How do you do fellow Phyzards? Today I’ll be making like The Rolling Stones and Rock your world with some more material physics (Yippee!). This is somewhat of a continuation of a post a made a while back, so if you’re wondering why I suddenly start talking about BTS, I’d suggest you take a look at Sending Cape Canaveral into space with C-moon .
As the title suggest we’ll be taking a look at how we figure out different attributes of materials, especially those that aren’t as straight forward. I’ll also be looking more into the experimental side, so that the theory on its own can take a back seat for a while. Don’t worry there will be much to learn either way, as I intend to prove during this blog. If you believe I didn’t succeed, well tuff luck! As you likely noticed I will continue to rock on with these horrible puns, but it may get boring so don’t take it for granite.
Tensile Stress
The main types of stress where going to be looking at today are tensile and shear stress, because these are also the ones relevant to that previous blog post, not to be sedimental or anything, and because this one would otherwise get out of hand.
To help with the explanations I will be making great use of diagrams throughout, which is to make the drilling of different rock types you’ll be undergoing less boring.
To kick things off we have tensile stress, which can be seen in the diagram below.
In this diagram, wonderfully constructed by what can only be the handsomest of physicists, you can see that tensile stress just the stress on an object which occurs when forces are applied to it in a length wise fashion.
This is directly mirrored on the atomic scale, because the bonds between molecules that go in the same direction as the pulling force are combatted. If the applied force isn’t strong enough to completely overpower the bond it will only stretch (very slightly, but exaggerated in the diagram) and return to normal if the force is no longer applied, but if not it will expand until it breaks, and then our sample will be six feet under.
It gets returned to normal because while our protagonist, the parallel bonds, stretch, the perpendicular bonds will narrow (if you stretch one side the other must become thinner). The forces between good and evil.. I mean the molecules are quadratically proportional to the distance so while the attraction of the molecules stretched away are practically zero, the repulsion (due to severe disgust towards each other) becomes extremely high.
So, the force has to increase to go even further, otherwise the repulsion will take the upper hand and the system will return like nothing ever happend (I THOUGHT WE HAD SOMETHING SPECIAL!!!!).
This breakage occurs because bonds between molecules decrease in strength over distance, so if we pull them away from each other the force also becomes weaker. They keep stretching until you hit a point where they are practically to weak to interact.
However, if no tensile force is applied, the bonds won’t continue to narrow, which is because there is also a repelling force between molecules, that forms because of the fact that electrons for example have the same charge. The break also only happens in between molecules, because atomic bonds in the molecules themselves are way stronger while the molecules have a somewhat more rocky relationship.
Shear Stress
Next in line we have the more fancy boulder stress type: shear stress, which is also pictured below. Shear stress works largely via the same mechanism, however, the bonds that eventually break go perpendicular to the direction of the applied stress.
As you can see, there exists a kind of balance between how the different bonds push and pull when a downward force is applied on one of the molecules, but not the other. In this case the bonds get pulled at and angle instead of lengthwise, which means that when it is pushed a distance down the bond only gets lengthened, or closer to breaking, at a smaller rate. This of course is thanks to our fellow Rock-head Pythagoras.
So, we would expect that the shear strength of most, not the special ones who do their own thing, rocks are higher than their tensile strength. The exception are when there are clear graining, because in that case the lengthwise and widthwise bonds have different strengths. Don’t lose your marble(s) over me going about my day, and blog, acting like they don’t exist, because that makes my life a whole lot easier.
However, you might wonder why it stretches to begin with, instead of just rotating very slightly and keeping the same preferred distance. The reason reason for this is that the molecule is also in a least energy costing state with the molecules next to it that move in the same direction. This means that the bond has to stretch somewhat for the other molecules to be the preferred distance from each other, 1,5 m distance was mandated after all. When it stretches too far, the same happens as for tensile strength, because of course shear stress just had to take tensile stresses thing, what a self centered goober (replace goober with any swear word you like).
Lastly, there are some aspects which both of them share, for example that they are both temperature dependent, which makes sense because adding temperature is just adding energy and the bonds break when enough energy is added. In this case it should be easier to break a material at higher temperatures, except when its too co(a)ld then the material becomes too brittle.
Furthermore, it is important, and a burden which we all have to carry, to remember that not all latices of bonds are squares, hexagons (the bestagons) also appear quite frequently. Now, I hear you cries of turmoil that you know have to learn how it works for each type, but fret not because it is practically the same and I am too lazy to make even more diagrams for the different possible latices.
With the knowledge of how things (which I will not summarise) do be doing, we can take a look at how we know the specific values that you may find floating around. We do this via the theoretical physicists worst nightmare, an experiment WITH real world applications (PUM PUM PUUUUUUM).
DTS
Our main man DTS, which means direct tensile strength, is based on the test with the same name. This is the most straight forward method of figuring out the tensile strength of any material, but if you couldn’t imagine it by yourself it’s illustrated somewhere. I also don’t need to give an explanation, because, I mean, you’re smart enough to get it right? (I believe in you :3).
Ok ok ok ok, I’ll say something about it. Let me see here….. the interesting thing about DTS is……. Ummmm….., the rock? Yeah idk. No but really, when you applied a force at one end of the setup on the cap connected to the specimen, but also hold down the other side (glue it to the ground for what I care) you actually also get a force from that side which counteracts the pulling force. These two forces which both pull the rock to opposite sides are actually what create the stress, and eventually the divorce.. I mean break.
ITS/BTS (OMG)
Here we are, we have finally reached the part where the Phyzards talk about het hit band BTS! Alas, for it is not, because BTS is also a way to test the tensile strength of Dwayne The Rock Johnson. However, this one and the more general term ITS are (as the name indicates) indirect tensile strength tests. And if you ask me where the B comes from, I will tell you it’s the B from Brazil (no really it is).
As seen above the mechanism is quite simple, where the only real difference between ITS and BTS is that BTS has a curved plate at the top and the bottom and has guide straps on both sides.
The way it functions is also easier to decipher than BTS’s lyrics, so that’s a plus. It relies mostly on het fact that most rock types (if not all) are more resilient to compression than to tensile stress. If the rock gets compressed it must expand in the other direction, just like when you stretch an object it narrows in the other direction. As such, the outward force is generated by the centre of the rock specimen pushing outwards, to the sides, which is the tensile stress. As long as the friction between the plates where it is held between and the rock itself is low, this force will be the same as what you put in as compression.
Shear strength testing
We’ve reached the final stretch, in the sideways direction, look at it go! It’s are good pal where rock actually gets beaten by shears (scissors). Just like before the diagram below is quite shellf (a shell is close enough to a rock okay!? I’m running out of puns) explanatory. I mean, it’s not ROCKet science or anything.
As can be seen the rock sample Is held stationary and pushed toward the centre from both sides. It has to be both instead of just one, because in the case you can’t use the normal forces of the ground or an object stuck down to it. This happens because if you were to use the wall for that you would also block either the entire thing (so nothing happens except compression) or if you have a small wall up to half of the hight it stats pivoting because of the torque the shearing force creates.
Lastly, a normal load has to be applied so that the sample will not start pivoting, which can still kind of happen, because a force from both sides isn’t to dissimilar to the small wall and one force), but has to move in the designated plane.
Comparison between direct and indirect methods
So, what can we expect from the results of these different measuring methods, and why would one be used instead of the other?
DTS, while seeming the most simple, actually causes the most complications and has been rapport to not always give rock solid (haha) results. This mostly happens because the samples may break in varies places except for the perfect centre, caused by imperfections for example, which makes it harder to get a consistent result. Indirect methods are more reliable, although they don’t lack the knack to crack in the wrong place, so they are more commonly used as a rock to lean on.
The funny thing is, the difference in measured values between indirect and direct methods seem to be mostly determined not by the test itself but by the types of rock which you test. DTS generally has a lower threshold than indirect methods, where the factor is 0,9 for metamorphic, 0,8 for igneous and 0,7 for sedimentary rock.
(Why don’t you back it up with a source?, I will. It’s not that I made it the F up. See?):
BTS does seem more complicated than general types of ITS, however, is this more elaborate nature warranted? Indirect methods sadly also suffer from the fractures not happening in the middle, yet BTS, due to its curved plates, suffers less from this issue. The curvature of the plates cause the a slight pressure from the sides pointing inward, which makes the centre more stressed (has a larger work load, not entirely dissimilar to phyzards.com) which makes it more prone to breaking, which is where we want it to break.
However, it does have the slight disadvantage due to BTS having more friction, which we can chalk up to the curvature of the plating, which makes it have more touching surface area, which makes it harder for the rock to expand sideways. Apart from this a very slight amount of force is lost due to it actually going to solely crushing the rock, but this should not differ that much between indirect methods.
Final Remarks
This has been a summary of what stresses can be and how we can identify their thresholds. This mostly shows how, although they have widely different values attached to them or look to operate completely differently, they work via the same logic, both in testing and in the fundamentals. However, there is one more thing:
Con(crete)adulations! (They keep getting worse by the minute), you are one of the probably two people (incl. my brother) who is reading this. My aim with this blog was mostly to put some more understanding behind my previous post and to shed some more light on the dark decrepit corners of experimental physics.
This was it, after a long blog I am (stalac)tired and am just going to lie down on my bedrock. And to all the readers, you still haven’t told me how you’re doing even though I asked you at the start, but also: rock on!
(EDITORS NOTE: bad pun count: 23)
Hans Stapel
0 Comments