Calculate the upper bound and lower bound of the elastic modulus of a Al composite that contains 20 vol.% of BN aligned, continuous fibers. The elastic modulus of Al and BN is 69 GPa and 90GPa, respectively.

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 =

                      = ( 3 * 69 ) / [ (0.8 * 69 ) + ( 0.2 *  3 ) ]

                      = 207 / 55.8 =  3.71 GPa