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# UD Composite Strength vs Angle Orientation

## UD Composite Strength vs Angle Orientation

(OP)
Hi,

I am trying to understand behaviour of UD composite as I increase an angle from 0° . Is this changing the same way for all types of fibres or has to be determined experimentally?

I thought it is related to transformation matrix formula for strength qx= q1*cos^2 (angle) + q2*sin^2(angle) + 2Tau*sin(angle)*cos(angle)

but compare with strength vs angle plots I found online it does not change quite the same way.

Thanks,

Stan

### RE: UD Composite Strength vs Angle Orientation

You can predict the stiffness values using laminate theory equations, including the transformation you list. But strength nerds to be determined from tests.

### RE: UD Composite Strength vs Angle Orientation

The formula you have is for rotating the stress component into the the direction of the fibres in your ply of material from your global direction. However, you also need to rotate the resultant strain back into the global x direction. As a result, you end end up with equations that are quartic (e.g. cos^4(theta)) rather than cubic. There is a free online course that provides an introduction to the mechanics of composite materials:

https://www.edx.org/course/composite-materials-ove...

Even though the course is almost over, if you enroll on it I would guess you'd have access to the materials for a while longer. You also get a free, but time limited, copy of MatLab to use to go through the exercises. I have a student doing an Industrial placement with my company and he's been taking the course. He thinks its been helpful in getting to grips with composites so it wold probably be worth you having a look at it. There are also plenty of books as well as materials online that will provide an introduction to the mechanics of composite materials; this one looks ok for a start on the matter of rotating stress and strain tensors: http://ocw.mit.edu/courses/materials-science-and-e...

Anyway, you specifically mention strength rather than stiffness. As SWComposites said:

#### Quote (SWComposites)

But strength nerds to be determined from tests.

You'll need some reliable experimental data to even get started with; don't underestimate who hard this might be to get if you don't have access to academic journal (and even a lot of the data available there shows some pretty huge variations in measured properties, even for UD prepregs

There are many theories about how the strength of laminates varies with layup and orientation....how reliable they are is certainly open to question (there are ongoing international program to investigate this, most well known are the 'World Wide Failure Exercises'). The many approaches available for predicting the effect of orientation on strength which can broadly be divided into four classes from the most simple to the more advanced:

Basic; based on comparison of calculated scalar quantities in different failure modes. Examples' max stress and max strain criteria. Pros: very simple and can differentiate between failure modes
Intermediate; Interactive criteria that take into account multiaxial load states. E.g Tsai-Hill, Tsai-Wu. Kind of like the composite materials equivalent of a Von Mises failure criteria. Pros; can account for mutliaxial stress states to a degree Cons; can't differentiate between failure modes
Advanced/Academic (homegenisation); Damage based models. E.g. Hashin, LaRC04. Pros; Can deal with vastly more complex stress states, more accurate and realistic than the above if implemented correctly. Cons; requires vastly more experimental data, the numerical tools to implement them and the expertise required to understand them
Advanced/Academic (multiscale modelling); tuned to the materials and situation at hand. Pros; can (theroetically) account for pretty much any phenomena. Cons; requires massive computational fire power, huge amounts of experimental data, will require a full fat commercial numerical package (e.g. Abaqus) or one coded/adapted for the task, plus a bespoke pre processor, etc...

Finally, I'm working on the basis that you're looking at UD prepreg material. If you're looking at textile based materials, be they woven or non-crimp fabrics, then things will get vastly more complicated.

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