Answer:
upper bound = 20.4 GPa
lower bound = 3.71 GPa
Explanation:
Given data:
20% of BN ( Vb )
80% of AI ( Va )
Elastic modulus of AI ( Eai ) = 69 GPa
Elastic modulus of BN ( Ebn ) = 90 GPa
lets assume the Modulus of the composite to be 3GPa ( value not given in question ) ( Em )
Calculate the upper bound of the elastic modulus
upper bound = Em*Va + Ebn * Vb
= 3 * 0.8 + 90 * 0.2
= 2.4 + 18 = 20.4 GPa
lower bound = [tex]\frac{Em * Eai}{Va*Eai +Vb*Em }[/tex]
= ( 3 * 69 ) / [ (0.8 * 69 ) + ( 0.2 * 3 ) ]
= 207 / 55.8 = 3.71 GPa
