Arrkhal typed his response while I was typing mine so there is probably some overlap.
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EDIT:My apologies to posters mendonca and PMantix as, in the process of reading the thread, grabbing quotes, and constructing this post and then rewriting it(it took me a couple hours) I confused which posts were attributed to which authors. I have put it in a spoiler so as to remove it from plain sight while preserving it for posterity. Again, I apologize for words said in error.....
Not sure if this really makes sense or represents fact, but these are my musings. So take them as you will.
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This is a basic fundamental idea of mechanical engineering (which I happen to have a degree in, btw )
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You should be more careful as an engineer. If you are going to try to lay it out for somebody as an engineer then don't hedge like you know nothing. Give an accurate representation of the facts or say nothing at all to begin with....Since weaponry is commonly made of a non-homogeneous material (folded steel)...
Folded steel is homogeneous because the composition is uniform throughout relative to the macroscale(scales relevant to our daily experience). At very small scales, sub-micrometer scales, almost nothing we deal with on a daily basis is truly homogeneous throughout, but we can ignore this because it only rarely matters. Wood and fiberglass are not homogeneous on scales that matter to us. Something like concrete, which
isn't strictly speaking homogeneous, can generally be thought of as homogeneous if the mixture is good and the internal aggregate is relatively small compared to the geometry of whatever it is used in, though there are application dependent exceptions. Fiber reinforced rubber is another example of this. Note that I am assuming the geometry isn't very complicated because that can open whole other cans of worms. Practically speaking, for our purposes all metals, stone, and most other materials in DF are homogeneous with the noteworthy exceptions of wood, cloth, silk, and bone(or similar) and in those cases hand waving can be involved. Bone as a material tends to be very complicated, doctorates have been done on the composition of bone as a material and I am not in any position to elaborate beyond saying it is complicated.
"what combination of properties make folded steel better for weapons than homogeneous steels?" and does this hold true for all weapons
To answer your question about why hand forged steel was used for weapons, it is because steel has a good combination of hardness and strength and the methods of manufacturing steel were conducive to making a blade. Material selection is often dominated by the ease of manufacture with the properties of a material playing second fiddle. If you can't make something out of a given material, either because you can't get enough of the material or you can't make it into the shape, then there is little point.
In the specific case of the katana, which I assume you are intending to refer to with your reference to folded steel, the answer is less simple. For that case I need to split hairs and it will require a little explanation.
The composition of, how it was treated with heat, and how it was forged will all affect the properties of a material like steel. That is, we call a very wide variety of carbon infused ferrous alloys "steel" but not all of them have exactly the same trace amounts of additives like beryllium, nickle, chromium, to name a few. This much you know. But the rate at which a given steel is cooled, reheated, cooled again, and the annealed(kept in a specific temperature range) will cause dramatic changes to the microscopic crystalline structure(not crystaline like
this, but like
this and
this). Lastly, how steel is worked into its final shape has a similar impact on its properties, this is why many tools, like pliers and wrenches, are made of drop-forged or cold forged steel. The act of shaping the virgin metal actually "strengthens" the material, to a point.
This page is a pretty good primer for the subject.
For a katana, the steel at the cutting edge of the blade was cooled more quicker so it is harder and takes an edge better but is a little brittle. While the steel at the back of the blade was cooled a little more slowly so it is softer and capable of absorbing more energy. Admittedly, I am leaving a lot of stuff out because people literally write books on this and have been for hundreds of years, but I hope this was at least a little enlightening. If you want to know more, then I suggest you consider getting a degree in metallurgy.
The image you attached shows really nicely how the material stress is affected by a fracture, that white area in the middle is entirely disconnected (by appearances, due to tensile forces, though since it's an intra-substance fracture rather than at the edges, I'm not sure) ...
The fracture size is exaggerated in the example picture given. The important feature in any fracture(as oppose to a break, a stress fracture, a shear, a puncture, or any other type of failure) is the "radius of curvature" which is a fancy way of saying how angled or sharp the fracture appears. The smaller and sharper the fracture the higher the stress concentration, though all fractures tend to propagate with cyclic loading. This can most easily be shown and appreciated by examination of the
fracture face. Smaller defects are a bigger concern than large fractures because major fractures are obvious and it is easy to predict how much load it can take while an initially small fracture will be nearly undetectable until it is too late. Brittle materials,
including some steel alloys, are much more prone to this kind of behavior than more elastic materials.
...or only swords and knives which must be ductile enough to bend slightly under stress without breaking ...
This is...all wrong.
Ductility, the ability to draw a material out into a wire or deform permanently under tensile stress, has little to do with with the manufacture or use of a bladed weapon. With regards to manufacturing you are probably thinking of malleability which is the ability of a material to be beaten into a flat sheet or deform permanently under tensile stress, is of relevance but is not unique to steel. I suspect that what you are thinking of is actually two things
young's modulus and the yield strength.
while still being hard enough to hold an edge and win hardness competitions vs. armor materials?
Hardness is complicated. Any kind of absolute scale is derived empirically using specific tests, and not from any one fundamental material property. Furthermore, you can't accurately transform one type of hardness test to another and because of this hardness is relative. For our purposes we can just say that the hardness of steel is almost ideal for use as a blade. Any way that Toady decides to work the material property balance in DF for both real and imaginary materials is up to him but I would shy away from a truly accurate real world model.
my expectation is that the layers, having different levels of strength vs various types of destructive force, ought to fare poorly at any specific finite test compared to a weapon made of a homogeneous material specifically suited for that purpose
Force is force. How it is applied is important. Generally, a composite material is actually better than any of the component materials by themselves
because they were designed to be used for whatever purpose they are functioning in. See my previous comments about homogeneous materials for other considerations.
(for example, a support cable ought to have tensile and shear strength whereas structural steel needs compression strength and whichever it is that prevents a beam from bowing out sideways due to compression forces)
Comparing a cable to a beam or a column--and yes the distinction is very important--is just not done. For one thing a cable or rope has no compressive strength to speak of along its axis of use.
Most materials have very similar tensile and compressive strengths with the exception of brittle materials like ceramics which have a higher compressive strength.
A given beam is almost certain to have
equal use for both tensile and compressive strength. For a simply supported beam, a force down on the top with two supports underneath at either end of the beam, the top of the beam will be under compression and the bottom will be under tension. A similar situation will occur if it is a cantilever beam.
A two force member is a member only in tension, such as a rope, chain, cable, or bracket. These tend to be very strong because when a two force member deflects(is stretched) it tends to get correct any eccentricity in loading.
A column on the other hand is almost entirely under compressive force which will exaggerate loading eccentricity when it deflects leading to buckling unless the length to width ratio is very very low(3 or 4 to 1). I can elaborate more if need be.
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Arrkhal typed his response while I was typing mine so there is probably some overlap.
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EDIT: Spelling and what grammar I could find.
Also, given the length of my and Arrkahl's responses I hope everyone can appreciate the complexities of these subjects.