Are we assuming some rod that would never corrode or otherwise break down for reasons unrelated to the pulling, then? Would this rod with this ever-so-slight pull on it break faster than, say, an identical rod floating in intergalactic space, due to creep it experiences? (I’m not sure that floating in intergalactic space actually fres us of literally all stresses on the rod, though.) Because it kind of sounds like this isn’t likely to be the reason the rod fails in a realistic situation, since something else is liable to get to it first.

I think this comment would be better placed under the original question.

Is creep a form of metal fatigue?

Creep in bars that are made in normal bar-like-materials (ie; not ice, nor solid iodine or any other fringe case) at "normal" temperatures (say; below 0.2 of homologous) produces noticeable displacements only in geologic timescales and that is why they are often written off as negligible. Stone bends at room temperature, slowly, which is why there are mountains.

@rubenvb Well, in order for the surface of the tectonic plate to be pushed up, the material inside the plate has to bend. There are geologic deposits, where layers of different types of stones are visibly folded over. Takes a lot of time, but at geological scales, minerals have a lot of plasticity.

It will only break if it hasn't turned into gaseous state by sublimation before ;-) en.wikipedia.org/wiki/Sublimation_(phase_transition)

This answer is misleading as a general answer. Sure, lead pipes show creep over time. But copper pipes do not. Many substances will show no observable creep over any reasonable timescale 9if the stress on the material is inside the elastic limit. The answer strongly depends on the specific material properties.

@matt_black I don't think so (misleading...) (I should say, however, I am not a physicist)... The lead pipes (as shown) only have the force of gravity (and to a lesser effect, whatever they contain at any given time). If one were to replace them with some other metal, and at the same time, exert an external force (perhaps hang a cinder block) and let it hang for a indeterminate-but-long period, even copper will deform. After all, the question asks about a very small (what is small, actually?) but constant force....

@rubenvb Well, if the tectonics pushed and the stone didn't give, you'd have sand or piles of crushed rock. The only mountains would be volcanic ones. Not the case though. It bends and even "flows" with force and time. Mother nature, acting on behalf of father entropy wears them down again though.

@matt_black are you sure copper pipes do not experience “creep”?

@Tim not under gravity with normal conditions.

@CGCampbell If the question were "is there always some force that would cause a material to permanently deform", then you would be right. But, for many materials a small force will never do that. To say otherwise is seriously misleading. Everything will deform given a large enough force; many things will never deform if the forces is small enough.

@Stian Yttervik: Yet there are plenty of places - faults - where the rock fractures rather than breaking. Also, I think you'll find that the folded rock layers have been heated to a temperature at which they're more ductile. (I'm not a geologist, though, so maybe a question for the Earth Science site?)

@cmaster-reinstatemonica Yes rocks bend. But they are also subject to very large forces so are hardly relevant to the general question about small forces.

The key here is the homologous temperature, i.e. material temperature divided by material melting point. For lead this is 0.5 at room temperature. For copper it is closer to 0.2. Vacancy movement, the primary cause of creep (to a first approximation) is an Arrhenius process, meaning creep is exponentially dependent on (homologous) temperature, as we see in the lovely diagrams above. This explains why lead creeps noticeably on the order of decades, but copper does not. A decade is 10^8 seconds for reference.

@jamesqf It is certainly more complicated (and interesting!) than solely volcanic! Granite, for instance, has a measured viscosity at standard temperature and pressure of about 4.5×1019 Pa·s. That is of course ridiculously viscous but still... It flows... Panta Rei, as the philosopher said.

Additionally, the normalized shear stress of a pipe supported to IPC codes is absurdly low, probably near the bottom of the graph. To get the exponential line to swing way down to that low normalized shear stress at 0.2 HT would be 10^<some large negative number> per second. Given a decade is 10^8 seconds, we're talking noticeable creep rates in copper pipe on the order of millions or billions of years, probably. I'm guessing it would fully oxidize or sulfurize long before then, assuming your building were still standing.

I suppose it really depends on how hard OP pulls the bar :)