Question

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.

Answer 1

upper bound = 20.4 GPa

lower bound = 3.71 GPa

Step-by-step 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 =
`(Em * Eai)/(Va*Eai +Vb*Em )`

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

= 207 / 55.8 = 3.71 GPa