Composite materials are made of at least two different materials combined to obtain superior strength and stiffness over a single material. The fiber arrangement is dictated by a tradeoff of cost, flexibility and performance. Composites exhibit orthotropy, meaning they have two orthogonal planes of symmetry in their material properties. The rule of mixtures is used to calculate the longitudinal modulus (E1) based on the fiber and matrix volume fractions and moduli. For a graphite/resin composite, the uncertainty in E1 was calculated to be between 134.54-167.67 GPa due to uncertainties in fiber modulus, matrix modulus and fiber volume fraction. The transverse modulus is calculated using springs in series, while other properties like the shear modulus and

1. Composite materials
• At least two different materials put together.
• Mostly to obtain superior strength and
stiffness.
Why not just use
the stronger material?

2. Fiber arrangement
• Fiber arrangement is dictated by tradeoff of
cost, flexibility, and performance.

3. Orthotropy
• Anisotropic materials with two orthogonal
planes of symmetry in properties.
• Ply is transversely isotropic.
• Large differences between E1 and E2

4. Rule of Mixture for E1
• Based on volume fractions 𝑉𝑓 and 𝑉
𝑚 =1-𝑉𝑓.
• Equivalent to two springs in parallel.
1
1
f f m m
f m
f m
f m f f m m
A E A E
AE
P P P
L L L
A A
E E E E V E V
A A
 

    
    

5. Example with uncertainty
• For a graphite fiber and resin matrix we have
from the manufacturer 222 ≤ 𝐸𝑓 ≤
238𝐺𝑃𝑎 3.35 ≤ 𝐸𝑚 ≤ 3.55𝐺𝑃𝑎
• Our uncertainty in volume fraction is 0.6 ≤ 𝑉𝑓 ≤ 0.7
• What is the uncertainty in 𝐸1?
1min
1max
222 0.6 3.35 0.4 134.54
238 0.7 3.55 0.3 167.67
E GPa
E GPa
    
    

6. Transverse modulus
• Two springs in series
• Obtain
• Other properties
2
1 f m
f m
V V
E E E
 
12
12
1 f m
f f m m
f m
V V
V V
G G G
  
   