someone help me out with lateral stresses, stock thickness, and grinds, pls

[hardheart]

Another goofy question pops into my head while sitting at the drive thru. What is the relationship between lateral stress on a blade, thickness, length, grind type & height?

If we go with the assumption that a force will be applied at the handle, levered against the flats and not the spine/edge, and at some point near the tip of the blade (since if you always applied the force the same distance from the handle, part of this is moot), can some statements be made about how the knife will perform for any given steel/heat treat when the dimensions are changed?

It's a few variables, but if you had something like a 6 inch blade, 1/4" thick, full flat grind to a zero edge-How does that compare to a half height saber grind, or full/half in 1/8" stock. What if you go from 6 to 8 inches? The change in length means a change in the lever arm, so what basically happens is easy to understand, but if you want the longer blade to fail at the same force as a shorter one, is there an easy way to say how much the thickness needs to increase, or how to adjust the grind?

How much strength would a knife get with a shallower grind/wider flats? And how would having a flat/hollow/convex grind affect the strength for the same height flat (even zero). Is it easily quantified and formulated?

Thinner knives cut better, but some knives have a requirement for prying ability placed on them by the user. Being able to calculate, or at least estimate, the amount of side load a knife could take at a given geometry, a geometry that maximized cutting ability for that strength needed, seems like a good thing. And would one be better off designing for a specific load capability, or just making the thickest knife reasonable and then seeing what it's limits are, changing the steel to a stronger one if needed.

 

[kel_aa]

I cannot answer your question fully, but here are some ideas that I hope will help. You can look for some civil engineering (statics) and material science or fracture mechanics text for more detail.

Take 2x4, put it on two sawhorses, and push down in the middle. The top surface is now under compression, while the bottom surface is now under tension. At every point in between the two sawhorses, the wooden beam is under stress. This is analogous to a knife under lateral stress (or any kind of stress). The force configuration is not the same, but the internal stress (compression and tension) in the material is what we are going at.

Now the material will start to fail when the stress exceeds the tensile strength or the compression strength. For steel (and most materials?) the tensile strength is lower.

Now a short foray into fracture mechanics:

When a stress risor such as a material flaw, crack, a scratch, a notch, a screw hole... is in the material, the local stresses in the material increases disportionately to the reduction in surface area. In other words, when you cut a sharp notch half-way into a material, it is not half as strong, it is less than half as strong. Hardened steel can fail via crack propagation (the local stress near the flaw exceeds the strength of the material and the crack propagates a near the speed of sound) with very little bulk yielding. The relationship between the stress limit as a function of flaw size is 1/ rt(flaw size). That is, if you can reduce the flaw size of half then the stress limit is increaed to 140%. Most designers will try to reduce the effect of stress risors, except the really cool knives like the Reality Based Folder...

Note all materials have stress risors. The bad ones have major flaws in the steel. The better ones are limited to surface scratches, carbide irregularies...

 

[hardheart]

So, the transition from a blade flat to the primary grind would localize stress?

 

[Cliff Stamp]

Being able to calculate, or at least estimate, the amount of side load a knife could take at a given geometry, a geometry that maximized cutting ability for that strength needed, seems like a good thing.

This is a well known problem, it is simple a loaded beam. You can find detailed calculations for any manner of loading which will tell you the internal stress at any point in the beam. The physical characteristics of the beam which give it its stiffness are summarized in the bending moment. For a rectangular object this is 1/12 a b^3. Where a is the length perpendicular to the load and b is the length parallel to the load.

So for example, a 2x4 section of wood has a bending moment of :

1/12 2*4^3=32/3

through its width (i.e, bend it on the edge), but only :

1/12 4*2^3=32/12

through the width. If you look at these ratios in general :

(1/12 a b^3) / (1/12 b a^3)=(b/a)^2

or the stiffness ratio is the square of the dimension ratio. So the 2x4 is :

(4/2)^2 = 4

times stiffer through the edge than through the width. For a knife this is really dramatic becaue they are so different. A typical bowie for example is 1/4" thick but 2" wide so the stiffness ratio is :

(2/(1/4))^2=64

Which means basically it is infinitely stiff through the width. This is true even of really weak knives, try to bend even a butter knife through its width. It is stiffer than even the heaviest tactical knives through their thickness. These moments are just one dimensional integrals = int(yx^2dx)

Which for a rectangle is easy as the width is constant (y=w), so you just get

w int(x^2dx)=w (1/3) x^3|bound[x=1/2h,-1/2h]=1/12wh^3

For other geometries, flat, hollow, convex, etc., the function y is dependent on h, but in all cases the integrals are just power series in x, or can be well approximated by similar so they are trivial to evaluate. If you do these calculations, which I have done in the past, you can see for example things like the scandinavian grinds are very weak for their weight/cutting ability vs full flat grinds. It also shows how for example a flat grind makes much more sense for both cutting ability and strength vs a sabre grind.

-Cliff

 

[hardheart]

Is there some advantage to a saber or low hollow grind on a large knife? I guess there could be additional mass for chopping, but then the reduction in performance caused by the geometry would seem to negate that somewhat.

I haven't done an integral in a decade, so I'm gonna have to find something online as a refresher. What I would like to attempt is a calculation of the strength of a saber ground blade, and what dimensions a fully flat blade would need to match. Too bad the width has to constantly change from the spine to the edge, freakin' calculus.

 

[Cliff Stamp]

Is there some advantage to a saber or low hollow grind on a large knife?

Yeah, it is cheap.

I guess there could be additional mass for chopping..

Axes are not sabre ground. You can get the same weight in a flat grind of suitable spine thickness which will also be stronger as well.

To do the integral with a flat blade you just replace y=h with y=mx+b so you end up with the first integral minus a very similar part. Note all of the integrals have to give :

(some number)w*h^3

Yes, you can calculate the thickness of a flat ground blade which is necessary to match the rigidity of a sabre ground blade, essentially you get a relationship between the height of the grind and the thickness multplier. I worked out a bunch of these integrals years ago, they are not overly surprising assuming you are not one of the masses which believe the hype/propoganda anyway.


-Cliff

 

[Steelhed]

So a saber grind would be stronger than a flat grind of equal width providing every thing else is the same (materials, length, height, etc.)? I can understand how a saber grind would be less expensive to produce than a full flat grind, but a saber grind would seem to have some advantages over a full flat ground in some instances, like say, sabers?

 

[Cliff Stamp]

So a saber grind would be stronger than a flat grind of equal width providing every thing else is the same ...

Same stock, yes. If you are forced to use a specific stock thickness, then you may need to use a partial height grind to achieve the necessary strength.

-Cliff

 

[Steelhed]

Well that explains why some swords are saber ground versus full flat or convex. You would want a sword to withstand side impacts and still be able to penetrate with a thrust (not all swords obviously). I don't see an obvious role for saber grinds in knives though, except daggers which are designed for a very specific function. So I would tend to agree that saber grinds are used to cover up deficiencies in the material used and to cut grinding costs. It would seem to me that combat knives would be better suited to their task using full flat or convex grinds, but with wider and thicker blade stock. Again daggers would be the exception.

 

[thombrogan]

It would seem to me that combat knives would be better suited to their task using full flat or convex grinds, but with wider and thicker blade stock. Again daggers would be the exception.

There's a reason why cleavers are, um, cleaver-shaped and it would stand to reason that a knife with similar geometry would be better at cleaving. Maybe we'll see 2.5-3.5" wide combat and field knives with spine thicknesses between 0.187" and 0.25" and a full-flat grind. Like some sort of exaggerated santoku pattern... hmm...

Anyone else read "Bloodgroove?"

 

[hardheart]

Same stock, yes. If you are forced to use a specific stock thickness, then you may need to use a partial height grind to achieve the necessary strength.

-Cliff

Course, then we get back to steel. Saber ground S30V or full flat 5160, or some such. And then you can come back to the cost of higher grinds, cause now you have to see what eats up belts faster or costs more to heat treat. Now, if we choose the steel based on application, would saber grinds have a place? Can/should a grind make up for the steel chosen?

I'm trying to see if there's a point beyond aesthetics, or making leftover stock of a weaker steel work in a heavy use application.

 

[Cliff Stamp]

Can/should a grind make up for the steel chosen?

That isn't an ideal perspective, you choose a steel which suits the geometry and allows you to optomize it. You NEVER hack a shape to try to suit a steel, that is a horrible choice. Again, in the past when you were forced to use scrap materials maybe, but now, especially with the cost of knives, this perspective is not valid. Costs of belts, heat treating, etc., are also irrelevant when you consider the price of most knives. .

-Cliff

 

[jdm61]

most of the ABS guys that I have been around lately are using a flat grind with a convex edge. I guess you get the strength. etc of the full flat grind with the edge geometry/ease of sharpening advantages of the convex grind. i have done a couple recently like that in 1080 and W2 , and even with my amateur skills, they cut like mad from the get go, even if the edge is a bit thick initially. They are also easier to do than a full convex. You set the edge and sharpen with a slack belt and I knock off the burr/wire on a stone. Using a strop would probably leave me with a sharper edge initially.

 

[Steelhed]

Thombrogan - Sorry, I didn't read "Bloodgroove," so not sure about your reference. If I follow you correctly though, I think you are making the same connection I am, i.e., some combat knives are made along the lines of a Santoku, very stout Santokus. I think the whole idea of combat knives is somewhat ambiguous. Most are simply all purpose tools designed to work in various applications, but not excell at any one thing. Fighting knives are another animal altogether, but history is full of various fighting knife patterns, including some I would certainly call cleavers. In any case I would think stronger steels would be preferred over more brittle varieties. A knife optomized for skinning, edge retention, and corrosion resistance would not make the best combat or fighting knife in my book.

 

[thombrogan]

"Bloodgroove" is a comic strip in the Nelson Arms Pub at Swordforum. The protagonist has just enough knowledge to be dangerous and frustrating.

 

[Steelhed]

thombrogan - Oh, so your comment was intended as some sort of subtle putdown. Hmm, next time perhaps you should spare the clever allusion and just say it plainly for us less informed protanganists. :jerkit:

 

[thombrogan]

If so, then I'm putting down myself. Bloodgroove originally wants a ninja sword like what's seen on Sho Kosugi's 1980s movies. When he reads the SFI primers on cutting ability written by Michael Pierce and Angus Trim, he wants a much wider ninja sword. When the SFI folks tell him that movie style ninja swords, let alone ones with double the normal width, didn't exist before the ninja movies, he wants two. While not wanting a chisel-tip or drop point, that's the boat I'm in. That's why my tastes are more geared towards cleavers and modified santoku patterns.

Last night, I had typed a rambling paragraph about the trade-offs one must make when seeking the balance between chopping and piercing (slashing was completely omitted), cutting ability and modes of durability (mostly hardness versus ductility though they're not totally in opposition), and mass versus movement (think Battle Rat versus pairing knife), but I left it off. It's a safe bet that you already know all of that stuff and more, so why put it? Well, now I see it would have provided the context in which Jedi penpal Bloodgroove isn't a slam or putdown, but a funny look at the boat most of us are rowing when seeking our best-suited large knife or sword.

Michael, I'm sorry I offended you.

 

[Steelhed]

Thombrogan - And thus the limitations of the written word and forums. My apology too for taking offense too quickly. I thought it out of character for you and should have asked exactly what you meant before I fired off my riposte.

Now that I do see the context I understand exactly what you're saying. Although I would never advocate wider swords per se, I can see some advantage to wider combat knives in the 6 to say 10 inch blade length category. You do sacrifice some lateral strength, but I think you gain in other areas like slicing ability.

Again, you have my apology as well.

 

[thombrogan]

Thanks, Michael.

For folks needing a stout, multi-task knife (my assumption of what a combat knife may be), something like Justin Gingrich's RD-6 or Swamp Rat's M6 may be more suitable (for piercing, prying, cutting, and batoning). For those with less constraints (don't have to carry 80 plus pounds of gear), a large santoku or cleaver pattern going straight from a 0.25" or greater spine to a thin edge some 2 to 4 inches away from the spine will provide more entertainment ala doubling one's supply of food or foliage ("Now there are 2 pieces of steak!").

 

[Steelhed]

Thombrogan - Yes, that was my thinking too. A round bar probably represents the best cross sectional geometry for resistance to lateral stress from any perpendicular direction. As the bar is flattened out strength decreases proportionally along the flats and rises proportionally along the width as the cross sectional geometry changes from round to rectangular, or in the case of the full, flat blade, to triangular. Assuming forging, the amount of material in cross section has not changed from the round to the flatter geometry, only its distribution. You can take this to the absurd and flatten the round bar out to something as thin as foil where you would no longer have any appreciable resistance to stress in any direction, so you can easily see that transistioning from a rounder cross section (saber grind) to a flatter cross section (flat grind) produces a point of diminishing returns. However, I think a sweet spot exists somewhere between the round and too flat where the blade geometry is optomized for chopping and thrusting with no bad tradeoffs against the ideal for either. Knives that come to mind include some Busses like the Satin Jack Tac, Steelheart, Battle Mistress and many very good customs made along these same lines. No one is using a saber grind to win the cutting contests.

I am not as acquainted with sword performace, but I could guess the saber grind represents the best compromise considering a sword's greater length compared to a knife and thus its exposure to higher moments of inertia and lateral stresses.