Polymer Engineering question related to Von Mises yield criterion

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SUMMARY

The discussion focuses on solving a proof question related to the Von Mises yield criterion in polymer engineering, specifically for a final exam extra credit problem. The problem involves determining values A and B using two simultaneous equations: one for uniaxial tension yielding (σ1 as fty and σ2=σ3=0) and another for uniaxial compression yielding. It is emphasized that for polymers, the yield strengths in tension (fty) and compression (fcy) differ, which is crucial for solving the equations. The final step involves analyzing the hydrostatic case where σ1=σ2=σ3=σ to solve for σ.

PREREQUISITES
  • Understanding of the Von Mises yield criterion
  • Knowledge of uniaxial tension and compression yielding
  • Familiarity with polymer material properties
  • Ability to solve simultaneous equations
NEXT STEPS
  • Study the derivation of the Von Mises yield criterion in detail
  • Explore the differences between tensile and compressive yield strengths in polymers
  • Learn how to solve hydrostatic stress conditions in materials
  • Review examples of simultaneous equations in engineering mechanics
USEFUL FOR

This discussion is beneficial for polymer engineers, materials scientists, and students preparing for exams in materials engineering, particularly those focusing on yield criteria and stress analysis in polymers.

kennyyip
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It is a proof question. Does anyone can tell me how to do this question?question 22.2
it is the question for extra credit for my final exam.
thank you so much.
 

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You can find A and B with two simultaneously equations.
For the first equation assume uniaxial tension yielding - i.e. take σ1 as fty and σ2=σ3=0.
For the second equation assume uniaxial compression yielding. This is a polymer so it makes sense that fty and fcy would be different values - and they have to be different values otherwise you'd find that A=0.

Once you have A and B, then consider the hydrostatic case - i.e. take σ1=σ2=σ3=σ. Solve for σ.
 

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