Elastomer stretched in tension and elongation

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SUMMARY

The discussion focuses on the behavior of an elastomer under tension, specifically using the Maxwell model to analyze stress relaxation. After 10 minutes of constant tension, the tensile stress dropped by 12%, leading to the calculation of the relaxation time, which is determined to be approximately 8 minutes. Additionally, it is established that the stress will decrease to 75% of its final value in 22 minutes, confirming the predictive capability of the Maxwell model in elastomer behavior.

PREREQUISITES
  • Understanding of the Maxwell model for viscoelastic materials
  • Familiarity with stress and strain concepts in materials science
  • Knowledge of exponential decay functions
  • Basic calculus for solving differential equations
NEXT STEPS
  • Study the derivation of the Maxwell model equations in viscoelasticity
  • Explore the implications of stress relaxation in elastomers
  • Learn about other viscoelastic models, such as the Kelvin-Voigt model
  • Investigate practical applications of elastomer stress analysis in engineering
USEFUL FOR

Materials scientists, mechanical engineers, and students studying viscoelastic behavior in polymers will benefit from this discussion, particularly those interested in the mechanical properties of elastomers under stress.

tone999
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Homework Statement



A strip of elastomer was stretched in tension and elongation and was held constant. After 10 minutes the tensile stress in the specimen dropped by 12%. Assuming that the elastomer behaves in accordance with the maxwell model:

(i) Calculate the relaxation time (to the nearest whole number)
(ii) Show that it takes 22 minutes for the stress to drop to 75% of its final value.


Homework Equations





The Attempt at a Solution



I take it we have to use the maxwell model equation here?

sigma (t) = sigma (0) e ^ -t/tau
 
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tone999 said:

The Attempt at a Solution



I take it we have to use the maxwell model equation here?

sigma (t) = sigma (0) e ^ -t/tau

I think so. Based on the information in the problem statement, what is the ratio,

sigma(t) / sigma(0),​
when t=10 minutes?
 

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