Hope this may help you!
https://www.researchgate.net/post/Can_necking_phenomenon_be_observed_in_any_kind_of_mechanical_test/1
Torsion is a pure shear test. Shear strains do not give rise to changes in the area subjected to the shear load. So necking cannot occur.
Assuming that the plasticity is an isochoric transformation, as the lenght of the specimen does not change during torsion (shear) test, the area subjected to the shear load remains constant.
The reason for necking in simple language is that it is energetically it is favorable for the material to undergo localized deformation in the necked area, rather than the whole length of the material would be strained. In other words necking can be seen as a relaxation mechanism in metals.
Mathematically necking occurs when the rate of change in true stress w.r.t. true strain becomes larger than the true stress. Such condition is like rolling the ball to the top pf the hill and watching it lower its energy by rolling down the curve. This condition is called Considere's criterion.
The simplest definition of the necking is so called localization of plastic deformation. There are two principal conditions for necking in a metallic material. The first one, it should exhibit considerable plasticity (>10% of elongation). The second, applied deformation scheme should allow observing the neck region in sample. Therefore, the uniaxial tension is the more appropriate geometry for study of this phenomena. The necking begins appearing on the third stage of plastic deformation of a metallic single crystal, when deformation relief is developing on the surface. TEM study is shown that dislocations begin transform into the small angle boundaries at this stage of deformation of single crystal.
I suggest a much simpler answer. Necking occurs in a tensile test because all the section is subjected to the same nominal stress field. Therefore, when it is triggered somewhere (for any reason such as local imperfection), that section reduces its extension and increases its stress continuously. Note that in all other non-decreasing sections the stress lowers or keep at least constant.
In torsion you do not have any section entirely stressed at its critical value because the stress varies linearly from its center to the borders. Therefore, the inner material (closer to the speciment axis) does not have any reason to start elongating abrouptly and it constrains the elongation of the outer material (read no neckling).
It is interesting to note that if you consider a hollow small-thickness cylinder the stress state changes and follows the approximate Bredt theory (almost constance of the stress state in the thickness). In this case, if you are able to avoid bukling occurence, you WILL experience a localization of the deformation (read NECKING).
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