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Engineering
Mechanical Engineering
Open die forging, von Mises related questions
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[QUOTE="Twigg, post: 6440351, member: 572426"] I think I've made a little more progress. At least I think I understand why the boundary condition ##\sigma_x = 2k## @ ##x=0## exists, but it doesn't explain why the author uses ##p=2k## @ ##x=0## in the lower limit of integration. I threw in a little quick diagram to help illustrate what I think is going on. As the dies close in on the workpiece, the edges of the workpiece deform by bulging outwards. Where this bulge starts, the dies no longer touch the workpiece, so there is no pressure by the dies on the workpiece at this point, so p=0 at this point. I exagerrated the bulge in my little sketch, but my gut tells me there has to be some bulge. I can do this experiment with playdough and the playdough would bulge, so it shouldn't be qualitatively different for steel? If my "bulging" hypothesis is correct, then since the material is yielding, ##\sigma_x + 0 = 2k## gives ##\sigma_x = 2k## at x=0 where the bulge starts. However, that conclusion contradicts the author's statement that ##p=2k## at ##x=0##. What gives?? I don't think ##\int \frac{dp}{p}## is even integrable from p=0, so I feel like I'm missing something. [ATTACH type="full" alt="1609898092109.png"]275705[/ATTACH] [/QUOTE]
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