Edge retention modeling


Background

Knifemaker Wayne Goddard has collected much data comparing the edge retention of steels, and makers such as Ed Fowler and Phil Wilson credit Goddard for the methods they use in evaluation of the edge retention. The method used by Goddard origionated as follows1 :

Twelve years ago I started using a standard test to test the cutting abilities of different knife steels. All the blades I prepare for this test are the same size, shape and thickness, being .125 in. thick and flat ground. The included angle is 12 degrees to 15 degrees, with a primary sharpening angle of 15 degrees per side; final sharpening is on a Norton Fine India stone. Cuts are made on the single strands out of a 1 1/4 in. hemp rope. The single strands are easier to handle. Three tests were conducted on each blade and the results averaged. Using a slicing cut, the strand is parted and cutting continues until the cutting edge loses its bite into the rope. This is about the same point that the edge loses its ability to shave hair.

In short, simply cut until a specific amount of blunting is reached. The measure of edge retention is the ratio of how much more one steel can cut than the other. Goddard later increased the precision by cutting the rope on a bathroom scale covered with newspaper which allows the stopping point to be set at a specific force and Wilson also adapted the same technique. Mike Swaim, who as a hobby studied various aspects of knife performance, also ran a number of edge holding tests on knives using a similar independently developed rope cutting test2

... for a sheer edge retention test, I simply cut through pieces of 3/8" hard-lay black polypropylene rope sucessively until the blades were so dull that they couldn't reliably make the cut in one pass over a cutting board without leaving ragged edges. A good sharp thin knife will leave a glassy looking smooth cut that almost looks fused. The duller the knife the more ragged the cut.

Mike extended the method by noting the performance at multiple intervals and therefore examined the nature of blunting. From the same post which refers to a 66 HRC 1095 paring knife from Alvin Johnston:

... still shaving arm hair at 10, 20 and a whopping 50 cuts. At 75 cuts knife started to just barely scrape, rather than shave. Still making glassy smooth cuts in the rope at 100 cuts, but by then edge was noticeably producing rolled burr.

Phil Wilson also measured the sharpness in intervals and noted the blunting was not a linear process. He developed a two stage model, noting that initial blunting was very rapid and then it decreased and eventually plateaued. Wilson attributed this early blunting being mainly deformation and late blunting being mainly wear3.

Early modeling attempts

Edge retention comparisons by the author noted just as Wilson described. An early example of such work was performed during reviews of two custom knives, a MEUK and Running Dog Traditional Tanto. The knives were compared for edge retention during slicing wood 4 with the sharpness measured by cutting 1/4" poly rope under 700 grams of tension 5. It was clear that blunting was not linear and followed Wilsons description, however there is to much noise in the data to quantify the exact nature of the curve.

Subsequent knife comparisons supported the hypothesis of two distinct blunting mechanisms. This was especially clear in a trial which compared low and high carbide steels shown by the graph on the right6. The two high carbide steel blades with a very high wear resistance, S30V (South Fork) and 10V (Coyote Meadow) show a large decrease in the rate of blunting in the late stage while the two low carbide steels, 52100 (MEUK) and 420J2 (Point Guard) continue to blunt at a more rapid rate. Further direct support for this nonlinear responce was given by Dr. Roman Landes whose book Messerklingen und Stahl7 showed edge retention graphs which had the exact same shape and also noted the different responce of high and low carbide steels.

Early attempts to model these measurements of edge retention used various power laws or just splines as a direct application of Wilson's two stage model for blunting. These however were not satisfactory because they did not allow ease of comparisons and have no physical significance to the coefficients. A model was subsequently developed from first principles to match the behavior in both regions and address all those issues.

Current model

Starting with the hypothesis that blunting is mainly edge deformation and wear; consider as an edge wears it thickens and thus it would take more wear to thicken (blunt) it the same amount as more material would need to be removed. Bending steel is much the same, it is easy to bend it a little, but as it bends it gets harder and harder to keep bending. Thus as an edge blunts by deformation it takes much more of the same work to keep the deformation increasing. Combining these two effects the rate of blunting should be inversely proportional to the amount of existing blunting. Thus the blunting B at a given amount of material cut x can be written as follows:

B(x)=a xb+c

If blunting followed the exact physical behavior noted then b would equal exactly 0.5 but consider effects such as of chipping which will weaken the edge and make it easier to deform and as well increase wear. Thus the model will allow b to take other values to account for chipping and other influences. The parameter a is determined by the strength and wear resistance of the steel and c just represents the initial sharpness, it is zero for a perfectly sharpened blade. Note how the blunting is determined does not matter, any representative measure of sharpness will do 5.

Since there are two paramaters which influence the rate of blunting, a and b, one steel can have superior edge retention at high sharpness but another steel can have superior long term edge retention. This is shown in the graph on the right. This subject was explored in detail by Dr. Roman Landes7 who classified steels in three types, I, II, II, according to their ability to hold a very push cutting sharpness at low angles. AEB-L is an example of a type I steel and ATS-34 is an example of a type III steel.

Note to model sharpness S(x) the function just has to be inverted producing :

S(x)=c/(1+a xb)

Application

These forumlas have been used extensively by the author to fit the edge retention data personally recorded such as an exhaustive comparisons performed on multiple S30V and ZDP-189 knives8. The model represented the data perfectly both in the early and late stage blunting. The b coefficents were all the same as would be expected as the steels are all similar in being very hard high carbide stainless. The difference in behavior was just the a coeffient was systematically larger for all S30V blades. The model also well represents similar hand data collected from other individuals9. It can also be readily applied to model the extended cutting ability of knives by realizing that the coefficient c can also include any constant wedging force on the blade so the sharpness equation can be extended directly to measured extended cutting ability.

As an example of such analysis, the graph on the right represents data digitized from graphs published by BUCK 10 and fitted to the above model. It compares the performance of a two blades steels and two edge configurations. It was used to promote the "Edge 2000" process, an enhancement by Buck in their sharpening methods to increase the intitial cutting ability and cutting lifetime of their knives. The angle was reduced to 14.5 degrees per side and a hard cardboard wheel replaced a cloth wheel to reduce the convexing of the final edge bevel which further makes the edge more acute11. In short, the 420HC blade with the "Edge 2000" profile radically outperforms the BG-42 blade with the more obtuse edge profile. When both have the "Edge 2000" process the BG-42 blade pulls ahead strongly after significant cutting. The data was modeled by the S(x) equation and as shown in the graph the fitted curves well represent the experimental data. The results of the fit are given in the following table.

Steel Edge Configuration a b c
420HC Edge 2000 0.37 (4) 1.34 (5) 10.4 (3)
BG-42 Pre-Edge 2000 2.4  (3) 0.64 (3) 12.5 (8)
BG-42 Edge 2000 0.44 (4) 0.97 (3) 10.9 (3)

Note when both blades have the "Edge 2000" configuration the a parameters are not significantly different but the b value is much lower for the BG-42 blade indicating its higher wear resistance. It is clear that the more acute edge does significantly better on the CATRA machine. It would have been interesting to see other angles tested to example if that was the optimal configuration.

Recap

A simple power equation has been proposed to model the loss of sharpness of knives in use. The equation has been successfully applied to data collected by hand by the author and others and as well CATRA results.

References

1 : Wayne Goddard, http://users.ameritech.net/knives/edge.html, 1997.

2 : Mike Swaim, rec.knives,1998.

3 : Phil Wilson, private communication, 1999.

4 : Cliff Stamp,Knife Review: Traditional Tanto by Running Dog Knives, 2001.

5 : Cliff Stamp, Measures of Cutlery Sharpness, 2007.

6 : Cliff Stamp,Review: South Fork, 2006.

7 : Dr. R. Landes, Messerklingen und Stahl, 2. Auflage, Wieland Verlag, Bruckmühl, Germany. Copyright 2006

8 : Cliff Stamp, Blade Comparisons, Copyright 2007

9 : Mike Cheshareck, Slicing edge retention: CPM-D2 (Spyderco Military) vs. D2 (Mel Sorg), Copyright 2007

10 : Catra Edge Testing Results, C. J. Buck, 2001

11 : Buck Knives, Technical Info, 2003


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Written: Jan. 2006 Updated: Aug. 2007 Copyright (c) 2006-2007 : Cliff Stamp