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 (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.)
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.