Visualizing the Tradeoff of Higher Hardness

New data from Larrin for 3V shows much better toughness/hardness, perhaps because the old data were based on a slower plate quench. So I have relabeled the old data and added the new data.
 
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There might be value in leaving the old 3v values since most 3v will not have used the new lower tempering temperature. Just mark it as such.
 
SharpBits said:
There might be value in leaving the old 3v values since most 3v will not have used the new lower tempering temperature. Just mark it as such.
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I would agree but I think it's now fairly common knowledge in the knife world that 3V does better at lower temperatures than the datasheet recommends.

Nathan the Machinist Nathan the Machinist what do you think of austenitizing temperature of 2000°F, plate quench, cryo, and temper at 400°F?
 
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I was trying to think of a way to visualize the effect of blade thickness and edge angle on toughness and edge retention at the same time.

A convenient mathematical relationship is that toughness is proportional to the cube of blade thickness, while edge retention is related both to the contact force at the blade tip and the thickness of the edge bevel: the larger the edge angle is, the thicker the edge bevel is, and the less contact pressure there is on the material being cut at the actual edge. As the edge wears away, contact pressure is reduced further until the blade ceases to cut.

Empirical data on edge angle and edge retention gives the relationship:

Edge Retention ∝ (sin(Edge Angle/2))^(-9/4)

If we reduce the blade thickness while keeping the bevel height the same, the bevel thickness decreases proportionally with blade thickness and we can get a simple relationship between toughness, edge retention and thickness.

Bevel Thickness ∝ sin(Edge Angle/2)
Edge Retention ∝ (Bevel Thickness)^(-9/4)
Edge Retention ∝ (Thickness)^(-9/4)

Since Toughness ∝ (Thickness)^3, we can use the results above to get the relationship:

Edge Retention ∝ (Toughness)^(-3/4)

And this can be visualized as such:

1000014067.png

The dotted lines show the effect of reducing the blade/bevel thickness (and edge angle), confirming that edge angle can be even more important than the steel type.
 
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New data from Larrin shows a significant improvement in toughness from Erasteel Magnacut! I added it to the chart, but note this is preliminary data with extrapolated edge retention. I also added Magnamax.

Please subscribe to Larrin's Patreon to read the details.

1000014066.png
 
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Now and then I see comments about some knife steel or other becoming unavailable accompanied by mild panic. The big picture is there's lots of choices available and some new ones are great. My second observation is many knife enthusiasts pursue edge retention at high prices to the exclusion of all else.
 
OoW4NqM.png


So if we can use geometry to trade toughness for edge retention, what does this mean for designing a knife? We can specify a toughness value and then calculate the optimal geometry to reach that toughness. We can then compare each steel at the same toughness by putting edge retention on the y axis and hardness on the x axis:

cDNV3CE.png


Interestingly, this graph will look exactly the same no matter which toughness value you choose, only the scale of the y axis will change. So I removed the units of edge retention, they don't matter! The best steels are going to be the ones that have the highest edge retention at a particular hardness. 3V is the best of the lower hardness steels and Z-max is the best of the high hardness steels, at least in the data I have. Magnacut, 4V, and K390 also do well in the middle range.
 
Last month, Blues Blues challenged me to create a chart showing optimal edge angles for each steel.

Blues said:
Now you just need a chart for optimal angles for each steel...

Stop being so lazy. ☺️

(I removed my post above so as not to confuse the matter once Synov Synov replied again.)
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I've been putting it off for a while and working on the best way to model this, but here it is:

https://docs.google.com/spreadsheets/d/10yKMxBDcGxStoWETouGL2cCZcc7rWdcz716Xf4WMSWg/edit?usp=sharing

This will calculate the optimal edge angle if you put in your desired tougness and hardness, along with two data points from Larrin Larrin 's tests of the steel you're using.

You can also do the same with a desired edge retention, or see the effects of changing the edge angle. Just put what you want next to the red names and the numbers next to the black names will change.
 
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And for those wondering, this is the model the chart is based on:

1000014617.png

R = edge retention
A = edge angle (dps)
H = hardness
T = toughness

Subscripts 1 and 2 indicate data points from Larrin Larrin 's tests

If anyone wants to know the details of how the model was constructed, let me know.
 
I’m not following what any of that means. Maybe you could create a diagram of what you are referring to with “blade thickness” and “bevel thickness.”
 
Larrin said:
I’m not following what any of that means. Maybe you could create a diagram of what you are referring to with “blade thickness” and “bevel thickness.”
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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?

file.php
 
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?

file.php
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And what does the blade thickness have to do with the edge toughness and edge retention?
 
All very interesting but beyond my ken, being a math phobic. If a knife cuts well and holds an edge a decent time, it's OK with me. So far, Magnacut is the best knife steel I've come across, albeit there are plenty of others I like, too, from high carbon steels to tool steels to stainless grades.
 
Larrin said:
And what does the blade thickness have to do with the edge toughness and edge retention?
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Not much, but you can think of this analysis as solely pertaining to the edge if you want.
 
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