1. D AY 33: C OMPOSITE M ATERIALS Composite Materials – Two Examples Types of Composite Materials Properties of Composite Materials

2. C OMPOSITE M ATERIALS HAVE BEEN WITH U S FOR A LONG TIME. 10 Then the slave drivers and the foremen went out and said to the people, "This is what Pharaoh says: 'I will not give you any more straw. 11 Go and get your own straw wherever you can find it, but your work will not be reduced at all.' " 12 So the people scattered all over Egypt to gather stubble to use for straw. 13 The slave drivers kept pressing them, saying, "Complete the work required of you for each day, just as when you had straw." 14 The Israelite foremen appointed by Pharaoh's slave drivers were beaten and were asked, "Why didn't you meet your quota of bricks yesterday or today, as before?" 15 Then the Israelite foremen went and appealed to Pharaoh: "Why have you treated your servants this way? 16 Your servants are given no straw, yet we are told, 'Make bricks!' Your servants are being beaten, but the fault is with your own people." 17 Pharaoh said, "Lazy, that's what you are—lazy! That is why you keep saying, 'Let us go and sacrifice to the LORD.' 18 Now get to work. You will not be given any straw, yet you must produce your full quota of bricks." What is the advantage of adding straw to the clay used in making bricks?

3. M ODERN C OMPOSITE M ATERIALS Show are some images of composites as they are used today.

4. M ODERN C OMPOSITE M ATERIALS Starting with the early passenger jets, the use of composite materials in the aerospace industry has grown steadily. Boeing 767

5. G RAPHIC ILLUSTRATING THE INCREASED USE OF COMPOSITES.

6. W HAT ARE THESE WONDERFUL MATERIALS ? A fiber. Remember the high, high performance of fibers loaded along their length? MaterialElastic Modulus ksi Strength ksi Density g/cc Hercules IM7 carbon fiber 400007901.78 DuPont Kevlar 149 fiber 260005001.49 Generic E- glass fiber 105005002.54

7. W HAT DO WE COMBINE WITH THE F IBER ? A matrix material. This is going to be a polymer, probably a thermoset, although thermoplastics have been used. MaterialElastic Modulus ksi Strength ksi Density g/cc Epoxy Generic 200022.51.06 PEEK (polyetheret herketone) 2000181.34 Polyimide48013.51.43 Applied Composites Polyester 400101.76

8. O THERS Rubber is a common matrix material. The modern tire is a perfect example of how composite materials can be engineered. Yummy!

9. H OW IT WORKS The matrix material 1. bonds to the fiber 2. Surrounds and protects the fiber 3. Causes the fiber to maintain orientation desired 4. Keeps the whole piece in shape The fiber carries most of the load in an efficient way The composite material has properties that are a blend of those of the matrix and the fiber.

10. A DVANTAGES AND D ISADVANTAGES Advantages 1. Superb strength to weight ratio 2. Allows material to be customized to the load 3. Very strong resistance to chemical attack 4. Some can be good at high temperature (Not all) Disadvantages 1. Price 2. Difficult to manufacture. 3. Difficult to design with (Their anisotropic, or oriented nature makes stress / strain calculations very tricky.

11. T YPES Particle. Concrete is the great example. We will not be studying these. Short Fiber. Fibers are short and randomly oriented. These materials are usually among the cheaper ones to manufacture.

12. L ONG F IBER OR C ONTINUOUS F IBER These are the highest performance. Not so easy to manufacture. Have built in directionality.

13. P ROPERTIES OF C OMPOSITES Several properties of composites can be calculated using the rule of mixtures. Let’s begin with the density of the composite. Suppose that V f is the Volume fraction of the fiber, and that V m is the volume fraction of the matrix material. Please note that V f + V m = 1. Next let  f be the density of the fiber, and  m is the density of the matrix material. The density  c of the composite is apparently  c =  f V f +  m V m.

14. T HE CONDITION OF I SOSTRAIN This applies to long fiber composites. Compressed or pulled along fiber direction. The fibers and matrix material have the same strain. The load is shared.  is the average normal stress. mm ff L AfAf AmAm

15. M ODULUS E IN I SOSTRAIN We assume Hookean Behavior. (Think carefully about this assumption!) We can divide by the constant strain shared by all components. Oh yes, we also multiply by L. We divide by A L, or Volume. The result is

16. T HE CONDITION OF I SOSTRESS This applies to long fiber composites. Compressed or pulled across the fiber direction. The fibers and matrix material have the same stress. The displacement  is shared.  is the average normal strain. mm ff A LfLf LmLm

17. M ODULUS IN I SOSTRESS We divide by the common stress, . Mulitply by A. Divide by the volume. The result is.

18. E XAMPLE Suppose we had 62% fiber content by volume. We are dealing with a Carbon Fiber – epoxy composite.

19. I SOSTRESS AND I SOSTRAIN Composite Modulus will lie somewhere between the two. Clearly Isostrain is the target condition.