# Do polymers undergo uniform plastic deformation?

I've learned that the yield stress of a polymer can be marked on the tip of the first curve on the stress-strain graph of a polymer undergoing a tensile strength test, like so:

As the yield stress - which marks the start of plastic deformation, and necking (which marks the beginning of localized plastic deformation) begin at the same strain, does this mean that polymers don't undergo any uniform plastic deformation and that they only undergo localized plastic deformation?

If so, why?

Help would be much appreciated, thanks.

The short answer is Yes, some polymer can undergo uniform plastic deformation.

Your question is about necking and neck stability. The criteria for the onset of necking is only related to the slope of the true stress $$\sigma$$ - true strain $$\varepsilon$$ curve, $$\frac{\mathrm{d}\sigma}{\mathrm{d}\varepsilon} > \sigma$$ You can find this equation in nearly every text book of material mechanics. It applies to all isotropic materials, not only to polymer, but also to steel, aluminum and etc.

The left hand side $${\mathrm{d}\sigma}/{\mathrm{d}\varepsilon}$$ represents the material's work (strain) hardening characteristics.

As explained in figure 2 of this blog, polymer undergoes different stages of hardening during deformation:

As the semi-crystalline polymer begins to deform, the stress causes the chains in the amorphous region to elongate and uncoil (b and c). At higher strains, the stress is transferred from the amorphous chains to the lamellae causing the crystalline lamellae to become oriented in the direction of the applied stress (d). Parts of the lamellae can break apart forming smaller fold blocks. With further levels of large elongations, the fold blocks continue to deform in the direction of the applied stress and the amorphous regions become highly elongated resulting in a fibrillar type structure.

This journal article explained the three stages of tensile tests of polymer:

1. Shortly after yielding, the polymer chains simply uncoil and, thus, the work hardening is too low for stable deformation, so necking initiates.
2. Necking evolution: the cross-section of the necking area shrinks.
3. Necking diffusion: As the lamellae become oriented, the work hardening increases rapidly and, to a certain degree, can stop the necking evolution. Then, the deformation becomes stable and the cross-sectional area at the location of necking does not reduce further. The deformation extends along the axial direction to the entire length of the testing region of the specimen. The specimen deforms uniformly in this stage.

The following is still a gross generalisation, but I hope it will address your question.

Polymers can be categorised as Thermosets and thermoplastics. The main difference between the two is that in thermoplastics the polymer chains are not "connected"/"linked" to other polymer chains. In the case of thermosets, there is crosslinking (this crosslinking means that at some/random points there is connection to another chain).

FIgure 1: Thermoplastic vs thermoset source:polymeracademy

As a result you get the following curves:

Figure 1: Typical stress strain curves for thermosets and thermoplastics source: polymer innovation blog

The crosslinking means that the chains (or strands) in the case of thermoplastic can move more freely. Also, when they are stretched they can slide (which accounts for the dip in the stress strain curve).

On the other hand the thermosets produce a more brittle linear behaviour. They may also exhibit necking during tensile testing. Sometimes though they might have a more brittle fracture.

There are also further differences when you look at amorphous or crystalline and other subcategories.