Stress relaxation in a thermoplastic member under tension
A long piece of thermoplastic is stretched between two rigid supports at a stress level of 6 MPa. After 25 days, the stress level is found to have decayed to one third of the original level. How long will it take for the stress level to reach one tenth of the original value?

Question

Accepted Answer

Substituting these data into Eq. (10.11)

[latex]\sigma (t)=\frac{k\Delta l}{A}e^{-({k}/{\eta })t} =\frac{k\Delta l}{A}e^{-{ t}/{\lambda}} [/latex] (10.11)

as modified for normal stress, we have,

[latex]3=6e^{-25/\lambda } [/latex]

Hence,

[latex]\ln \left\lgroup\frac{3}{6} \right\rgroup=\frac{-25}{\lambda } [/latex] (or) [latex] λ=36.1 [/latex] days.

Therefore,

[latex]\ln \left\lgroup\frac{1}{6} \right\rgroup=\frac{-t}{36.1 } [/latex] (or) [latex] t=64.6 [/latex] days.

Question 10.3: Stress relaxation in a thermoplastic member under tension A ...

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