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.)