Rubber particles are sometimes dispersed in an epoxy matrix to increase its resistance to the propagartion of cracks. Rubber has a Young's modulus of Erubber=0.001GPa. For a composite with 15 volume percent rubber particles uniformly dispersed in an epoxy matrix, give numerical values for the upper Eupper and lower Elower bounds of the composite.

To calculate the upper and lower bounds of the composite's Young's modulus, we need to consider the rule of mixtures. According to this rule, the Young's modulus of a composite material is determined by the volume fractions and Young's moduli of the constituent materials.

1. Calculate the Young's modulus of the epoxy:
Since the rubber particles are dispersed in an epoxy matrix, the epoxy will be the main material determining the overall Young's modulus. Let's assume the Young's modulus of the epoxy (Eepoxy) is a known value.

2. Calculate the Young's modulus of the composite:
The Young's modulus of the composite (Ecomposite) can be determined using the rule of mixtures equation:
Ecomposite = Vepoxy * Eepoxy + Vrubber * Erubber

Vepoxy: Volume fraction of the epoxy matrix (85% or 0.85)
Eepoxy: Young's modulus of the epoxy
Vrubber: Volume fraction of the rubber particles (15% or 0.15)
Erubber: Young's modulus of rubber (given as 0.001 GPa)

Plugging in the values, we get:
Ecomposite = 0.85 * Eepoxy + 0.15 * 0.001 GPa

3. Calculate the upper Eupper and lower Elower bounds of the composite:
The upper and lower bounds can be determined by assuming the volume fractions in the extreme cases:
a) All the space is occupied by epoxy (0% rubber volume fraction)
b) All the space is occupied by rubber particles (100% rubber volume fraction)

Upper bound (Eupper): In the case of 0% rubber volume fraction (all epoxy), the equation becomes:
Eupper = 0.85 * Eepoxy + 0.15 * 0 = 0.85 * Eepoxy

Lower bound (Elower): In the case of 100% rubber volume fraction (all rubber particles), the equation becomes:
Elower = 0 * Eepoxy + 1 * 0.001 GPa = 0.001 GPa

Therefore, the upper bound (Eupper) would be 0.85 times the Young's modulus of the epoxy, and the lower bound (Elower) would be 0.001 GPa.