Question

A composite is produced from a titanium alloy reinforced with aligned silicon carbide fibres. The elastic moduli of titanium and silicon carbide are 118 GPa and 380 GPa respectively. The composite contains approximately 50% titanium and 50% fibres.

• a.Calculate the overall modulus of the composite, explaining your calculations and the assumptions you have made when it is loaded: Show all working and formula used:
  • i.along the direction of fibre length
  • ii.perpendicular to the fibre length.

    (8 marks)

• b.Explain briefly why a material might show different yield behaviour in tension and compression when loaded cyclically.

Answer 1

Question a: Rule of mixtures is used to determine the modulii of composites in two directions.

The underlying assumptions:

1. There is a perfect bonding between fibers and matrix.

2. The fibers are uni directionally arranged in matrix.

Question b: The effect is known to be Bauschinger effect.

It is a property of materials where the material's stress/strain characteristics change as a result of the microscopic stress distribution of the material. For example, an increase in tensile yield strength occurs at the expense of compressive yield strength. Titanium is well known to exhibit this phenomenon.

The figure above shows cyclic loading of a material. When the material is loaded in tension, it reaches its yield at point-1. However, when material is loaded beyond yield and the stress is reversed such that it is in compression, the yield point-2 occurs at lower stress. This value is lower than the yield stress when the material is loaded directly in compression (point-3).