- introduction to composite materials - review of stress and...

M2794.007700 Smart Materials and Design

School of Mechanical and Aerospace Engineering Seoul National University

http://[email protected]

- Introduction to Composite Materials

- Review of Stress and Strain

1

April 6, 2017

Prof. Sung-Hoon Ahn (安成勳)

GENDER INNOVATIONS

2

© Sung-Hoon Ahn

Gender In Engineering Education

▪ Pregnant Crash Test Dummies:

- Rethinking Standards and Reference Models

3

Female crash test dummies

The Challenge• Conventional seatbelts do not fit pregnant women properly

(Weiss et al., 2001).• Even a relatively minor crash at 56km/h (35 mph) can cause

harm. With over 13 million women pregnant (European Unionand USA) each year, the use of seatbelts during pregnancy is amajor safety concern (Eurostat, 2011; Finer et al., 2011).

Method: Rethinking Standards and Reference Models• The male body is often defined as the norm and serves as the primary object of study.• In this case, crash test dummies were first developed to model the U.S. 50th percentile man (taken as

the norm).• This means that other segments of the population were left out of the discovery phase in design.• Inattention to humans of different sizes and shapes may result in unintended harm.

Gendered Innovations:

1. Taking both women and men as the norm may expand creativity in science and technology. From thestart, devices should be designed for safety in broad populations.2. Analyzing sex has led to the development of pregnant crash dummies and computer simulations.

© Sung-Hoon Ahn

▪ Cases

4

Imaging equipment for organ toxicity models

Materials for protective shielding

▪ If your team project is related to Gendered Innovations, there will be a 2% of extra grade

Gender In Engineering Education

© Sung-Hoon Ahn

Emotional ICT industrial products

5

0

1

2

3

4

Roughness Stiffness Temperature Familiarity

Male

Zirconia difference Alumina difference

Aluminum difference Polycarbonate difference

0

1

2

3

4

Roughness Stiffness Temperature Familiarity

Female

Zirconia difference Alumina difference

Aluminum difference Polycarbonate difference

• Devices that are used in public

• There are various gender issues on the material of the product

• Grip, scratch, pattern of cover material, color, etc.

Difference between Blind touch and touch

INTRODUCTION TO COMPOSITE MATERIALS

6

© Sung-Hoon Ahn

Basic types of materials

▪ Metal

▪ Polymer

▪ Ceramic

▪ Where do we use engineering composites?

▪ Aerospace structures

• Commercial 5 ~ 10 % weight

• Business jet

• Military

• Satellite ~ 100% structural parts

▪ Sports goods : tennis rackets, golf shaft, ski, …

▪ Automobile, ship

▪ Biomedical : hip joint

7

Metal

Polymer Ceramic

Composite

© Sung-Hoon Ahn

Why do we use composite?

▪ High E/ρ

▪ High σ/ ρ

▪ Fatigue life

▪ Corrosion

resistance

8

Ashby chart[1]

[1] The CES Edupack Resource Booklet 2 – Material and Process Charts, © Granta Design (2009)

© Sung-Hoon Ahn

What is composite material?

▪ Two or more materials (metal, polymer and/or ceramic)

▪ Consist of two or more phases in macroscopic scale

▪ Mechanical performance and properties are designed to be superior

to those of the constituent materials acting independently

• Phase ~ Constituent : Alloys (X)

• Macroscopic scale(~fiber dimension) > Grain size(molecular dimension)

▪ cf) Characteristic dimensions (general)

9

100 nm 100 μm 1 mm

Atomic Micro scale Meso scale Macro scale

© Sung-Hoon Ahn

▪ Homogeneous

▪ Independent of location

▪ Scale/characteristic volume dependent concept

▪ Heterogeneous/inhomogeneous

▪ Properties vary from point to point

Classifications of materials

10

Heterogeneous Homogeneous/Quasi Homogeneous

10 mm 10 μm

© Sung-Hoon Ahn

▪ Isotropic

▪ Properties are the same in all direction

▪ Infinite number of plane of material symmetry

▪ Anisotropic

▪ Properties vary with direction

• Zero plane of material symmetry(general anisotropy)

▪ Orthotropic

▪ 3 mutually perpendicular plane of symmetry

▪ Most metal, ceramic and polymer : homogeneous and isotropic

▪ Continuous fiber reinforced composite : (Quasi) homogeneous and

anisotropic material

▪ cf) Functionally graded material (FGM)

▪ Continuously varied properties

Classifications of materials

11

Matrix

Fiber

© Sung-Hoon Ahn

Behavior of general anisotropic material under loading

▪ Response of various materials under uniaxial normal and pure shear loading

12

Isotropic

Anisotropic (or orthotropic material loaded along nonprincipal directions)

Orthotropic (loaded along principal material directions)

N N

N

Top view

Side view

N

N

© Sung-Hoon Ahn

Types of composite materials

▪ Reinforcement

▪ Strengthen

▪ Fibers L/D >> 1 : “fiber reinforced composite”

▪ Particles L/D ~ 1 : “particulate composite”

▪ Matrix

▪ Polymer, metal and ceramic

▪ cf) “Laminated composite”

▪ Thin layers bonded together

▪ Bimetal, clad metal and plywood

13

L

D

Fiber

Particle

L

D

© Sung-Hoon Ahn

Why fibers?

▪ Stronger than bulk

▪ Griffith’s experiment (1920)

• Glass fiber

• Less (surface cracks) that would induce failure

▪ Size effect

14

SiC whisker(0.5 micro meter dia.)

Multiwall CNT(20 nano meter dia.)

© Sung-Hoon Ahn

Other materials

▪ Other materials showing similar behavior

▪ Polymer fibers : highly aligned polymer chains

▪ Whisker

• Single crystal : lower dislocation density than a polycrystalline solid

• L/D ~ 100

• Strongest reinforcing material

• Eg) Iron crystal theoretical strength : 200GPa

Iron whisker : 13GPa

Iron bulk : 0.5 ~ 0.7 Gpa

15

Fiber

Vs.

Bulk

Vs.

© Sung-Hoon Ahn

Typical fiber materials

▪ Typical fiber materials

▪ Glass

• Cheap

• Strong

• Low modulus

▪ Boron

• Tungsten/carbon substrate

▪ Carbon (graphite/pitch)

• Aerospace

• Cost is an important factor

▪ Kevlar, aramid, polyamid

▪ SiC (Silicone Carbide)

• Very high temperature

16

© Sung-Hoon Ahn 17

CAD/CAM integration

Global collaborationUS design, manufactured around the world

Higher efficiency – composite materials (40~55% weight)

Boeing 787

Applications of reinforced plastic

PART: Wing box

CO: Mitsubishi Heavy Industries

Japan

PART: Vertical tail assembly

CO: Boeing Fredrickson

Washington,Canada,Australia

PART: Movable trailing edges

CO: Hawker de Havilland

Australia

PART: Leading edges

CO: Spirit Aerosystems

Kansas, OklahomaPART: Wing-to-body fairing

CO: Boeing Winnipeg

Washington,Canada,Australia

PART: Cargo doors, access doors

CO: Saab Aerostructures

Sweden

PART: Center wing box

CO: Fuji Heavy Industries

Japan

PART: Engine Pylons


Kansas, Oklahoma

PART: Naoelles

CO: Goodrich

North Carolina

PART: Engines

CO: General Electric

Ohio

PART: Forward fuselage


Kansas, Oklahoma

PART: Fixed trailing edge

CO: Kawasaki Heavy Industries

JapanPART: Horizontal stabilizer,center fuselage, aft fuselage

CO: Alenia/Vought

Italy, Texas

PART: Fuselage, wheel well

CO: Kawasaki Heavy Industries

Japan

PART: Landing gear

CO: Messier-Dowty

France

PART: Passenger doors

CO: Latecoere

France

PART: Engines

CO: Rolls-Royce

U. K.

PART: Wingtips

CO: Korean Airlines-AerospaceDivision

Korea

http://100.naver.com/100.php?id=769693























© Sung-Hoon Ahn

Thermoset and thermoplastics

18

Thermoset Thermoplastic

Epoxy Polyethylene

Polyester Polystylene

Phenolics Polypropylene

Bismaleimide (BMI) Polyetherether ketone (PEEK)

Polyimide Polyethersulfone

Undergo chemical change Non-reacting

Process irreversible Post-formable

Low viscosity High viscosity

Long cure (~ 2hr) Short process time

Lower process temperature High process temperature

Good filler wetting Rapid processing

Long process time High process temperature

Restricted storage (Refrigeration) Less chemical solvent (Resistance)

© Sung-Hoon Ahn

Classification by reinforcement

19

▪ Particulate filler

▪ Discontinuous fibers/whiskers

▪ Continuous fibers

© Sung-Hoon Ahn

Matrices

▪ Functions of matrix

▪ Fiber alone can not support longitudinal compression

▪ Weight reduction (usually low density than fiber)

▪ Cost reduction (cheaper than fiber, mtotal=mfiber+mmatrix)

▪ Protect fiber from environmental attack

• eg. Ultra violet degradation, chemical attack

20

© Sung-Hoon Ahn

Type of matrices (tempertature)

▪ Polymer

▪ Thermoset

• Epoxy

• 120°C/250°F for sporting goods, 175°C/350°F for aerospace

• Polyimide

• 370°C/700°F

▪ Thermoplastic

• PEEK

• Polysulfone (400°C/750°F)

▪ Metal

▪ Aluminum, Magnesium ( ~ 800°C/1500°F)

▪ Titanium (900°C/1700°F)

▪ Ceramic

▪ Glass, Si3N4, Al2O3, SiC (1000~1500°C)

▪ Carbon

• C-C : Aircraft brake (~2600°C/4700°F)

21

© Sung-Hoon Ahn

Lamina and Laminate

▪ Lamina (ply)

▪ A layer of unidirectional fibers or woven fabric

▪ Orthotropic material

▪ Laminate

▪ Made up of two or more laminas (plies)

▪ Ply orientation

▪ Angle between reference x-axis & fiber orientation in a counter

clockwise direction

22

x

y

loading

© Sung-Hoon Ahn

Lamina and Laminate

▪ Stacking sequence

▪ Configuration indicating the exact location or sequence of each ply

▪ From the bottom ply

▪ Example of laminate designation

▪ Unidirectional : [0]

▪ Angle : θ [θ]

▪ # (number) : repeated group of plies

▪ s : symmetric

▪ T : total ( to distinguish from symmetric)

▪ - (over bar) : symmetric about mid-plane ply

▪ Ex : [(0/±45)2]s

23

1

n...

© Sung-Hoon Ahn

Stacking sequence

▪ Notation

▪ [0]

▪ [θ]

▪ Number : repetition of group

▪ s : symmetric

▪ T : total

▪ Q:▪ [(0/45)2]→[0/45/0/45]

▪ [(0/45)2]s→[0/45/0/45/45/0/45/0]

▪ [(0/±45)2]s→[0/+45/-45/0/+45/-45/-45/+45/0/-45/+45/0]

24

[0°/45°/-45°/0°]

© Sung-Hoon Ahn

General material properties

▪ General material properties

▪ Material constant : 1, 2, 3 direction

▪ Fiber volume ratio

25

comp

fiber

fv

vv

1

2

3

V fiber

© Sung-Hoon Ahn

Analysis level

▪ Analysis level

▪ Micro mechanics

• Fiber & matrix

• Fiber failure

• Tensile, buckling and spliting

• Local matrix failure

(tensile/compression)

• Interface failure

▪ Macro mechanics

• Lamina level

• Consider as homogeneous and anisotropic

• Average stress, strength

▪ Lamination theory

• Laminate level

• CLT (Classical Lamination theory)

• Structure level26

Matrix Fiber

Ply (lamina)

Laminate Structure

Load

Micro mechanics

Macro mechanics

TemperatureMoisture

Hygrothermal

© Sung-Hoon Ahn

Manufacturing processes

1. Prepreg

1. Autoclave : 20 ~ 100 psi (138 ~ 689 kPa)

2. Vacuum : 1 atm (14.7 psi, 101 kPa)

3. Hot press : plate

2. Filament winding

1. Pressure vessel

2. Shaft

3. Pultrusion

1. Simple cross section

4. Molding

1. SMC (Sheet Mold Compound)

2. BMC (Bulk Mold Compound)

3. RTM (Resin Transfer Molding)

5. Automation of layups

1. Tape layup

2. 3DP with short fiber

6. Honeycomb

1. High stiffness by geometric design

27

12

3bhI

b

h

Hh

b b

B

12

33 bhBHI

© Sung-Hoon Ahn

Elastic behavior of unidirectional lamina

▪ Objectives

▪ Isotropic E, ν : anisotropic elastic constant ?

▪ Transformation of σ, ε

▪ Behavior of isotropic materials

▪ Axial loading

▪ Shear loading

28

1E

)(1

3211 E

G

11

)1(2

EG

E, ν : only 2 elastic constant

© Sung-Hoon Ahn

Scalar, vector and tensor

▪ Scalar (Scalae) – “stairs”

▪ Tensor of order zero

▪ A pure number

▪ Mass of car, temperature of body….

▪ Vector (Vectus) – “carried”

▪ Tensor of order 1

▪ Magnitude & direction

▪ Position, velocity, force

▪ Tensor (Tensus) – “tension”, “stretched”

▪ Hamilton, Irish

▪ Tensor of order 2 and higher

▪ Stress inside solid, fluid, moment of inertia (Ixx Ixy)

29

0

∞

[1], [10]

987

654

321

© Sung-Hoon Ahn

Vector algebra

▪ Dot (scalar) product

▪ : map a vector to scalar

▪ Cross (vector) product

▪ : map a vector to vector

▪ Dyad (direct) product

▪ Map into a vector parallel to

30

cosvuvu

uvcosθ

v

uθ

u

evuvu )sin(

sinvuvu

vu

e

u

vθ

baT Tensor

v a

avbvbavbavba )()( Tensor

© Sung-Hoon Ahn

Indicial notation

▪ Indicial notation (simple way to represent tensors)

▪ A vector in 3D space

31

332211 eAeAeAA

321 , , eee : unit vector

Symbolic notation

ii eAAx

y

2e1e

3e A

z

Symbolic indicial

121

3

2

1

AAAor

A

A

A

A

Matrix notation

iAA Indicial notation

© Sung-Hoon Ahn

Convention

▪ An unrepeated subscript has a range over which it takes all values

▪ eg) i=1, 2, 3

▪ A repeated subscript implies summation over the range of permissible

values

▪ eg) dyadic product

▪ eg) dot product

▪ eg) cross product

32

332211 eAeAeAA 332211 eBeBeBB

))(( 332211332211 eAeAeAeAeAeABA

313121211111 eeBAeeBAeeBA



jiji eeBA

332313

322212

312111

BABABA

BABABA

BABABA

Matrix

ji BA i,j=1, 2,3

indicial

ii vev iivuvu

kjiijk evuvu

zero are indices moreor twoif 0

npermutatio odd has k) j, (i, if 1

npermutatioeven has k) j, (i, if 1

ijkPermutation symbol

© Sung-Hoon Ahn

Coordinate transformation

33

X1

X2

2e1e

3e

X3

1e

2e

3e

A

332211 eAeAeAA

)()()( 3132121111 eeAeeAeeAA

3132121111 AAAA

jiij eewhere

jiji AA

ij Cosine of the angle between the i-th primed axis and the j-th unprimed axis

Vector

1X

2X

3X

© Sung-Hoon Ahn

1. 2-D transformation

2. Transformation of 2nd order tensor

Coordinate transformation

34

X1

X2

1X 2X

θ

θ

cos),cos(

sin)90cos(),cos(

sin)90cos(),cos(

cos),cos(

2222

1221

2112

1111

XX

XX

XX

XX

2

1

2

1

2221

1211

cossin

sincos

cossin

sincos

X

X

X

X

ij

kljlikij AA

© Sung-Hoon Ahn

Number of elements in stiffness/compliance matrix

81 general

36 symmetry of stress-strain

21 symmetry of material constant

9 orthotropic case3 mutually perpendicular planes of material symmetry

5 Transversely isotropic

2 isotopic

Stress-strain in anisotropic material (3D)

35

klijklij C

klijklij S 3,2,1,,, lkji

matrix Stiffness : ijklC matrix Compliance : ijklS

1 ijklijkl SC

jiijjiij &

jiijjiij SSCC &

3

2

1

3

2

1

66

55

44

332313

232212

131211

3

2

1

3

2

1

C

C

C

CCC

CCC

CCC

66552322

4433221312 ,2

,, CCCC

CCCCC

2, 1211

665544332211

CCCCCCCC

&E

© Sung-Hoon Ahn

▪ Plane stress

▪ no stress in thickness direction

3

2

1

3

2

1

3

2

1

0

0

0

Stress-strain in anisotropic 2D

36

0)()( 2131233

© Sung-Hoon Ahn

Stress-strain in anisotropic 2D

37

3663

222112

2

33

2323221

23

2313122

12111

2

33

1323121

33

1313111

C

QQ

C

CCC

C

CCC

QQ

C

CCC

C

CCC

2

33

231

33

133

C

C

C

C

1 11 12 1

2 21 22 2

3 66 3

Into matrix form

0

0

0 0

Q Q

Q Q

Q

3

2

1

66

2221

1211

3

2

1

00

0

0

S

SS

SS

In matrix form

© Sung-Hoon Ahn

How to measure the material constants?

▪ Test 1

▪ Test 2

38

102

2

01

1 1

1

122 12 1 1

1

1211 12

1 1

1

1( , )

E

E

S SE E

2 2

2

211 21 2 2

2

2122 21

2 2

1

1( , )

E

E

S SE E

12 2112 21

1 2

S SE E

111

12 21

222

12 21

21 1 12 212

12 21 12 21

66 12

1

1

1 1

EQ

EQ

E EQ

Q G

© Sung-Hoon Ahn

Transformation of stress and strain

▪ Loading axes

▪ Principal mat. Axes

39

),( yx

)2 ,1(

1

2

y

x

22

22

22

2

2

nmmnmn

mnmn

mnnm

T

sin

cos

n

m

s

y

x

T

3

2

1

s

y

x

T

2

1

2

13

2

1

© Sung-Hoon Ahn


▪ Q : How to get off-axis stress-strain relation?

40

y

x

xy

y

x

xy

xyxy

xy

xyxyxy

TTQT

QQT

TT

Q

][

1212

1

1212121212

1

1212

1

ss

xy

xx

Q

Q

QQQQQ

cossin)2(2sincos 22

6612

4

22

4

11

3122

1

sxyxy 2

1

2

1

© Sung-Hoon Ahn

Smart materials and design H.W. #3

1) For a high strength (HS) carbon fiber/epoxy lamina, calculate the on-axis stiffness

matrix, [Q]1,2 (E11 =131.0 GPa, E22 = 11.2 GPa, ν12 = 0.28, G12 = 6.55 GPa)

2) Assuming it is isotropic lamina, calculate the on-axis stiffness matrix, [Q]1,2 (E11

= E22 = 131.0 GPa, ν12 = ν21 = 0.30, G12 = G21 = 6.50 GPa)

3) Using the [Q]1,2 matrix in problem 1), calculate the off-axis stiffness matrix [Q]x,y

of the cylinder where the fiber angle is 45° from the x-axis

4) Write the transforming code (Matlab) from [Q]1,2 to [Q]x,y

42

12

x

y45 °

© Sung-Hoon Ahn

Classical lamination theory

▪ Composite beam

▪ N-plane displacement

43

x

zw.

y

wzvv

x

wzuu

0

0

2

0

2

0

0

2

0 0

2

x

x x

y y y

xy

u u wz

x x x

z

vz

y

u v u v wz

y x x x x y

0

0

0

x x x

y y y

xy s s

z

00 0

2

2

s

s

u v

x x

w

x y

© Sung-Hoon Ahn

Classical lamination theory

44

KE

1k

layer thk

Ref. plane

x

y

s

0

0

0

layerth

xx xy x

y

sk k k

x x

y y

s sk k

for k

Q Q

Q z Q

© Sung-Hoon Ahn

Failure

▪ Failure theories : How to define failure of composite?

▪ Max. stress

▪ Max strain

▪ Tsai – Hill

▪ Tsai - Wu

▪ Parameters

45

F1t F1c F2t F2cF2 or F6

© Sung-Hoon Ahn

Failure

▪ Tension along the fiber▪ fiber breakage & matrix failure

▪ Tension normal to the fiber

▪ matrix cracking

▪ Shear

▪ matrix shear out

▪ Compression along the

fiber

▪ Compression normal to the

fiber

46

Micro buckling shear out in fibers kinking

Matrix failure

REVIEW OF STRESS AND STRAIN

47

© Sung-Hoon Ahn

Review of isotropic stress analysis

▪ Isotropic 2 material constant,

▪ Displacement Strain Stress Force

▪ Stress

▪ 6 components

48

Failure

&E

ux

u

E

zxyzxyzyx ,,,,,

x

y

z

1F

2F

3F

4F

5F

6F

1 Component per side (Normal)

2 Component per side (Shear)

iF

1iF

2iF

For cube of unit dimension

© Sung-Hoon Ahn


▪ Known relations

▪ For Normal stresses equilibrium of forces & moments

▪ For shear stresses

49

0

0

0

z

y

x

F

F

F

),,(

Components 3

zyx

xx

y

y

0

0

0

z

y

x

F

F

Fyx

yx

xy xy daForce

db

© Sung-Hoon Ahn


▪ Transformation

50

0

0

0

z

y

x

F

F

F

Moment

zyyz

xzzx

xyyx

old

0 dadbM xyyxc

),,(

)(

Components 3

zxyzxy

zyx ,σ,σσ

Vector

Tensor

jiji AA new

kljlikij AA

kljlikij oldnew

1

y

θx

2

cosinedirection ij

new

old

dbda

© Sung-Hoon Ahn


▪ Biaxial stress transformation

51

xy

y

x

nmmnmn

mnmn

mnnm

22

22

22

12

2

1

2

2

oldnew T

sin

cos

n

m

Cf.) reverse direction (1,2) →(x,y) 2,1

1

, ][ Tyx

)]([)]([ 1 TT ITT )()(

cos A

sin A

1y

x

2

A

cos Ax

12

)cos ( Axy

sin Ay )sin ( Axy

01 F

02 F

© Sung-Hoon Ahn


▪ Strains

▪ Biaxial stress transformation

52

x

u

y

u

y

u

x

u

yxxy

y

y

xx

xx

uEngineering shear strain

xuy

x

y

x

xy

x

u

y

u yxxy

2

1

Tensorial shear strain

xy

y

x

xy

y

x

TT

12

2

1

12

2

1

22

xy

© Sung-Hoon Ahn

Stress analysis of simple geometrics

loading Geometry stress

Axial load

Bending

Torsion

Pressure

53

A

Nσ x N

A

I

Myσ x

I

Mcσ max

M

x

u

Iy, dAyI 2

J

Tcτ max

J

Trτ xy

T r

Jr, dArJ 2

r

tr,

tP x

zy

2t

rPx

t

rPσ y

Pσz

© Sung-Hoon Ahn


▪ For linear elastic case, the stresses can be added together

▪ Failure

54

T MPN

E

E

rP

I

My

A

Nx

2

Yielding (Ductile)Fracture (Brittle)

'yS>

< Yield strength

><

Surface energy to propagate

crackStrain energy

© Sung-Hoon Ahn


▪ Von Mises

55

Principal direction (No shear)

'6662

1

'2

1

2

1

222222

2

12

13

2

32

2

21

zxyzxyxzzyyx

pppppp

© Sung-Hoon Ahn

General σ & ε (anisotropic case)

▪ Simplified notation

56

klijklij

klijklij

S

C

321 , , i,j,k,l

1CS

ijklijkl

elements8134

General elastic constant Cijkl , Sijkl

from symmetry of stress, strain as in isotropic case

jiij

jiij

36 element

(6×6)

3612

2531

142323

333

222

111

1

3

21122

33

© Sung-Hoon Ahn

General σ & ε (anisotropic case)

▪ Symmetry of elastic constant

57

3612

2531

142323

333

222

111

2

2

2

Engineering shear strain!!

151131141123

131133121122111111

CCCC

CCCCCC

Work per unit volumei

i By differentiation

jiijii C2

1

2

1W

i

i

W

jiji C

- introduction to composite materials - review of stress and...

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