# Composites Part 2 Flashcards

What does a composite material consist of, in the context of FRPs?§

High modulus reinforcing fibers embedded in a low modulus polymeric matrix.

In FRPs what does the matrix do?

Load can be transferred between fibers due to elasticity in the matrix. The matrix also serves to separate and protect the fibers.

What does the stiffness and strength of a FRP depend on?

- Proportions of fiber and resin
- Distribution and orientation of fiber
- Type of fiber
- Type of resin
- Length of fiber (or discontinuous fiber)
- Void content

Why do properties vary throughout an FRP structure?

because FRP materials are non-homogeneous and anisotropic

What is the stress strain behaviour of a FRP like?

The behaviour of an FRP under load is elastic up to the point of failure with no yield point or plastic behaviour. The strain to failure is also low with a correspondingly small amount of work done. This lack of yielding makes the material very notch or stress concentration sensitive, therefore localized stresses have to be critically analysed

Can you draw the stress strain graph for a FRP?

yes or no

in the numerical index system associated with orthogonal axes, what do x1, x2 and x3 coincide with?

x1 - coincide with fiber axis

x2 - coincide with transverse in-plane

x3 - out of plane

what are the symbols for longitudinal stiffness and transverse stiffness?

longitudinal - E1

transverse - E2

What do the mechanical properties of a FRP depend on?

- the properties of the constituent materials, the reinforcement and matrix and in particular the quantity and orientation of the fiber

What are the different fiber orientations?

- random (e.g. CSM)
- bi-directional (e.g. woven)
- unidirectional

For random orientation and in-plane only, what are the properties in different directions?

- the FRP has equal properties in all directions (psuedo isotropic)

For bi-directional orientation, what are the properties in different directions?

the FRP has equal properties in the 2 directions

For unidirectional orientation, what are the properties in different directions?

the properties are greatest parallel to the fiber

If the same amount of fiber was used in each case, which FRP would have the highest mechanical properties, unidirectional or random?

UD would have the highest mechanical properties and random the lowest

How do the properties change with different directions in UD?

the properties of a UD FRP are only superior in the direction parallel to the fibers, just a small angle away from the fiber-axis and the mechanical properties drop off considerably to very low values. The transverse properties of the FRP, perpendicular to the fiber direction, are close to that of the base resin.

What are the typical fiber volume fractions obtainable for the different orientations?

UD - 50-70%

bi-directional - 30-55%

random - 15-35%

What model is used to analyse axial loading?

Voigt model

What model is used to analyse transverse loading?

Reuss model

What is the voigt estimate/ rule of mixtures equation?

Ec = EfVf + Em(1-Vf)

note Lc = Lf = Lm

What implicit assumption does the rule of mixtures make?

That poisson ratios of fiber and matrix are the same, thus ignoring the elastic constraints caused by differential contractions

What is the rule of mixtures for elastic modulus in fiber direction (including fiber efficiency factors)?

E1 = A.EfVf + EmVm E1 = A.EfVf + Em(1-Vf)

Fiber efficiency factor, A:

- Aligned: A=1 (aligned parallel)

- Aligned: A=0 (aligned perpendicular)

- Random 2D: A=3/8 (2D isotropy)

- Random 3D: A=1/5 (3D isotropy)

What is the Reuss estimate/ inverse rule of mixtures equation?

1/Ec = Vf/Ef + Vm/Em

–> Ec = EfEm/EmVf+Ef(1-Vf)

Why is it much easier to compare the properties of composite materials on a volume fraction basis?

Because the densities of the constituents need to be considered with the weight fraction basis.

How to convert between weight fraction and volume fraction?

Wf = rho_f Vf/ rho_f Vf + rho_m(1-Vf)

Wf + Wm = 1

Can you draw a diagram/graph comparing the predictions for longitudinal modulus (E1) and transverse modulus (E2) varying with volume fraction Vf?

Yes or no

What are the issues with Reuss model?

Reuss model is a simplified representation (does not describe the real composite perpendicular to the fibers)

a) it ignores constraints due to strain concentrations in the matrix between the fibers

b) it assumes that the transverse stiffness of the fiber is the same as its longitudinal stiffness

c) it does not consider packing geometry. Real packing is even less regular than either of these idealised geometries.

What is poissons ratio of an isotropic material defined as?

The negative ratio of the lateral strain, e2, when a stress is applied in the longitudinal (x1) direction, divided by the longitudinal strain, e1, ie v=e2/e1

What are the two in plane poissons ratios for composites?

- v12, called the major poisson ratio (relating to the lateral strain, e2, when a stress is applied in the longitudinal x1 direction), v12 = e2/e1
- v21, the minor poissons ratio (relating to the strain in the x1 direction when a stress is applied in the x2 direction).

does major poissons ratio obey the rule of mixtures?

yes

What is anisotropic?

When the properties of a material vary with different crystallographic orientations, the material is said to be anisotropic

What is isotropic?

When the properties of a material are the same in all directions, the material is said to be isotropic