in a plate shape geometry you may measure global values of young's modulus poisson's ratio and shear modulus by impulse excitation technology (acoustic method). The problem is however that your material is anisotropic so that the you have different properties in different directions depending on the orientation of the reinforcement fibers.
If you have access to the equipment you could try Resonant Ultrasonic Spectroscopy (RUS). The torsional mode will give you the Shear Modulus while the flexural mode will give you the Elastic modulus. Once you determine the resonant frequency, you can vary the amplitude of the signal to simulate fatigue conditions. We have used this for a number of polymer and ceramic composites.
Concerning fatigue, first fix the direction of interest (shear, tension, compression....). Then, measure the static strength in that direction on a statistical number of samples, say 15 coupons, and take the average of ultimate strength, Su. The fatigue tests should be done by fixing the maximum applied stress at a percentage of the average strength previously calculated (for example use 70, 50 and 30% of the ultimate strength, Su). The amplitude of stress is fixed if the loading ratio R=Smin/Smax is fixed. Normally you can use R=0.1. Several tests (at least six) should be done at each loading condition given the statistical nature of fatigue in composites.
However, the argument is rather complex. I suggest reading the following papers:
- D'Amore, A . Grassia, L. Phenomenological approach to the study of hierarchical damage mechanisms in composite materials subjected to fatigue loadings(Article) Composite Structures Volume 175 (2017) pp. 1-6
- Alberto D’Amore, Luigi Grassia "Constitutive law describing the strength degradation kinetics of fibre-reinforced composites subjected to constant amplitude cyclic loading" Mechanics of Time-Dependent Materials Volume 20, Issue 1, February 2016 ISSN, 1 September 2017, Pages 1-6: 1385-2000 (Print) 1573-2738 (Online)
- Alberto D’Amore , Massimiliano Giorgio, Luigi Grassia “Modeling the residual strength of carbon fiber reinforced composites subjected to cyclic loading” International Journal of Fatigue 78 (2015) 31–37