2015 Composites Lab1

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Composite Materials

Lab 1

Alexandros Iliopoulos

Artemis Kalteremidou

November 25 2015







1. Elastic behaviour of composite lamina –

Micromechanics (Chapter 3)1.1 Micromechanics concepts

1.2 Engineering parameter calculation

2. Elastic behaviour of composite lamina – Macromechanics (Chapter 4)

2.1 Anisotropic compliance and stiffness matrix

2.2 Transformation



Micromechanics

Single layer with material coordinate system



Micromechanics

Unit cell modeling

Figure: Unit cells within the material



Micromechanics

Unit cell modeling

Figure: Single unit cell



Micromechanics

Problem 1 (3.1 in book)

Derive the expressions

for fiber volume ratio and determine its maximum value in each case.



Micromechanics






Micromechanics




1. Elastic behaviour of composite lamina – Micromechanics (Chapter 3)

1.1 Micromechanics concepts


2. Elastic behaviour of composite lamina – Macromechanics (Chapter 4)


2.2 Transformation





Micromechanics

1) Mechanics of material approach

Assumptions for rule-of-mixtures

1) Fiber: isotropic (or transversely isotropic), homogenous, regular array, linear elastic, as line

2) Matrix: isotropic, homogenous, linear elastic

3) Bonding: no gap



Micromechanics


Rule of mixture for E1

1

1 1 1 1

1 1 1 1

1

f f m m

f f m m

f m f m

f f m m

P A A A

AE A E A E

A A E E E A A

E V E V E



Micromechanics


Rule of mixture for E2

2

2 2

2

2

f f m m

f m f f m m

f m

f m

f m

f m

m f f m

B B V B V B

V V V V

E E

V V E

E E

E E E

V E V E



Micromechanics


Rule of mixture for 12

2

12

1

2 12 1

2 2 1 1

12 1 1 1

12

f m f f m m f f m m

f f m m

f f m m

B B B

B B B BV BV BV BV

B BV BV

V V



Micromechanics

2) Halpin-Tsai semi-empirical relation for E2



Micromechanics

Summary for engineering parameter calculation

Mechanics:

Halpin-Tsai:



Micromechanics




Micromechanics




Micromechanics


h



Micromechanics

Problem 6 (3.13 in book) - Solution

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 11

1.5

2

2.5

3

3.5

4

4.5Mechanics of material approach

Vf

E 2 / E m

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 11

1.5

2

2.5

3

3.5

4

4.5Halpin-Tsai relation

Vf

E 2 / E m

Mi h i



Micromechanics








Macromechanics



Macromechanics

Single layer with material coordinate system

Macromechanics



Macromechanics

Stress in 1 direction

Macromechanics



Macromechanics

Stress in 2 direction

Macromechanics



Macromechanics

Shear stress in 23 direction





Macromechanics



Macromechanics

Stiffness matrix for orthotropic material

Macromechanics



Macromechanics

Compliance and stiffness matrix for isotropic and transversely isotropic material

Macromechanics



Macromechanics

Plane stress

Macromechanics



Macromechanics

Plane stress compliance matrix

Macromechanics



Macromechanics

Reduced stiffness matrix



1. Elastic behaviour of composite lamia – Micromechanics (Chapter 3)

1.1 Micromechanics concepts


2. Elastic behaviour of composite lamia – Macromechanics (Chapter 4)


2.2 Transformation



Macromechanics



Stress vector rotation

Macromechanics



Strain vector rotation

Macromechanics



Transformed reduced compliance

Macromechanics



Transformed reduced compliance

Macromechanics




Macromechanics




Macromechanics






Any questions:[email protected]

kkaltere@vub ac be

2015 Composites Lab1

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