Quantifying sharp

Introduction

For centuries, men have sharpened tools, knives, swords and razors.  With the proliferation  of disposable utility blades and cartridge razors, what was once a commonplace skill has become a lost art, practiced mostly by knife enthusiasts, hand tool woodworkers and men who shave with straight razors.   Whether sharpening by hand with hones and abrasives can produce a finer edge than industrial scale, mechanized sharpening seems likely, but it is something we will investigate.  Undoubtedly, the modern preference for mechanized and disposable sharpening is the choice of convenience rather than  a confirmation of quality.

In principle, there are two general approaches to quantifying “sharp” or the keenness of a blade’s edge.  The simplest and most common is through comparison and evaluation of use.   Comparing the force to cut, the smoothness of the chiseled wood, the thinness of the sliced vegetable, or the closeness of the shave provides a relative quantification of sharp.   Such comparisons are more than sufficient to allow a practitioner to develop and evaluate a honing  procedure.   To a Scientist, this phenomenological approach begs the questions of why? and how? and provides little insight into how  the process can be improved.

My approach will be to use electron microscopy to physically observe the geometry and polish of the edge and to quantify the edge width and bevel angle.  The goal is to provide an understanding of what is happening at the blade’s edge. The centuries old design of a straight razor provides the ideal system for scientific study of sharpening.  Honing on a flat surface with the bevel and spine contacting the hone fixes the angle of the apex.  The steel used in a straight razor is hardened and tempered to optimize the achievable keenness.  In our experiments, the use of a straight razor will allow us to fix the honing angle at the value determined by the spine thickness and blade width.

The expression razor sharp undoubtedly refers to the fact that the keenness required of a  functional straight razor is very near the limits of what the physical properties of steel permits.  In other words, as sharp as it gets.  I will show that the apex of the blade must be thinned to about 100nm (one tenth of a micron) to comfortably shave facial whiskers.  At the same time, the limit of what can be achieved with honing and stropping of a steel blade is on the order of 50nm.  The intriguing aspect of a straight razor edge is the fact that it can be evaluated in a especially sensitive way, slicing hard whiskers from some of the softest and most sensitive skin.  This provides an added layer of complexity, identifying the properties of a blade that affect the selectivity of cutting whiskers over cutting skin.  Correlation of the microscopic edge characteristics to the shaving performance is also a topic to be investigated.

SEM Imaging

The scanning electron microscope allows imaging of a honed blade’s edge (or apex) at sufficiently high magnification and contrast to assess the polish of the bevel, the uniformity of the edge and to make relative comparisons of sharpness.

Below, two SEM images taken edge-on of honed blades.  Both images were recorded at the same magnification, providing clear evidence that one blade is keener than the other.

GMN200

10kx edge view of a razor after Gokumyo 20k hone

CHO1K_10k

10kx edge view of a razor after Chosera 1k hone

Although relative comparison of keenness is possible from the edge-view images, quantification of the keenness is challenging without the perspective provided by cross-sectioning of the blade.  A focused ion beam (FIB) is used to cut a cross-section perpendicular to the edge.  From the SEM image, the geometry of this cross-section can readily be measured to determine the edge width and bevel angle.

DMT1200_X_measured

SEM image of a FIB-milled cross-section with edge geometry measurements

In the above image, the bevel angle near the apex is 19 degrees and the edge width at 3 microns from the apex is 1.65 microns.

In summary, SEM imaging and FIB cross-sectioning allows measurement apex geometry; the edge width, the bevel angle near the apex, and the thickness at a distance from the apex.  With these measurements, it will be possible to quantify the results of various hones, stones, strops and the techniques of their use.