.)
N = Cycles to failure103 105 107 109
unsafe
safe
S = stress amplitude
case for Al (typ.)
N = Cycles to failure103 105 107 109
unsafe
safe
S = stress amplitude
Adapted from Fig. 8.17(a), Callister 6e.
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
dadN
= ∆K( )mtyp. 1 to 6
~ ∆σ( ) aincrease in crack length per loading cycle
• Failed rotating shaft--crack grew even though
Kmax < Kc--crack grows faster if
• ∆σ increases• crack gets longer• loading freq. increases.
crack origin
Adapted fromFig. 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 SurfaceFatigue Crack
Fatigue Striations in AlEach striation
One loading cycle Crack extension
Fast Fracture
Improving Fatigue Life
1.Impose a compressivesurface stress(to suppress surfacecracks from growing)
N = Cycles to failure
moderate tensile σmlarger tensile σm
S = stress amplitude
near zero or compressive σm
Adapted fromFig. 8.22, Callister 6e.
--Method 1: shot peening
2. Remove stressconcentrators.
bad
bad
better
better
--Method 2: carburizing
C-rich gasput
surface into
compression
shot
Adapted fromFig. 8.23, Callister 6e.
Creep
• Occurs at elevated temperature, T > 0.4 Tmelt• Deformation changes with time.
timeelastic
primary secondary
tertiary
T < 0.4 Tm
INCREASING T
0
strain, εσ,ε
σ
0 t
Adapted fromFigs. 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 recoverystress exponent (material parameter)
strain rateactivation energy for creep(material parameter)
applied stressmaterial const.
• Strain rateincreasesfor larger T, σ
10
20
40
100
200
Steady state creep rate (%/1000hr)10-2 10-1 1
ε s
Stress (MPa)427C
538C
649C
Adapted fromFig. 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.)
εs = K2σn exp −
QcRT
⎛
⎝ ⎜
⎞
⎠ ⎟
.
Creep Failure
• Failure:along grain boundaries.
time to failure (rupture)
function ofapplied stress
temperature
T(20 + log t r ) = L
L(103K-log hr)
Str
ess
, ksi
100
10
112 20 24 2816
data for S-590 Iron
20appliedstress
g.b. cavities
• Time to rupture, tr
• Estimate rupture timeS 590 Iron, T = 800C, σ = 20 ksi
T(20 + log t r ) = L
1073K
24x103 K-log hr
Ans: tr = 233hr
Adapted fromFig. 8.45, Callister 6e.(Fig. 8.45 is from F.R. Larson and J. Miller, Trans. ASME, 74, 765 (1952).)
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.)
Summary
• Engineering materials don't reach theoretical strength.
• Flaws produce stress concentrations that causepremature failure.
• Sharp corners produce large stress concentrationsand 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 15Mechanical 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 mechanicalresponse compare to ceramics and metals?
Polmer Microstructure - Review
• Polymer = many mers
C C C C C CHHHHHH
HHHHHH
Polyethylene (PE)
mer
ClCl Cl
C C C C C CHHH
HHHHHH
Polyvinyl chloride (PVC)
mer
Polypropylene (PP)
CH3
C C C C C CHHH
HHHHHH
CH3 CH3
mer
Adapted from Fig. 14.2, Callister 6e.
• Covalent chain configurations and strength:
Branched Cross-Linked NetworkLinear
secondarybonding
Direction of increasing strengthAdapted 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.--Annealing causes
crystalline regionsto grow. % crystallinityincreases.
crystalline region
amorphous region
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
0
unload/reload
0
brittle failure
plastic failure
20
40
60
2 4 6
σ(MPa)
ε
x
x
semi- crystalline
case
amorphous regions
elongate
crystalline regions align
crystalline regions
slide
8
onset of necking
aligned, cross- linked case
networked case
Initial
Near Failure
near failure
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 TBrittle 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.--decreases ductility (%EL)
• Annealing after drawing...--decreases alignment--reverses effects of drawing.
• Compare to cold working in metals!
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.)
Tensile Response: Elastomer Case
• Compare to responses of other polymers:--brittle response (aligned, cross linked & networked case)--plastic response (semi-crystalline case)
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 Nature and Properties of Engineering Materials, 3rd ed., John Wiley and Sons, 1987.)
initial: amorphous chains are kinked, heavily cross-linked.
final: chains are straight,
still cross-linked
0
20
40
60
0 2 4 6
σ(MPa)
ε 8
x
x
x
elastomer
plastic failure
brittle failure
Deformation is reversible!
Thermoplastics vs. Thermosets
• Thermoplastics:--little cross linking--ductile--soften w/heating--polyethylene (#2)
polypropylene (#5)polycarbonatepolystyrene (#6)
• Thermosets:--large cross linking
(10 to 50% of mers)--hard and brittle--do NOT soften w/heating--vulcanized rubber, epoxies,
polyester resin, phenolic resin
Callister, Fig. 16.9
T
Molecular weight
Tg
Tmmobile liquid
viscous liquid
rubber
tough plastic
partially crystalline solid
crystalline solid
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.)
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