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’t 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? (12 points)

Answer 1

- Given F: 630 KN € Young's modalus (E) = Stressla) Strain (E) we also know یا f A A: cross sectional area II (4)?cm? 4 A= TT x (4x10) mm a = 630x 103 501.3u mpa. ūCUX 1037 E = H = 001 E- 501:34 50,134 Mpa. ol 50134. Gran 0.01 Young's modulus of Epoxy resin (EY) = 3.2 Gpa. Youngles modulus of fiber (Ef) = 72.4 Gpe. The volume of the fraction fiber E=Vrert Vf Ef -(1)

2 here Vr= volume percentage of epory resin If = volume volume percentage of fiber Eq CD Can be written E = CI-V) Ert VEF so.134 = (1-16) 32-4 + vf (12.6) 69:2 Vf. = 46.934 Uf = 46.934 69.2 . vf 06782 V = 67.82 5.