### Technical Resource

Composite Engineer’s Viewpoint, Rik Heslehurst PhD, MEng, BEng(Aero), FIEAust, FRAeS, CPEng

##### In this article we look at the issue of volume ratio versus weight ratio in the design and fabrication of composite structures.  Are they not the same thing?  What is the relationship between volume ratios and weight ratios?

As the composites industry has grown there has become a bit of a divide between the language of the composite design engineer and the composite fabricator.  Specifically, how each group describes the ratio of fibre to resin in the composite structure.  The design engineer refers to the fibre/resin ratio in terms of volume of fibres to volume of resin.  On the other hand, the composite fabricator will talk of the fibre/resin ratio in terms of fibre-to-resin weight ratios in the composite structure.  Are they not the same thing?  Well, no they are not (with the exception of one specific condition), but they are related.  Each term has a very important relationship to the engineer or fabricator, and each are essential in their development of the final composite component.

The discussion herein relates to wet resin lay-up techniques.  Here the fabrication process will wet out the fibres with a wet resin system, i.e. the wet lay-up process, resin infusion processes and resin injection processes.

The basic engineering properties of a composite material can be determined by either experimental stress analysis (testing) or theoretical mechanics (micromechanics).  The micromechanics approach utilises knowledge of the individual fibre and resin properties, and the proportionality of fibres to the resin in the lamina (ply).  A rule of mixtures approach can best be used to derive the majority of the composite lamina properties.  For example the lamina axial modulus is derived from:

Ex = EfVf + EmVm

Where:   Ef  is the fibre modulus of elasticity

Em  is the matrix (resin) modulus of elasticity

Vf  is the fibre volume ratio

Vm  is the matrix volume ratio

Vf + Vm = 1, with zero voids

When fabricating composite materials and structures from dry fibre (rovings or cloth form) and pouring liquid resin onto the fibres, the correct ratio of weights of fibre and resin are required.  For example, the called-out ratio of say 60:40, requires a ratio of 60% fibre weight to 40% resin weight.

This resin weight is measured out, poured over the fibre system and worked into the fibres. This is referred to as wetting out the fibres

FIBRE VOLUME AND WEIGHT RATIO RELATIONSHIP

While the fibre weight ratio is easily determined by simple weighing, the fibre volume ratio is quite difficult to determine.  Typically, an ASTM test method is employed which requires destruction of a small sample.  However, the determination of fibre volume ratio can be derived from the fibre/resin weight ratio.  The approach is as follows:

1. The fibre weight is based on the areal weight and a known or measured planar area.

2. After processing, the composite laminate weight is measured.

3. The resin weight is the difference between the composite and fibre weights:

Wresin = WcompositeWfibre

4. From vendor data we obtain the density of both the fibre and the resin systems (Technical Data Sheets – TDS, or Safety Data Sheets – SDS). (If not available from vendor data, the density can be determined experimentally.)

5. Now calculate the volume of the fibres in the composite:

6. Then determine the fibre/resin weight ratio and the fibre/resin density ratio.

7. Calculate the fibre/resin volume ratio:

8. Now determine the matrix volume ratio:

9. Finally, calculate the fibre volume ratio:

An example of the above is shown in the following extract of an excel spreadsheet.  The input data is shown in italics and the calculated results are underlined.

Using the relationship established earlier, we can estimate the required fibre-to-resin weight ratio for a required fibre volume ratio.  This will then give a more reliable approach in achieving the required engineering properties of the composite material.  Rearranging the earlier equations gives the following design expression:

So, for example, if the required fibre volume ratio is 60%, then using a glass fibre/epoxy resin system with a density ratio of 2.0 requires a fibre/resin weight ratio of 75:25.  Whereas, using a carbon fibre/epoxy resin system with a density ratio of 1.425 requires a fibre/resin weight ratio of 68:32.  Finally, for an aramid fibre/ epoxy resin system with a density ratio of 1.142 requires a fibre/resin weight ratio of 63:38.

To achieve appropriate structural performance for a composite material, the fibre volume ratio plays a crucial role.  The engineering designer uses the fibre volume ratio to derive the lamina properties and thus after lamination, structural properties.  But to achieve the required fibre volume ratio in wet lay-up processes the fabricator requires the fibre weight to resin weight ratio.  This paper provides the mathematical expression that relates fibre volume ratio to fibre weight ratio.  The expression is dependent on the ratio of the fibre and resin densities.  This relationship clearly identifies the importance of low fibre densities when compared with the resin density.

In the next article we consider the impact of fabric composite stacking arrangements.  Do I nest or stack woven cloth?  What is the impact on structural performance and deformation behaviour? I also welcome questions, comments and your point of view.  Feel free to contact me via rikheslehurst@gmail.com.  I may publish your questions and comments, and my response in future newsletters.