A unidriectional, continuously reinforced glass fiber composite has Vf=60 volume percent fibers in a matrix of epoxy. Glass has a Young's Modulus of Eglass=70GPa; epoxy has a Young's Modulus of Eepoxy=2GPa
(a) Give numerical values for
(i) the Young's Modulus for loading along the fiber axis (E1) and
{ii) the Young's Modulus for loading perpendicular to the fiber axis (E1) .
A unidirectional, continuously reinforced glass fiber composite has ππ=60 volume percent fibers in a matrix of epoxy. Glass has a Young's Modulus of πΈππππ π =70πΊππ; epoxy has a Young's Modulus of πΈππππ₯π¦=2πΊππ
(a) Give numerical values for
(i) the Young's Modulus for loading along the fiber axis (πΈ1) and
{ii) the Young's Modulus for loading perpendicular to the fiber axis (πΈ2) .
please help with this problem.thank you
Please help with this problem
To find the Young's Modulus for loading along the fiber axis (E1) and perpendicular to the fiber axis (E2), we can use the rule of mixtures. The rule of mixtures allows us to calculate the effective properties of a composite material based on the properties of its constituents and their volume fractions.
For a unidirectional composite with volume fraction Vf = 60% fibers and (1 - Vf) = 40% epoxy matrix, we can calculate the effective Young's Modulus as follows:
(i) Young's Modulus for loading along the fiber axis (E1):
E1 = Vf * Eglass + (1 - Vf) * Eepoxy
Substituting the given values:
E1 = 0.60 * 70 GPa + 0.40 * 2 GPa
Calculating the values:
E1 = 42 GPa + 0.8 GPa
E1 = 42.8 GPa
(ii) Young's Modulus for loading perpendicular to the fiber axis (E2):
E2 = 1 / (Vf / Eglass + (1 - Vf) / Eepoxy)
Substituting the given values:
E2 = 1 / (0.60 / 70 GPa + 0.40 / 2 GPa)
Calculating the values:
E2 = 1 / (0.857 GPa + 0.2 GPa)
E2 = 1 / 1.057 GPa
E2 = 0.946 GPa
Therefore, the numerical values for the Young's Modulus for loading along the fiber axis (E1) and perpendicular to the fiber axis (E2) are 42.8 GPa and 0.946 GPa, respectively.