Rockwell C Linearity Study

[EOU]

ROCKWELL C LINEARITY STUDY
contributors:
Edge On Up & Jan Svancara
 
Foreword: Over the past few months we have worked closely with Jan in preparing this study. These words are ours though and it is not our intention to obligate Jan to each proposed fact and detail contained in this opening statement. We'll be hearing more from Jan in subsequent posts and then it will be, proverbially, "straight from the horse's mouth". We hope that old saying translates well into Jan's native language. We admit, in advance, to being poor discussion leaders on this subject having never been present while a Rockwell test was  conducted but that doesn't curb our curiosity concerning what Rockwell numbers mean in a practical sense. We haven't been able to find a study that correlates one Rockwell number to another in relatable terms. Perhaps one of our members has. If so, we'd sure like to hear about it here.
 
We confess to being a curious bunch around here and that's not always a good thing. The surface hardness of a sharpened steel edge has little  to do with measuring its sharpness level but still, we find ourselves wondering "how much harder is Rockwell 60 is than Rockwell 30?". We've noticed that we're not alone in this curiosity. We've seen and heard the question, using some set of Rockwell test numbers, asked many times and no one seems to have even a good guess at an answer. We've had our thinking caps on here and now we're ready to, at least, begin a discussion of the question. We don't think that we can answer the question in its entirety but do have some confidence that we can begin to get our arms around the subject. With the help of our good friend Jan, who happens to be the curious sort as well, we're going to try and find out just how long our shirt sleeves are. Please keep in mind that none of us pretend to be some sort of "metallurgical Rockwell whisperers" here. We're only attempting to apply, what we feel, are common sense observations and calculations to an often asked question. We'll begin with a little background:
 
The Rockwell was, originally, a 0-100 scale utilizing a round ball indenter. We see that engineering types now disagree on the useful upper extent of the Rockwell C.  Some say 65 and others, 70 or 80. A 0-100 scale makes for easy calculations though when pondering the relationship between one Rockwell test number and another. If the scale is linear then the answer to our question (how much harder is 60 than 30) can be quickly arrived at;  its twice as hard. If you've ever hand sharpened a Rockwell 55 knife and then a Rockwell 62 knife though you're likely to suspect that it required far more than 10% or 12%  more elbow grease than a linear relationship would demand, to accomplish the task. Anecdotally then, we might suspect that the scale is not linear. One close look at the shape of a Rockwell C indenter tends to confirm our anecdotal suspicions.


 
The  indenter shape  has evolved as well. The Rockwell C scale was born along with the 120⁰ sphericonical  indenter. This new test was found to be more suitable for harder steels, the kind of steel that knife makers utilize. Each increment on the scale represents a penetration depth of .002mm (.0000788 inches) or about 1/80,000th of an inch for we metrically challenged Americans. In 1918, a reading of "0" would have meant that the indenter fell on some very hard material, presumably a diamond surface, and a reading of 100 would have meant that the indenter had fallen on very soft material. It is our understanding that a Mr. Wilson of the Wilson Mechanical Instrument Company changed that around in the 1920's. We assume that this reversal was instituted by Mr. Wilson because he thought that a higher level of hardness should be represented by a higher (greater) number. This scale reversal has caused us some consternation when thinking about the linear or non-linear aspects of the Rockwell C because, with today's Rockwell C scale, less is more and vice versa.
 
The scale is, presumably, a differential one in that it is measuring the difference in penetration depth between, first, an applied minor load (10kg) and then the 150kg major load. This study does not attempt to calculate or compensate for the minor or "pre-load" penetration depth because it is believed to be inconsequential to our results and ambitions here.
 
The geometric shape, a sphericonical cone, of a Rockwell C indenter suggests that the Rockwell C scale cannot be linear. As the indenter travels deeper into the test sample it presents a larger and larger surface area to the sample. Each tick downward on the Rockwell C scale represents an additional .002mm penetration into the test sample. Since the Rockwell C uses a fixed force (150kg) the hardness of the test sample  determines the depth of penetration. So, now we have the rub; while the indenter is traveling deeper into the sample, indicative of a softer material, the contact surface area is increasing which should make it increasingly more difficult for the indenter to penetrate. This then would then seem to have some mitigating effect in calculating the "softness" of a material.
 
 
This increase in surface area of the indenter can be calculated and then presumed that this increase has proportionate effect on the linearity of the measured results. In a subsequent post here we will present those calculations for common Rockwell C measurements.
 
The foregoing is an attempt to open a conversation. Perhaps this has all been figured out already and we, along with a number of other people, just haven't been exposed to the information. Your input will not only be appreciated but is hereby solicited.
 

[Mark Reich]

My first thought of the three scales was wrong, and I simply don't have time ponder their relevance. I shouldn't even have tried, since it's not germane to the question.    

I think, "How hard is this malleable material?" is a difficult question. So difficult, that someone had to come up with a different kind of ruler to measure it within practical limits. I think they simply had to standardized the ruler, and the question is self answering. 

The question, "How much harder is RHC 61 than RHC 60" is answered by the measuring device. It's not linear, it's not a percentage, it's a question that needs an answer, not a definition.

No need to over analyze. I'm pretty sure it's already been analyzed to practical limits. You buy the same ruler everyone else is using. Just use the ruler properly and everyone will get the same answer every time. 

I think it's been proven to work as well as it needs to work. 

Actually, I think a very similar question may be, "How sharp is this edge?" As long as everyone is using the BESS media ruler, and gravity holds, the edge will always measure the same for everyone. 

I might add, "as long as the inclusive angle of the edge is within practical limits". Otherwise, BESS measurements are actually more linear, but that might add relevance.

IMHO, if Mr.  Mike and Mr. Jan have even spent so much as a few days trying to quantify the RHC scale, and aren't coming up with an answer, that tells me it's something that simply doesn't have a mathematical formula. I know it's hard to believe, because it sure seems like it ought to able to be explained mathematically, but if you can't find the formula for something that's been used for a century, there might not be one.

[Bubby]

I'm interested in knowing. Its something I've wondered about for a long time. I doubt that the answer is going to pop out in this forum but if no one ever asks the question I can guarantee that there will never be an answer. I think that this is something that could be answered and probably has been already. We've just haven't heard about it yet.

[Jan]

It will be a year since Mike invited me to discuss hardness measurements. At first I did not want to participate because I thought it was a mature engineering discipline, as Mr. Mark wrote about it. But the challenging Mike's question "How much harder is HRC 61 than HRC 60?" made me to accept invitation to the discussion.

Hardness is the property of metal to resist permanent change of shape.  Greater hardness means greater ability to resist to be permanently bent or broken when a load is applied. Hardness also means resistance to abrasion, scratching, wear, cutting or penetration.

The industry standard for knife steel is Hardness Rockwell Scale C often abbreviated as HRC and sometimes as Rc also. For steels HRC is related to tensile strength.

       

The HRC numbers are given by the depth of penetration of a small diamond-tipped cone of 120° included angle under certain load (150 kgf). Each HRC number represents 2 microns of indentation. When the penetration depth increases by 2 microns (≈0.000 08") than the HRC hardness decreases by 1 HRC number.

   

You tube video prepared by Materials Science 2000 provides explanation how the Rockwell hardness test is performed. https://youtu.be/G2JGNlIvNC4

The HRC number is calculated from the penetration depth h measured in mm as:

Rockwell Hardness HRC = 100 – h/0.002

The HRC numbers range from 0 to 100 HRC for diamond, but common knife steels hardness is form some 45 to 65 HRC. 

To be continued until we find an answer to the question: "How much harder is HRC 61 than HRC 60?".

[Mark Reich]

Mr. Mike, what can you make of the HRC numbers we generated yesterday?

[Mike Brubacher]

I'm still thinking about it Mark and you already know what a drain thinking is on me. Just so you all know, Mark and I ran some tests yesterday where Mark tested three different hardness levels of steel and each at two different load levels, 100KG and 150KG with his hardness tester.

Generally, I think the results indicated what we already suspected and that is that the Rockwell C is more nonlinear at higher levels of hardness than lower levels. At the lowest level the numbers didn't seem to quite follow and that is what still perplexes me. I think that it is a valid experiment but should be conducted with a series of incremental test blocks of known hardness. The differential readings between 100 and 150KG loads and between test blocks might give us a good idea of what the nonlinearity looks like.  I've got another post that I'm going to try and find time to put up later today that casts some new light on the Rockwell linearity question so all our experimentations may become moot.

[Jan]

Generally, I think the results indicated what we already suspected and that is that the Rockwell C is more nonlinear at higher levels of hardness than lower levels.

Mike, I can unequivocally confirm that the non-linearity of the HRC scale increases with the increasing hardness of the steel.

Tomorrow I will post a figure which documents this behavior of the HRC scale.

Jan

[Jan]

IMHO, if Mr.  Mike and Mr. Jan have even spent so much as a few days trying to quantify the RHC scale, and aren't coming up with an answer, that tells me it's something that simply doesn't have a mathematical formula. I know it's hard to believe, because it sure seems like it ought to able to be explained mathematically, but if you can't find the formula for something that's been used for a century, there might not be one.

Mr. Mark, I worked with Mike independently on this topic, and for a long time it looked like we will not find a formula that would describe the non-linearity of the HRC scale. That's why we worked with hardness charts relating hardness, indenter area and pressure generated by the conical tip of the indenter.

Finally, when we were correcting minor numerical differences between our results, the Holy Spirit has enlightened us, and we succeeded to find a very simple formula that describes the non-linearity of the HRC scale. We will post it here soon.

Jan

[EOU]

Well, ask and ye shall receive. Sometimes anyway. An industrial customer of ours happened across this Rockwell Study thread and sent us a link this morning to an outside forum thread. We read the thread and then copied the page and edited it so that the post could be displayed here minus extraneous material and links. The article is credited to a 2014 post by Mr. Tony Yan on Metallurgical Bladesmithing Forums. In our opinion it is extremely well written and if you'll follow this link http://www.hypefreeblades.com/forum/view...=694#p5656 you can read the post in its original form. If you read the thread in its entirety you'll see that our own Scott Livesey participated in the discussion. Here's the key - Mr. Yan asserts that the Vickers Hardness Scale is, essentially, linear. We have looked briefly and found, at least, one other article that supports Mr. Yan's assertion. 

  http://www.finetubes.co.uk/uploads/docs/...s_2014.pdf which says in part; " The Vickers hardness range is proportional, so a material of HV 400 is twice as hard as a material having a HV = 200" 

This was news to us at EOU. So what does this mean for the question posed by this thread? Vickers to Rockwell C conversion charts are common. One need only to correlate any two Rockwell C readings with the corresponding Vickers readings and then to calculate the percentage difference between Vickers readings. You would then know how much harder one Rockwell C number is than another with some certainty. The accuracy of this calculation would be contingent on the precision of the conversion chart and the linearity of the Vickers Scale. We assume that various folks have produced a number of different conversion tables and that they might vary to some degree (just like grit conversion tables). Barring new information or arguments to the contrary, we may have, as close and as good an answer as we are ever going to get given the vagaries of the Rockwell C test method. Here is Mr. Yan's article with our edits;

   

First of all, I don't like the Mohs hardness scale, nor do I like the Rockwell hardness scale. Instead, I tend to prefer the Vickers hardness scale. Here are the reasons why:

Mohs hardness has almost zero engineering in it, so as you go up the Mohs scale, the jumps in hardness are almost random. For example, you may think, "Oh, with a Mohs hardness of 9, sapphire/ruby is almost as hard as diamond which has a Mohs hardness of 10." This is extremely misleading: diamond is actually four times harder than sapphire. In the Mohs scale, 10 is only 11% more than 9, but not 400% more. So why doesn't the Mohs scale have more entries between 9 and 10? Because there are very few rocks which are harder than sapphire yet softer than diamond. Mohs hardness was created for identifying rocks, and it is based on rocks which are common and somewhat consistent in hardness (ie: like quartz). (To see that diamond is "actually" 4x harder than sapphire, we'll consider Vickers hardness.)


Next is Rockwell Hardness. What's "wrong" with Rockwell Hardness? Actually not too much. But Rockwell Hardness is non-linear. You might think that a Rockwell Hardness of 100 HRC is "twice as hard" as metal with 50 HRC. But this is simply not true. In fact, if you go through the definition of Rockwell Hardness, you will find that an infinitely hard material will have a Rockwell Hardness of 100 HRC. Not that HRC is used to measure anything above about 70 HRC. But you can see the non-linearity of Rockwell Hardness in the chart above. If you actually plotted the curve all the way to 100 HRC, the Vickers Hardness would go to infinity.

So why use Rockwell Hardness at all? Because, it is easy to measure. Relatively speaking, you can buy a Rockwell tester that is quick, cheap, and accurate enough for serious metallurgy. You can buy a Rockwell hardness tester for hundreds to thousands of dollars. Although the absolute accuracy of most HRC testers is only +/- 0.5 HRC, the relative accuracy is very good. This is because it is difficult to calibrate an HRC tester. When doing a measurement, you first calibrate the machine to the hardness of a "standard sample". But it turns out that a "standard sample" can only be manufactured to a tolerance of about +/- 0.5 HRC. So it's kind of like a weighing scale which is +/- 0.5 kg in absolute accuracy, but is much more accurate (say +/- 1 gram) for figuring out if something is heavier or lighter than something else. Those of you into metrology will recognize this as the technical difference between accuracy and precision.

At this point, you might wonder, "What is hardness anyways?" The short answer is, we don't know! In fact, there is no definition or understanding of what hardness is from first principles. So instead, we define hardness based on a procedure: put a specifically shaped diamond tip on the sample, and press it into the sample with a specific force for a given amount of time. Then measure how "big" the indentation is. All the various types of micro-hardness tests (like Rockwell, Vickers, Brinell, Knoop) are variations on this type of indentation test. They differ in the shape of the diamond tip, the force and duration applied, and how they measure "size" of the indentation. But if you were to ask a physicist what is the fundamental basis for these measurements, he couldn't tell you. And at this time we cannot figure out how to predict or even define "hardness" from the fundamental laws of the universe.

This should be contrasted with other quantities. For example, strength and toughness are defined in terms of fundamental physics. Strength is the force required to break a material, and toughness is the energy required to break a material. We do have fundamental definitions of force and energy, so in this sense we do have definitions which are based on first principles. The various types of strength (compressive, tensile, sheer, etc.) and toughness (Charpy impact, fracture, tensile, etc.) are based on different ways a material can break. We're just measuring either the force or the energy of breakage in different situations. For some discussion on strength and toughness, see the section called "Strength and Toughness of Materials" in an earlier post of mine:

 What is Vickers Hardness? The Vickers hardness test is very similar to Rockwell hardness, except for a few differences: First, the diamond indenter is a pyramid rather than a cone with a rounded nose. Next, the hardness score is not the depth of penetration. Instead, Vickers hardness is basically the force applied to the indenter divided by the area of indentation. Superficially, it has the same units as pressure (force / area), although the meaning is different. So if we had an infinitely hard material, then no indentation would form. Therefore, the area of the indentation is zero. Then the Vickers hardness would be the applied force divided by an infinitely small area (zero). This means that an infinitely hard material would have an infinite Vickers Hardness.

For details on Vickers Hardness, go look at Gordon England's website. Here is a diagram of the diamond indenter which is a square pyramid, and a diagram of the indentation it leaves.

   

So what's good about Vickers Hardness? First of all, it is "linear" in a technical sense. Infinitely hard materials will have infinite Vickers hardness. Furthermore, experiments show that Vickers Hardness is roughly proportional to the compressive strength of materials. That is, if you made a plot of compressive yield-strength versus Vickers Hardness, you would get a graph that was roughly a line. (See link above for discussion of strength.) Finally, Vickers Hardness is practical for measuring an incredibly wide variety of materials. Rockwell Hardness is only practical from about 20 HRC to 70 HRC. But Vickers is practical over a much wider range.

If Vickers Hardness is good, then why isn't it used more often? Well, Vickers Hardness is expensive and difficult to measure in practice. To find the area of the indentation, you need a high resolution microscope, and you need to optically measure the size of the indentation. Doing this accurately is actually a bit tricky. Compare this to Rockwell, where you just measure the depth the indenter penetrates; you can imagine this could be as simple as using a micrometer to measure how much the indenter has moved. Rockwell Hardness is simple enough that the machine can automatically measure the indenter's position. For Vickers Hardness, you can't just have the machine go and return a hardness value; instead you need to go through some procedure for measuring the area. Keep in mind that the area of the indentation is slightly complicated, because the material pushed aside will affect the area of the indentation pit.

Because it is more complicated to measure, Vickers Hardness is typically not used in manufacturing.

[EOU]

Sorry Jan, while I was composing you posted. Its like you tell the kids "look both ways before you cross the street". I need to look to see what might have happened in the previous few minutes before I hit the "post" button.