Prob,6.5
Define ROM relation for modulus,
> E1:=(Ef,Em,Vf) -> Vf*Ef+(1-Vf)*Em;
,,)E1,= ( Ef Em Vf) → Vf Ef + (1? Vf Em
50% E-glass in epoxy,
> 'E[1](GPa)'=E1(76,2.4,.5);
E
1
( GPa ) = 39.20
60% HM carbon in epoxy,
> 'E[1](GPa)'=E1(340,2.4,.6);
E
1
( GPa ) = 204.96
60% Kevlar in epoxy,
> 'E[1](GPa)'=E1(124,2.4,.6);
>
E
1
( GPa ) = 75.36
Specific modulus (E/density),
ROM density relation,
> rho1:=(rho_f,rho_m,Vf) -> Vf*rho_f+(1-Vf)*rho_m;
,,)ρ1,= ( rho_f rho_m Vf) → Vf rho_f + ( 1? Vf rho_m
Glass/epoxy,
> 'rho[1]'=rho1(2540,1300,.5);
ρ
1
= 1920,
> Digits:=3:'(E/rho) (MPa-m^3/kg)'=39.2e3/1920;
3

E
ρ
m
MPa?
= 20.4
kg
Carbon/epoxy,
> 'rho[1]'=rho1(1860,1300,.6);
ρ
1
= 1640,
> '(E/rho) (MPa-m^3/kg)'=205e3/1640;
3

E
ρ
m
MPa? = 125.
kg
Kevlar/epoxy,
> 'rho[1]'=rho1(1450,1300,.6);
ρ
1
= 1390,
> '(E/rho) (MPa-m^3/kg)'=75.4e3/1390;
3

E
ρ
m
MPa?
= 54.2
kg
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