Is it possible to cut harder material with a less hard material – for example cut a steel rod with iron blade ?
[Physics] Is it possible to cut harder material with a less hard material
classical-mechanicsmaterial-science
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If you cut something by pushing a blade directly into it, here's what happens: On first contact of blade with material, only the very thin edge of the blade is touching the material, the force per unit area is very high, and the blade cleaves the material very easily. That's why it's almost trivially easy to make score marks in things like aluminum using a sharp blade. But once the blade starts to penetrate, the opening into which the blade is descending must be forced open wide enough for the body of the blade to pass. This is accomplished mostly by the wedge-shaped sides of the blade pushing the material apart. Most of the resistance to the blade is due to the friction of the sides of the blade against the material, and to the energy required to deform the material outward to make room for the blade. In some circumstances, the leading edge of the blade may make little or no contact with the material being cut once the blade has descended past a certain point--the "cutting" is actually accomplished by forcing the sides of the crack apart, causing the material ahead of the blade to tear apart.
Imagine cutting a piece of cheese by pressing a wire through it. Obviously, the thinner the wire, the less force it will take to cut the cheese. What is the limit as the diameter of the wire approaches zero? I suspect (but don't know for sure) that it would be the molecular binding energy that you mentioned. But since any real wire would have to be thick enough not to break, we can never reach this theoretical limit.
As an aside, a similar thought process is used in designing laser cutters and EDM wire cutters. The more tightly focused the laser beam (or the thinner the EDM wire), the less material has to be vaporized, and the less energy it takes for a given length of cut.
They are two different things.
"Springyness" is called elasticity. This is described by a modulus of elasticity, also for elongation called Young's modulus $Y$. Looking at a stress-strain curve [source] as below, the elasticity is the slope of the straight line in the elastic region.
- If you are not familiar with a stress-strain curve, consider it as a curve resulting from a test of a material. If you pull the material sample with larger and larger stress $\sigma$ (force per area), you attain this curve (strain $\epsilon$ is elongation in percentage of the original length). The elastic region is where the material returns to initial state. The plastic region is where permanent deformation is done; it might still be "springy" but will not return all the way to initial state. (If the curve starts to bend downwards before the failure point, that area is furthermore called necking; but is not shown here.)
"Hardness" is different and is not described by the modulus of elasticity or similar. The more pure and perfect your material microstructure is, if it for example is a crystal, the softer it is. If there on the other hand are errors in the crystal - errors like dislocations, impurities and other atomical defects as well as other imperfections as grain development - the material gets harder. Then rows of atoms in the lattice of the crystal have a much harder time "stretching" and "slipping" and "sliding" around. For lower grain sizes the hardness as a rule-of-thumb increases, called the Hall-Petch rule (though there is a limit).
It is all about adding disturbances to bring tension inside the lattice, keeping the atomic positions fixed. What a heat treatment does, is in fact to trap impurity atoms inside the lattice. The old iron smiths from thousands of years back utilized this without knowing the cause. When they heated up steel, at a certain temperature it changed it's stable crystal type. Carbon atoms from the ashes in the open fires where mixed into tiny gabs and spaces in unit cells here and there on the atomical scale. Cooling it down fast (quenching in a bucket of water) closed the lattice and changed the unit cell structure rapidly, since the prefered crystal type is different for lower temperatures. Carbon atoms may be trapped, and impurities where hereby added. The steel was much, much harder.
The Japanese Katana Samurai swords from ancient times are examples of mechanical hardening on top of the heating treatment. They hammered the metal flat, folded it, hammered it, foled it, and did this for many, many layers. The resulting microscale disturbances were violent and the crystal structure was full of imperfections and very much harder that typical heat treated hardened steel.
The microstate changes for different temperatures can be overviewed with a phase diagram like this [source]:
- Pure iron is all the way to the left, and the more to the right you go along the axis, the more carbon is added. Each area is a specific phase, and phases have different crystal types (different atomic arrangements for each unit cell) for different temperatures (and composition). This does not tell how the microstructure looks, just what phases are prefered. Because even at a state of prefered phases in this diagram, you can violently mess the structure itself around mixing up all the grain orientations from the above described methods of heat treatment, mechanical treatment etc.
Best Answer
It depends on your definition of "cutting".
Hardness of a material relates to its yield strength - the stress it can sustain without plastic deformation. Push a "soft" material with a sharpened point into a "harder" material, and the tip will go blunt because the soft material deforms. This is why diamond powder is often used to coat grinding wheels etc - the diamond has very high hardness and doesn't go blunt under normal circumstances. Of course it is just carbon, and when heated sufficiently it will undergo chemical reactions - so even with diamond you have to watch the cutting speed to prevent the tip from getting too hot and going blunt.
But there are many instances of "soft" material cutting harder material - even the Romans knew this, and the poet Ovidius Nero wrote
(Approximate translation: the drop hollows the stone not by force but by repeatedly falling)
The pressure that a water jet can produce during cavitation; the momentum of.a soft sand grain burrowing into a hard coating; the heat generated when laser light hits a surface; the heat of electrons decelerating as they hit an anode - all these and more can be mechanisms of material removal which can be used to shape an object - "cut" it. Typically the mechanism is that local pressure, while exceeding the yield stress of the "soft" material, cannot be dissipated because of the speed of impact.
An example is the impact of a drop of water with a surface. During the early phase of the impact, the curved front of the drop is flattened as it hits the surface; during this phase the contact point between the drop and the surface travels supersonically, meaning that the shock wave that builds up inside the drop remains attached to the contact point, and the pressure inside the drop builds up considerably (source: "ELSI conference: invited lecture Liquid impact: theory, experiment, applications", JE Field, Wear 233–235 1999 1–12):
As the contact point slows down when the contact angle increases, the pressure eventually can escape, resulting in a jet of water across the surface which creates terrific shear stresses. This results in a very characteristic damage shape:
This particular example is for plexiglass (polycarbonate) which is a great material for studying the subsurface cracking - but the same thing happens with harder material. Source of the above image: http://blog.kmt-waterjet.com/category/waterjet-technology/ . If you are interested in learning more about this, consult the proceedings of the ELSI conferences that were held in Cambridge (UK) during the 80's and 90's (Erosion by Liquid and Solid Impact). A good start would be the above referenced lecture by Dr JE Field who was the conference's organizer.
So yes - if your definition of cutting is broad enough to include "able to remove material", then a soft material can cut a harder one.