4 Micromechanics

The Micromechanics chapter contains most, if not all, of the formulas in Chapter Micromechanics of the textbook. Here you can use CADEC to predict the moduli, strength, coefficient of thermal expansion (CTE) and moisture expansion, as well as thermal and electrical conductivity, mass diffusivity, and so on.

Note: If you work with composite properties that you obtained from the vendor, or testing, etc., you can skip this chapter and go directly to Macromechanics. This is usually the case if you work with prepregs.

Micromechanics allows you to predict the properties of the composite lamina as a function of the fiber, matrix, and amount of fiber (in relation to matrix) that you want to use. All processing methods except prepreg layup let you use whatever fiber, matrix, and fiber volume fraction you want in order to optimize the composite material for weight, cost, performance, sustainability, etc.

The properties of fibers and matrices are much more readily available than those of composite materials. Besides, the composite properties listed by the manufacturer can vary depending on your manufacturing conditions that could be different from theirs. Manufacturer’s properties are fixed for the fiber volume fraction they used. Yours aren’t.

The fiber volume fraction $V_ f$ is the volume of fiber per unit volume of composite. A value of 0.5, or 50%, means that 50% of the volume of the composite is occupied by the reinforcement. This does not mean 50% by weight because the fiber density $\rho _ f$ is different (higher) than the matrix density.

Volume fractions add up to one. For a 2-component composite (matrix plus reinforcement), $V_ f+V_ m=1$.

The fiber mass (or weight) fraction $W_ f$ is defined as the ratio of fiber mass to composite mass. Again, mass fractions add up to one, i.e., $W_ f+W_ m=1$.

If you decide the volume fraction you want to use, then CADEC will help you calculate the density of the lamina $\rho _ c$. Armed with that, you can easily calculate the weight fractions:

  $\displaystyle  W_ i=\frac{\rho _ i}{\rho _ c}V_ i  $   (4.1)

where i=f,m; that meas the same formula can be used to compute the fiber (f) mass density and the (m) mass density. More on [2, Chapter 4].

Chapter, Micromechanics has 35 pages that compute a lot of things. A view of the Left Menu Tree with the Micromechanics chapter partially expanded is shown here:


Figure 4.1: Partial view of the Left Menu Tree with Micromechanics partially expanded. Click the Back button on your browser to return to your previous page.

Some peculiarities of this chapter are discussed next. First, the results are organized into three categories: Unidirectional, Random, and Textile, according to the type of reinforcement used.

All three categories have the same structure shown for Unidirectional in the figure below. That is, the have calculations for Moduli, Hygrothermal, Transport, Strength, and Fracture Toughness properties. Also, all the results in this chapter are displayed in uniform format. Let’s use the Density page to illustrate it.

Micromechanics predicts the property of a Lamina that you have previously defined in My Documents, My Laminas. So, the first thing you do on a Micromechanics page is to select the lamina for which you want results. You select the lamina using the dropdown selection box Lamina right below the page title.

Below the dropdown box used to select the lamina, CADEC displays the equation used to do the calculation. If the equation is too long, a reference to the textbook is given.

Next, only the relevant properties used in the formula are displayed. The values are retrieved from the definition of the fiber and matrix, plus the fiber volume fraction. Immediately below you see the result that you are looking for, in this case, the density of the lamina.

Notice that units are given for both data and results. Also notice that the values, which have been retrieved from the database, are in editable fields. This means that you can change them right here on this page. In this way, all 35 pages in Micromechanics work like a graphic calculator. Change the data and you get the results, both in numerical and graphic format. However, the changes you make here to data are not saved to the database. In other words, you changes do not alter your definition of fiber and matrix that you did in My Documents. This is done on purpose because your data could be used in other objects, such as laminates and other objects, and you would not want to inadvertently ruin some other objects while you are experimenting with values in this page. If your trials here indicate that you should permanently change the data, then you must go to My Documents and make permanent changes there.

Below the numerical result we can see a plot for the property calculated as a function of the fiber volume fraction. The plot is labeled to show where your current design is (Vf=0.3 and density=1.6 $\textrm{g/cm}^3$ in the figure). Also, labels indicate the extreme values that the property could take if the fiber volume fraction were to take limit values, 0 and 1 in this case. The plot is trivial for density because the predictive equation is a linear function of volume fraction. However, in other cases the plot may be very instructive, giving you a sense of whether or not is worth increasing/decreasing the volume fraction for the result that you can achieve. Don’t forget that increasing the fiber volume cost you money, so you want to make it worthwhile. A good example is the page for transverse modulus $E_2$.