2 Consider the composite system below EA 100 MPa EB 200 MP

2. Consider the composite system below:

EA = 100 MPa EB = 200 MPa

Estimate its effective composite modulus (Etotal) in the vertical direction. Justify your answer indicating Voigt and Ruess bounds.

Solution

For a two phase composite made of two different isotropic materials A and B whose Young’s moduli are EA and EB, and Poisson ratios are vA and vB, respectively, the Voigt limit for the Young’s modulus of the composite is given as

Effective E max = EA fA + EB fB

Where fA and fB are the volume fractions of the two materials, and thus fA+fB=1. The lower limit (i.e. the Reuss limit) for the Young’s modulus of the two-phase composite is given as

Effecttive E min= EA EB/ (EafB + EB fA)

In this case we can assume fA = fB = 1 since values are not specified so

Emax = 100 + 200 = 300MPa

Emin = 100*200/100+200 = 66.66Mpa