Material Science – Will a Metal Bar Eventually Break if Pulled with a Constant Small Force

Question

Let's say I have a strong metal bar. I pull it apart with a very small constant force — obviously it doesn't break. However, this would disturb the internal configuration. If I let go, then eventually the internal configuration would return to what it was before I started pulling on the bar. However, if I keep pulling on the bar long enough, would the bar eventually break, no matter how small the force is?

Answer 1

Yes, the rod will ultimately break—barring any other failure mechanism that occurs first.

(Depending on the material and conditions, you may need to wait a very, very long time, but your mentions of "long enough" and "ultimately" suggest that you're interested even in glacially slow processes, so to speak. Read on to hear about one such class of processes.)

The reason for inevitable failure is that at any finite temperature—which is any actual temperature—there's a finite chance that any particular molecular bond will fail under a pulling force. This is called creep, or time-dependent deformation under an applied load. Creep is often assumed to be negligible at less than about a third (or a half, or two-thirds) the material's homologous temperature, as reflected in various answers and comments on this page, but is always active in every material around us.

Creep is frequently characterized using a deformation mechanism map, which identifies which creep mechanism (e.g., viscous flow, dislocation creep) predominates under the specific temperature and applied stress and displays the predicted strain rate (e.g., $10^{-10}\,\mathrm{s}^{-1}$, with approximately evenly spaced lines reading $10^{-5}$, $10^{-6}$, $10^{-7}$, and so on indicating an exponential rate decrease with decreasing temperature):

Copper, ice, and olivine are shown together here to emphasize the commonality of creep in material types that aren't often grouped together. Creep is universal.

The following generic form is typical:

In these maps, we find various regimes marked power-law creep in addition to boundary and lattice diffusional creep. Now, it's a common outcome when comparing various kinetic processes that because of the exponential dependence of rate on the activation energy, we see an interplay of predominance between processes with higher or lower reactant concentrations and higher or lower activation energies. Here's what I mean:

1. The regime of grain boundary and surface diffusion typically dominates at lower temperatures and lower stresses because the bonding at interfaces is poor and allows more mobility, corresponding to a lower activation energy for physical rearrangement. This is the regime in which engineering materials are typically implemented; the creep rate is generally negligible when considering the lifetime of the system, structure, device, or object. However, when you hear about turbine blades being grown as single crystals at great effort and expense, it's to eliminate problematic grain boundary creep:

_{F. L. VerSnyder and E. R. Thompson, Alloys for the 80’s, R. Q. Barr, Ed., Climax Molybdenum Co., 1980, p. 69, reprinted in Hertzberg's Deformation and Fracture Mechanics.}

2. At higher temperatures, lattice or bulk diffusion (i.e., diffusion within the host material) often dominates because there are many more atoms in the bulk than along interfaces. In other words, these bulk atoms are better bonded and less likely to flow than interface atoms, but there are so many of them that sufficient thermal activation causes their effect to add up. Now, I realize your question focuses on metals, but I'll add that in polymers, long molecular chains may slide past each other at an appreciable rate given that the glass transition temperature or melting temperature may not be much higher than room temperature. Consider the creep of PVC resin at 20°C (i.e., room temperature), showing that creep in engineering materials doesn't require searing temperatures or geological time scales:

3. Larger stresses tilt the energy landscape such that the effective barriers to dislocation movement are lowered. In this way, dislocations are driven to carry plasticity through the material via a combination of glide and climb (power-law creep, so named because the rate increases exponentially with increasing stress). At a certain stress in certain materials, dislocations glide easily and nearly instantaneously; we call this stress the yield strength and in engineering contexts often ignore the nuance of slow creep in favor of a yield–no yield dichotomy. In other words, we replace the fanning out of lines representing strain rates of, say, $1\,\mathrm{s}^{-1}$ (representing a fast rate) to, say, $10^{-10}\,\mathrm{s}^{-1}$ (representing a slow rate) with a single horizontal line called the yield strength.

It's important to note that regardless of which mechanism dominates under a certain set of conditions, all valid creep mechanisms for a particular material are acting all the time, although the rate may be minuscule.

Finally, a classic example of noticeable creep is the sagging of lead pipes over decades:

Given enough time, this sagging arc will accentuate and fail by material pinching off, in the manner of any viscous fluid. Lead's low melting temperature means that room temperature corresponds to a quite-high homologous temperature, so prominent creep observations of a familiar metal become accessible over a human lifespan. Make no mistake, however: the pipes could be made of any other material, and such sagging would simply be a matter of time. In the long term, elasticity is an idealization, albeit a very reliable one for many metals and ceramics (and some polymers) at familiar temperatures and over familiar time scales. Many of the other existing answers appear to rely on this idealization, but it sounds like you're asking about the nuances of the very long term. This answer is intended to address one such nuance.