for the following composite material stressed under isostrain conditions.
The composite consists of a continuous glass‐fiber‐reinforced‐epoxy resin produced by
Using 60 percent by volume of E-glass fibers having a modulus of elasticity of
Ef =7.24× 〖10〗^4 MPa and a tensile strength of 2.4 GPa and a hardened epoxy resin with a
Modulus of Em = 3.1 × 〖10〗^3 MPa and a tensile strength of 0.06 GPa.
calculte the the fraction of the load carried by the fiber
Which material is a composite?(1 point)
gold
silicon
aluminum
polycarbonate
To calculate the fraction of the load carried by the fiber, we need to determine the tensile strength and modulus of elasticity for the composite material.
First, let's calculate the tensile strength for the composite material using the Rule of Mixtures:
σ_c = V_f * σ_f + V_m * σ_m
Where:
- σ_c is the tensile strength of the composite material
- V_f is the volume fraction of the fiber
- V_m is the volume fraction of the matrix
- σ_f is the tensile strength of the fiber
- σ_m is the tensile strength of the matrix
Given:
- V_f = 0.60 (volume fraction of E-glass fibers)
- σ_f = 2.4 GPa (tensile strength of E-glass fibers)
- V_m = 0.40 (volume fraction of hardened epoxy resin)
- σ_m = 0.06 GPa (tensile strength of hardened epoxy resin)
σ_c = 0.60 * 2.4 GPa + 0.40 * 0.06 GPa
σ_c = 1.44 GPa + 0.024 GPa
σ_c = 1.464 GPa
Next, let's calculate the modulus of elasticity for the composite material using the Rule of Mixtures:
E_c = V_f * E_f + V_m * E_m
Where:
- E_c is the modulus of elasticity of the composite material
- E_f is the modulus of elasticity of the fiber
- E_m is the modulus of elasticity of the matrix
Given:
- E_f = 7.24 × 10^4 MPa (modulus of elasticity of E-glass fibers)
- E_m = 3.1 × 10^3 MPa (modulus of elasticity of hardened epoxy resin)
E_c = 0.60 * 7.24 × 10^4 MPa + 0.40 * 3.1 × 10^3 MPa
E_c = 4.344 × 10^4 MPa + 1.24 × 10^3 MPa
E_c = 4.468 × 10^4 MPa
Now, we can calculate the fraction of the load carried by the fiber:
Fraction of load carried by the fiber = σ_f / σ_c
Fraction of load carried by the fiber = 2.4 GPa / 1.464 GPa
Fraction of load carried by the fiber ≈ 1.64
Therefore, the fraction of the load carried by the fiber is approximately 1.64.
To calculate the fraction of the load carried by the fiber in the composite material, we need to consider the volume fractions and the material properties of the glass fibers and the epoxy resin.
Given:
- Volume fraction of glass fibers, Vf = 60% = 0.6
- Modulus of elasticity for glass fibers, Ef = 7.24 × 10^4 MPa
- Tensile strength for glass fibers, σf = 2.4 GPa = 2.4 × 10^3 MPa
- Modulus of elasticity for epoxy resin, Em = 3.1 × 10^3 MPa
- Tensile strength for epoxy resin, σm = 0.06 GPa = 0.06 × 10^3 MPa
First, let's calculate the modulus of the composite material, Ec.
Ec = Vf * Ef + (1 - Vf) * Em
= 0.6 * 7.24 × 10^4 MPa + (1 - 0.6) * 3.1 × 10^3 MPa
Next, let's calculate the tensile strength of the composite material, σc.
σc = Vf * σf + (1 - Vf) * σm
= 0.6 * 2.4 × 10^3 MPa + (1 - 0.6) * 0.06 × 10^3 MPa
Now, we can calculate the fraction of the load carried by the fiber, Ff.
Ff = (σc - Em) / (Ef - Em)
Substituting the previously calculated values,
Ff = (σc - 3.1 × 10^3 MPa) / (7.24 × 10^4 MPa - 3.1 × 10^3 MPa)
Therefore, to calculate the fraction of the load carried by the fiber, you can substitute the values into the equation for Ff and perform the necessary calculations.