3.1.3 Just For You
|We still have to look at questions iv) and v) of your homework, the tensile testing of soft metals like copper (Cu) or gold (Au) and hard metals like steel. Did you come up with a result?|
|The figure below gives the answer in the form of real stress-strain diagrams for a bunch of different metals. To demonstrate a few points of tensile testing with respect to steel and sword making, I have done a number of tensile stress experiments just for you, the reader of this hyperscript.|
|That's a damned lie, of course, because it wasn't me but my able assistants who actually did the experiments - they wouldn't let me ruin their treasured (and expensive) testing equipment.|
|The scale shows "Megapascals" (MPa) and, as promised, I give you another idea here of what that means.|
|Consider your weight. If you are a guy like me, we take it to
be 100 kg (OK, just once: about 220 pounds). If you climb up a rope (I doubt that you can
do this if you are a guy like me, but let's just assume you can), you are pulling at that
rope with a force of 100 kg × 9,81 m/s2 = 981 kgm/s2 = 981 N. That's
about the maximum force you can produce: pulling with all your weight. |
How thick should the rope be to take your weight?
|If you don't use extremely strong monofilament, somewhat
less than a square centimeter should be fine, let's say 0,3 cm2 (= 3 · 105
m2). That corresponds to a rope with a diameter of about 0,6 cm = 6 mm. Sort
of like this: O |
The stress in the rope then would be
| Of course, the
psychological stress that professors like me can produce
in undergraduates taking an oral exam will exceed that by far but it's not measured
in MPa. That's just another reminder that mere words are just mere words. Real |
|Now let's focus on the major point: The stress - strain curves we get for ductile materials as shown above are completely different from the ones we had before for brittle materials|
|This is indicated for the steel ST 37N curve. Stop your machine at some point like the one indicated, release the stress and the strain will be permanent (about 15 % for the example shown). The specimen is now permanently longer. It has been plastically deformed.|
|Now let's look at the other major features of those curves.|
|1. Eventually, after the specimen have been elongated to some final value indicated by the star, all specimen fracture as shown before. This is just an expression of the first law of materials science that we will encounter in full glory presently.|
There are four kinds of steel in the figure. One (St 37N) is just as easily deformed as copper
or aluminum, while the C45 type seems to be much harder
in the sense that you have to apply far more stress to elongate it a few percent permanently
or plastically. |
So, in pronounced contrast to their stiffness , all steels are not equal when it comes to their resistance to plastic deformation.
You know, of course, that there are different kinds of steel with respect to hardness from what you know or have heard about swords. The question then is if there is some kind of relation between hardness and what we have here.
There is. I'm coming to that. But first let's look at what else is of interest.
|3. All curves run through a maximum stress shortly before they break. That means that if you elongated the materials up to that maximum, it now becomes easier to elongate them some more up to fracture. In other words: the ductile materials give you a fair warning that they are about to break, just like rubber. But in contrast to rubber, that becomes stiffer just before it breaks, ductile materials appear to become "weaker" (once more we lack a proper word) right before fracture.|
4. Once more: if you release the stress at any one point to the right of the "perpendicular
" part in the beginning, the strain does not go back
to zero. The specimen stays elongated. |
The curves shown are thus the "upward curves", showing what happens if you increase the stress, strain and thus elongation. They are completely different from the "downward" curve. The downward curve simply goes almost straight down as indicated for the steel (ST 37N) curve at one point.
|Now let's look at the not-so-obvious features. As a little surprise for you, I had a few more tests done; look at the next figure:|
|What we see is that one and
the same kind of steel shows rather different behavior in tensile testing. |
That's good. What that means is that you can change the properties of a given piece of steel by doing proper things to it like hammering it, or heating it, cooling it rapidly, and so on.
Here we are at the very beginning of the science of making swords.
|So what was done to the steel in the figure above and what has changed?|
|Well, curve 1
shows the properties of the steel "as bought". That's what you get when you buy
C15 steel. The steel is pretty hard to deform. The machine
needs to apply something like 700 MPa to elongate it just 1 %. It fractures after it was strained
to about 1,5 %. |
If you would pull at the specimen with all your might, your measly 30 MPa or so applied to a wire of that steel would just elongate it by about 0,04 %. You wouldn't notice this.
Curve 2 shows the steel after I annealed
or normalized it. That simply means that the
steel was kept at a temperature around |
What you see is that after annealing / normalizing the steel, we need only half the stress from before to elongate it 1%. We can also strain the steel now to more than 3% before it breaks.
It appears that keeping steel hot for some time tends to make it easier to deform or "softer".
|Curve 3 is exactly
the same annealed steel as that in curve 2 but some devious person (might have been me) secretly
strained it to about 2 % before giving it to the engineer
in charge of the tensile test machine without telling him.
Being smart, he might see that this piece of steel has been in a tensile test machine before (the big jaws of the machine leave traces), but being smart myself, I had removed all traces before I pass on the specimen.
For my engineer (or anybody else), this specimen looks no different from the ones he tested before. There is no (easy) way of telling that it had been pre-stressed.
|We have a major point here. Somebody gives you a piece of metal for a tensile
test, and there is just no (easy) way of knowing if somebody hasn't pulled at it, banged it
with a hammer, or done God knows what to the specimen, changing its properties in a major
way before it was given to you. |
In other words:
|This is a major point. Consider the difference to brittle materials:|
have deformed a brittle material like glass (without breaking
it, of course) in any conceivable way to his hearts contents. But when you come into possession
of that glass, it behaves exactly as if all of that had
not happened. It's history is not important at all. |
Ductile materials obviously have a kind of "memory" where information about what has happened in the past is stored. This is rather weird, think about it! The corresponding "how?" question is obvious and doesn't need to be spelled out in detail. The answer to it will contain much of what you need to know about the art of sword making. That will exercise us quite a lot in what follows.
|There are two more interesting points to be made about our three stress - strain curves from above:|
|1. If we move curve 3
to the right, it matches perfectly with curve 2 if we start
it at around 2 % deformation.(curve 3a). In other words:
if we stop the deformation of the sample represented by curve 2 at the circle and then release
the stress, the strain would go down as shown by the green arrow. The sample is now permanently
or plastically deformed, it is longer than it was before the test by about |
If we take this sample and test it again, counting the strain from 0 %, we get curve 3.
In essence we just continued where we left off. Our specimen "remembered" its past; its history is somehow stored in its structure. But if you don't know the history of your piece of steel, you would tend to see it as something different from the steel of curve 2. It is "harder" but less ductile, and it breaks earlier.
|2. Looking once more at
the stress- strain curves above for the C15 steel, we note another peculiarity: In the beginning
- for about the first 0,1 % of elongation - all three specimen behave exactly
the same way. The stress - strain curves are linear and have the same slope. When we looked
a brittle material, we identified the slope of a stress - strain curve with its Young's modulus.
Can we do the same thing here again? |
Yes, we can. In the straight parts of the diagrams above we just deform the steel elastically. Release the strain and the specimen goes right back to its original length as indicated by the arrows.
So we can assign a Young's modulus modulus to ductile materials too, we just need to keep the stress /strain at a level low enough to have only elastic behavior. We are going to look at this more closely in the next sub-chapter. Now you know why I could discuss Young's modulus for all materials in the preceding sub-chapter.
By the way, I also proved now experimentally the claim I made before: Three rather different kinds of steel have one and the same Young's modulus because the slope of all three curves is the same, indeed.
|What the experiment has given us is a first glimpse at hardening mechanisms and softening mechanisms.|
|There are several mechanism to harden metals. What we did to the C15 steel in the figure above is called deformation hardening, strain hardening or work hardening. Different words but meaning the same Work hardening is just one of several hardening mechanisms we will encounter.|
|Temperature treatments known as annealing or normalizing, meaning
that you keep your steel hot for a while, seem to soften
steel. Well, they dobut only if you do it right (furnace
with controlled atmosphere and temperature, very slow cooling down, ...). |
If you just shove your steel it into a fire and take it out again, you might be in for a surprise. For example, if you cool your steel down rapidly after it was hot some time, it might not be softer but much harderprovided the temperature and the carbon content was high enough.
In a fire, you also might either add a bit of carbon or remove some, depending how exactly you hold your steel into the fire or coals. What you take out of the fire then is a different material since a little bit of carbon, as you know of course, typically hardens steel.
|So working with iron and steel is tricky.
What about the remaining 90 or so elements of the periodic
table? Or just the 20 or so major metals? Can we also make them harder or softer like iron
/ steel? |
The answer to this "what" question is: yes, in principle.
And now we are stuck with a lot of "why? and "how?" questions!
© H. Föll (Iron, Steel and Swords script)