AERO 214

Introduction to Aerospace Mechanics of Materials

Lecture 2

Materials for Aerospace Structures

• Aluminum

• Titanium

• Composites: Ceramic Fiber-Reinforced Polymer Matrix Composites

• High Temperature Materials: Superalloys and Ceramics

Mechanical Behavior: Elastic and Plastic

F

bonds

stretch

return to

initial

2

1. Initial 2. Small load 3. Unload

• Elastic, no remaining deformation upon unloading

• Due to stretching of bonds

Elastic Deformation

F

Linear Elastic

Non-Linear Elastic

• Modulus of Elasticity, E: (also known as Young's modulus)

10

• Hooke's Law:

Linear Elastic Isotropic

s

Linear- elastic

E e

13 0.2

8

0.6

1

Magnesium,

Aluminum

Platinum

Silver, Gold

Tantalum

Zinc, Ti

Steel, Ni

Molybdenum

Graphite

Si crystal

Glass-soda

Concrete

Si nitrideAl oxide

PC

Wood( grain)

AFRE( fibers)*

CFRE*

GFRE*

Glass fibers only

Carbon fibers only

Aramid fibers only

Epoxy only

0.4

0.8

2

4

6

10

20

40

6080

100

200

600800

10001200

400

Tin

Cu alloys

Tungsten

<100>

<111>

Si carbide

Diamond

PTFE

HDPE

LDPE

PP

Polyester

PSPET

CFRE( fibers)*

GFRE( fibers)*

GFRE(|| fibers)*

AFRE(|| fibers)*

CFRE(|| fibers)*

Metals

Alloys

Graphite

Ceramics

Semicond

Polymers Composites

/fibers

E(GPa)

Based on data in Table B2,

Callister 6e.

Composite data based on

reinforced epoxy with 60 vol%

of aligned

carbon (CFRE),

aramid (AFRE), or

glass (GFRE)

fibers.

Comparison of Elastic Moduli

3

1. Initial 2. Small load 3. Unload

• Plastic means permanent! • Permanent set • Proportional/elastic limit • Yielding point

F

linear elastic

linear elastic

plastic

Plastic Deformation in Metals

15

• Simple tension test:

(at lower temperatures, T < Tmelt/3)

Plastic Deformation in Metals

tensile stress, s

engineering strain, e Elastic

initially

Elastic+Plastic at larger stress

permanent (plastic) after load is removed

e p plastic strain

16

when ep = 0.002

Tensile Properties

tensile stress, s

engineering strain, e

0.002

17

Room T values

sy(ceramics)

>>sy(metals)

>> sy(polymers)

Based on data in Table B4,

Callister 6e.

a = annealed

hr = hot rolled

ag = aged

cd = cold drawn

cw = cold worked

qt = quenched & tempered

Comparison of Yield Strength Graphite/ Ceramics/ Semicond

Metals/ Alloys

Composites/ fibers

Polymers

Yie

ld s

tren

gth

, s

y (M

Pa)

PVC

Ha

rd t

o m

ea

su

re ,

s

inc

e i

n t

en

sio

n,

fra

ctu

re u

su

all

y o

cc

urs

be

fore

yie

ld.

Nylon 6,6

LDPE

70

20

40

60 50

100

10

30

2 00

3 00

4 00

5 00 6 00 7 00

10 00

2 0 00

Tin (pure)

Al (6061) a

Al (6061) ag

Cu (71500) hr Ta (pure) Ti (pure) a Steel (1020) hr

Steel (1020) cd Steel (4140) a

Steel (4140) qt

Ti (5Al-2.5Sn) a W (pure)

Mo (pure) Cu (71500) cw

Ha

rd t

o m

ea

su

re,

in c

era

mic

ma

trix

an

d e

po

xy

ma

trix

co

mp

os

ite

s,

sin

ce

in t

en

sio

n,

fra

ctu

re u

su

all

y o

cc

urs

be

fore

yie

ld.

H DPE PP

humid

dry

PC

PET

¨

18

Maximum possible engineering stress in tension

• Metals: occurs when noticeable necking starts. • Ceramics: occurs when crack propagation starts. • Polymers: occurs when polymer backbones are aligned and

about to break.

Adapted from Fig. 6.11,

Callister 6e.

Tensile Strength (TS)

Ductile vs Brittle Failure

Very

Ductile

Moderately

Ductile Brittle

Fracture

behavior:

Large Moderate %AR or %EL Small

Adapted from Fig. 8.1,

Callister 7e.

• Ductile: warning (large plastic deformation) before fracture

• Brittle: No warning

ductile brittle

Ductile vs Brittle Failure

17

• Evolution to failure: Necking is the localization of damage

100 mm

Fracture surface of tire cord wire

loaded in tension. Courtesy of F.

Roehrig, CC Technologies, Dublin,

OH. Used with permission.

Moderately Ductile Failure

necking

s

void nucleation

void growth and linkage

shearing at surface

fracture

Tensile strain at failure, %EL:

20

%AR

Ao A f

Ao

x100

• Note: %AR and %EL are often comparable. crystal slip does not change material volume. %AR > %EL possible if internal voids form in neck.

%EL

L f Lo

Lo

x100

Adapted from Fig. 6.13,

Callister 6e.

Ductility

Reduction in the area at failure, %AL:

• Ability to absorb energy up to fracture

21

smaller toughness- unreinforced polymers

Engineering tensile strain, e

Engineering

tensile

stress, s

smaller toughness (ceramics)

larger toughness (metals, PMCs)

• Usually ductile materials have more toughness than brittle one • Areas below the curves

Toughness

0

f

W de

s e

True Stress & Strain

iT AFs

oiT lne

ee

ess

1ln

1

T

T

• Curve fit to the stress-strain of plastic deformation:

s T K e T n

“true” stress (F/A) “true” strain: ln(L/Lo)

hardening exponent: n = 0.15 (some steels) to n = 0.5 (some coppers)

22

• Curve fit to the stress-strain response:

True stress & strain

n

TT Kes n = hardening exponent

n = 0.15 (some steels)

n = 0.5 (some copper)

Material

Elastic

Modulus (E)

[GPa]

Strength (S)

[MPa]

%

Elongation

Aluminum

Al 7075-T6 71.7 Yield Strength: 505 11% 2810 25.5 0.18

Titanium

Ti-6Al-4V 113.8 Yield Strength: 830 14% 4430 25.7 0.187

Epoxy 2.41 Tensile Strength: 40 5% 1300 1.85 0.031

Carbon Fiber 230 Tensile Strength: 4000 2% 1780 129.2 2.25

Carbon fiber-Epoxy

Composite

(Vf=60%)

Longitudinal: 220 Tensile Strength: 760 0.3

1700

129.4 0.447

Transverse: 6.9 Tensile Strength: 28 0.4 4.06 0.016

Properties of Common Aerospace Structural Materials

Hardness

Hardness • Measure of resistance to localized plastic deformation • Simple, non-destructive, not a well-defined material property

1. Scratch hardness: Mohs scale, 2. Indentation hardness: Rockwell, Vickers, Brinell, Shore 3. Rebound (Dynamic) hardness: Leeb, scleroscope

• Larger hardness:

• smaller indent • resistance to plastic deformation or cracking in compression • better wear properties

increasing hardness

most plastics

brasses Al alloys

easy to machine steels file hard

cutting tools

nitrided steels diamond

Indentation Hardness

Brinell Hardness (HB)

10 mm sphere

F= 10,000 N measure size of indent after removing load

d D Smaller indents mean larger hardness.

• D=10 mm hardened steel

• Keep at least 3 indentation diameters away from the edge or previous mark

• Hardness can be related to tensile strength • For steel: TS (MPa) = 3.45 × HB

Appendix

Stress and strain are point-wise and can vary over the space.

Photoelasticity

c07f14

Stress-strain of iron at several temperatures

Stress-Strain Behaviors of Polymers

brittle polymer

Plastic polymer

elastomer

Tensile strength of polymer ca. 10% that of metals

Strains – deformations > 1000% possible (for metals, maximum strain ca. 10% or less)

elastic modulus – less than metal

37

Dislocation Motion Dislocations & plastic deformation

• Cubic & hexagonal metals - plastic deformation by plastic shear or slip where one plane of atoms slides over adjacent plane by defect motion (dislocations).

• If dislocations don't move,

deformation doesn't occur! Adapted from Fig. 7.1,

Callister 7e.