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How can I use the rule of mixtures to calculate the properties of a composite material?

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What is the rule of mixtures and how can I use it to calculate properties of a composite material?

gzukerman5

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The rule of mixtures is a very simple and reasonably accurate way of predicting the stiffness of a composite based on the volume fractions of the constituents (i.e. fibres and matrix) and their corresponding stiffness. Assuming that all the fibres are aligned in one direction, the stiffness of the composite can be calculated as follows:

Ec = Ef*Vf + Em*Vm.

Ef – stiffness of the fibres,

Vf – volume fraction of the fibres, 

Em – stiffness of the matrix, 

Vm – volume fraction of the matrix. 

To predict the strength of a composite, such an approach is much more inaccurate, as the strength highly depends on the quality of the bond between the matrix and the fibre. Furthermore, in a laminate comprised of multiple layers with different fibre orientations, final failure does not always coincide with onset of damage. Damage may start at a load significantly lower than the load at which final failure occurs.

In order to predict when damage starts and how it evolves requires modelling of the matrix and fibres, the main subject of micro-mechanics

 More simplified, but still quite evolved approaches to predict the strength of composite laminates compared to the rule of mixtures are: Maximum Stress and Strain Failure Theories, Tsai-Hill Failure Theory, Tsai-Wu Failure Theory.

francisco.saraiva

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