I know the ratio at which the cross sectional area changes to length is Poisson's ratio but is this why necking is more apparent in some materials than others or is the necking effect only dependent on the material's ductility?


It is important to think about the underlining physics of a tensile test. What material are you testing? What is the geometry you are testing? How much global strain is being applied? With these questions in mind, I think it is necessary to think about this problem both in terms of elastic and plastic deformations.

Consider the stress-strain behavior for two materials, one with no plasticity (traditionally rubbers) and one that exhibits plasticity (traditionally metals). First let's focus on the elastic material. It is possible to imagine a situation were differences in Poisson's ratio manifests as differences in necking behavior. One might consider there to be necking in a simple rectangular tensile specimen. In this situation the boundary conditions are such that displacements at the ends of the specimen are zero. Therefore, during deformation a curved edge profile might develop. For perfectly elastic deformations this is where it is clear that differences in Poisson's ratio might affect the relative necking between two materials. If the Poisson's ratio is zero, then we would not expect there to be any geometric changes in the sample--the rectangular specimen just gets longer. However, on the other end of the spectrum, if the material is incompressible, $\nu = 0.5$, the initial and final configurations must have the same volume. Geometrically this means, given the fixed zero displacement boundary conditions of our test, there needs to be some distribution of deformation, necking, within the specimen.

In the context of plasticity the picture gets a bit more complicated. The short answer is that the final geometry of a tensile specimen will be dependent on its material properties. This includes both the plastic and elastic behavior (including the Poisson's ratio) of the material. Materials that are more ductile have a higher strain to failure, and this feature, when comparing elastically similar yet plastically dissimilar materials, predominately drives differences in necking behavior. If you have two materials, one which can withstand 2% strain and one 20% (assuming $\epsilon_{yield} = 1\%$), each increment of strain the second material can withstand relative to the first will contribute to differences in the final geometries of the specimens. In this example the failure of the material is driving the final configuration of the neck.

Finally, it is important to realize that one necking starts to occur things are no longer as simple as they appear. Once the specimen starts to neck the stress state with in the gage is, if it ever really was, no longer uniform. This means that at the smallest section of the neck stresses increase (dropping crosssectional area) and new components of stress start popping up.


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