MIGNAL":3s4b2euv said:
If you can't reduce a difficult engineering problem to just one A4 sheet of paper you will probably never understand it.

Page 8 and I'm still none the wiser.
Sorry

probably my fault, using technical terms like 'stress' without explaining them.
materials
Just for the sake of (some attempt at) clarity, I'll try to explain a bit about stress, as used in engineering and materials science world. It's not quite the same thing as the stress all of us encounter in everyday life; though I suppose there are parallels of a sort.
An engineer would define 'stress' as a way of measuring a material's capacity to cope with the loads applied to it, and define the point at which the material can't cope with the loads, and fails. A simple example would be a crane cable holding up a load. The cable would have a tensile stress in it, because it's in tension. The stress is defined as the load applied divided by the cross-sectional area affected by that load. So if the crane cable had a cross sectional area of 1 square inch, and the load was five tons, the stress in the cable would be 5 tons per square inch.
The load applied to the cable would tend to stretch it a little bit, and the amount by which it stretches (the extension) divided by it's original length gives another figure engineers use quite a bit - strain. Up to a point, if you divide the figure for stress by the figure for strain, you end up with a constant, called the Modulus of Elasticity (or sometimes. Young's Modulus). Note the word elasticity - that's because up to a point, many materials behave like a piece of elastic - apply a load, and they deform a bit, but take the load off again, and they return to their original shape.
However, that's only up to a point - after that point, they deform permanently. In other words, they behave plastically. That point is known as the 'yield point'. Keep on applying load, and they keep on deforming permanently - up a point. THAT point is when the material gives up and breaks - the Ultimate point.
Thus, a piece of (say) mild steel subjected to gradually increasing tension load will behave elastically up to it's yield point, then plastically up to the Ultimate Tensile Strength of that grade of steel.
Each material has it's own points for Yield and Ultimate, often quoted by material suppliers.
Just to make life more interesting, you can modify the yield and ultimate for many materials by such actions as heat treatment or cold work. A piece of spring steel in it's annealed - soft - state will have quite a low yield point, and a longish plastic range. However, harden and temper it, and it will have a very long elastic range - a high yield point - but a much shorter plastic range thereafter, but it's Ultimate will be much higher than it was when it was soft. Conversely, a blacksmith or forgemaster can heat the spring steel to a suitably high temperature when it will have a very low yield, but a very long plastic range - so he can do a lot of drastic shaping without causing the steel to fail. Also, if you take your piece of soft spring steel and cold work it (hammer it, bend it, draw it through dies or whatever) you will increase it's yield point by work-hardening it. This is very noticeable with metals like copper and brass. Once it's hard - high yield point, short plastic range - you can soften it again by annealing, thus restoring a low yield point and large plastic range.
Confused yet? You will be!
Stresses are 'tensile' if the material is being stretched, and 'compressive' if it's being squeezed. (There's also shear stress, which happens when the load applied is trying to 'shear' the material - bolts, rivets and shear pins often see a stress of this type.)
Now, let's consider our saw blade. If it's just lying on the bench, it's not subject to any stress. If it's picked up, and the toe end bent round so that the blade takes up a curve, it's effectively acting as a beam (a cantilever, in this case). Beams see both tensile and compressive stresses; if you take a piece of flat steel and bend it into a gentle curve, the outer side of the curve is now a little bit longer than it was when straight, and the inner side a little bit shorter. The outer side is thus in tension, and has a tensile stress, and the inner side in compression, and has a compressive stress. The line through the middle remains the same length, and sees no stress - that's the 'neutral axis'. Thus, our bent saw blade is in tension on the outside of the bend, and in compression on the inside, with stresses to match.
It now gets complicated. So far, we've only considered stresses resulting from externally applied loads or forces. However, there exist another sort of stress known as 'internal stresses', or sometimes, residual stresses -
https://en.wikipedia.org/wiki/Residual_stress . They have been known about for quite a long time, but even now are not well understood, perhaps because they are very difficult to measure. They can be a problem, or they can be beneficial. They tend to find an equilibrium within a piece of material, so a piece of steel - such as a sawblade - just sitting on a bench on it's own, can appear stable, and under the influence of no loads (and hence stresses) applied to it. There can, however, be stresses IN the saw blade. If any loads are then applied externally, the stresses resulting from those loads add to the internal stresses.
Most failures of relatively strong materials like spring steels tend to happen when a crack starts in part of a component under tensile stress. The crack runs quite fast, and the component breaks in two. It's much harder to start a crack in part of a component under compressive stress. Try bending a stick of wood, then putting a nick or sawcut in the tensile (stretched) side of the bend - it'll break sooner. Not so if the sawcut is in the compressed side.
Let's now imagine some way in which we could manipulate the internal stresses in the saw blade such that the surface layers were in compression (and to balance the stress distribution, the centre was in tension). When the saw lay on the bench, it would be stable, because no external forces were applied. Now let's pick up the saw and bend the blade into a curve, as before. Now, the outer side, which had a tensile stress in it as soon as the bend started, starts with compressive stress, so as the bend develops, the stress comes from compressive, back to zero, and only then starts to become tensile. Thus, the maximum tensile stress the surface sees is lower than in the saw blade with no internal stresses. Cracks start in materials with tensile stress in them; less tensile stress, less chance of cracks starting.
Way back in the mists of time, blacksmiths discovered that if they peened the tensile side of leaf springs, the springs lasted much longer. They didn't know why, they just knew it worked. It works because peening a surface (or rolling it lightly, or shot-peening it -
https://en.wikipedia.org/wiki/Shot_peening ) puts a compressive internal stress in the surface. Thus, the maximum tensile stress the spring surface saw was lower than one not so peened, so cracks were less likely to start, so the spring was less likely to break.
Springs and saws are made from pretty much the same grade of steel (sometimes in the same works, in times gone by). Not hard to see that what works for springs would also apply to saws (which are just wide, flat leaf springs with teeth on one edge).
Thus, I think 'tensioning' is a process that makes sawblades less likely to snap in use, and it's done by peening the surface of the saw blades. Light rolling would work too, as would shot peening. I've no idea why it's called 'tensioning', but as the idea came from spring-making practice, maybe that has something to do with it.
Well - that's the brief :shock: explanation. I don't know if it's the full answer to the question of what 'tensioning' is, but it seems plausible from the materials science standpoint.
Right. I'm off for a rest after that!