麻省理工学院：《polymer engineering》p4 17

I McCrum Prob. 4.17 [ restart: with(inttrans): Digits: =4: L Compute shift factor for 50C relative to 20C >a50:=exp((De1ta[H]/R)*(1/(273+50)-1/(273+20))); 94639R a50:=e >De1ta[H]:=145e3;R:=8.314;"a50'=a50; △a:=145000 R:=8.31 a50=.003974 L Define step function and relaxation modulus [>u: t->Heaviside(t) Ere1:=t→>2*t^(-0.09)*10^9; Erel:=t→2000000000 I Compute stress and plot alpha: =.0001: sigma: alpha*E rel(t/a 50)*(20-50)+ a1pha*Ere1(t-3600)*u(t-3600)*(50-20); 36481037-+600010 Heaviside(t-3600) (t-3600)° plot(sigma(t),t= 1. 3800, thickness=3) 2004006008001200-16002002400-2800-3200300

McCrum Prob. 4.17 > restart:with(inttrans):Digits:=4: Compute shift factor for 50C relative to 20C > a_50:=exp((Delta[H]/R)*(1/(273+50) - 1/(273+20))); a_50 :=      ∆ 30 H − 94639 R      e > Delta[H]:=145e3;R:=8.314;'a_50'=a_50; ∆H := 145000. R := 8.314 a_50 = .003974 Define step function and relaxation modulus > u:= t -> Heaviside(t): > E_rel:= t-> 2*t^(-0.09)*10^9; 1 E_rel := t → 2000000000 t .09 Compute stress and plot > alpha:=.0001:sigma:= alpha*E_rel(t/a_50)*(20-50) + alpha*E_rel(t-3600)*u(t-3600)*(50-20); + .6000 107 Heaviside( t − 3600 ) σ := −.3648 107 1 t .09 ( t − 3600).09 > plot(sigma(t),t=.1..3800,thickness=3); Page 1

L Compute stress after 3600+100s t: =3700;'sigma 3700s (MPa)I=sigma/1e6; t:=3700 sigma 3700s( MPa)=2.222

Compute stress after 3600+100s > t:=3700;'sigma_3700s (MPa)'=sigma/1e6; t := 3700 sigma_3700s( MPa ) = 2.222 Page 2