Compare the Young's modulus E∗ of two open-cell foams. Which Young's modulus is higher? Recall that C1=1.
1. polystyrene: (Es∼3.5GPa), ρ∗/ρs=0.3
2. Al 7075-T651: (Es∼72GPa), ρ∗/ρs=0.1
E∗PS (in GPa):
E∗Al (in GPa):
Select the correct answer:
Polystyrene has a higher Young's modulus
Al 7075-T651 has a higher Young's modulus
Al 7075-T651 has a higher Young's modulus
To compare the Young's modulus of two open-cell foams, we need to calculate the effective Young's modulus (E∗) for each foam by taking into account the density ratio (ρ∗/ρs) and the Young's modulus of the solid material (Es).
The formula to calculate the effective Young's modulus (E∗) is:
E∗ = ((1 - α) * Es) / (1 + α)
Where α is the porosity of the foam given by the ratio of the density ρ∗ of the foam to the density ρs of the solid material (α = ρ∗/ρs).
For the given foams:
1. Polystyrene:
Es = 3.5 GPa
ρ∗/ρs = 0.3
First, calculate the porosity (α):
α = ρ∗/ρs = 0.3
Then, apply the formula to calculate E∗:
E∗ = ((1 - 0.3) * 3.5) / (1 + 0.3)
E∗ = (0.7 * 3.5) / 1.3
E∗ = 2.45 GPa
So, E∗PS = 2.45 GPa.
2. Aluminum 7075-T651:
Es = 72 GPa
ρ∗/ρs = 0.1
Similarly, calculate the porosity (α):
α = ρ∗/ρs = 0.1
Then, apply the formula to calculate E∗:
E∗ = ((1 - 0.1) * 72) / (1 + 0.1)
E∗ = (0.9 * 72) / 1.1
E∗ = 59.76 GPa
So, E∗Al = 59.76 GPa.
Comparing the values obtained:
E∗PS = 2.45 GPa
E∗Al = 59.76 GPa
Hence, Al 7075-T651 has a higher Young's modulus (E∗) than polystyrene.