T and Strain Rate: Thermoplastics

Adapted from Fig. 15.3, Callister 6e. (Fig. 15.3 is from T.S. Carswell and J.K. Nason, 'Effect of Environmental Conditions on the Mechanical Properties of Organic Plastics", Symposium on Plastics, American Society for Testing and Materials, Philadelphia, PA, 1944.)

20

40

60

80

00 0.1 0.2 0.3

4°C

20°C

40°C

60°Cto 1.3

σ(MPa)

ε

Data for the semicrystalline polymer: PMMA (Plexiglas)

• Decreasing T...--increases E--increases TS--decreases %EL

• Increasingstrain rate...

--same effectsas decreasing T.

Elastic, Viscoleastic and Viscous Behavior

Input: Constant Stress

Response: Viscoelastic

Response: Elastic

Response: Viscous

Time Dependent Deformation

• Stress relaxation test: • Data: Large drop in Erfor T > Tg.

(amorphouspolystyrene)

• Sample Tg(C) values:PE (low Mw)PE (high Mw)PVCPSPC

-110- 90+ 87+100+150

103

101

10-1

10-3

105

60 100 140 180

rigid solid (small relax)

viscous liquid (large relax)

transition region

T(°C)Tg

Er(10s)

in MPa

Adapted from Fig. 15.7, Callister 6e. (Fig. 15.7 is from A.V. Tobolsky, Properties and Structures of Polymers, John Wiley and Sons, Inc., 1960.)

Selected values from Table 15.2, Callister 6e.

--strain to εο and hold.--observe decrease in

stress with time.

• Relaxation modulus:time

strain

tensile test

εo

tσ( )

Er (t ) =

σ(t )εo

More on the Relaxation Modulus

Schematic Er(t) for a thermoplastic Er(t) for amorphous polystyrene

More (again!) on the Relaxation Modulus

A: Crystalline isotactic

B: Lightly cross-linkedatactic

C: Amorphous

Relaxation Modulus: Polystyrene

Fracture of Polymers

Crazing (thermoplastics)Formation of localized yieldingFibrillar bridges between microvoidsMolecular chain reorientation + bridge fibers

= increased fracture toughness

Crazing in Polyeythylene Oxide

Fatigue in Polymers

Fatigue in polymersLess studied than in metalsStrong dependence on testing frequency (why?)

Melting and the Glass Transition Temperature

Melting Temperature TmTransition to a viscous liquidCan occur over a range of TDepends on sample history!

Glass Transition Temperature TgAmorphous or semicrystalline polymersTransition

Rubbery solid to a rigid solid

Factors Influencing Tm and Tg

Melting Temperature

Tm ↑ as chain stiffness ↑e.g., add double bonds on chain

Tm ↑ with bulky side chains or polar side groupse.g., polypropylene: Tm = 175 °C; polyethylene: Tm = 175 °Ce.g., polyvinyl chloride: Tm = 175 °C; polyethylene: Tm = 175 °C

Tm ↓ with significant side branchingWeaker interchain interactions, low density

Similar trends for the Glass Transition Temperature

Cross-linking: Tg ↑

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.)

Liquid Crystalline Polymers

Summary

• General drawbacks to polymers:-- E, σy, Kc, Tapplication are generally small.-- Deformation is often T and time dependent.-- Result: polymers benefit from composite reinforcement.

• Thermoplastics (PE, PS, PP, PC):-- Smaller E, σy, Tapplication

-- Larger Kc

-- Easier to form and recycle• Elastomers (rubber):

-- Large reversible strains!• Thermosets (epoxies, polyesters):

-- Larger E, σy, Tapplication

-- Smaller Kc

Table 15.3 Callister 6e:

Good overviewof applicationsand trade namesof polymers.

Chapter 16:Composite Materials

ISSUES TO ADDRESS...

• What are the classes and types of composites?

• Why are composites used instead of metals,ceramics, or polymers?

• How do we estimate composite stiffness & strength?

• What are some typical applications?

Terminology/Classification

• Composites:--Multiphase material w/significant

proportions of ea. phase.• Matrix:

--The continuous phase--Purpose is to:

transfer stress to other phasesprotect phases from environment

--Classification: MMC, CMC, PMC

• Dispersed phase:--Purpose: enhance matrix properties.

MMC: increase σy, TS, creep resist.CMC: increase KcPMC: increase E, σy, TS, creep resist.

--Classification: Particle, fiber, structural

metal ceramic polymer

woven fibers

cross section view

0.5mm

0.5mmReprinted with permission fromD. Hull and T.W. Clyne, An Introduction to Composite Materials, 2nd ed., Cambridge University Press, New York, 1996, Fig. 3.6, p. 47.

Composite Survey: Particle-I

Particle-reinforced Fiber-reinforced Structural

• Examples:-Spheroidite steel

matrix: ferrite (α) (ductile)

particles: cementite (Fe3C)

(brittle)

-WC/Co cemented carbide

matrix: cobalt (ductile)

particles: WC (brittle, hard)

-Automobile tires

matrix: rubber (compliant)

particles: C (stiffer)

60µm

Vm:

10-15vol%! 600µm

0.75µm

Adapted from Fig. 10.10, Callister 6e. (Fig. 10.10 is copyright United States Steel Corporation, 1971.)

Adapted from Fig. 16.4, Callister 6e. (Fig. 16.4 is courtesy Carboloy Systems, Department, General Electric Company.)

Adapted from Fig. 16.5, Callister 6e. (Fig. 16.5 is courtesy Goodyear Tire and Rubber Company.)

Composite Survey: Particle-II

• Elastic modulus, Ec, of composites:-- two approaches.

• Application to other properties:-- Electrical conductivity, σe: Replace E by σe.-- Thermal conductivity, k: Replace E by k.

Fiber-reinforced StructuralParticle-reinforced

Data: Cu matrix w/tungsten particles

0 20 40 60 80 100

150200250300350

vol% tungsten

E(GPa)

lower limit:1

Ec= Vm

Em+

Vp

Ep

c m m

upper limit:E = V E + VpEp

(Cu) (W)

“rule of mixtures”

Adapted from Fig. 16.3, Callister 6e. (Fig. 16.3 is from R.H. Krock, ASTM Proc, Vol. 63, 1963.)

Composite Survey: Fiber-I

• Aligned Continuous fibers

Fiber-reinforcedParticle-reinforced Structural

• Examples:

From W. Funk and E. Blank, “Creep deformation of Ni3Al-Mo in-situ composites", Metall. Trans. A Vol. 19(4), pp. 987-998, 1988. Used with permission.

fracture surface

matrix: α (Mo) (ductile)

fibers:γ’ (Ni3Al) (brittle)

2µm

--Metal: γ'(Ni3Al)-α(Mo)by eutectic solidification.

--Glass w/SiC fibersformed by glass slurryEglass = 76GPa; ESiC = 400GPa.

From F.L. Matthews and R.L. Rawlings, Composite Materials; Engineering and Science, Reprint ed., CRC Press, Boca Raton, FL, 2000. (a) Fig. 4.22, p. 145 (photo by J. Davies); (b) Fig. 11.20, p. 349 (micrograph by H.S. Kim, P.S. Rodgers, and R.D. Rawlings). Used with permission of CRCPress, Boca Raton, FL.

(a)

(b)

Composite Survey: Fiber-II

• Discontinuous, random 2D fibers

Fiber-reinforcedParticle-reinforced Structural

• Example: Carbon-Carbon--process: fiber/pitch, then

burn out at up to 2500C.--uses: disk brakes, gas

turbine exhaust flaps, nosecones.

• Other variations:--Discontinuous, random 3D--Discontinuous, 1D

fibers lie in plane

view onto plane

C fibers: very stiff very strongC matrix: less stiff less strong

Adapted from F.L. Matthews and R.L. Rawlings, Composite Materials; Engineering and Science, Reprint ed., CRC Press, Boca Raton, FL, 2000. (a) Fig. 4.24(a), p. 151; (b) Fig. 4.24(b) p. 151. (Courtesy I.J. Davies) Reproduced with permission of CRC Press, Boca Raton, FL.

(b)

(a)

Composite Survey: Fiber-III

σ(x)

• Critical fiber length for effective stiffening & strengthening:

Fiber-reinforcedParticle-reinforced Structural

fiber length > 15

σf dτc

fiber diameter

shear strength offiber-matrix interface

fiber strength in tension

• Ex: For fiberglass, fiber length > 15mm needed• Why? Longer fibers carry stress more efficiently!

fiber length > 15 σ f d

τc

Shorter, thicker fiber:

fiber length < 15 σ f d

τcσ(x)

Longer, thinner fiber:

Poorer fiber efficiency Better fiber efficiency

Adapted from Fig. 16.7, Callister 6e.

Composite Survey: Fiber-IV

Fiber-reinforcedParticle-reinforced Structural

• Estimate of Ec and TS:--valid when

-- Elastic modulus in fiber direction:

--TS in fiber direction:

efficiency factor:--aligned 1D: K = 1 (anisotropic)--random 2D: K = 3/8 (2D isotropy)--random 3D: K = 1/5 (3D isotropy)

fiber length > 15 σ f d

τc

Ec = EmVm + KEf Vf

(TS)c = (TS)m Vm + (TS)f Vf (aligned 1D)

Values from Table 16.3, Callister 6e. (Source for Table 16.3 is H. Krenchel, Fibre Reinforcement, Copenhagen: Akademisk Forlag, 1964.)

Composite Survey: Structural

Fiber-reinforcedParticle-reinforced Structural

• Stacked and bonded fiber-reinforced sheets-- stacking sequence: e.g., 0/90-- benefit: balanced, in-plane stiffness

• Sandwich panels-- low density, honeycomb core-- benefit: small weight, large bending stiffness

Adapted from Fig. 16.16, Callister 6e.

Adapted from Fig. 16.17,Callister 6e. (Fig. 16.17 isfrom Engineered MaterialsHandbook, Vol. 1, Composites, ASM International, Materials Park, OH, 1987.

honeycombadhesive layer

face sheet

Composite Benefits

• CMCs: Increased toughness • PMCs: Increased E/ρ

• MMCs:Increasedcreepresistance

20 30 50 100 20010-10

10-8

10-6

10-46061 Al

6061 Al w/SiC whiskers σ(MPa)

εss (s-1)

E(GPa)

G=3E/8K=E

Density, ρ [Mg/m3].1 .3 1 3 10 30

.01.1

1

10102

103

metal/ metal alloys

polymers

PMCs

ceramics

Adapted from T.G. Nieh, "Creep rupture of a silicon-carbide reinforced aluminum composite", Metall. Trans. AVol. 15(1), pp. 139-146, 1984. Used with permission.

fiber-reinf

un-reinf

particle-reinfForce

Bend displacement

Summary

• Composites are classified according to:-- the matrix material (CMC, MMC, PMC)-- the reinforcement geometry (particles, fibers, layers).

• Composites enhance matrix properties:-- MMC: enhance σy, TS, creep performance-- CMC: enhance Kc

-- PMC: enhance E, σy, TS, creep performance• Particulate-reinforced:

-- Elastic modulus can be estimated.-- Properties are isotropic.

• Fiber-reinforced:-- Elastic modulus and TS can be estimated along fiber dir.-- Properties can be isotropic or anisotropic.

• Structural:-- Based on build-up of sandwiches in layered form.