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Thread: Hi on katanas

  1. #1
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    Question Hi on katanas

    Is it better to have hi or no hi on your katana blade? I can see where it would lighten the blade, but some of the forum posts I have read describe how hi is essentially removing material from the blade and this makes it weaker. On the other hand, you have some historical Japanese blades with hi, some of which surely must have been used in warfare. But then I see new swords with no hi meant for cutting, and those with hi meant for iaido. Hmmm!
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    Re: Hi on katanas

    Originally posted by Henry C. Frederick
    Is it better to have hi or no hi on your katana blade? I can see where it would lighten the blade, but some of the forum posts I have read describe how hi is essentially removing material from the blade and this makes it weaker. On the other hand, you have some historical Japanese blades with hi, some of which surely must have been used in warfare. But then I see new swords with no hi meant for cutting, and those with hi meant for iaido. Hmmm!
    it's a matter of preference. Some Iaido practitioners prefer to have a hi because it allows them to guage their technique by the "woosh" sound it creates; if there is no woosh sound the blade is misaligned in the cuts.
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    I've also read that hi may in fact make the blade stiffer, like the waves in corrugated cardboard.

    More applicable to antique nihonto than to a pristine modern sword maybe, but "The New Generation of Japanese Swordsmiths" says this about hi:

    "Originally the object was to reduce the weight and improve the cutting ability of the sword; later the grooves served as decoration. Another purpose for the hi was to restore a sword's balance after it had been shortened, or to conceal a flaw in the blade. In either of these cases, the hi was known as an ato-bi (groove added later)."

  4. #4
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    Originally posted by Kevin Courter
    I've also read that hi may in fact make the blade stiffer, like the waves in corrugated cardboard.

    Stiffer *per unit weight*. If you look at the bending moment equations in a mechanics textbook, you'll find that if you take any cross section of material in any shape and remove material from it without changing any of the exterior dimensions, it will be less rigid in all axis.


    If you keep the same amount of material and change the cross section, all bets are off.

    As an example take this overall shape

    ********************
    ********************
    ********************
    ********************
    ********************


    This will have a certain stiffness in each axis of bending.

    Now take a chunk of material away from it

    *** ************
    ********************
    ********************
    ********************
    *** ************


    There is no way for this cross section to be more rigid than the old one. It's simply got less material to resist deformation.

    There are 100 asterisks in the first box; there are 90 in the second shape. So I took away 10% of the material. But I bet I didn't take away 10% of the rigidity. So per unit mass, the second design is superior, but on an absolute basis, it is not.

    If you can avoid buckling issues, the largest contributors to overall blade stiffness are material properties (elastic modulus) and overall cross section dimensions, basically the width and height of the cross section in the longest dimension. This is why I-beams are so prevalent in contruction--they're an easy to manufacture shape that is very, very stiff per unit mass.

    dhc
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    cool way to explain it!

    So to go the other direction with it...

    You could make the blade with 10% extra material, planning to scrape/remove that 10%, and wind up with a blade of the same weight as a "standard" katana, but stiffer, ne?

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    Originally posted by Kevin Courter
    cool way to explain it!

    So to go the other direction with it...

    You could make the blade with 10% extra material, planning to scrape/remove that 10%, and wind up with a blade of the same weight as a "standard" katana, but stiffer, ne?
    Yes, but understand that to make a "stiffer" blade, you either need to make it thicker or wider (given, say, a constant 28" length) or both. I seem to recall this being referred to as a more "full" blade when comparing new swords to old ones, and the assumption being that the old swords started out that way but after many repolishings were made thinner.
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  7. #7
    Be *really* careful here because this is incredibly complex. Even in these examples, the word "stiffer" needs to be clarified with reference to resistance to a force in some direction. These are complex shapes and adding a bo-hi makes it even more complex.

    The bottom line is to remember that *adding* a bo-hi to a blade will not make it stiffer. Period. It will allow the removal of material while minimizing the stiffness loss *in certain dimensions*. But not in others. Blades with bo-hi are vastly more likely to bend, break, and *especially* corkscrew. The worst, most difficult bends to remove from a blade are those bloody corkscrew bends.

    Bo-hi are incredibly popular among the iai crowd. The "divine wind" sound of swinging a blade with bo-hi is pretty cool. But a high shinogi can also give a similar sound and quite frankly, you can learn to listen to most any blade to get some feedback as to its orientation. Its just not gonna be heard across the dojo.

    That quote from "New Generations" kinda bugs me. When I first read it I wondered if what they meant was more along the lines of "Originally the object was to reduce the weight and improve the handling of the sword..." Regardless, the rest of the quote is right on target. Mostly bo-hi were added to cover up things like a ware' (grain opening) up in the shinogi-ji. Or to lighten a sword after shortening. It is a good solution to the problem *after the fact*. From a purely performance standpoint when making a new sword however, they're not adding anything. If you look at the subtle variation of cross sectional geometry, you'll find the swords of the Yamato-den as an example. High shinogi. Meaning the shinogi-ji surface angle back to each other and form a thin mune. So the sword has more of a diamond shaping. This helped reduce mass and move the center of balance back towards the hands. The blade gets faster but minimizing the loss of stiffness in most directions.

    Today many Japanese smiths install bo-hi on their blades because its another aspect of the artistic side of the craft. And because they're popular among buyers. A well-done bo-hi is nice to look at, just like nicely done horimono. But as functional improvements in the sense of structural integrity during cutting? Nah...
    Keith Larman
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    Originally posted by Keith Larman
    Be *really* careful here because this is incredibly complex. Even in these examples, the word "stiffer" needs to be clarified with reference to resistance to a force in some direction. These are complex shapes and adding a bo-hi makes it even more complex.

    In a very real way it doesn't matter. If you take any cross section and remove material without altering the original outline (other than the material removed) there is no coordinate system in which the moment of inertia is less. None.

    For any cross section the flexural rigidity is defined basically as

    D = E x J / (1- v^2), where E is the elastic modulus (an essentially constant material property given a given alloy of steel), and v is poisson's ratio. J is the integral form of the geometic moment of inertia per unit width.

    That moment of inertia is defined solely by the geometry of the cross section, and it gets larger with increasing dimension. So if we keep the exterior bulk shape of the sword constant, but remove the material for the bo-hi, the geometric moment of inertia MUST go down, in any coordinate system.

    The removal of the material for the bo-hi in a katana, however will hardly remove any material in the plane of the cut direction. So the stiffness that way won't go down much. In the direction of the flat of the blade, the flexural rigidity will go down more, but since the overall dimension hasn't been reduced, it won't go down much (the resistance to bending increases as the cube of the thickness, as I'm sure you know).

    So while the overall shape is fairly complex, the overall principle is not.

    Thinking about it, you can make a reasonable but not exact approximation of a katana blade by taking a trapezoidal cross section beam and setting it on top of a triangular one. With a bo-hi, it would be a thick section I-beam on top of the same triangle.

    dhc
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  9. #9
    All that is true, but the forces a blade experiences in real world cutting can be very complex. We don't cut with perfect form, even perfect bad form, and not in a vacumn (i.e., the targets have their own properties as well). The rigidity as a idealized concept is one thing. But there is a lot of complex stuff going in a blown cut. It depends on the angle of attack, how well the swordsman maintains (or doesn't maintain) that angle, the amount of drawing through the target, the amount of rotation, the amount of force, the nature of the target itself (hard hollow bamboo is very different from heavy rolled tatami from light rolled beach mats,, etc.)... Angled cuts, as an example, bring the behavior of the cross section traveling through a dense medium and acting much like a wing on a plane. But with a guy holding the other end often with his weight pushing down on the blade (at whatever angle its now at) as it passes through. That was more the point I was trying to make. The forces experienced are not all just straight impact like forces. But are pulled cuts with off angles, curving paths, dense materials, and a guy flying the thing possibly trying to power through the poor cut...

    There is a reason swords actually used for cutting generally don't have bo-hi. Those with bo-hi don't last very long, especially if the targets are difficult or the swordsman is less than perfect.

    So I don't disagree with you at all. But I also wanted to point out that the forces experienced are quite complex.

    But bo-hi are fine for cutting if you always have perfect form. ;-)
    Last edited by Keith Larman; 01-30-2003 at 09:05 PM.
    Keith Larman
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  10. #10
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    Originally posted by DouglasCole


    In a very real way it doesn't matter. If you take any cross section and remove material without altering the original outline (other than the material removed) there is no coordinate system in which the moment of inertia is less. None.

    For any cross section the flexural rigidity is defined basically as

    D = E x J / (1- v^2), where E is the elastic modulus (an essentially constant material property given a given alloy of steel), and v is poisson's ratio. J is the integral form of the geometic moment of inertia per unit width.

    That moment of inertia is defined solely by the geometry of the cross section, and it gets larger with increasing dimension. So if we keep the exterior bulk shape of the sword constant, but remove the material for the bo-hi, the geometric moment of inertia MUST go down, in any coordinate system.

    The removal of the material for the bo-hi in a katana, however will hardly remove any material in the plane of the cut direction. So the stiffness that way won't go down much. In the direction of the flat of the blade, the flexural rigidity will go down more, but since the overall dimension hasn't been reduced, it won't go down much (the resistance to bending increases as the cube of the thickness, as I'm sure you know).

    So while the overall shape is fairly complex, the overall principle is not.

    Thinking about it, you can make a reasonable but not exact approximation of a katana blade by taking a trapezoidal cross section beam and setting it on top of a triangular one. With a bo-hi, it would be a thick section I-beam on top of the same triangle.

    dhc
    One problem with oversimplifying Sword this way. The material properties are not a constant. The steel contains a large variety of different crystaline structures and grain sizes with varying properties. Even simple cross-sectional gradients will show a coresponding gradient in mechanical properties from the heat treatments.
    Also Stress does not flow through a simplified object like the rectangle and the triangle cross-sections the same as they would on a shape that contains many sets of radious contours like a katana does. I Cant argue with your math, but The material, behavior, and shapeing are combined to form a very unique set of properties that go beyond simple shapes and constant values.
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    Originally posted by Keith Larman
    Bo-hi are incredibly popular among the iai crowd. The "divine wind" sound of swinging a blade with bo-hi is pretty cool.
    Aren't you confusing kamikaze (divine wind) with tachikaze (sword wind)?

    And as one who belongs to the "iai crowd", I confess that I use tachikaze as an indicator of how my hasuji's doing. It's no guarantee of perfect hasuji, but enough to tell a crappy cut from a mediocre one (the range where I'm usually at ). It has absolutely nothing to do with "coolness"! I wish that notion could be dropped. Seeing as how bo-hi is far from an unusual feature in historical blades, I have difficulties seeing that it was such a crappy design as some seem to suggest. (Not to argue against what has been stated above, most of which I'm sure is precise and factual.) We seem to be obsessed about perfect, fool-proof blades. The swordsman is just as important.

    For "coolness" I'd rather go with a silver koshi-yujo habaki, or perhaps some black micarta mekugi...

    Edited to add: Just to make it clear, I wasn't intending to enter into a polemic with this post, and certainly not to cast doubt upon what has been said by persons vastly more knowledgeable than myself. Re-reading the thread, I find some really good arguments against bo-hi in modern-day cutting blades, and I don't really see it as a must in an iaito either, actually.
    Last edited by A. Bakken; 01-31-2003 at 01:13 AM.
    Aage

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    Originally posted by Keith Larman
    All that is true, but the forces a blade experiences in real world cutting can be very complex. We don't cut with perfect form, even perfect bad form, and not in a vacumn (i.e., the targets have their own properties as well). The rigidity as a idealized concept is one thing.
    I agree that the forces applied can be quite complex, but the rigidity concept is not. My original point was very simple--all other things being equal, removing material from a blade of a certain cross section will never stiffen or make more rigid the blade. Period. It may remove more weight than rigidity, in which case some people may call that a gain, but the absolute rigidity will never go up, no matter what direction or combination of directions you're dealing with.

    I would probably also add that because "J" in my formula above (well, not really mine of course) is listed as the "integral form," all complexities of shape are accounted for.

    So the DEFLECTIONS are complex, because the forces are complex; the rigidity as a function of blade length, call it D(x), can be fairly precisely known. The geometrical considerations of overall shape will much dominate the stiffness considerations caused by slightly different compositions of steel from place to place. Elastic modulus (inherent material stiffness) doesn't change that much with forging, although strength and toughness and hardness do very much.


    But there is a lot of complex stuff going in a blown cut. It depends on the angle of attack, how well the swordsman maintains (or doesn't maintain) that angle, the amount of drawing through the target, the amount of rotation, the amount of force, the nature of the target itself (hard hollow bamboo is very different from heavy rolled tatami from light rolled beach mats,, etc.)... Angled cuts, as an example, bring the behavior of the cross section traveling through a dense medium and acting much like a wing on a plane. But with a guy holding the other end often with his weight pushing down on the blade (at whatever angle its now at) as it passes through. That was more the point I was trying to make. The forces experienced are not all just straight impact like forces. But are pulled cuts with off angles, curving paths, dense materials, and a guy flying the thing possibly trying to power through the poor cut...

    There is a reason swords actually used for cutting generally don't have bo-hi. Those with bo-hi don't last very long, especially if the targets are difficult or the swordsman is less than perfect.

    So I don't disagree with you at all. But I also wanted to point out that the forces experienced are quite complex.

    But bo-hi are fine for cutting if you always have perfect form. ;-)
    The orignal quote I was responding to likened bo-hi to corrugated cardboard. I was merely pointing out that the analogy was imprecise.

    dhc
    Last edited by DouglasCole; 01-31-2003 at 05:36 AM.
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    Originally posted by Patrick Hastings


    One problem with oversimplifying Sword this way. The material properties are not a constant. The steel contains a large variety of different crystaline structures and grain sizes with varying properties. Even simple cross-sectional gradients will show a coresponding gradient in mechanical properties from the heat treatments.
    Also Stress does not flow through a simplified object like the rectangle and the triangle cross-sections the same as they would on a shape that contains many sets of radious contours like a katana does. I Cant argue with your math, but The material, behavior, and shapeing are combined to form a very unique set of properties that go beyond simple shapes and constant values.
    The properties of any real-world structure are fairly unique. There is nothing inherently magical about a sword--the shape is actually rather simple (although subtle and beautiful) when compared to many other structures in nature and engineering.

    If you look at the picture I've just tried to attach, you can see that the two are the same except I removed two circular grooves from the cross-section, a simplistic bo-hi. The second shape will simply have lower resistance to bending than the first.

    The forces causing bending may be very complex; the material stifness resisting it may also be complex, but even with inhomogenieties, won't vary by much (don't confuse strength with stiffness--very different!). The geometry change involved dominates.

    Two final point from me on this: I'm not saying "yay bo-hi" or "boo! bo-hi bad!" I'm pointing out that, as Keith mentioned, there's nothing simple about blade design. A blade with a bo-hi should be designed that way from the start, because if you're going for a blade of a certain rigidity, that very same blade with a bo-hi will ALWAYS be less resistant to deflection than one without. But you don't have to keep the cross-section the same, and that's where the art and science of design come in.

    Next, I want to point out that "stiffness" and "rigidity" are two different things. Stiffness is an inherent material property. Rigidity is the product of inherent properties and geometrical considerations. Two bars of the same alloy have the same stiffness regardless of size or geometry; with any change in size or geometry, those same identical material bars will have different rigidities.

    dhc
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    Two bars of the same material of the same section will always have the same stiffness IF they also have the same microstructure.

    Usually, blades with bo-hi have a thicker mune and shinogi-ji, which plays into what you were saying about changing the section geometry.

    I can make tachikaze with nearly any sword, as can most of the guys I know who cut well. It IS louder and slightly different in blades with bo-hi, because the turbulence sets up a different resonance than a "normal" blade without the bo-hi.

    The bottom like here is, if you like them, fine, if you don't like them, that's fine too. The fact that a blade has or has not bo-hi indicates nothing else, it wither has or has not bo-hi. There COULD BE something more, like camoflaging ware, or not.

    I don't like cutting them, and charge a lot for doing it because I don't like it, and I am not happy unless I do a good job, which takes a great deal of time. So mostly I don't. Most of the serious cutters I know do not use swords with bo-hi, because they tend to bend easier than thos without. (because all other things are not equal)
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    Originally posted by Howard Clark
    Two bars of the same material of the same section will always have the same stiffness IF they also have the same microstructure.

    I'm pretty sure that the elastic modulus ("stiffness") of steel is independent of microstructure to a very large degree, although the strength of the steel, as well as the strain at which permanent deformation sets in, is highly dependent on microstructure.


    From "Deformation and Fracture Mechanics of Engineering Materials," by Richard W Hertzberg:

    As a result, while heat treatment and minor alloying additions may cause the strength of a steel alloy to change from 210 to 2400 MPa [about 30,000 to 350,000psi -dhc], the modulus of elasticity of both materials remains effectively unchanged--about 200-210 GPa
    So everything we know how to do with steel can change the strength by ten times, but can eke out maybe a 5% change in stiffness.

    Microstructure largely affects hardness and strength, resistance to creep, and of course resistance to permanent deformation. Resistance to elastic, non-permanent deformation (and thus rigidity in the technical sense of the word) does not depend on much other than what atoms are involved and their interatomic distances.

    I make no judgement about the aesthetic value of bo-hi, and I believe I have been agreeing with you that a sword without bo-hi will serve as a more rigid, and better cutting, weapon than the same sword with one.

    dhc
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    Originally posted by Howard Clark
    I don't like cutting them, and charge a lot for doing it because I don't like it, and I am not happy unless I do a good job, which takes a great deal of time. So mostly I don't. Most of the serious cutters I know do not use swords with bo-hi, because they tend to bend easier than thos without. (because all other things are not equal)
    For what it's worth, I've checked out your website, and greatly admire your work--acquiring one is definitely on my "to-do" list!

    dhc
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  17. #17
    Originally posted by A. Bakken


    Aren't you confusing kamikaze (divine wind) with tachikaze (sword wind)?
    Actually, no, it was an inside joke among a few friends of mine I train with and sometimes teach, some who also lurk here. It started in a very old thread we had on this forum many years ago that most have probably forgotten.

    And as one who belongs to the "iai crowd", I confess that I use tachikaze as an indicator of how my hasuji's doing. It's no guarantee of perfect hasuji, but enough to tell a crappy cut from a mediocre one (the range where I'm usually at ).
    Geez, Aage, lighten up. I wasn't being critical. I've been involved with iai for a while myself... Too long apparently. It has its purpose but frankly you get the same feedback from any sword, just not as loud. And you will also find that you can get really good tachikaze and still have your hasuji as well as overall form off.

    Might I also add that my personal iaito that I train with has bo-hi.

    It has absolutely nothing to do with "coolness"! I wish that notion could be dropped. Seeing as how bo-hi is far from an unusual feature in historical blades, I have difficulties seeing that it was such a crappy design as some seem to suggest.
    Why isn't it cool? Geez, it makes a neat sound. You even talked about how it makes a sound for your own training? The whole sword thing has a "coolness" factor. So what? I wasn't being disrespectful. Heck, I've been known to say "Cool..." when demonstrating a sword technique if it goes particularly well.

    And with respect to historic blades... Blades made in periods of heavy use rarely had bo-hi. Many you see today are ato-bi (horimono added after the fact) for exactly the reasons listed. Adjusting balance on a shortened sword is one very good reason. But if you're making a *new* blade, there are vastly better ways of getting proper weight and balance without adding bo-hi. Removing ware' is a very common other reason for bo-hi. So again, the bo-hi are installed to "fix" an issue with the blade.

    Of course there are smiths who liked to carve. Some rather famous.

    Its not a case where its a terrible thing to do, just that it does introduce some compromises into the blade.

    Today many modern smiths in japan do them because the market demands them and the smiths see it as another means of expressing their ability and craftsmanship. The artistic side of it is critical to smiths today in order to advance their careers. And many who collect the work of these top level smiths rarely cut with their blades.

    And again, there is a reason shinken sold for tameshigiri both here and in Japan generally don't have bo-hi.
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    Originally posted by A. Bakken


    Seeing as how bo-hi is far from an unusual feature in historical blades, I have difficulties seeing that it was such a crappy design as some seem to suggest. (Not to argue against what has been stated above, most of which I'm sure is precise and factual.) We seem to be obsessed about perfect, fool-proof blades. The swordsman is just as important.

    If I gave the impression of stating otherwise, that was not my intent. Simplistically, my thougth process was like this:

    1. Someone posted that he'd heard bo-hi added stiffness

    2. I posted that (a) you cannot take a blade, remove material, and get a more rigid blade as a result, and (b) I pedantically ( I can admit it) pointed out that stiffness and rigidity are not quite the same thing.

    Now, the fact that I've been comparing two IDENTICAL blades with and without a groove doesn't give the, er, groovy concepts their proper due. I-beams (the ultimate bo-hi) are used in construction because they are a cross section that maximizes the resistance to deflection per unit weight This means that two swords of equal mass can have very different rigidities.

    The easiest way to accomplish this would be to, by design, shift the material that you "take out" of the bo-hi and "putting it back" in the cutting direction.

    So at constant mass, the blade with the bo-hi probably has the advantage, as the smith can choose to make the blade longer from spine to edge.

    What is the extent of variation in this dimension in these blades? Is it pretty uniform, as too thin is undesirable and too thick is ahistorical? Or is there as much variation as I've seen in western-style swords (from really thin to two or three inches at the base?)

    dhc
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    Originally posted by Keith Larman
    Geez, Aage, lighten up.
    I suggest we all lighten up, and don't start a trench war on this subject, as that would surely be very depressing.









    Aage

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    Yes, I agree. I wish no heavy disagreement either, because I don't really care "that" much about it, anyway.


    I have always wondered about the modulus of elasticity measurements (assuming there are such, and that it is not all theoretical), and how they are made, and would like to prepare specimens and see the test done on them. I am not from Missouri, but you can see it from here, almost, and I am very stubborn. It is not that I disbelieve, neccesarily, only that I would like to see the test done to better understand the subject matter. Strength, resistance to deformation, hardness, microstructure, all those things make sense to me. This other measurement of elasticity, I apparently am having trouble with. I don't get it how that could remain so close to the same, regardless of condition, it just does not compute for me.
    It is not the destination, it is the journey.

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    Originally posted by DouglasCole


    I'm pretty sure that the elastic modulus ("stiffness") of steel is independent of microstructure to a very large degree, although the strength of the steel, as well as the strain at which permanent deformation sets in, is highly dependent on microstructure.


    From "Deformation and Fracture Mechanics of Engineering Materials," by Richard W Hertzberg:



    So everything we know how to do with steel can change the strength by ten times, but can eke out maybe a 5% change in stiffness.

    Microstructure largely affects hardness and strength, resistance to creep, and of course resistance to permanent deformation. Resistance to elastic, non-permanent deformation (and thus rigidity in the technical sense of the word) does not depend on much other than what atoms are involved and their interatomic distances.
    Thanks that puts things in a better perspective for me and answers a Queastion I dont have to ask now

    I Dont care much about BoHi, My interest in this thread is more about the Modulus
    Patrick Hastings
    "A man without patience lives in hell"
    "He o hitte
    shiri Tsubome"

  22. #22
    Join Date
    Jan 2003
    Location
    Minneapolis, MN
    Posts
    139
    Originally posted by Howard Clark
    Yes, I agree. I wish no heavy disagreement either, because I don't really care "that" much about it, anyway.


    I have always wondered about the modulus of elasticity measurements (assuming there are such, and that it is not all theoretical), and how they are made, and would like to prepare specimens and see the test done on them. I am not from Missouri, but you can see it from here, almost, and I am very stubborn. It is not that I disbelieve, neccesarily, only that I would like to see the test done to better understand the subject matter. Strength, resistance to deformation, hardness, microstructure, all those things make sense to me. This other measurement of elasticity, I apparently am having trouble with. I don't get it how that could remain so close to the same, regardless of condition, it just does not compute for me.
    In the simplest form, the speed of sound through a material is computed as the square root of the stiffness divided by the density (sqrt (E/p)).

    So if you measure the speed of sound in a material by sending an ultrasonic pulse through a material of known density, you can calculate the inherent stiffness of the material.

    One thing that is an important geek-driven caveat/cover your butt factor is that all this elasticity stuff goes out the window once the material starts deforming plastically.

    One experiment you could do is to take two steel bars, possibly of differing alloys, but one is annealed and the other is fully forged. A circular or square cross section will do.

    support the bar end fully, and hang weights off the other end. The annealed bar will deflect a certain amount, but it will probably take a permanent set. The forged bar will deflect the same amount, but will return to true. Or at least, it shoud, if the cross-sections are constant from bar to bar.

    So, you can either find a university, bring them samples, and have them do the ultrasound thing, or make up some alloy steel bars (make 'em thin, so you don't need a ton of weight to deflect them).

    One way to do this would be to support the bar and tie a laser pointer to the end. Mark where the laser hits a wall, fairly far away ( so you have good sensitivity to movement). hang a weight on it, and then remove it; ensure the dot returns to where it started (no permanent deformation induced). If so, hang the weight again, and mark where the dot went.

    Now, take the other bar, and repeat. The key is that the cross sections of the bars be the same, the unsupported length be the same, and you use the same weight.

    Mechanics predicts the maximum deflection of the end of the bar is equal to:

    d = [ Load x Length^3 ] / [ 3 x Elastic Modulus x Moment of Inertia]

    Moment of inertia is equal to h^4/12 for a square bar of dimension h x h; for a rectangular bar of height h and width b, it's I = b x h^3 / 12

    Basically, you can see from the math that if the cross section is constant, as well as the unsupported length, and you hang a weight on it, the only controlling thing that can change is the modulus of elasticity.

    Hey! I have an idea. Take a piece of long rod-stock that you have forged and quenched. Do the above measurement. Then anneal the bar, which will weaken it, but preserve the shape and length. Then repeat the measurement. If I'm not totally off my rocker, the bar should deflect the same amount (within five percent or so), as the only thing that can change is the Elastic Modulus.

    Sorry for the long-winded message, but I wanted to try and give you some things you could try on your forge at home.

    If you're bored, most of what I've just said can be found in Hertzberg's book on Deformation and Fracture (mentioned in a previous post), while the bending stuff can be found in Gere and Timoshenko's book Mechanics of Materials. Dry engineering texts, to be sure, but pretty readable, as such things go.

    Dr. Doogie, signing off.
    Last edited by DouglasCole; 01-31-2003 at 12:31 PM.
    _________________
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    Made weak by time and fate, but strong in will
    To strive, to seek, to find, and not to yield.
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  23. #23
    Join Date
    Mar 2002
    Location
    Westfield Mass
    Posts
    268
    If a bo-hi is cut into a blade that has already been polished, does the entire blade need to be re-polished? or just the newly cut bo-hi.
    Tim Mailloux

  24. #24
    Join Date
    Feb 2002
    Location
    Salem, Oregon
    Posts
    1,927
    Originally posted by Howard Clark
    Yes, I agree. I wish no heavy disagreement either, because I don't really care "that" much about it, anyway.


    I have always wondered about the modulus of elasticity measurements (assuming there are such, and that it is not all theoretical), and how they are made, and would like to prepare specimens and see the test done on them. I am not from Missouri, but you can see it from here, almost, and I am very stubborn. It is not that I disbelieve, neccesarily, only that I would like to see the test done to better understand the subject matter. Strength, resistance to deformation, hardness, microstructure, all those things make sense to me. This other measurement of elasticity, I apparently am having trouble with. I don't get it how that could remain so close to the same, regardless of condition, it just does not compute for me.
    I think Im starting to get a clearer picture myself this mesurement has generally been pretty muddy for me aswell. The Modulus is a ratio of the Stress versus strain. To calculate the number you need a Stress strain diagram including the reduction in cross-section. Useing any given point below the yeild (the elastic range) you have a Temporary reduction in cross-section becuase it will spring back in the elastic range(a temp strain). So the Stress divided by the corresponding reduction of cross-section gives you a number that remains constant throughout the elastic range on the stress strain diagram. The greater the strain the greater the reduction in cross-section and that is porportional so the modulus stays the same. Apparently most steels are very similar in Modulus though the yeilds and ultimates can vary wildly. Just thinking aloud here I dont know If i Have that totally accurate, but for the first time it actually makes sence to me
    Last edited by Patrick Hastings; 01-31-2003 at 02:05 PM.
    Patrick Hastings
    "A man without patience lives in hell"
    "He o hitte
    shiri Tsubome"

  25. #25
    Join Date
    Feb 2002
    Location
    Wichita, KS
    Posts
    1,754
    Originally posted by Howard Clark
    I am not from Missouri, but you can see it from here, almost, and I am very stubborn.

    Howard,

    Would you be referring to our friends in the "show me" state, called such because you have to draw them a picture so they understand? Sigh, after that comment, I'll have to watch out that my friends in Missouri don't decide to make me regret saying that..

    Chris
    Christopher A. Holzman, Esq.
    Moniteur d' Armes
    "[T]he calm spirit is the only force that can defeat instinct, and render us masters of all our strengths" -Settimo Del Frate, 1876.

    Author of The Art of the Dueling Sabre
    ViaHup.com - Wiki di Scherma Italiana

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