A new composite grappling hook was purchased for the overhead crane in the turbi

Question

  A new composite grappling hook was purchased for the overhead crane in the turbine building, but the manufacturer lost all records of the volume of fibers used in the process. He is able to say that the fibers are E-glass and the matrix is epoxy, but he doesn%u2019t know the percent of fibers. While a density measurement could estimate the make-up, you decide to test the force at which 1% strain occurs. Carefully gripping the shaft of the hook (which is 4 cm in diameter), you find that a force of 630kN is necessary to create 1% strain. What is the fiber percentage in the material?

Explanation / Answer

youngs modulus of composite=stress/strain=630 E3/pi*2^2 E-4*0.01=50.159 E9 Pa=50.159 GPa

E of epoxy resin=3.2 Gpa

E of fibre=72.4 GPa

Ec=Vr*Er+Ef*Vf

here f stands for fibre and r stands for resin and c stands for composite

==> 50.159=(1-Vf)*3.2+Vf*72.4

==> Vf=0.678

==> volume fraction of fibre= 67.8 %

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