Sharpness vs Cutting Ability

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CATRA, Sharpness, and Cutting Ability

I got several good comments on the article about CATRA edge retention testing regarding sharpness and cutting ability. The edges tested with more acute angles (20° edge is more acute than 50°) started out cutting better and remained that way through the standard 60 cuts. However, the measured width of the edge with the worn 20° edges was larger than with the 50°. So this leads to a question: which was sharper? And if the 50° was indeed sharper due to its narrower edge then why was it not cutting as well?

20° worn edge (23 microns)

50° worn edge (17 microns)

Sharpness

Despite the seeming simplicity to defining sharpness, there is no agreed upon definition [1]. The two most common definitions that are used are:

1. The force required to make a cut
2. The radius or width of the edge

This image comes from [2]

Definition one relies on cutting while definition two is essentially a geometrical definition. In other words, in one case it is defined by how difficult it is to actually make a cut, while the other is concerned with defining what a sharp edge shape is. However, either case is more complicated than it might first appear.

Force Required to Make a Cut

In a study performed with scalpels and razors on soft rubber substrate, the displacement and force applied to cut through the material was measured [3][4]. The setup was the following, where the blade was pressed into the rubber [3]:

The rubber is soft and pliable and therefore it deforms to some extent before the blade begins cutting into the rubber [3]:

There are different stages to the cutting of the rubber, from the initiation of the cut (a), then the rubber traveling around the knife edge and up the sides (b), the knife then entering the rubber completely (c), and then steady state cutting (d) [3]:

Measuring the cutting you then get the following graph showing the change in force and displacement during cutting into the rubber [3]:

The top shows the force vs displacement while the bottom shows the stiffness vs displacement. The bottom graph provides an alternative view that can make the changes in behavior more apparent. There is a somewhat subtle change at 2 mm in the top graph, for example, where the graph changes to a new slope which is the point where the cut initiates in the rubber. That change is much more visible in the bottom graph. The region labeled B shows where the rubber is passing over the knife, C is the onset of steady state cutting and D is steady state cutting.

When the experiment was repeated with a blunt blade the effect of sharpness on the test is easily evident [3]:

The blunt blade required twice the displacement to initiate the cut (4 vs 2 mm), and over 2.5x increase in force from 3.8 N to 9.7 N. For the blunt knife there is a decrease in stiffness following the initiation of the cut. The overall force required to displace the blade 30 mm into the rubber was also much higher, about 88 N for blunt and 30 N for the sharp blade.

So when measuring sharpness what should be measured? The peak force that is reached during steady state? The force required for cut initiation? The displacement required for cut initiation? Those things must be decided to propose a sharpness test.

Radius or Width of Edge

Defining sharpness based on the shape of the edge itself may appear simpler on the surface. A sharp and a dull edge can be easy to distinguish in some cases based on the edge radius [5]:

However, cross-sectioning blades and using microscopy to measure the edge radius is not particularly convenient, and measuring the edge width head-on isn’t much better as it still requires microscopy. Furthermore, there may be more effects than simply the edge radius. For example:

1. Consistency of edge. Where should the edge be observed? What is the effect of variability in edge radius?

2. Edge roughness. Some edges have changes in height; does that affect sharpness?

The edge has high roughness; the edge does not reach a uniform point [6]

3. Edge finish and friction. In some cases it is possible to have a poorer finish but still a small edge radius, or a high finish with a large edge radius. How does that impact the edge sharpness?

The top edge has a rough finish while the bottom edge has a fine finish [6]

4. Edge straightness

5. Edge angle

6. Coatings. Edge coatings are relatively rare in knives but are sometimes present on razor blades

Therefore despite the seeming simplicity of defining sharpness with edge radius or width it is not necessarily a perfect definition. Also I prefer to define sharpness by an actual measure of cutting rather than leaving it to geometrical definitions. Otherwise it may not be known what variables actually improve cutting behavior.

Correlating edge radius and force to cut

Experiments comparing the radius of the edge and the force required to initiate a cut show a very strong correlation [7]:

From those graphs it is clear that the edge radius is the most important factor for cut initiation, with perhaps a small secondary effect of edge angle. A finite element model simulation of edge sharpness found an effect of edge angle [4], but that hasn’t been confirmed experimentally as far as I am aware. While the above graph shows sharpness vs edge radius with relatively dull knives, the correlation works with sharper edges as well [4]:

Cutting Ability

When it comes to making complete cuts the effect of edge angle is very strong. A test was performed with beet topping using knives with either single bevel (asymmetric) or double bevel (symmetric) with a range of edge angles [8]:

The cutting force required for cutting through the beets increased with increasing edge angle. Interestingly, double bevel edges cut with less force at the same angle as the single bevel edges. The single bevel edge was equal to a 10-15° greater double bevel edge. So despite the similar sharpness (edge radius), the force required is much greater to cut through the beets with a more obtuse edge. The force required for the complete cut is sometimes referred to as “cutting ability” though that is not a well-defined term. The CATRA edge retention test measures cutting ability rather than sharpness. So while the sharpness is reduced over the course of the test the CATRA machine itself is measuring the change in overall cutting ability and this property is reduced throughout the test through changes in sharpness. When comparing different edge angles, however, a more obtuse edge cuts less cardstock because of its reduced cutting ability even if its sharpness, or edge radius, is superior to the more acute edge.

This reduction in cutting ability with more obtuse edges has been repeated on carrots and potatoes with single bevel knives as well [9][10]:

Effect of Sharpness on Cutting Ability with Different Materials

Sharpness does not have the same effect with cutting all materials. Some are more difficult to initiate a cut and some are more difficult to cut through either due to friction or from the energy required to propagate the cut through the material. The graphs below show the cutting force vs displacement for a sharp edge (black) along with a dull edge (grey) with different foods [7]:

On one extreme is the pumpkin flesh where there is almost no difference in behavior between the sharp and dull edge. The pumpkin fractured easily and therefore the displacement to begin a cut was small. On the other end of the spectrum is asparagus and ham where because they are soft materials which easily deform, sharpness is a significant factor for allowing it to be cut. With the two cheeses, the semi-hard gouda is less affected by sharpness than the softer Bergkäse for similar reasons. The friction that resists cutting is much higher with cheese and ham than asparagus which is why the force to cut continues to increase to a greater extent with those foods.

Available Sharpness Measurement Systems

CATRA is perhaps best known for their edge retention tester, but they also produce a sharpness tester. The sharpness tester uses a rubber test media and the blade is pressed slowly into the rubber until a small drop in load is measured indicating that the cut has been initiated [11]:

A type of test that has been used for nearly 100 years is the cutting of taut thread/string where the force required to cut through the thread is measured [12]. Because the thread is thin and the cut propagates easily then the test measures the force required for initiation of the cut. Edge On Up [13] makes a simple scale-based testing system that is made for a standardized test media called BESS. Their sharpness test is also reported to correlate strongly with edge width [14].

Slicing vs Pushing

Most of the tests referenced above other than the CATRA edge retention test uses a push cut rather than a slicing cut. It is possible to define sharpness and cutting ability differently for slicing. The force required for slicing is lower than for push cutting [15][16][17]. For example, it has been claimed that a coarser edge finish cuts longer or more aggressively when slicing. This is an area that still needs further study.

Conclusions

Defining Sharpness

Based on all of the above information I think the best definition for sharpness is the energy required for initiating a cut. Using energy incorporates both force and displacement necessary for the cut initiation because energy is the area under the force-displacement curve. Using only force/weight or displacement can still be a useful simplification. Sharpness correlates very strongly with edge width/radius but I don’t personally like that as a definition of sharpness because I prefer an objective test that uses actual cutting. Different test media will lead to different values, of course. To compensate for this fact one proposed method is the Blade Sharpness Index (BSI) [3] that divides the energy required for cut initiation by the fracture toughness (energy) of the test media which results in a dimensionless number. In the study where they developed the BSI they looked at two materials with different fracture energies and the BSI values were similar for both. In a later study by other researchers, BSI was found to work well when testing with food [7]. A BSI value of zero is an infinitely sharp blade and higher values indicate lower sharpness.

Defining Cutting Ability

Cutting ability is the energy required for cutting. It includes a complete cut rather than simply the cut initiation. Many have experienced cutting with very thin knives that seem to cut even when dull, particularly for cutting tasks that do not require high sharpness. Creating a definition or independent test for cutting ability is somewhat more difficult. Factors such as friction of the material being cut adds complications that don’t allow a simple division by fracture toughness such as with the BSI. It includes many more variables such as depth of cut, edge geometry, shape and dimensions of the knife, etc. Also separating “cutting ability” from “sharpness” isn’t easy or even necessarily possible since the sharpness also greatly affects cutting ability. The first cut of the CATRA edge retention tester is perhaps the most standardized test available for cutting ability but that test isn’t perfect because even the first cut wears the edge which means that low wear resistance steels have lower values for the first cut than a high wear resistance steel. CATRA recommends using the first three cuts but that is even more affected by wear resistance. There has been some attempt to define and measure cutting ability in the German literature [18][19][20][21] but not much in English that I have been able to find.

Re-evaluating CATRA Edge Retention

So getting back to the CATRA edge retention test referenced at the beginning of this article. It is clear that the more acute edges, such as the 20° edge, cut better and longer than the 50° edge. That is due to the superior cutting ability of the 20° edge. At the end of the test the 20° edge had a larger edge width than the 50° edge, which indicates that it had lower sharpness than the 50° edge. So with the CATRA test the cutting ability of the dull 20° knife was superior to the 50° knife though the sharpness was better on the 50° at the end of the test. However, the 50° edge had also cut much less overall cardstock. If the 50° knife had performed sufficient cutting for the same amount of cardstock the situation may have been reversed. These factors are important to account for when comparing edge geometries, sharpening methods, and different edge retention tests. When designing an edge retention test the different variables matter: at what point the test ends, push/slice cutting, whether the test measures cutting ability, sharpness, or both, the material being cut, etc. I think the CATRA edge retention test is a good one but it must be understood that other tests are still possible and may give somewhat different results.

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[1] Reilly, G. A., B. A. O. McCormack, and D. Taylor. “Cutting sharpness measurement: a critical review.” Journal of Materials Processing Technology 153 (2004): 261-267.

[2] http://www.hroarr.com/wp-content/uploads/2014/04/sharpness.pdf

[3] McCarthy, Conor T., M. Hussey, and Michael D. Gilchrist. “On the sharpness of straight edge blades in cutting soft solids: Part I–indentation experiments.” Engineering Fracture Mechanics 74, no. 14 (2007): 2205-2224.

[4] McCarthy, Conor T., A. Ní Annaidh, and Michael D. Gilchrist. “On the sharpness of straight edge blades in cutting soft solids: Part II–Analysis of blade geometry.” Engineering Fracture Mechanics 77, no. 3 (2010): 437-451.

[5] Adamovsky, Michael Francis Anthony. “The Effect of Cutting Blade Geometry and Material on Carbon Fiber Severing as Used in High-Volume Production of Composites.” (2015).

[6] Verhoeven, J.D. “Experiments on Knife Sharpening.” (2004).

[7] Schuldt, S., G. Arnold, J. Kowalewski, Y. Schneider, and H. Rohm. “Analysis of the sharpness of blades for food cutting.” Journal of Food Engineering 188 (2016): 13-20.

[8] Moore, M. A., F. S. King, P. F. Davis, and T. C. D. Manby. “The effect of knife geometry on cutting force and fracture in sugar beet topping.” Journal of Agricultural Engineering Research24, no. 1 (1979): 11-27.

[9] Ciulica, L. G., and F. Rus. “Experimental regarding the determination of the optimum cutting angle using a single edged knife.” Bulletin of the Transilvania University of Brasov. Forestry, Wood Industry, Agricultural Food Engineering. Series II 5, no. 1 (2012): 135.

[10] Ciulica, L. G., and F. Rus. “The influence of the knife constructive and functional parameters on the process of cutting vegetables.” Bulletin of the Transilvania University of Brasov. Forestry, Wood Industry, Agricultural Food Engineering. Series II 4, no. 2 (2011): 105.

[11] http://www.catra.org/pages/products/kniveslevel1/st.htm

[12] Age, Iron. “On the Sharpness Testing of Safety Razor Blades.” Iron Age 131, no. 981 (1933): 981.

[13] http://edgeonup.com/index.html

[14] http://knifegrinders.com.au/Manuals/Sharpness_Chart.pdf

[15] Zhou, Debao, and Gary McMurray. “Slicing cuts on food materials using robotic-controlled razor blade.” Modelling and Simulation in Engineering 2011 (2011): 36.

[16] Zhou, Debao, Mark R. Claffee, Kok-Meng Lee, and Gary V. McMurray. “Cutting,’by pressing and slicing’, applied to the robotic cut of bio-materials. II. Force during slicing and pressing cuts.” In Robotics and Automation, 2006. ICRA 2006. Proceedings 2006 IEEE International Conference on, pp. 2256-2261. IEEE, 2006.

[17] Phan, Andrew Vinh. “Determination of cutting forces with asymmetric wedged blades.” (2014).

[18] Landes, R. “Messerklingen und Stahl.” Aufl. Bad Aibling: Wieland Verlag (2006).

[19] Hendrichs, Fr. “über ein Verfahren zur Prüfung der Schneidfähigkeit von Messerklingen.” Maschinenbau 7 (1928): 1012.

[20] Knapp, Werner. “Über Schneidfähigkeit und Schneidhaltigkeit von Messerklingen.” PhD diss., Buchdr. der Bergischen Zeitung, 1928.

[21] Klemm, Heinz. Die Vorgänge beim Schneiden mit Messern. Akademie Verlag, 1957.