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Converging on Delamination, February 2011

Composite Analysis Tips

Using Micromechanics to Determine Lamina Properties

In designing with composite materials, it is often necessary to determine the resulting engineering properties when varying the types and proportions of the fiber and matrix constituents. For example, what are the effects of changing matrix material or increasing fiber volume?

The answers could be determined by test – but that would cost a great deal in time and money. If we want to optimize our lamina and experiment with different composition, we cannot afford to use Test to determine behavior. Instead, we use analysis.

If we know the properties of the fiber and matrix we wish to use – from vendor data sheets for example – how do we then determine the combined property set? There are two options discussed here:

1. Perform the full set of classical derivations
2. Use CompositePro's Micromechanics tool to derive your properties

The Classic Approach

We first determine E₁ using the Rule of Mixtures in the fiber direction:

Imagine a single ply with load "P" in the fiber direction.

Divide both sides by A_C

Volume fractions are defined as:

Substituting, we get:

We can differentiate both sides with respect to strain as follows:

Finally, since we are working within the linear range of the material, dσ/dε is linear and is the definition of Modulus. Thus:

We continue with determination of E₂.

In the 2 direction, P_C=P_V=P_m

This gives:

Solving for Modulus, E₂:

Since σ_f = σ_m = σ₂:

And, if you have LOTS of time, you can continue your derivations to determine G₁₂, ν₁₂, ε₁, ε₂, CTE’s, K’s (Moisture Responses), etc. Even with spreadsheet tools, this can be a VERY time consuming and error prone process when estimating properties for several composite combinations.

Micromechanics with Helius:CompositePro

Fortunately, Helius:CompositePro handles these types of calculations in one easy module – and it uses a more advanced formulation by implementing Micromechanics.

Helius:CompositePro’s micromechanics module utilizes a detailed finite element model of a fiber/matrix unit cell that features a uniform hexagonal distribution of parallel fibers embedded in a matrix material. The micromechanical finite element model utilizes the properties of fiber and matrix materials specified by the user, in addition to the fiber volume fraction specified by the user. It then determines the composite material’s elastic properties (e.g., moduli and Poisson ratios) by using the model to simulate the various fundamental load/deformation relationships of the composite material.

Using the New Lamina from Micromechanics, you can determine over two dozen engineering constants for your lamina with the click of a mouse. Simply select your fiber and matrix properties from a library of pre-populated materials – or create your own by adding to the material data library. Then select your fiber and matrix volume fractions. (If the user only has fiber and matrix weight fractions, then Helius:CompositePro’s Vf-Wf Converter can be used to convert weight fractions to volume fractions.) Hit "Calculate" and your lamina properties are presented.

The new lamina material can be entered in the Helius:CompositePro material database by clicking the Save button that appears under the Results tab. Once the new lamina is entered into the material database, the lamina material can then be used to define new laminates.

With the micromechanics tool in CompositePro, you can run this calculation over and over again with countless different l combinations without the time and potential error involved in hand calculations or spreadsheet tools.

To learn more about the many composite analysis features available in Helius:CompositePro, visit www.firehole.com/compositepro/ or email compositepro@firehole.com.