# 230404 - Composite Materials Flashcards

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

Youngs modulus and Poisson ratio.

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

Youngs modulus and Poisson ratio.

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

Youngs modulus: tension. Poisson ratio: torsion.

How do you quantify the ratio between fibers and matrix?

This is important to find the mechanical properties of the laminate.

1. Mechanics of Materials approach.

2. Elasticity Solutions. Tsai.

3.

Volume fraction

Fiber volume vs. Total volume

Matrix volume vs. Total volume

Two different classic ratio alternatives:

Mass fraction ψ and Volume fraction Φ.

- MMA (Mechanics of Materials Approach) Young’s Modulus E1

Direction 1

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.

- MMA (Mechanics of Materials Approach) Poisson’s Ratio

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

- MMA (Mechanics of Materials Approach) Young’s Modulus E2

Direction 2

- 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.

- MMA (Mechanics of Materials Approach) Shear Modulus

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.

- Elasticity Solutions. Tsai.

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

- Halpin-Tsai:

Concentric cylinders surrounded by matrix.

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

Experimental Assessment of the theoretical predictions

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