# A problem with quantifying ductility of a material

The textbooks I'm referring to for studying strength of materials say that we can quantify ductility using percentage elongation or percentage reduction in area up to failure point. The higher the percent elongation higher the ductility.

However this way of quantifying ductility appears misleading to me for the following reason:

If I consider rubber for example, the percentage elongation in it will be high, that will imply (by what is written in bold) that it has a high ductility, but rubber is not ductile, because the elongations are not plastic. So won't this method of using percentage elongation to measure ductility be misleading? Because according to it rubber will be ductile, but in reality it is not.

I was expecting post elastic strain to be a measure of ductility.

• By your own definition, why isn’t rubber ductile? Sep 25 '21 at 14:00
• Because ductility is a property of the material by the virtue of which it is able to undergo large plastic deformations before failure. Rubber does undergo large deformations before failing but these strains are not plastic, so rubber can't be ductile. Sep 25 '21 at 14:04
• But the way you explained the situation what is then wrong? Or are you using the wrong words, or even, examples? Sep 25 '21 at 14:06
• What I want to mean is, percent elongation for rubber will be high, which would mean that rubber is ductile (according to what is written in books that a higher % elongations means the material is more ductile), but we know for sure that rubber isn't ductile. So this method of quantifying ductility using % elongation, is misleading, because by it rubber is ductile, but we know it is not. Sep 25 '21 at 14:12
• Who is this "we" you are talking about? You or me? Perhaps you should quote what the texdbooks say about ductility and start your question from there. Sep 25 '21 at 14:15

Rubber is a hyperelastic material. It doesn't fall under the typical Ductile or Brittle categories.

Percentage elongation and percentage reduction in length or area basically refers to permanent elongation or reduction, after the material has undergone any sort of plasticity (i.e. surpassing the yield strength of the material). If it experiences elongations or reductions in length after surpassing Yield Strength, and up until reaching the Ultimate Strength (after which it fractures) then it is more ductile. That is what the textbook is implying. It is not asserting the elongation or reduction in length/area when the material is still in the elastic range.

Rubber doesn't have high ductility since it cannot undergo high elongations and reductions in length/area after surpassing its Yield Strength before failing.

Chewing gum, for example, has high ductility. It means that when stretched from an initial length (and surpassing its Yield Strength but not reaching its Ultimate Strength), it won't come back to its original shape and will remain stretched at zero loadings, which means it has been highly permanently elongated. Then if you stretch it even more, it will fracture/break.

• Actually, the % elongation that the book is talking about is given as (Lo-Lf/ Lo )*100, where Lo is the initial length at the start, not the length corresponding to yield point. As in this link en.wikipedia.org/wiki/… . Everything would've made perfect sense to me if it would've been written as you wrote, that elongations are after the elastic range Sep 25 '21 at 15:03
• A brittle material can have high elongations before fracturing so according to the link and equation that you mentioned, does it make the brittle material more ductile? No right. Sep 25 '21 at 15:19
• This was only the thought confusing me, these equations can call my brittle materials ductile. If a person doesn't know from before hand that a material is brittle or ductile, then by using these equations and getting high elongations he would conclude that the material is ductile,. But in reality it may be brittle (because these elongations could be elastic) Sep 25 '21 at 15:29
• The equations are written just for the introductory understanding of the concept of elongations/reductions of the length or area. But if you go in more deep, the equations become even more complex. For example, true stress-strain curve where the strains are not calculated from the initial length but from the contemporary lengths which keeps on changing over time. But ductile is actually the measure of how much the material can endure and absorb strain energy before failing and it depends on much it elongates before failing. Sep 25 '21 at 15:43

Rather than getting hung up on the words, consider their usage. The authors' definition may only make sense in a specific context that that they were trying to convey.

Ductile was about the ability to draw a material into a wire. The word or its roots may even preceed quantification of structural properties, but that's somewhat irrelevant. What is relevant is whether meaning gets across. For a textbook, that may mean: Use these equations when solving homework while understanding that these theoretical scenarios behave close enough to reality to be useful.

Malleable was about the ability to hammer a sheet. Physically that would mean using impact to apply large forces to cause a material to expand out of axis to the impact. While most material can expand laterally when pressed, not all will avoid shattering from the localization of the impact, and not all will retain cohesion if pressed.

Ductile was about the ability to draw into a wire. Physically that would mean tension in place of malleable's compression. Rather than area, resulting length would be the measurement.

Both of these (along with every other phrase or statement) come with unsaid caveats. For example: What is cohesion anyway? Different materials have different structural strengths and so bonds are relative. Could we then consider certain liquids to be a very malleable and ductile material so long as the molecules attract somewhat? I can start with a drop of water in the form of a bead on my anvil, and slowly press a hydrophobic hammer into it until it's scattered evenly across the entire anvil. Must be very malleable indeed. Sure I couldn't get it to retain that spread flat shape if I removed it from the anvil, but I can hammer some copper foil to the point where it would break if I peeled it off the anvil too.

The caveat that is most important that people seem to be forgetting these days: All statements are only true where they are true. If your math/model/logic are not following reality, it's not reality that's wrong. Observe reality rather than accepting statements to mean what you think they mean. Do not, for example, take that definition of ductility and some unrelated statement of rubber's elongation to mean that you can simply pull it into a wire at room temp and pressure. Verify the applicability and relation. If you can't verify before the application, leave room to react when the application of theory fails.

• Hammer: a multi-purpose variable pressure hand tool. Sep 25 '21 at 17:57