ASE324: Aerospace Materials Laboratory

Instructor: Rui Huang

Dept of Aerospace Engineering and Engineering MechanicsThe University of Texas at Austin

Fall 2003

Lecture 13

October 16, 2003

Introduction to composite materials

• Two approaches can be used to engineer mechanical properties of materials:– Intrinsic modification (e.g., alloying)– Extrinsic modification (composite)

– Nanomaterials: nanocrystals and nanocomposites

Composite approach

• Certain property (e.g., strength) of a material may be improved by mixing with other materials.

• The host material commonly known as matrix and the other material(s) known as reinforcement(s).

• Almost infinite arrays of properties can be designed via composite approach.

Examples of composite materials

• Wood is a natural composite that consists of hemi-cellulose fibers in a matrix of lignin.

• Concrete is an artificial composite that consists of sand, cement, and stone.

• More commonly, polymer matrix composites are reinforced with glass or carbon fibers (e.g., pole vaults, tennis racquets)

Matrix materials

• Polymer: reinforced to improve stiffness and strength

• Metal: reinforced to provide creep resistance at high temperature

• Ceramic: reinforced to improve fracture toughness

Types of composite materials• Fiber-reinforced composites

– Wood: cellulose fibers in lignin matrix

• Laminated composites– Plywood, sandwich panels

• Particulate composites– Rocket propellant: aluminum particles in polyurethane

• Hybrids, such as laminated fiber-reinforced composites

Laminated fiber-reinforced composites

• Laminae: flat layers, each with unidirectional fibers.

• Laminate: a stack of laminae of various fiber orientations.

• Tailor the directional dependence of material properties (anisotropy)

Mechanical properties of composites

• Inhomogeneous: properties depend on position (micro-mechanics)

• Anisotropic: properties depend on direction (macro-mechanics)

Elastic modulus• Fiber-reinforced composites

Direction 1

Direction 2

)1(1 fmff VEVEE −+=1

2

1−

−+=

m

f

f

f

EV

EV

E

Direction 1

• Same strain in fibers and matrix.• But different stresses (inhomogeneity).

• Total force:• Average stress:• Average modulus:

mmff AAP σσ +=

)1(1 fmffmf

VVAA

P−+=

+= σσσ

)1(1

11 fmff VEVEE −+==

εσ

Direction 2

• Total elongation:• Total strain:• Average modulus:

mmff hh εεδ +=

)1(2 fmffmf

VVhh

−+=+

= εεδε

1

2

22

1−

−+==

m

f

f

f

EV

EV

Eεσ

•Same stress in fibers and matrix•But different strains

Elastic anisotropy

σ

Matrix

Composite Ef

Em

E1E2

Fiber

ε

E1 = E2 if Ef = Em (homogeneous, no reinforcement)

Particulate composites• E1 and E2 are the upper and lower limits for the

elastic modulus of particulate composites.

Poisson’s ratio

Transverse strains:

fff ενε −=' mmm ενε −=' 1εεε == mf

)1(''2 fmff VV −+= εεε

Major Poisson’s ratio:)1(

1

221 fmff VV −+=−= νν

εεν

2112 νν ≠Minor Poisson’s ratio:

Shear modulus

σ12σ12

σ21

σ21

Composite shear strain:)1(12 fmff VV −+= γγγ

Composite shear modulus: 1

12

1212

1−

−+==

m

f

f

f

GV

GV

Gγσ

Compliance matrix• Under plane-stress condition:

=

12

2

1

333231

232221

131211

12

2

1

σσσ

γεε

sssssssss

compliance

For isotropic elastic materials:

Ess 1

2211 ==G

s 133 = E

ss ν−== 2112 032312313 ==== ssss

Two independent constants: E, G, or ν (independent of orientation)

( )ν+=12EG ( )121133 2 sss −=

Composite complianceDirection 2

=

12

2

1

33

2221

1211

12

2

1

0000

σσσ

γεε

sssss

Direction 1

• Four independent elastic constants (plane orthotropic)

111

1E

s =2

221E

s =12

331G

s =

1

2121 Es ν

−=2

1212 Es ν

−=

1221 ss =2

21

1

12

EEνν

=

Summary

• Introduction to composite materials– Matrix and reinforcement– Laminated fiber-reinforced composites

• Mechanical properties of composite materials – Inhomogeneous and anisotropic.– Elastic deformation of fiber-reinforced composites:

plane orthortropic compliance matrix