230404 - Composite Materials

Question 1

How many material parameters are involved in 3D Hookes Law?

Answer 1

Youngs modulus and Poisson ratio.

Question 2

How many material parameters are involved in 2D Hookes Law?

Answer 2

Youngs modulus and Poisson ratio.

Question 3

How many material parameters are involved in 1D Hookes Law?

Answer 3

Youngs modulus: tension. Poisson ratio: torsion.

Question 4

How do you quantify the ratio between fibers and matrix?

Answer 4

This is important to find the mechanical properties of the laminate.
1. Mechanics of Materials approach.
2. Elasticity Solutions. Tsai.
3.

Question 5

Volume fraction

Answer 5

Fiber volume vs. Total volume
Matrix volume vs. Total volume

Question 6

Two different classic ratio alternatives:

Answer 6

Mass fraction ψ and Volume fraction Φ.

Question 7

1. MMA (Mechanics of Materials Approach) Young’s Modulus E1
   Direction 1

Answer 7

Direction 1 (along the fiber orientation).
* Linear relation: Fiber volume increases –> Modulus increases.
* Parallel arrangement of the fiber and the matrix, two parallel springs. Derived from the hooke’s law.
* Equal strain.
* Rule of mixtures or Voigt rule.

Question 8

1. MMA (Mechanics of Materials Approach) Poisson’s Ratio

Answer 8

• Linear ratio between both Poisson’s ratio. Fiber volume increases –> Lamina Poisson’s ratio increases.

Question 9

1. MMA (Mechanics of Materials Approach) Young’s Modulus E2
   Direction 2

Answer 9

• Non linear: fiber volume increases –> Lamina Modulus increases.
• Direction 2 (perpendicular to the fiber orientation):
  Serial arrangement of fiber and matrix, two serial springs.
• Equal stress.
• Inverse rule of mixtures or Reuss rule.

Question 10

1. MMA (Mechanics of Materials Approach) Shear Modulus

Answer 10

Non linear.
* For ISOTROPIC materials: Shear Modulus is not independent from Young’s Modulus and Poisson’s Ratio
** G = E = [2(1+ν)]
* For COMPOSITE materials: it’s an independent variable.

Question 11

2. Elasticity Solutions. Tsai.

Answer 11

The fibers are not perfectly parallel, surrounded by the matrix AND in contact with each other.
K and C parameters.
- Young’s Modulus:
* E1 (linear) but with a k (filament misalignment factor), 0.9 < k < 1
* E2 (non-linear) with a factor C, 0 < C < 1
- Poisson’s ratio: not so good. C factor from linear to non linear
- Shear Modulus: C factor from linear to non linear

Question 12

3. Halpin-Tsai:

Answer 12

Concentric cylinders surrounded by matrix.
Two adjusting parameters: η and ξ, either found experimentally or by equations (not very precise).

Question 13

Experimental Assessment of the theoretical predictions

Answer 13

Adjusting the Halpin-Tsai parameters with the method of least squares offers usable values.