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 10
7
Heaviside( t? 3600 )
σ,=?.3648 10
7
1
t
.09
( t? 3600)
.09
> plot(sigma(t),t=.1..3800,thickness=3);
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Compute stress after 3600+100s
> t:=3700;'sigma_3700s (MPa)'=sigma/1e6;
t,= 3700
sigma_3700s( MPa ) = 2.222
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