Question

If the tensile strength of the Kevlar 49 fibers is 0.550 x 106 psi and that of epoxy resin is 11.0 x103 psi, calculate the strength of the composite material that contains 79 percent by volume of Kevlar 49 fibers. The answer should be in psi with 0 decimals of accuracy.

Answer 1

`\sigma_(tot) =436810 psi`

Step-by-step explanation:

Notation

`\sigma_(fib) =0.55x10^6 psi` represent the tensile strength for the Kevlar 49 fibers

`\sigma_(epox) =11x10^3 psi` represent the tensile strength for the epoxy resin

79% by volume is made of Kevlar 49 fibers

The rest 100-79=21% is made of epoxy resin

Tensile strength is a "measurement of the force required to pull something such as rope, wire, or a structural beam to the point where it breaks". Can be defined as "the maximum amount of tensile stress that it can take before failure".

For this case we need to use a basis of calculus since we don't know the total volume but we can assume a reference value on order to make the calculations.

If we assume a total volume of
`V_(tot)=1 in^3` we can do the follwoing balance:

`\sigma_(tot)V_(tot)=\sigma_(fib)V_(fib) +\sigma_(epox)V_(epox)`

We can replace the values given:

`\sigma_(tot)=(0.55x10^6 psi)(0.79) +(11x10^3 psi)(1-0.79)`

`\sigma_(tot) =436810 psi`

So then the strength of the composite material is :
`\sigma_(tot) =436810 psi`