Answer:
upper bound = 20.4 GPa
lower bound = 3.71 GPa
Explanation:
Given data:
20% of BN Â ( Vb )
80% of AI Â ( 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
