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- TL;DR Summary
- Hung up on two steps in a derivation of mechanics in open die forging. First question is a supposedly von Mises stress that looks to me like a Tresca stress. Second question is a confusing boundary condition.

Hey folks!

I had a hard time finding accessible resources on open die forging. If you have a better source, that'd be just as good as an answer to these questions. I've been following this slideshow, and my questions are about steps in this derivation I don't follow.

First up, one page 6 "Force balance in the x-direction", I don't follow the last step. It says it's the von Mises yielding criterion, but to me ##\sigma_x + p## looks like the Tresca criterion. I would've expected ##\frac{1}{\sqrt{3}}[\sigma_{x}^2 + \sigma_x p + p^2]^{1/2}## for von Mises. Am I missing something? I have a funny feeling it has something to do with how the author is working in 2D but I can't put a finger on it.

Second question is about the boundary condition on page 8 "Sliding region". The author explicitly says at ##x=0##, that ##\sigma_x = 2k##. But in the lower limit of integration on the left hand side integral, he says at ##x=0##, that ##p = 2k##. They can't both be true because per the yield criterion on page 6, ##\sigma_x + p = 2k##. What gives? My understanding is that the stress won't exceed the yield criterion because if the material temporarily exceeds the yield point it will squish and flow around until the stress returns to the yield point. Is that right? Additionally I don't feel like I understand where this boundary condition ##\sigma_x = 2k## at ##x=0## comes from. Can anyone fill me in?

Thanks all!

I had a hard time finding accessible resources on open die forging. If you have a better source, that'd be just as good as an answer to these questions. I've been following this slideshow, and my questions are about steps in this derivation I don't follow.

First up, one page 6 "Force balance in the x-direction", I don't follow the last step. It says it's the von Mises yielding criterion, but to me ##\sigma_x + p## looks like the Tresca criterion. I would've expected ##\frac{1}{\sqrt{3}}[\sigma_{x}^2 + \sigma_x p + p^2]^{1/2}## for von Mises. Am I missing something? I have a funny feeling it has something to do with how the author is working in 2D but I can't put a finger on it.

Second question is about the boundary condition on page 8 "Sliding region". The author explicitly says at ##x=0##, that ##\sigma_x = 2k##. But in the lower limit of integration on the left hand side integral, he says at ##x=0##, that ##p = 2k##. They can't both be true because per the yield criterion on page 6, ##\sigma_x + p = 2k##. What gives? My understanding is that the stress won't exceed the yield criterion because if the material temporarily exceeds the yield point it will squish and flow around until the stress returns to the yield point. Is that right? Additionally I don't feel like I understand where this boundary condition ##\sigma_x = 2k## at ##x=0## comes from. Can anyone fill me in?

Thanks all!