P3.2: The material of a tension link is changed from a Ti-6A1-4V (aged) titanium
ID: 1862229 • Letter: P
Question
P3.2: The material of a tension link is changed from a Ti-6A1-4V (aged) titanium alloy to a uniderectional continuous Gy-70 carbon fiber-expoxy. The stress-strain curve of the epoxy resin is shown below. Calculate the volume fraction of GY-70 fibers required in the composite link to match the modulus of the titanium alloy.
HInts: Find the modulus of Ti and carbon fiber from table
Get Em from graph
Solve E(L) = EfVf+Em(1-Vf) for Vf
. Calculate the volume fraction of GY-70 fibers rerquired in the composite link to match the modulus of the titanium alloy.
Also, estimate the tensile strength of the composite link and compare its strength-weight ratio with that of the titanium alloy. Consider a unidirectional continuous fiber lamina containing brittle, clastic fibers in a elastic, perfectly plastic matrix. The stress-strain diagrams for the fibers and the matrix are shown onExplanation / Answer
modulus of carbon fibre is 138 Gpa.
for the given titanium alloy is 113.8 Gpa
from the graph, the slope is the youngs modulus .
= 9/.02=450 ksi=3.1 GPa
From formula
E(Ti alloy)=E(fibre)(Vf)+E(epoxy)(1-Vf)
113.8=138(Vf)+3.1(1-Vf)
113.8=Vf*134.9 +3.1
=>110.7/134.9=.82
i.e 82% is the required volume fraction
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