Polymer Engineering question related to Von Mises yield criterion

kennyyip

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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afreiden

You can find A and B with two simultaneously equations.
For the first equation assume uniaxial tension yielding - i.e. take σ1 as f_ty and σ2=σ3=0.
For the second equation assume uniaxial compression yielding. This is a polymer so it makes sense that f_ty and f_cy 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.