Chapter 16: Composites - Armstrongengineering.armstrong.edu/cameron/composites.pdf1 ISSUES TO...

1

ISSUES TO ADDRESS...

• What are the classes and types of composites?

• What are the advantages of using composite

materials?

• How do we predict the stiffness and strength of the

various types of composites?

Chapter 16: Composites

2

Composite • Combination of two or more individual materials

• Design goal: obtain a more desirable combination

of properties (principle of combined action)

– e.g., low density and high strength

3

• Composite: -- Multiphase material that is artificially

made.

• Phase types: -- Matrix - is continuous

-- Dispersed - is discontinuous and

surrounded by matrix

Terminology/Classification

Adapted from Fig. 16.1(a),

Callister & Rethwisch 8e.

4

• Dispersed phase: -- Purpose:

MMC: increase sy, TS, creep resist.

CMC: increase KIc

PMC: increase E, sy, TS, creep resist.

-- Types: particle, fiber, structural

• Matrix phase: -- Purposes are to: - transfer stress to dispersed phase

- protect dispersed phase from

environment

-- Types: MMC, CMC, PMC

metal ceramic polymer

Terminology/Classification

Reprinted with permission from

D. Hull and T.W. Clyne, An

Introduction to Composite Materials,

2nd ed., Cambridge University Press,

New York, 1996, Fig. 3.6, p. 47.

woven fibers

cross section view

0.5 mm

0.5 mm

5

Classification of Composites

Adapted from Fig. 16.2,


Small dispersed particles

impede motion of

dislocations

Stiffer particulate bears

fraction of load, restrain

matrix movement in vicinity

6

• For which particle reinforced composite would

bond strength be more important?

• What geometric/spatial properties of particles in

dispersed phase would influence performance?

7

Classification: Particle-Reinforced (i)

• Examples: Adapted from Fig.

10.19, Callister &

Rethwisch 8e. (Fig.

10.19 is copyright

United States Steel

Corporation, 1971.)

- Spheroidite

steel

matrix: ferrite (a)

(ductile)

particles: cementite ( Fe

3 C )

(brittle) 60 mm

Adapted from Fig.

16.4, Callister &

Rethwisch 8e. (Fig.

16.4 is courtesy

Carboloy Systems,

Department, General

Electric Company.)

- WC/Co

cemented

carbide

matrix: cobalt (ductile,

tough)

particles: WC (brittle, hard) :

600 mm

Adapted from Fig.

16.5, Callister &

Rethwisch 8e. (Fig.

16.5 is courtesy

Goodyear Tire and

Rubber Company.)

- Automobile

tire rubber

matrix: rubber (compliant)

particles: carbon

black

(stiff) 0.75 mm

Particle-reinforced Fiber-reinforced Structural

8

Classification: Particle-Reinforced (ii)

Concrete – gravel + sand + cement + water

- Why sand and gravel? Sand fills voids between gravel particles

Reinforced concrete – Reinforce with steel rebar or remesh

- increases strength - even if cement matrix is cracked

Prestressed concrete - Rebar/remesh placed under tension during setting of concrete

- Release of tension after setting places concrete in a state of compression

- To fracture concrete, applied tensile stress must exceed this

compressive stress


threaded

rod

nut

Posttensioning – tighten nuts to place concrete under compression

10

• Elastic modulus, Ec, of composites: -- two “rule of mixture” extremes:

• Application to other properties: -- Electrical conductivity, se: Replace E’s in equations with se’s.

-- Thermal conductivity, k: Replace E’s in equations with k’s.



(Fig. 16.3 is from R.H.

Krock, ASTM Proc, Vol.

63, 1963.)

Classification: Particle-Reinforced (iii)

lower limit:

1

E c

= V m

E m

+ V p

E p

upper limit: c m m E = V E + V p E p


Data:

Cu matrix

w/tungsten

particles

0 20 4 0 6 0 8 0 10 0

150

20 0

250

30 0

350

vol% tungsten

E(GPa)

(Cu) ( W)

11

Classification: Fiber-Reinforced (i)

• Fibers very strong in tension

– Provide significant strength improvement to the

composite

– Ex: fiber-glass - continuous glass filaments in a

polymer matrix

• Glass fibers

– strength and stiffness

• Polymer matrix

– holds fibers in place

– protects fiber surfaces

– transfers load to fibers


12

Classification: Fiber-Reinforced (ii)

• Fiber Types – Whiskers - thin single crystals - large length to diameter ratios

• graphite, silicon nitride, silicon carbide

• high crystal perfection – extremely strong, strongest known

• very expensive and difficult to disperse


– Fibers

• polycrystalline or amorphous

• generally polymers or ceramics

• Ex: alumina, aramid, E-glass, boron, UHMWPE

– Wires

• metals – steel, molybdenum, tungsten

13

Fiber Alignment

aligned

continuous

aligned random

discontinuous



Transverse

direction

Longitudinal

direction

14

• Critical fiber length for effective stiffening & strengthening:

• Ex: For fiberglass, common fiber length > 15 mm needed

Classification: Fiber-Reinforced (v)


c

f d

s

2length fiber

fiber diameter

shear strength of

fiber-matrix interface

fiber ultimate tensile strength

• For longer fibers, stress transference from matrix is more efficient Short, thick fibers:

c

f d

s

2length fiber

Long, thin fibers:

Low fiber efficiency

c

f d

s

2length fiber

High fiber efficiency

17

Composite Stiffness:

Longitudinal Loading

Continuous fibers - Estimate fiber-reinforced composite modulus of

elasticity for continuous fibers

• Longitudinal deformation

sc = smVm + sfVf and c = m = f

volume fraction isostrain

Ecl = EmVm + Ef Vf Ecl = longitudinal modulus

c = composite

f = fiber m = matrix

18

Composite Stiffness:

Transverse Loading

• In transverse loading the fibers carry less of the load

c= mVm + fVf and sc = sm = sf = s

f

f

m

m

ct E

V

E

V

E

1

Ect = transverse modulus

c = composite

f = fiber m = matrix

isostress

Ect EmEf

VmEf VfEm

Example 16.1

• A continuous and aligned glass fiber-reinforced

composite consists of 40 % vol of glass fibers having an

elastic modulus of 69 Gpa and 60 % vol of a polyester

resin that, when hardened, displays a modulus of 3.4 Gpa.

a. Compute the elastic modulus of the composite in the longitudinal

direction

b. If the cross-sectional area is 250 mm2, and a stress of 50 Mpa is

applied in this longitudinal direction, compute the magnitude of

the load carried by each of the fiber and matrix phases.

c. Determine the strain that is sustained by each phase when the

stress in part (b) is applied.

?

?

?

?

50

250

?

4.3

69

6.0

4.0

composite reinforced-fiber glass aligned and continuous -

:statement Problem

2

f

m

m

f

allongitudin

c

cl

m

f

m

f

F

F

Mpa

mmA

E

GpaE

GpaE

V

V

s

kNF

kNF

FF

GpaE

AFFF

VE

VE

F

F

VEVEE

m

f

mf

cl

cmfc

mm

ff

m

f

mmffcl

860.0

640.11

: and in equations two theUsing

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:Solution

:Theory

s

3

3

1069.1

1069.1

:Solution

//

//

:Theory

m

f

m

mmm

m

mm

m

mm

f

cff

f

ff

f

f

f

mfc

E

AVF

E

AF

E

E

AVF

E

AF

E

s

s

Example 16.2

• Compute the elastic modulus of the composite

material in example 16.1, but assume that the

stress is applied perpendicular to the direction of

fiber alignment.

?

4.3

69

6.0

4.0

composite reinforced-fiber glass aligned and continuous -

:statement Problem

ct

m

f

m

f

E

GpaE

GpaE

V

V

GpaE

EVEV

EEE

ct

mffm

fm

ct

5.5

:Solution

:Theory

25

• Estimate of Ecd for discontinuous fibers:

-- valid when fiber length <

-- Elastic modulus in fiber direction:

efficiency factor: -- aligned: K = 1 (aligned parallel)

-- aligned: K = 0 (aligned perpendicular)

-- random 2D: K = 3/8 (2D isotropy)

-- random 3D: K = 1/5 (3D isotropy)

Values from Table 16.3, Callister &

Rethwisch 8e. (Source for Table

16.3 is H. Krenchel, Fibre

Reinforcement, Copenhagen:

Akademisk Forlag, 1964.)

Composite Stiffness


Ecd = EmVm + KEfVf

15s fd

c

26

Composite Strength


• Estimate of for discontinuous fibers:

scd*

2. When l < lc

sc d *

c

dVf sm(1Vf )

l

sc d * s f

*Vf 1 c

2

sm (1Vf )

1. When l > lc

l

l

27

• Laminates -

-- stacked and bonded fiber-reinforced sheets

- stacking sequence: e.g., 0º/90º

- benefit: balanced in-plane stiffness Adapted from

Fig. 16.16,

Callister &

Rethwisch 8e.

Classification: Structural


• Sandwich panels -- honeycomb core between two facing sheets

- benefits: low density, large bending stiffness

honeycomb

adhesive layer face sheet



(Fig. 16.18 is from Engineered Materials

Handbook, Vol. 1, Composites, ASM International, Materials Park, OH, 1987.)

28

Composite Benefits

• PMCs: Increased E/r

E(GPa)

Density, r [mg/m3]

0.1 0.3 1 3 10 30 0.01

0.1

1

10

10 2

10 3

metal/ metal alloys

polymers

PMCs

ceramics

Adapted from T.G. Nieh, "Creep rupture of a

silicon-carbide reinforced aluminum

composite", Metall. Trans. A Vol. 15(1), pp.

139-146, 1984. Used with permission.

• MMCs: Increased

creep

resistance

20 30 50 100 200 10

-10

10 -8

10 -6

10 -4

6061 Al

6061 Al w/SiC whiskers s (MPa)

ss (s-1)

• CMCs: Increased toughness

fiber-reinf

un-reinf

particle-reinf Force

Bend displacement

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• Composites types are designated by: -- the matrix material (CMC, MMC, PMC)

-- the reinforcement (particles, fibers, structural)

• Composite property benefits: -- MMC: enhanced E, s, creep performance

-- CMC: enhanced KIc

-- PMC: enhanced E/r, sy, TS/r

• Particulate-reinforced: -- Types: large-particle and dispersion-strengthened

-- Properties are isotropic

• Fiber-reinforced: -- Types: continuous (aligned)

discontinuous (aligned or random)

-- Properties can be isotropic or anisotropic

• Structural: -- Laminates and sandwich panels

Summary

30

Core Problems:

ANNOUNCEMENTS

Reading: 16.1-16.5

16.10, 16.11,

16.13

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