Visualizing the Tradeoff of Higher Hardness

Larrin said:
Which of the equations use blade thickness instead of edge thickness?
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Oh, none of them. The assumption is that blade thickness will be changed proportionally with edge thickness so that we don't have to worry about the complexities of the blade possibly affecting the toughness of the edge.
 
Blues said:
The fact that you took my wry comment to heart is both impressive and bewildering. Hopefully it will prove useful for all the time and effort invested.
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I was mostly ignoring it, but my mind tends to wander to math problems in the shower, so you can consider this work the accumulation of a month's worth of shower thoughts. Several dead ends this week and finally a breakthrough yesterday when I found the correct set of assumptions for the model to work.
 
Synov said:
Blade thickness is just the standard meaning, for example a PM2's blade thickness is 3.7 mm at the thickest part.

Bevel thickness is the same thing but along the profile of the bevel, so it's the base of an isosceles triangle.

If you reduced the thickness of C proportionally throughout the blade you would get B. Did that explain it?

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The bevel thickness you speak of is what most call Behind the edge(BTE) measurement. The reality is that just putting a XX degree edge on a knife doesn't make it equal to the other knife if it has the same XX degree edge. Equal BTE certainly bring the edges closer to being equal,

I'm not sure what you are trying to do in the pic above. Seems to me that B, C and D are all the same with just different bevel angles and BTE thickness. And if all three had the same BTE and the same angle, they would be identical. So for example, when I put a 9 dps edge on a knife it will look like B. A 15 dps will look more like C and a 25 dps will look more like D. The difference in edge retention is simple. On hard materials D will survive better than B. But on soft materials, like rope wear will be minimal and the steeper angle will last longer as it stays thinner and can continue to cut far longer. Just logic here. So you can take a simple steel and put edge B on it and it will outperform magnacut with edge D.

So what is the calculated DPS of this knife and how does this flat ground profile with that measure edge fit into your picture?
yMXMCYW.jpg
 
I realize that this may be dumb but it is stuck in my head lately. Where would obsidian be on the chart, assuming it was knapped by someone reasonably skilled? I have an idea but nothing to prove it or back it up.
 
DMG said:
I realize that this may be dumb but it is stuck in my head lately. Where would obsidian be on the chart, assuming it was knapped by someone reasonably skilled? I have an idea but nothing to prove it or back it up.
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Edge retention would be high, toughness would be ridiculously low, I think. That would be my guess. Way sharper than any steel but like glass in toughness.
 
Cobalt said:
Edge retention would be high, toughness would be ridiculously low, I think. That would be my guess. Way sharper than any steel but like glass in toughness.
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More or less what I am thinking as well. I have knapped obsidian (or attempted to) and my hands had tiny cuts i could not really feel when they happened.
 
Cobalt said:
The bevel thickness you speak of is what most call Behind the edge(BTE) measurement. The reality is that just putting a XX degree edge on a knife doesn't make it equal to the other knife if it has the same XX degree edge. Equal BTE certainly bring the edges closer to being equal,
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Not really, I'm talking about the thickness along the entire profile of the bevel, including the edge. These numbers are comparisons between knives that have the same bevel heights but different edge angles. Bevel thickness is determined by those two numbers. So the same edge angle will produce the same bevel properties. If we only really care about toughness at the edge, then these results should be applicable to any knife, at least in relative terms. But it's not saying two knives with different BTEs but the same edge angle will behave the same. You have to compare like to like.
Cobalt said:
So what is the calculated DPS of this knife and how does this flat ground profile with that measure edge fit into your picture?
yMXMCYW.jpg
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If you had data on the steel it's made from you could plug it into the model and it would tell you how to change the dps to reach the properties you want.
 
DMG said:
I realize that this may be dumb but it is stuck in my head lately. Where would obsidian be on the chart, assuming it was knapped by someone reasonably skilled? I have an idea but nothing to prove it or back it up.
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Individual shards and small sections of an obsidian knife can be sharp but the overall blades are generally less sharp than a well sharpened steel knife. Toughness is of course terrible.
 
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Synov said:
If you had data on the steel it's made from you could plug it into the model and it would tell you how to change the dps to reach the properties you want.
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That's presuming that data is available for the steel. So if the knife above was made from 3V, what number would you get.
 
Cobalt said:
That's presuming that data is available for the steel. So if the knife above was made from 3V, what number would you get.
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That's why I said "if" you had data, but I don't understand what you're asking. You could put in the hardness and edge angle of your knife to predict what the toughness and edge retention would be. Then if you wanted more edge retention or toughness you would put in the number you want and it would give you a new dps you could change the knife to.
 
Synov said:
That's why I said "if" you had data, but I don't understand what you're asking. You could put in the hardness and edge angle of your knife to predict what the toughness and edge retention would be. Then if you wanted more edge retention or toughness you would put in the number you want and it would give you a new dps you could change the knife to.
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How much empirical data did you use creating this formula to test that it works.
 
Cobalt said:
How much empirical data did you use creating this formula to test that it works.
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All of Larrin's data at 15 dps (if there are 3 or more data points for the same steel then you can input 2 of them and predict the others) and the data he used for his analysis of edge retention at different edge angles, which I think is a mix of his own tests and data he got from corporate testing.

The only thing that isn't based on empirical data is the assumption that toughness is proportional to the cube of thickness, which I think is a rather uncontroversial assumption and probably more accurate than the empirically-based correlation of edge retention to edge angle.
 
badmatt said:
heres a visual of high hardness steel and its downside. ZDP-189 @ 67.2 HRC

CQGJ7JV.jpeg
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As Synov said that is that steel. All steels have a point where hardness reduces toughness. Some have two peaks. Its not as simple as a bell curve sometimes
 
Synov said:
All of Larrin's data at 15 dps (if there are 3 or more data points for the same steel then you can input 2 of them and predict the others) and the data he used for his analysis of edge retention at different edge angles, which I think is a mix of his own tests and data he got from corporate testing.

The only thing that isn't based on empirical data is the assumption that toughness is proportional to the cube of thickness, which I think is a rather uncontroversial assumption and probably more accurate than the empirically-based correlation of edge retention to edge angle.
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There are many experimental reports on the effect of thickness on impact toughness. None of them say it is proportional to thickness cubed.
 
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