# 6.12: Questions

- Page ID
- 35958

## Quick questions

*You should be able to answer these questions without too much difficulty after studying this TLP. If not, then you should go through it again!*

In mechanical loading experiments, involving large stresses and long durations, to measure the transverse stiffness of a composite, the experimental values are sometimes lower than the Halpin-Tsai prediction (some even lower than the Equal stress calculation.) Why might this be?

**Answer**-
Correct. Inelastic deformation and creep of the matrix increases the strain for a given applied stress. Since

\[E=\frac{\sigma}{\varepsilon}\]

a larger strain leads to a smaller Young’s Modulus.

How would you determine the total energy absorbed during fracture of a composite from its stress strain curve? (multiple choice)

**Answer**-
B

\[\begin{array}{l}

\sigma=\frac{\text {Force}}{\text {Area}}, \quad \varepsilon=\frac{\text {Extension in the direction of the force}}{\text {Original length}} \quad \sigma \times \varepsilon=\frac{\text {Force} \times \text {Extension}}{\text {Volume}} \\

\text {Work done}=\text {Force} \times \text {Extension}=\sigma \times \varepsilon \times \text {volume}

\end{array}\]

What is the most significant energy absorbing mechanism during composite failure?

**Answer**-
D. Additional work is required for frictional sliding

What is the combined work done per unit crack area required for crack deflection and fibre pull-out in a 60 % long-fibre composite? (Data: τ_{i*} = 40 MPa, G_{ic} = 8 J m^{-2} , fibre radius r = 7 μm, pull-out length x_{0} = 840 μm.)

**Answer**-
C

Pull-out aspect ratio s = x

_{o}/ 2r = 840 / (2*7) = 60

\[\begin{array}{l}

G_{c d}=f_{S} G_{i c}=0.6 \times 60 \times 8=288 \mathrm{Jm}^{-2} \\

G_{\mathrm{cp}}=4 \mathrm{fs}^{2} r \tau_{\mathrm{i}^{*}}=4 \times 0.6 \times 60^{2} \times\left(7 \times 10^{-6}\right) \times\left(40 \times 10^{6}\right)=2.4 \mathrm{MJ} \mathrm{m}^{-2}

\end{array}\]

∴ Work per unit crack area ≈ 2.4 MJ m^{-2}.

## Deeper questions

The following questions require some thought and reaching the answer may require you to think beyond the contents of this TLP.

For a laminate made up of 50% volume fraction carbon HS fibres and Nylon 6,6 matrix with a stacking sequence of 0 / 15 /50 / 55 / 60, at what loading angle is the Poisson contraction the minimum?

**Answer**-
D

How would you describe a laminate, composed of two constituents, with a stacking sequence of 0/45/80/45/0 subjected to a uniaxial tensile stress at a loading angle of 20 degrees?

**Answer**-
C

What is the axial stiffness of a long-fibre composite composed of glass fibres arranged in a hexagonal array in an epoxy matrix ? (Data: Glass fibre: E_{f} = 76 , fibre radius = 3.9 μm, spacing between centres of adjacent fibres = 8 μm Epoxy: E_{m} = 5 GPa.)

**Answer**-
Correct.

Calculate the axial failure stress for a composite composed of 30% borosilicate glass matrix and 70 % kevlar fibre, assuming that if one of the components fails the entire applied load is transferred to the other component.

Data: Kevlar fibre: σ_{fu} = 3.0 GPa, E_{f} = 130 GPa.

Borosilicate glass matrix: σ_{mu} = 0.10GPa, E_{m} = 64 GPa

What further assumptions do you need to make?

**Answer**-
Correct.