For a given laminate made of composite material (composed of fibers oriented in a carefully designed sequence coated and embedded in a matrix material), where can I begin estimating the stiffness and/or strength of the material? How can I know (within a beginning estimate tolerance) how to design a part out of composite materials?
There are quite a few ways to find out the stiffness and/or strength of a composite material, with a good understanding of the materials that make up the composite material.
1. Pre-engineered composite materials
Several materials, prevalent mainly in the aerospace industry, are pre-engineered and pre-designed. GY70/339 is a common carbon fiber epoxy used extensively with highly tested properties. The material is a prepreg, which means the fibers are pre-oriented and the matrix to fiber ratio is carefully controlled in the factory selling the material. The roll must be kept in careful thermal control to prevent the pre-impregnated roll from curing before desired.
2. Simple formula used for rough estimation
From a far enough point, a very simple rule-of-mixtures can be used for a lot of situations using composites. This includes when one of the materials is even missing. Unfortunately, the rule of mixtures can only figure out stiffness, not strength. Note the major differences in definition. Most other methods for estimating materials can only measure stiffness, with strength being better defined as a maximum strain, then an actual strength.
3. More complex empirical formula
Beyond the rule of mixtures, there are more and more complex formulas that can be utilized. For example, the Halpin-Tsai formula is utilized frequently. Although semi-empirical, it is used in plenty of applications that need good rough estimates to investigate the plausibility of a design. More complex methods can be seen by various sources, but usually this is considered acceptable with follow up material testing.
4. Highly complex formulas which still need testing
State-of-the-art is considered Mil Handbook 17F, Section 3, Chapter 5, which starts on page 211 of the reference. Section 5.2 gives estimates for each layer, than 5.3 combines each layer into an orientation based laminate using matrix methods. These are complex but understandable formulas. As you get further into the document, you will notice that while this system is considered good enough for people who can't afford testing, stress concentration factors, fatigue factors, etc are completely unknown - if you need the system to be more reliable testing will be required, or you can use heavy safety factors and use these equations (10:1 is frequently used in pressure vessel applications, with 5:1 allowable for emergency circumstances, such as seismic and wind loading).
Hopefully this will be helpful to people asking "where do I begin" when it comes to composite material design.