Hard work hardening

My last chilean girlfriend made her thesis on dislocation theory. I never thought I would actually use that. She asked me once about tensors and we almost break up. She said I'm a bad teacher. My wife would agree on that. Also my phd student. 

So don't complain I didn't if this doesn't make any sense.

In one of Mark's comments, he explains the reason for "ploughing" and "brushing" (sen and miyagi in japanese) the blade:

"The reason this is done, is friction in use is reduced, and this (and the process of setting) work hardens just the surface, which means the burr breaks away with less ductile bending - more like glass - just where a cutting edge is created, sharper and longer wearing, yet still easily sculpted to correct shape." 

Enters scientific mind. From wiki:

Work hardening, also known as strain hardening or cold working, is the strengthening of a metal by plastic deformation. This strengthening occurs because of dislocation movements and dislocation generation within the crystal structure of the material. Many non-brittle metals with a reasonably high melting point as well as several polymers can be strengthened in this fashion. Alloys not amenable to heat treatment, including low-carbon steel, are often work-hardened. Some materials cannot be work-hardened at low temperatures, such as indium, however others can only be strengthened via work hardening, such as pure copper and aluminum.

Dislocations are defects in the crystalline structure of the material.  They are the first to move/appear when you strain it. If you have a perfectly ordered crystal and you strain it, it will first develop dislocations, and then it will break. If you create enough dislocations the metal will be harder.

Increase in the number of dislocations is a quantification of work hardening. Plastic deformation occurs as a consequence of work being done on a material; energy is added to the material. In addition, the energy is almost always applied fast enough and in large enough magnitude to not only move existing dislocations, but also to produce a great number of new dislocations by jarring or working the material sufficiently enough.

 This is the key to the hard work of work hardening. The yield stress increases as the root of the number of dislocations, so if you want a 4 times harder material you need 16 times more dislocations. Assume that the number of dislocations is a linear function of the time you work the material and you get the idea of how much you need to work to get a saw ten times better.

Figure 1: The yield stress of an ordered material has a half-root dependency on the number of dislocations present.

Now, how do you work harden the material? Wiki lists two of our interest: shaving and burnishing.

The shaving process is a finishing operation where a small amount of metal is sheared away from an already blanked part. Its main purpose is to obtain better dimensional accuracy, but secondary purposes include squaring the edge and smoothing the edge. Blanked parts can be shaved to an accuracy of up to 0.025 mm (0.001 in)

and

Burnishing is the plastic deformation of a surface due to sliding contact with another object. Visually, burnishing smears the texture of a rough surface and makes it shinier. Burnishing may occur on any sliding surface if the contact stress locally exceeds the yield strength of the material.

The shaving I can manage with a file, but it would be nicer to have a proper sen. I need to find out how to best do the burnishing.  And this is beautiful. First you make furrows on the steel (Remember that poem of Hölderlin "Es brauchet aber Stiche der Fels/ Und Furchen die Erd"?) that then will be burnished. You need to make furrows since otherwise you don't have enough force to exceed the yield stress of the material. This really shows a deep, almost poetic, understanding of steel by the japanese blacksmiths.

Western jewellers also know about this btw: "jewellers will construct structurally sound rings and other wearable objects (especially those worn on the hands) that require much more durability (than earrings for example) by utilising a material's ability to be work hardened. While casting rings is done for a number of economical reasons (saving a great deal of time and cost of labor), a master jeweller may utilise the ability of a material to be work hardened and apply some combination of cold forming techniques during the production of a piece."

Now, the most interesting part for me comes here:

The increase in strength due to strain hardening is comparable to that of heat treating. Therefore, it is sometimes more economical to cold work a less costly and weaker metal than to hot work a more expensive metal that can be heat treated, especially if precision or a fine surface finish is required as well. The cold working process also reduces waste as compared to machining. (My emphasis.)

So, you remember those lovely lamination lines from your favourite chisel? A good work hardened saw is the same, but you have just one metal. When you work on the surface you are actually creating a "hard steel back" and a soft core, all without welding, without heat. Furthermore, "During cold working the part undergoes work hardening and the microstructure deforms to follow the contours of the part surface. Unlike hot working, the inclusions and grains distort to follow the contour of the surface, resulting in anisotropic engineering properties." Chupate esa mandarina, as Redoles would say.

This reminds me of Bolaño. Roberto Bolaño is probably the greatest writer that south america has produced since Borges. He always talks about these young guys walking next to the abyss. One false step and you die, literally. Poetry lives there, walking next to it but without falling. A perfect saw would be something like that. Bring the steel to the edge of its properties, just before it breaks it's at its best. Make the teeth as long as possible, the surface as brittle as possible and tension the blade as much as you can.  This will bring you just a little bit closer to the edge, but god knows it's worth it.