DIY tensile strength testing
For these kind of tests you could rely on the ASTM standards. They define test procedures and test specimen sizes for different types of tests. Or you can derive a specimen yourself based on these standards (e.g. for my bachelor's degree I used an alternative notch impact specimen as I was bound to the amount of available material of the turbine rotor blade the specimens were taken from). Considering the material, you could device up a contraption made from extrusion profiles or something.

Please do note that to get reasonable results, you would have to do a lot of tests as the spread in results is probably even more than in metals. 

The company I work for does this, these material qualification programmes run for long times (years, as we also do fatigue and creep testing), and a lot of samples are tested to qualify for use in Aerospace applications.