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Non-Newtonian liquids can change their viscosity as a function of shear stress. Shear thinning liquids are those liquids whose viscosity decreases with shear stress. The examples I have seen of such liquids include ketchup and whipped cream.

Is there such a thing as a liquid whose viscosity changes catastrophically? I.E. it acts as something close to a solid, but becomes liquid fairly suddenly at a certain shear stress?

Catastrophic shear thinning liquid

If so, do these substances have a name, and where can I find out more about them?

Rocketmagnet
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Yes; this is sometimes called a complex liquid/fluid with a yield stress or a viscoplastic material or, in the case of specific models, a Herschel–Buckley fluid or a Bingham plastic, for example:

Granular materials and ductile metals exhibit similar behavior of flow to some degree after a load threshold is exceeded.

This and the associated Wikipedia article should give plenty of search terms to explore.

Chemomechanics
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