Hello,
We are producing composite materials which consist of plies stack on each other at different angles (like 0°/90°, 45°/45°, 15°/75°,30°/60°).

For the 0°/90° case, we have the same tensile strength in X and Y (principle) directions.

I want to estimate the maximum stress that a laminate(for instance 15°/75°) can withstand from the 0°/90° test. i found some document (actually it is from MIT's open courses).
There it is written:

sigma1=sigmaX.cos2teta+sigmaYson2teta+2taoXYsintetacosteta
another formula for sigma 2 and a formula for new tao12.
Here teta is the angle from the x acis to the 1 (fiber) axis.

Can I use this formula to estimate my maximum stress for different ply angles?

 

Best Regards,
Sartor

Provided the 2s are for squared (cos or sin(theta))² that will correctly rotate stresses in the x, y and xy plate directions to the 1-direction (usually the fiber direction) in a ply. Presumably your other two formulas are correct (all three are generally combined into the so-called transformation matrix).

If you have woven plies then the 0 (or 90) degree strengths are the basic 0 degree ply strength and you can use the formulas ok. Even if the plies are unidirectional this should still work, but the 0/90 layup strength is not the basic ply strength.

NB: I assume that your 15/75 and 30/60 stacks are actually 15/-75 and 30/-60. Also your stacks either need to be symmetric about the centerline or a symmetric weave, probably twill or plain. (It's good practice to make the laminate symmetric in any case.)
 

Short answer - the equations you listed are valid for transformation of applied stresses; however, they are not directly related to strength prediction, which, to do it accurately, is very complicated.  Strength prediction involves failure mechanisms in the fiber, matrix and interface.  What you will find in most text books is over simplified at best, often wrong.  Start by reading this paper:  

Hinton, M. J., Kaddour, A. S. and Soden, P. D., "A Comparison of the Predictive Capabilities of Current Failure Theories for Composite Laminates, Judged Against Experimental Evidence", Composite Science and Technology, Vol. 62, 2002, pp. 1725 – 1797

Then dive into the referenced papers.

Or, just run tests on your various laminates.

 

Were you intending to assume that the fiber stress would be the same at failure for the angle plies as in the 0/90 test? SW is right to advise caution. The all 45° laminates will fail in in-plane shear, quite a different failure mode from the 0/90s. This is also true for the 30/-60. The 15/-75 is a bit borderline, but will still fail with a lower fiber stress than the 0/90.
 

You should also consider if there is a need to put holes/bolts in the structure or to have residual strength after an impact.  Those are typical design conditions that will dramatically reduce strength from the unnotched (pristine) strength.

In either of those cases, you will need to look at very different approaches than the simplified academic theories.  

And as SWComposites has mentioned, the basic formulas can not always be translated into a confident prediction of strength due to the complex nature of composites.  This is why industry often relies on semi-empirical approaches, which add the necessary confidence via testing.  

Brian
www.espcomposites.com