Rubber particles, roughly 1mm in diameter, have been added to an epoxy resin to increase its resistance to crack growth. Estimate the Young's modulus of the composite, given that the Young's moduli of the epoxy and the rubber are, respectively, 2GPa and 10MPa, and that the volume fraction of the rubber particles is 5%.
E (in GPa):
E= (Er*Ee)/(ErVe+EeVr)
To estimate the Young's modulus of the composite, we can use the rule of mixtures, which considers the volume fraction and Young's modulus of each component.
The rule of mixtures states that for a composite material made of different components, the overall properties can be estimated by taking a weighted average of the properties of each component, based on their volume fractions.
In this case, the composite is made up of epoxy resin and rubber particles. Given that the volume fraction of the rubber particles is 5% (0.05), we can calculate the Young's modulus of the composite as follows:
E_composite = V_epoxy * E_epoxy + V_rubber * E_rubber
Here, V_epoxy and V_rubber are the volume fractions of epoxy and rubber, respectively, and E_epoxy and E_rubber are their respective Young's moduli.
Plugging in the given values:
E_composite = 0.95 * 2 GPa + 0.05 * 10 MPa
Converting the Young's modulus of rubber from MPa to GPa:
E_composite = 0.95 * 2 GPa + 0.05 * 0.01 GPa
Simplifying the equation:
E_composite = 1.9 GPa + 0.0005 GPa
Calculating the final answer:
E_composite = 1.9005 GPa
Therefore, the estimated Young's modulus of the composite is approximately 1.9005 GPa.