It doesn’t matter how sophisticated your failure model is. Your results will still be inaccurate because their inputs – the local fields – were based on incorrect initial assumptions. It is like building a fancy house on top of a weak foundation – it is a waste of time and money.
So let’s understand the root of these inaccuracies.
In the first model, the assumption is that under uniaxial tension, the strains on the fibers and resins are the same, while the stresses are proportional to each constituent’s moduli. That is not quite true, but luckily, fiber mechanical properties are normally one order of magnitude larger than resin properties. Therefore, it is common for the axial direction response to be fiber-dominated with the influence of resin being quite small. Under those circumstances, the experimental results show acceptable agreement with the first model equation.
This explains why Rule of Mixtures can still be reasonably applied in practice to axial response of continuous fibers despite the geometric inaccuracies of the model, even for this given composite. However, the bigger problem lies in the prediction of transverse direction properties, as we discuss below.
In the second model, the extra assumption is reversed: the stresses on the fibers and the resin are the same, while strains are now inversely proportional to each constituent’s moduli. However, this time you can’t count luck, as this model is much more inaccurate than the first one. This is partially because the fibers will “protect” portions of the resin from stress while causing other resin areas to be over-stressed, as seen in the below image of the fringe patterns of microscale stress distribution.
So much for equivalent stresses among constituents – the stresses are not constant, not even throughout the same constituent! But the consequences of that go beyond simply predicting wrong moduli.
In reality, damage initiates sooner than one would predict by using Rule of Mixtures. Therefore, your Rule of Mixtures-based design is not so safe anymore.
So what? You can always overdesign, right? Wrong!