麻省理工学院：《polymer engineering》Prob. 6.5

Prob. 6.5 Define rom relation for modulus El:=(Ef, Em, vE) VE*Ef+(1-VE)*Em; E/: =(Ef, Em, V- VfEf+(1-v Em 50%o E-glass in epoxy E[1](GPa)'=E1(76,2.4,.5); E1(GPa)=392 60%HM carbon in epoxy >"E[1](GPa)"=E1(340,2.4,.6); E1(GPa)=204.96 60% Kevlar In epoxy >E[1](Gpa)"=E1(124,2.4,,6); E1(GPa)=75.3 Specific modulus(E/density) Rom density relation rhol:: =(rho f, rho m, vE)-> vE*rho f+(l-vE)*rho m; pl: =(rho f, rho m, rho f+(1 -rho >'rho[1]'=rho1(2540,1300,.5); p > Digits:=3:'(E/rho)(MPa-m^3/kg)=39.2e3/1920; 20.4 kg ho[1]"=rho1(1860,1300,.6); p >'(E/rho)(MPa-m^3/kg)'=205e3/1640; MP kg Kevlar X\ >'rho[1]'=ho1(1450,1300,.6); P >'(E/rho)(MPa-m^3/kg)"=75.4e3/1390; MP 54.2 kg

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); E1( GPa ) = 39.20 60% HM carbon in epoxy: > 'E[1](GPa)'=E1(340,2.4,.6); E1( GPa ) = 204.96 60% Kevlar in epoxy: > 'E[1](GPa)'=E1(124,2.4,.6); > E1( 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); ρ1 = 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); ρ1 = 1640. > '(E/rho) (MPa-m^3/kg)'=205e3/1640; 3       E ρ     m       MPa − = 125. kg Kevlar/epoxy: > 'rho[1]'=rho1(1450,1300,.6); ρ1 = 1390. > '(E/rho) (MPa-m^3/kg)'=75.4e3/1390; 3       E ρ     m MPa −       = 54.2 kg Page 1