The volume fraction of particles in a WC-particle Cu-matrix CERMET is 0.84 Calculate the minimum expected elastic modulus, in GPa, of this particle reinforced composite. The moduli of the two components are 682 GPa and 110 GPa, respectively. Use what you know about these composite phases to discern which modulus is which.

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nuhulawal20 nuhulawal20 · Answer 1 · 2021-05-04T03:22:44+02:00

Answer:

the minimum expected elastic modulus is 372.27 Gpa

Explanation:

First we put down the data in the given question;

Volume fraction [tex]V_f[/tex] = 0.84

Volume fraction of matrix material [tex]V_m[/tex] = 1 - 0.84 = 0.16

Elastic module of particle [tex]E_f[/tex] = 682 GPa

Elastic module of matrix material [tex]E_m[/tex] = 110 GPa

Now, the minimum expected elastic modulus will be;

[tex]E_{CT[/tex] = ([tex]E_f[/tex] × [tex]E_m[/tex] ) / ( [tex]E_f[/tex][tex]V_m[/tex] + [tex]E_m[/tex] [tex]V_f[/tex] )

so we substitute in our values

[tex]E_{CT[/tex] = (682 × 110 ) / ( [ 682 × 0.16 ] + [ 110 × 0.84] )

[tex]E_{CT[/tex] = ( 75,020 ) / ( 109.12 + 92.4 )

[tex]E_{CT[/tex] = 75,020 / 201.52

[tex]E_{CT[/tex] = 372.27 Gpa

Therefore, the minimum expected elastic modulus is 372.27 Gpa