Lecture 4

Question 1

What are the 3 influencing parameters to longitudinal strength?

Answer 1

Fibre volume fraction

Failure strain of the fibre

Failure strain of the matrix

Question 2

When does the matrix fail first?

Answer 2

εf > εm

When there is a low volume fraction, the composite will fail when the matrix fails.

When there is a high volume fraction multiple matrix fracture occurs prior to failure of the composite

Question 3

When does the fibre fail first?

Answer 3

εm > εf

When there is a high volume fraction the composite fails when the fibres fail

When there is a low volume fraction multiple fibre fractures occur prior to failure of the composite.

Question 4

Explain the failure procedure when the matrix fails first

Answer 4

The matrix will fail as the εf > εm. The load is then transferred to the unbroken fibres.

At low volume fractions the fibres are unable to support this additional load and the composite fractures.

At high volume fractions the additional load on the fibre is insufficient to cause fibre fracture, however the matrix is already broken.

Question 5

What are the two equations relating the matrix ultimate tensile strength and the fibre ultimate tensile strength when the fibre fails first.

Answer 5

At low volume fraction: σmu = σ1T = σm(1-νf)

At high volume fraction: σfu = σ1T = σf νf + σm* (1-νf)

Where σm* = Em εf
(as the fibre is failing first)

Question 6

Explain the so called “cross-over” point that is known as the critical volume fraction when the fibre is failing first.

Answer 6

This is the point where the failure mode crosses over from fibre to matrix.

The point can be found by equating the two failure mode equations:

σ1T = σfνf + σm*(1-νf) = σm(1-νf)

Thus νf = σm - σm* / σf - σm* + σm

Where σm* = Em εf
(as the fibre is failing first)

Question 7

Explain the size effect

Answer 7

The longer the specimen, the weaker the composite as there are more chances of flaws being present. So technically speaking the longitudinal tensile failure stress is not a single value and depends on the sample size.

Question 8

What are two important parameters effecting fibre buckling (longitudinal compressive strength).

Answer 8

Matrix modulus

Fibres misalignment

Question 9

What is the in-plane shear strength dominated by?

Answer 9

Matrix properties because the cracks propagate along the fibres and do not break them.

For a high volume fraction the in-plane shear strength is less than the shear strength of the matrix.

For a low volume fraction the in-plane shear strength is fairly equal to the shear strength of the matrix as the matrix is more flexible or ductile.