This effect also applies to polymers! Perhaps even more so. Take a polyethylene bag (LDPE) and stretch the material in one direction. You might notice the material becomes thinner but also stronger. This is due to the polymer chains becoming aligned. Eventually you get "drawn fibers" where the molecular strands are aligned with the fibers for optimum tensile strength.
it varies a lot with polymers, and it's a different effect. steel is entirely crystalline; ldpe is mostly amorphous. a big part of what's happening in the strain hardening of ldpe, aside from making it uniaxially oriented, is that it's crystallizing; the crystalline domains become larger, greatly reducing the amorphous volume fraction. (there are also other ways of achieving this effect, such as annealing, which you will notice softens steel rather than hardening it.) ldpe's strength isn't determined by crystal dislocation density in the same way as steel's, and of course steel doesn't have polymer chains to align
HDPE is also what Nalgenes and the like are made of (or used to be anyway), and is very popular for storing chemicals as well. It is very nearly completely inert.
you cunninghammed me: nalgenes are polycarbonate, which is a lot less inert
all the polyethylenes are relatively inert, because polyethylenes are in some sense just heavy paraffins. paraffin is germanized latin for 'relatively inert'