Strength and Fibre Orientation

When considering the effect of fibre orientation on the strength of a composite material made up of a continuous aligned fibres embedded in a matrix, it should be recognised that there are 3 possible modes of failure...

• 1. Tensile fracture parallel to the fibres (whether the fibres fail or the matrix fails will depend on the particular combination of fibre and matrix materials as well as the volume fraction of fibres)

  2. Shear failure of the matrix as a result of a large shear stess acting parallel to the fibres ,

  3. Tensile failure of the matrix or fibre/matrix interface when stressed perpendicular to the fibres. 

We have already determined suitable expressions for the strength of a composite when tested parallel to the fibres, We'll call this strength X. We also know the tensile strength of the matrix material which we'll call Y. The shear styrength of the matrix can be determined using the Tresca criteria and is simply Y/2. In order to examine the effect of orientation on strength we need to make use of Mohr's Circle to establish the state of stress aligned parallel and perpendicular to the fibres and then to equate these stresses with the appropriate failure stress of the composite in each those directions.

For failure to occur, the applied stress must be increase until either 

These equations are plotted out below and since failure is a "weakest link" phenomenon, fracture will occure at whichever criterion is reached first and so the mechanism of failure changes from tensile failure of the fibres to shear of teh matrix to tensile failure of the matrix as the fibre angle is increased from 0 to 90°.

Failure under Mutliaxial Stress States (Plane Stress) - Tsai-Hill

When two mutually perpendicular stresses and/or a shear stress is applied to the composite we need to be able to define a failure criterion. Tsai and Hill have established a suitable fracture criteria based on maximum strain energy, rather than considering stress and strain. This maximum strain energy approach allows us to ignore the fact that failure can occur because either a stress has exceeded a critical value (e.g. the stress resolved perpendicular to the fibres has exceeded the tensile strength of the matrix) or the strain has exceeded a particular value (e.g. the strain resolved parallel to the fibres has exceeded thefibre fracture strain). The Tsai-Hill maximum strain energy formulation is:-

Which we can see for the case of a uniaxial stress applied parallel to the fibres 

,

Perpendicular to the fibres 

, 

Simple shear 

is the result that we would expect.

The following MathCad exercise will allow you to examine the effects of orientation on strength.