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The invariants affect the shape of the yield surface. The von Mises condition assumes that the yield surface remains cylindrical in principal stress space. If you want pressure-dependence (the circular cylinder becomes a circular cone), then you add the first invariant into the mix. If the yield surface varies depending on whether you are in pure triaxial ...


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This is an added effort in response to your question after your latest update. In the situation above, if a < d (beam depth), practically we can replace the uniform load with a concentrated load, and say it is justified by the Saint-Venant Principle. However, it will run into problems with the actual behaviors from the beam theory if we proceed to check ...


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I would like to add something to the already existing answer here. Yes, it would be considered as an application of Saint Venant's principle. Since the law just mentions about replacing a point force with an equivalent distributed force over the area and vice versa, it can be an externally applied force or it can be a reaction force, so it doesn't matter. ...


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Yes it is correct. This is not a dire t answer but can shed some light on the question. We do a lot of simlar substitution of point load for distributed loads and vice versa. we do the same exchenge between point loads to one moment e g, in bolted hangar roof beam to column or bolted brackets supperting a beam. in the elbow bolt group we find the CG of the ...


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Yes, I think you can say so if you reverse its concept exactly the way it is concerned. The explanation (of the concept) below is quite straightforward and precise: Saint-Venant's Principle simply states that the stress measured at any point on an axially loaded cross section is uniform given that the measured location is far enough away from the point of ...


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The other answers describe the "materials science" mechanisms of iron vs. temperature. I'm going to add this: Matter "tries" to reach a minimum energy state whenever possible. In general, then, if you cool something as slowly as possible, you'll come closest to a solid which is a perfect crystalline structure. See "annealing."...


6

You are mixing apples and oranges. Many steels harden by rapid cooling, but very few other metals do that; specifically, only aluminum bronze and certain titanium alloys. Many metals will strengthen by age hardening; Rapid cool softens, and then time at a lower temperature strengthens them. There are a myriad of combinations, like HSS (high-speed steels). ...


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The effects of heating-quenching a metal is explained below Transformation hardening is the heat-quench-tempering heat treatment cycle addressed earlier in this article. It's used to adjust strength and ductility to meet specific application requirements. There are three steps to transformation hardening: Cause the steel to become completely austenitic by ...


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In short the heat treatments in steel change the phase of iron between the following phases: Austenite Cementite Martensite Bainite Ferrite Perlite. (Actually quenching does not allow low temperature phase changes to occur, so effectively the phases are sort of "frozen" in their high temperature equivalents). Figure 1 : example of continuoous ...


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Assuming the following stress tensor: $$A = \begin{bmatrix}100,20,0\\20,0,20\\0,20,50\end{bmatrix}$$ you can find the eigenvalues and eigenvectors in octave/matlab A = [100, 20 ,0 ;20 ,0,20; 0,20 ,50] [k,l] = eig(A) The printout is k = 0.169653 -0.132430 -0.976565 -0.935341 0.290482 -0.201883 0.310410 0.947672 -0.074586 l = Diagonal ...


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