REQUEST: Knife throwing and metal fatigue, materials science. Let's see some data.

[chiral.grolim]

There is a common belief that knife throwing, even accurate knife-throwing, impresses a severe level of stress on the knife and can lead to fatigue and sudden failure, and that this is absolutely the case in hardened knives (e.g. 58 - 60 Rc) which will fracture from the stresses induced by accurate throwing within a short span of time (e.g. the life-span of the thrower).

However, I have yet to come across or be directed to hard data describing (as a value) the level of stress impressed upon ANY knife by an average accurate throw from an average human being into an average piece of wood. Nor have I come across any hard data describing (as a value) the fatigue life or limit of any knife.

What I have encountered is various individuals insisting that this common belief is true but offering no actual data to back it up other than anecdotes of knives breaking after being thrown. However, I have encountered a much greater number of anecdotes and demonstrations of knives NOT breaking after being thrown, and all of this regards knives that were apparently not specifically designed to be thrown or endure the stresses of such activity.

So, with nothing but anecdotes to go on, my conclusion is that some hardened knives cannot endure the stresses of being thrown and others can, and that the notion that all hardened knives are unable to endure throwing is a myth.

As much as I like myths, I would like the veil of ignorance lifted just ever so slightly by the application of scientific method and the collection of data. It may be that such data has already been collected, and if so please point me to it. Please note, I am not requesting anecdotes like, "Well, I've thrown my knife hundreds of times and it's still fine," or "I threw my knife a few hundred times but one day it just broke in half!" I am not requesting that people simply go out and throw their knives until failure is induced.

Here is what I am looking for (and please make suggestions/improvements to the method):

1) Take a common batch-manufactured fixed-blade knife hardened to 58-60 Rc and have an average user or a collection of average users throw the blade accurately (perhaps the most difficult part) a number of times into a common target (e.g. pine) to give a clean set of data points (minimize outliers). Use high-speed cameras and a measured-grid to help calculate the force of impact and the level of bending in the blade and the frequency of oscillations after each impact (commonly cited as the direct cause of fracture), and thereby achieve a mean value for the stress induced by throwing the knife.

2) Take a new, relatively unstressed sample (since we hypothesize that throwing induces rather a lot of stress, we do not want to perform the next test on the same sample), and bring this one to its fatigue limit in a controlled fashion or find a way to calculate/predict it by measuring some other attributes (so that no knife need be destroyed in these tests). Plug these values into the Goodman Relation and present the outcome.

Hypothesis confirmed or negated for this particular knife?

3) Repeat the process with another knife with similar features (especially hardness) but with one major differing element, e.g. steel composition.

The goal of course is to lay to rest either the myth itself or the notion that it is a myth. What attributes of a knife need be accounted for to produce a hardened thrower with a fatigue limit above the level of stress induced by throwing.


Thank you in advance for any and all assistance.

 

[Bigfattyt]

IBFL

Sounds like you have a new mission in life. Take out a loan (for the necessary equipment, knives, high speed cameras and equipment for inducing and measuring the stress, etc). Then you will need to quit your job.


I will eagerly await the results.

Oh, I forgot, I have been throwing knives for about 25 + years. I have broken knives throwing them. I have broken them at the handle/tang handle transition. I have broken them at the tip.

I also have one particular knife that I have thrown for that entire time without breaking it. A WWI bayonet with a 12 inch blade. It took a slight set from throwing, but is still in one piece. I have some throwing knives that have made it a decade of hard throwing with out more than mild tip damage.

CS thrower and the GI tanto have held up for 10 years or so. No sets or breaks.

The bayonet has been thrown hour and hours at a time for a decade straight at targets out as far as 55 feet.

I believe that knife is likely a spring steel, or medium carbon but am not sure.

Throwing imparts a lot of stress on a knife. Impact, sudden side load lateral stress, and vibration.

One example I show people is to have them stab the target as hard as they can and look at how deep they can stick the knife. Then have them throw the same knife at the same target. The difference in penetration is amazing. The bigger knives will still be humming when you pull them out of the target.


Sorry, no large batches of identical knives. No high speed cameras, no equipment to measure anything.

 

[Lagrangian]

Hi chiral.grolim,

Sorry I have no hard advice or experience for you; I know almost nothing about throwing knives.

I was just wondering if engineering books on metal fatigue and impact toughness would be helpful? Presumably, engineers have done experiments to measure the toughness and strength of metals under repeated shocks. There may also be journal papers on this kind of thing, so if you're at a university, you probably have access.

The idea isn't necessarily to use current engineering data or papers as the ultimate basis. The idea is simply to see what kinds of tests have already been performed on metal fatigue and shock resistance. It will be up to you to decide if these tests are relevant to knife throwing, and if so, to consider how such tests might be modified. It's also interesting to learn about things like the methodology, statistical significance, and experimental protocols they use.

Among us are a few metallurgists, like Roman Landes, who have published books and papers about metallurgy and knives. Unfortunately for us, Roman Landes' book is in German (d'oh!) and he doesn't post often, probably because it is too much work trying to communicate with the various fan-boys and the like. However, now and then, he does come by and post, and will answer a question or two.

I myself do not have a background in metallurgy, so I don't know what a reasonable test should be. In a real experiment, you need to have some idea of what variables to control for ahead of time. Otherwise, you may end up doing a perfectly scientific tests (with fully documented data, double-blind unbiased protocols, controls, and statistical analysis) which are useless, because you were unaware of some confounding variable (for example, quality and evenness of heat-treatment, or defects introduced during casting/forging). Of course this is experimental science, so it is impossible to know (and therefore control for) all the confounding variables. However, what you can do, is learn what confounding effects engineers have encountered historically, and which ones they consider to be important in modern engineering. Maybe you can learn from that, and then go from there. (Standing on the shoulder's of giants, and so on.)

I would like to get beginner's background in the area by reading a book or two on metallurgy (such as Prof. Verhoeven's free book on metallurgy and heat-treatment for knife makers), and engineering books on metal fatigue and strength of materials. As far as I can tell, Verhoeven's book is free and it is downloadable:
_Metallurgy of Steel for Bladesmiths & Others who Heat Treat and Forge Steel _ by John Verhoeven (2005)
http://www.feine-klingen.de/PDFs/verhoeven.pdf

A different book by Verhoeven (different title, and different date) can be purchased at Amazon.com, or found in the library:
_Steel Metallurgy for the Non-Metallurgist_ by John Verhoeven (2007)
http://www.amazon.com/Steel-Metallu...=sr_1_1?s=books&ie=UTF8&qid=1336673766&sr=1-1

I remember when I was an undergrad, and an engineering friend said to me,"Did you know, for aluminum there is no known lower bound on fatigue limit!" I don't know if I understand what he was saying, but I think he meant that there is no known lower limit on how small a repeated stress on aluminum can be that does not cause metal fatigue. As my friend said, even an ant repeatedly walking over an aluminum beam would eventually cause it to fail by metal fatigue (as far as engineers can tell). This is in contrast to other materials (spring steel?), where if the repeated stress is below some threshold, you can cycle the repeated stress indefinitely without causing metal fatigue (so far as engineers can tell).

In this wikipedia article is the following plot. I believe the vertical axis is the size of a cyclic stress (or maybe strain?), and the horizontal axis is the number of cycles the part can survive before breaking. I may not understand this quite right, but you can go read the Wikipedia article on it and from there go to textbooks, etc.
https://en.wikipedia.org/wiki/Fatigue_limit

If you do any tests, please let us know. Same goes for if you find any good books, tutorials, or published papers.

Sincerely,
--Lagrangian

 

[chiral.grolim]

Lagrangian,
Thank you for the reply.
From my investigations so far, I have come across only a general estimate confirming the wikipedia page you linked which I also linked in a post on another recent thread (about Junglas throwing), namely that the ultimate tensile strength of 1095 hardened to 60 Rc is around 300,000 psi, and that below stress levels of ~1/2 that there is no limit to the number of elastic cycles which the material can endure... IF it is structurally sound with even carbide distribution. But I haven't found any information on how much force is generated by throwing a knife into a target and what the average remaining force is left to vibrate the knife. 100,000 psi (<1/2 the UTS) converts to 70,000 Newtons per square centimeter... but how to disperse that force load on the length of the knife....

I found a webpage describing the average knife throw at a speed of ~50 km/h which calculates to <50,000 Newtons of impact force from throwing a 12 oz knife, and most of that force should be absorbed into the material struck on impact... Even throwing a knife as large as the Junglas (22oz) 50 km/h into a target only generates 87,000 Newtons prior to dispersion. How much of the force of impact absorbs into the material being struck? 50%? More? Less? With values like that, how is it possible that throwing a knife into an object accurately by hand EVER results in blade failure from a sound implement? Or are all these broken throwing knives the result of major deflection off of surfaces that reflect the energy back into the knife?

That's why I'd like to see someone do an actual measurement. Maybe I will contact that Mythbusters show on Discovery...

 

[Lagrangian]

Hi chiral.grolim,

Just a quick question: How are you computing impact force from velocity? I ask because a lot of things (too many) affect impact force beyond velocity. For example, airbags reduce impact force in a car crash. (And thank goodness for that! )

Another problem is possibly shock-waves generated upon impact. This may not be a significant factor for throwing knives into wood. But in other cases, I know it matters. For example, when shooting glass with a bullet, I'm pretty sure the shock-wave generated in the glass matters, and it can reflect back and forth a few times within the glass. Shock waves can do weird stuff like focus (just like any wave can). Does it matter for knife throwing? I think probably not... but I don't know that it doesn't matter because I've not looked into any of the relevant engineering, nor done any testing/measuring.

By the way, defects in materials do matter. For example, on paper, glass is incredibly strong. It has a tensile strength that his higher than steel. Yes, glass, on paper, can support more tension than steel. The problem is, a tiny microscopic defect on the surface of glass will easily grow into a big crack. In fact, it will do so instantly (I'm fairly sure this crack-growth is faster than the speed of sound in air, just like a balloon popping has the rubber pulling back faster than the speed of sound). This is why in practice, no bridges are made of glass.... However, glass fibers are relatively defect free. This is why fiberglass materials are so darn strong.

Actually, I shouldn't say "on paper" here. Researchers have created small samples of virtually defect-free glass, and wow are they strong and flexible. They have _experimentally confirmed_ that defect-free glass has a higher tensile strength than steel. But it was non-trivial to make such a glass sample. And if you even just touched the sample with your fingers, you would probably ruin it. There is a discussion about this in the book
_The New Science of Strong Materials or Why You Don't Fall through the Floor_ by J. E. Gordon (2006)
http://www.amazon.com/Science-Mater...5481/ref=sr_1_3?ie=UTF8&qid=1336685255&sr=8-3

btw, Gordon's book is rather dated, even-though the copyright date is 2006. It's a "new printing with new forward" of an original book from 1968. Sadly, Gordon did not live see the full bloom of powered metallurgy and the revolution in composite materials and ceramics. Although he seems to have foreseen the revolution in composite materials. It's a fairly nice book even so, and only uses some high school math in the early chapter or two. The rest is almost free of math, so it is okay for a general audience. Despite being dated in these ways, I recommend this book.

By the way, here is what I think is the best general audience book on strength of materials (general audience, virtually zero math): This book I _highly_ recommend, and I suggest you read it before Gordon's book or instead of Gordon's book (if you could only read one of them). It is a much more entertaining and exciting, and is very modern (talks about why the Titanic sank, modern ceramic anti-tank armor, and the Corningware in your dinner-plate).
http://www.amazon.com/Why-Things-Br...8834/ref=sr_1_1?ie=UTF8&qid=1336684773&sr=8-1

Similarly, it could be that, under ideal circumstances, steel has a very high fatigue limit which, on paper, you would never hit by knife throwing. But in practice, the knives may have numerous defects which lower the toughness. Sadly, if this is the case, then you would need to run around quantifying the metallurgical quality of your throwing knives. This is probably a lot of work, and might require fancy equipment, and possibly breaking a lot of knives to study them.

If this is not the case, then there is hope that back-of-the envelope calculations could give you a reasonable estimate, which you could then refine by testing. Best of luck!

Sometimes I wish the real world, as fascinating as it is, wasn't so complicated to engineer.

Sincerely,
--Lagrangian

 

[idaho]

Sorry for the language, I have big problem with using correct expressions.

In the source thread there is a photo of broken ESSE knives. It is a good example where thrown knives break.
a) tip
b) halfway trough
c) blade-handle transition
Every type of breakage have different source.
a) tip. Tip of blade is in most knives smaller in profile and thickness. It means that is will bend/flex more under same force. But, unfortunately it cannot offer enough elongation/elasticity to withstand this force. Throwing knives have much bigger/thicker tips. Problem solved.
b) Knife snapping halfway trough. I believe it is VERY hard to break knife in this spot with sticking throw. BUT if you miss, and hit sideways then impact resistance comes to play. And most knife steels have low impact resistance. The smaller the area of object, and the harder the hit object is the more stress is deployed to the blade. Using medium carbon, low hardness steel and more thickness will solve this problem.
c) blade-handle transition. Every "corner" on the knife with diameter lower than specific value for each steel/HT will create a weakspot. And weakspot is 100 or even 100 times less impact resistant. Impact, not slow bending. Of course serrations, sharp choil, or even vertical grind lines - it all creates weak spots. And last but not the least - steel impurities. They are there always.

Use clean lines knife to avoid this problem. Cold steel TFT and other good throwers, some bayonets(Sig57) are good examples how to avoid this problem.

To sum up. I don't believe that FATIGUE (caused by numerous medicore force and bending) plays major role in breaking the knife (maybe in the breaking the tip). Excessing the knife resistance ONCE causes knife to break.

 

[Lagrangian]

Idaho, Thanks for your post! I don't know much about knife throwing or knives breaking, so it was interesting to read and think about your post. Especially your thinking that fatigue is not the main factor in failures.

btw, In your point (c) you mention "weak spots." I think this is also known as "stress concentration." For example, they say airliners have round windows, because rectangular windows are more likely to crack at their corners. This is because forces get "concentrated" at sharp features (in particular holes with corners).
https://en.wikipedia.org/wiki/Stress_concentration

Sincerely,
--Lagrangian

 

[TennToadsticker]

Rather than offering any scientific insights on metal fatigue, I thought I'd share data from 3 years of throwing at targets made of pressure-treated 2 x 6 boards as well as poplar logs. We are talking hundreds of throws for each weapon. Here's a list of what held up well and what didn't:

Still going strong:
Glock FM78 field knifes--these 3 knives are my best throwers; all are a bit scratched but are still in superb condition
Condor 12" throwers--very solid, but their tips are fairly thick and don't stick well unless you throw them very hard
SOG Fasthawk Tomahawk

Damaged/destroyed:
Cold Steel Kukri--I've destroyed two of these; both broke inside the handle; I know they aren't meant for throwing but I learned how to do it and they make the most amazing sound on the way to the target. When they stick, their length makes them really wobble. Perhaps this might have something to do with the metal fatigue.
Gil Hibben set--although I used these for a while and really liked them, I soured on them after 2 out of 3 broke near the tip during the middle of a throwing competition.

I can't say enough about the Glock field knives as throwers. They are well balanced, and smooth.

I hope this information is helpful.

 

[Lagrangian]

Hi TennToadsticker,

Thanks! It's not scientific or anything, but just as a knife enthusiast, I would love to see pictures of the knives you're talking about (whether or not they're pics of them intact or broken), just to get some idea of their geometry and size. If it is not a hassle, maybe you could put the knife next to a ruler in the pictures? If any of that that's too much trouble, then it's no big deal.

Sincerely,
--Lagrangian

 

[Davefromva]

This sounds like a case for "MYTHBUSTERS!" Oh yes, I said it..lol

 

[Lagrangian]

Maybe we should create a new Youtube show called,"Knife Busters!"

 

[chiral.grolim]

This sounds like a case for "MYTHBUSTERS!" Oh yes, I said it..lol

Maybe we should create a new Youtube show called,"Knife Busters!"

...That's why I'd like to see someone do an actual measurement. Maybe I will contact that Mythbusters show on Discovery...

http://community.discovery.com/eve/forums/a/tpc/f/9741919888/m/25319568011

Yes, I did. ... because they have access to the money & tools required to accomplish the goal, and I bet it would have significant entertainment value as well

 

[TennToadsticker]

Unfortunately, I threw away the broken Hibbens, but still have the Kukri. The other problem is that I'm an old-schooler who's never learned how to upload pics. I'd welcome advice/tutorials. If I can figure it out, I'd be glad to take a group shot of the GlockFM78, Kukri, and one of the Condors.

 

[chiral.grolim]

So I've been trying to educate myself further on the stresses involved in throwing a knife and the material properties of various steels.

From my previous post about average knife throwing speed, throwing a 12oz knife into a target at 50km/hr calculates to a kinetic energy level of the center of mass (ignoring rotational KE at this point) before impact = 3281.8 Joules.

I have become convinced that idaho is correct, that fatigue due to cyclic loading with lateral stress is the wrong path to follow, that any sound steel knife at 58 - 60 HRC is strong enough to endure the vibrations without fracture, the stress & strain are too low to reach yield strength and exceed the range of elastic deformation (in which the steel experiences virtually NO fatigue).

Impact toughness is the key, measured in Joules per cubic meter. Since cubic meters are rather large for the volume of steel involved in this scenario, I propose cubic centimeters (cc) = 0.000001 cubic meters.

Let's assume our hardened 1095 knife is 340g, approximately 30cm long x 4cm wide x 0.5cm thick (net 60 cc), center-of-mass traveling 14 m/s, kinetic energy at impact = 33.32 J, and the if the blade absorbs ALL of this energy at impact, thats 0.555 J/cc (Joules per cubic centimeter).
I found some data graphing impact toughness (via Charpy) of 1095 steel at ~60 HRC in the 15 - 20 foot-pounds range, 1 foot pounds = 1.35581795 joules, so 15 ft-lbs = 20.4 Joules. Now, I'll need someone to explain to me what unit of volume/area that value covers, but if it is the Charpy standard, that's 5.5 cc, so 3.7 J/cc. That's 6.67X the amount of energy per cc required to endure the impact of the knife being thrown...

What am I missing? From that amateur math, I can see how thin edges could fracture & chip on impact but not how a knife could lose a large portion of the tip or the entire blade snap away... unless something was terribly wrong to begin with.

Help?

 

[Lagrangian]

A few minor thoughts, but nothing major:

(1) The rotational energy of a thrown knife is significant, and should probably be added to the equation.
(2) Impact toughness has to do with the energy adsorbed by the region deformed and broken. It is unlikely the entire volume of the knife is what we should be looking at. Although exactly what we should be looking at, is a good question. For example, if I break a knife by the Charpy test, well the sample could be longer than the Charpy holder and simply stick outside of the machine. I believe this will have almost no affect on impact toughness, because all of the force and energy is focused into the sample's notch which is cut out for the Charpy impact test.
(3) Shocks could be important to fatigue; I just don't know enough about material science here. But my impression, is that a shockwave could induce high local stresses. Maybe not; but I just don't know enough.
(4) It may be time to actually learn some strength of materials. Like actually read a book or take a class. Or watch free online-courses (say from MIT, Stanford, etc.) about strength of materials.
(5) If you do break a throwing knife, then save it. It is now forensic evidence for failure. After you know more about strength of materials, you may be able to examine it and figure out how it failed. Or at least, you may be able to find some professor or engineer who is willing to take a quick look at it. From what I've seen from documentaries on transportation accidents, the detailed structure of the break can be analyzed to understand why it failed.
(6) Failure might not be from fatigue per se, but progressive failure due to a flaw in the knife?
(7) I don't know all the details of a Charpy impact toughness test. But here is what I believe is true, from some casual reading (not any formal study):
(a) The Charpy impact test is just one of several tests for toughness.
(b) The Charpy test is for a specific geometry (shape of sample). If you were to change the shape of the sample, you would get a different value for the impact toughness. Why? Because the failure depends partly on how the sample deforms before breaking, as well as effects such as fracture propagation and stress-concentration. In particular, stress-concentration is highly influenced by the shape of the sample.
(c) Some very elementary non-technical material about the Charpy test is in the book _Why Things Break_ by Eberhart. It's a non-technical book, so don't expect to give you an understanding that will allow you to calculate failure rates. Eberhart's book (as well as wikipedia) are just about the level at which I understand the Charpy test. (Okay, I lied slightly; as a physics major, I know more, but not a lot more.)

Without knowing proper metallurgy, or strength of materials, I would not want to run around plugging stuff into formulas, at least not for stuff that I didn't feel I had a understanding of at the level of an undergraduate textbook. I've read a couple of popular science books on strength of materials and learned a lot, however they were mostly non-technical in nature. Probably next for me is a technical book on strength of materials, and an intro-ish book on metallurgy.

Sincerely,
--Lagrangian

 

[Big Mike]

Failure might not be from fatigue per say, but progressive failure due to a flaw in the knife?

That's the key right there.

As others have deduced, the type of cyclic loading we study as common fatigue is not the problem here.

The failures are caused by repeated random shock loading events.

Repeated, as in with each throw.

Random, as in every impact is different.

Each of the random stress events works on the microscopic flaws that exist in all steel.

Not that there is a flaw in the knife, it's just that steel is not perfect.

The accumulated stresses of these random impacts slowly work on the flaws.

Propagation of these flaws is the kind of "fatigue" these knives encounter.

Over time, and with the right stress load, one or several of these flaws weakens the blade enough to break.




The failure is more like a jack hammer bit failing from repeated stress events then a bridge girder failing from cyclic loading caused by traffic passing over it.


I suspect that the more uniform nature of PM steel would make a longer lasting thrower.



Just one engineer's two cents.




Big Mike

 

[Lagrangian]

Hi Big Mike,

Thanks for your input! (Hey, a real engineer!)

Couple of additonal thoughts:

(1) You mention that steels is not perfect, and so has microscopic flaws. These are not flaws in the manufacturing of the knife, but just the microscopic defects that exist in all steels, to various degrees. I think this is very interesting, and it sounds a lot, to me, like my example with glass. Defect-free glass has been shown (ie: experimentally shown) to have a tensile strength higher than steel. But in practice, micro-defects in the surface of the glass can easily grow into large cracks. Once the crack grows beyond some critical length, it basically explodes in size, causing the glass to fracture. So, how strong is glass in practice? There isn't a simple answer to this: it depends on how many microdefects are introduced into the glass surface, and that can vary wildly depending on manufacturing and real-world usage. Plus there is a ton of technologies and techniques for toughing glass (ie: tempered glass, laminated glass, chemically strengthened glass, differentially heated/annealed layers, Corningware, etc.) Each of these glasses not only has some specialized techniques applied, they also are affected by manufacturing quality. It would be hard to quantify them all. I believe, that something similarly complicated happens for steel. The only difference is that steel is more ductile and less brittle.

(2) I don't know much material science. But here's a senario that I could imagine (speculate): Random shocks do not have much affect on the internal structure of the steel grains. However, there could be micro-flaws on some grain boundaries. Some of these micro-flaws might grow slightly after being subjected to random shocks. Once these microcracks become long enough to join together, they may form a defect which is larger than a critical crack length. Once the defect is larger than the critical crack length, the steel may be weak at a macroscopic level which we can experience as the knife breaking upon impact.

Now before the _real_ engineers and the _real_ metallurgists start shooting me for being a bozo, let me repeat: I am _not_ a metallurgist, and the above is simply _wild speculation_. I am _not_ proposing this wild speculation as the truth. Instead, this speculation is given as an example to non-specialists (myself included), as a possibility for how complicated things _could_ be, even in a "simple steel". This speculation is simply at the level of explanations I've read about in non-technical popular-science books on strength of materials. Namely the two books I mentioned in an earlier post for this thread (Eberhart's book, and Gordon's book).

(3) The notion of a critical crack-length is fairly basic in material science. I learned about it in Gordon's book, and am still rather fascinated by it. The theory for it, is based on a simplified model for materials. If you remember your high school physics, then we have Hooke's Law, which says a spring's force is (approximately) linear in the displacement (F = -kx). Hooke's law is a simplification of real materials, which are not linear. But for small displacements, most things are very close to being linear. Hooke's law applies to idealized one-dimensional springs (you either stretch or compress these springs, there is nothing else you can do to them). It turns out, you can generalize Hooke's law to two and three dimensional springs. You might think of them as a rubber sheet and a rubber cube. Each tiny infinitesimal bit of these sheets or cubes, acts like a tiny grid of linear springs. Using materials which can be approximated as linear springs, and using some energy analysis (such as surface energy, and fracture toughness), it is possible to do a mathematical analysis that shows there is a critical crack length. Roughly speaking, if a crack is smaller than this critical crack length, then it is unlikely to grow. But a crack which is bigger than the critical crack length will grow explosively when stress is applied. Things in the real world are much more complicated, as real materials are not linear, and cracks can grow by other mechanisms, such as corrosion.

There are lots of details in the above, which I don't know. But as a physics major who has read Gordon's popular-science book, I can give the rough description you just read. And I do so, without feeling extremely bad. But, I do feel a somewhat bad, because I'm talking about things I don't understand.

Sincerely,
--Lagrangian

P.S. The two books I mention are:

_The New Science of Strong Materials_ by J. E. Gordon (revised edition 2006)
http://www.amazon.com/Science-Mater...=sr_1_1?s=books&ie=UTF8&qid=1337124264&sr=1-1

_Why Things Break_ by Mark Eberhart (2004)
http://www.amazon.com/Why-Things-Br...8834/ref=sr_1_1?ie=UTF8&qid=1337124330&sr=8-1

 

[chiral.grolim]

Thank you all for keeping this conversation going. I am hoping that a metallurgist or someone with real numerical values or the tools to produce the proper calculations takes the time to bother weighing in on the predictive mathematics at least.

I am not a professional mathematician or metallurgist or even an engineer, my area of expertise is the biomedical sciences. But as a scientist, the lack of published material data demonstrating the supposed principle that throwing hardened knives destroys them irks me. That is why, amateur that I am, I am trying to come up with at least a general mathematical demonstration of the supposed principle, using only the basic physics and limited numerical data I have available to me.
I understand the underlying theories of "why things break" and while I haven't read the book suggestion, I am sure it is an entertaining & educational read and may purchase it for my children's home-schooling curriculum (when they are old enough). But I am trying to get beyond the theories to the actual math. Minute flaws can expand with repeated stress, but how minute can the flaws be or how powerful / how many repeats of the stress before growth and induced failure?
Or assuming an un-"flawed" piece of steel, i.e. no occlusions in the matrix beyond what is "normally" present, such that grain size and type is the predominant factor in the microscopic structure - an idealized situation. If we start there (which is where the metallurgists and indeed all scientists start, forming "macro-principles" to govern the behavior of materials, establish a "normal" value before discussing the principles involved in the specific situations of flaws), what sort of values do we find and how do those values weigh in on the outcome of a specific event? In this case, how do geometric design, impact toughness, & tensile strength (objective properties of materials in an idealized state) effect transfer of energy in the object when its momentum is altered, e.g. it goes from rotating and travelling at velocity to stationary upon impact with another object. While I do not have the skill required (or time to learn those skills) to cobble together the precise predictive mathematical equations (involving both angular and linear kinetic energy), I feel that someone here might or might be able to do as I have done with greater accuracy, namely calculating the kinetic energy of the knife in motion as well as the total energy load required to induce failure of the knife under different stresses. My calculations MUST be way off...


And yes, according to Crucible's data, refinement of molecular composition, grain distribution, and minimization of grain size that can be accomplished via PM techniques can more than double the impact toughness of steel. Phil Wilson has written articles about optimizing heat-treatment protocols to acquire the highest level of impact toughness achievable when a knife blade is taken to a high hardness, i.e. trying to balance the two for specific applications. But Wilson talks almost exclusively about the very edge of the knife, not about its structural integrity as a whole. With broken throwing knives, the edge does not exclusively receive the blow and may be intact while the blade is broken in half.
Something very interesting in the articles I have read from forgers and metallurgists is that high carbon low-alloy steels like 1095 can have very narrow ranges at which hardness & toughness can be brought to a balanced maximum, and missing it can result in a blade that is too brittle at the edge...

 

[Lagrangian]

I understand the underlying theories of "why things break" and while I haven't read the book suggestion, I am sure it is an entertaining & educational read and may purchase it for my children's home-schooling curriculum (when they are old enough). But I am trying to get beyond the theories to the actual math. (...) My calculations MUST be way off...

Hi chiral.grolim,

Not sure why I'm feeling a bit uneasy.

The current theories of "why things break" cannot be ignored if you want to understand the math. You cannot "get beyond the theories to the actual math." You must go _through_ the theories to get to the math. There are several reasons for this:

(1) Applied math _always_ occurs within some conceptual framework. That framework may be a combination of phenomonology and pure theory. If one does not understand the framework, then one does not actually understand the math.
(2) Our understandings of why things break, is almost always an over-simplification. It is only after we have judiciously over-simplified, that we can do mathematics on the problem. This is where phenomonology and experiments matter: they helps us understand which simplifciations are reasonable. It is necessary, I think, to understand the context of the oversimplification to do the math.

We expect our simple question to have a simple answer.

But in science, we are often (very often) surprised to be in a situation where the answer has mind-boggling complexity. It behooves us to be respectful the possibility of such complexity.

Since you are in the biomedical sciences, I may be able to pull out some examples of naive questions having insanely complicated answers:

(1) In high-school, we learn than DNA unzips when a cell divides, and then each half is completed to make two copies. Sounds simple, right?
But it's not simple... It's almost ridiculously complicated. Consider than a human cell has about 2 billion (?) base pairs, and has a total length of about 2 meters. How the heck does 2 meters of DNA get packed into a 10 micron cell not get tangled/knotted up? Well, it turns out DNA is packed in a very organized, but very very complicated manner (super-coiling with a ton of helper proteins and spools). Given that it is all coiled up, how does it "unzip" ? Well... that's a huge area of research. As far as we know, the unzipping starts at multiple areas, and during the unzipping, the twist and coiling of the DNA has to be manged as well. So there are helper enzymes (topo-isomerases) that help twist/untwist the DNA. How this huge complicated dance actually happens is still a large area of research. Last I heard, tons of stuff about chromosome centromere's are poorly understood. From this example, it is easy to imagine that some naive question about DNA replication could have an answer so complicated, it is still an area of research.
http://en.wikipedia.org/wiki/Mechanical_properties_of_DNA

(2) We look at things. So our eyes simply track stuff right? Seems simple.
But it's not simple. Our eyes have several different kinds of jitters (saccades) some fast, some slow, some large, some small. They all have various kinds of biomechanical details, which I don't know. However, interestingly, some of them appear to have some degree of chaos (ie: chaos of dynamical systems). And there was some suggestion that schizophrenics may have different types of saccades that non-schizophrenics. Why is this? I think it's not well understood. My undergraduate perception teacher did a crazy demo for us and showed that we can smoothly track a tossed ball, or a moving finger. However, as hard as we tried, our eyes could not focus upon and smoothly move along the edge of the table. Instead, our eyes simply jumped from spot to spot along the table-edge. You can do this demo yourself, but having a very bright pin-point light in the background, which will leave an after-image in your eye. If when your eye moves smoothly, the afterimage will be a smooth line. When your eye jerks or jumps, you will see bright spots in the path of the after image, which is where your eye stopped for a fraction of a second. As a class, we were shocked; despite being alive for two decades, most of us did not know this about our own eyes.
http://en.wikipedia.org/wiki/Saccade
http://www.ijo.in/article.asp?issn=...ume=48;issue=1;spage=15;epage=9;aulast=Sharma

(3) With all the talk of iPads and iPhones, one might wonder about the resolution limit of human vision. Seems simple... Just give me a number as the answer right?
Well, human vision isn't so simple. For resolution, you might naively think that the size of a retinal rod or cone is the limiting factor for resolution in vision. Afterall, if a pixel images onto the retina with a size smaller than a rod or a cone, how could we see it? Well, it turns out there are various forms of so-called hyper-accuity, where we see features that are smaller than a retinal rod or cone. A standard example of this is called vernier accuity. Imagine I take a thin line, and cut it into two line segments. You take one of the line segments and move it a tiny bit in a directin perpendicular to the line. So you have two lines which are parallel, and almost join together to make along line, but there is a tiny break. Our ability to perceive that break is amazingly good, and is known as vernier accuity. In other words, when the break in the line is imaged onto your retina, the break itself is smaller than a rod or cone. So how can we see it? Well, it turns out that our eyes and brain combine information from the length of the line segments, and in effect, do something like "fit a line" to each side of the break. Even if each point on the line is seen with some inaccuracy, by combining multiple points along the line, the line's position can be accurately determined. So actually, it is quite complicated. A general number can be given for the resolution of human vision, but it often makes several assumptions about the conditions (such as brightness/contrast) and type of resolution (often it is not vernier accuity that is of interest in movies/video, but other measures of visual resolution).
(btw, I may have a technical error, and it could be that "size of rods and cones" should be replaced by "the size of the spacing between rods and/or cones.")
http://en.wikipedia.org/wiki/Hyperacuity_(scientific_term)

If you wanted do biomedical mathematics on (1), (2), or (3), I think you really do have to understand the theory first. Similarly, for metal breakage, I think you need to understand theory and engineering before you can do a calculation. If you want to get to the actual technical math involved right away, then you should be reaching for an undergraduate or graduate textbook on strength of materials, or enrolling in a class. At least, that is my opinion. Unfortunately, this does not give a quick or simple answer.

For example, you ask a simple question such as, how does the shape of the knife affect it's stresses during impact? Well, to really analyze this, you may have to do a finite-element-analysis of the knife as it collides. There may be some rules of thumb about stress concentration and so forth, but in something as dynamic as an impact fracture with shockwaves, I don't know if such rules still apply. This is not easy, which is why engineering structures have failed due to unexpected stress concentration due to shape (ie: unexpected stress-concentration exceeding the fatigue limit on metals, leading to unexpected failure due to metal fatigue). Supposedly, this happened in the passenger aircraft, the de Havilland Comet.
http://en.wikipedia.org/wiki/Comet_airliner#Accidents_and_incidents

If it were easy to just calculate impact toughness, probably engineers would do this. But it seems rather complicated, to me. I _think_ this is why engineers do a Charpy impact test: because they don't actually know how to compute impact toughness from first principles.

Sincerely,
--Lagrangian

P.S. Sorry about this post... It is too long, and maybe too ranty. If you hated (or liked) this post, you can let me know, and I'll consider adjusting my content and etiquette to match.

 

[KnifeThrowing]

Chiral and Lagrangian, thank you for starting and nursing this topic! This is the broadest collection of ideas on the topic I have ever read. And since I'm running a knife throwing website for around 10 years, getting in contact with countless throwers, you can accept this as empirical evidence that the question of throwing knives breaking is indeed a very difficult one.

I have come so far to describe the physics of knife throwing in a model that has become accepted. But, concerning breaking, I have to say with Chiral:

What I have encountered is various individuals insisting that this common belief is true but offering no actual data to back it up.

Concerning:

Or are all these broken throwing knives the result of major deflection off of surfaces that reflect the energy back into the knife?

I have never seen (or heard of) a knife breaking upon a contact that would have resulted in a god stick. Rather, it's when the knives hit the target with the flat of the blade, or, killer, hit the upper edge of the target (e.g. the log).

Among us are a few metallurgists, like Roman Landes, who have published books and papers about metallurgy and knives. Unfortunately for us, Roman Landes' book is in German (d'oh!)

Thank you; just added this to my reading list!