Rockwell C Linearity Study

[Jan]

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.

Mr. EOU, it is perfect that your industrial customer draw your/our attention to the article posted by Tony Yan in 2014. I know this article well from my recherché done last year. It is really extremely well and simply written.
 
As independently confirmed by Tony Yan the problem with Rockwell hardness is that the HRC numbers have no fully clear physical definition and no physical dimension. The Rockwell hardness scale is nonlinear, so we cannot say that diamond with 100 HRC is twice as hard as a steel with 50 HRC.

And now back to Mike’s tricky question: "How much harder 61 HRC is then 60 HRC?".

If the HRC would be a linear scale than the answer would be "61 HRC is by 1.66 % harder than 60 HRC" (1/60 * 100 = 1.66). But because the HRC is nonlinear this answer is not correct.

As a homework I related the HRC numbers to the pressure generated by the surface of the conical indenter. Having the relation between HRC and the pressure of the indenter I was able to determine the percentage increase of hardness between two HRC numbers. To some extent I went in the footsteps of Mr. Robert and George Vickers, who calculated Vickers scale alike, but almost one hundred years earlier.




Example 1: From the graph above we can estimate that 61 HRC steel is by 5% harder than 60 HRC steel. Similarly we can say that 59 HRC steel is by 5% softer than 60 HRC steel. That answers Mike’s tricky question.


Example 2: From the graph above we can estimate that 51 HRC steel is by 4% harder than 50 HRC steel. Similarly we can say that 49 HRC steel is by 4% softer than 50 HRC steel. Such a soft steel is used e.g. for throwing axes, because they must absorb brute impact force without breaking

Jan

P.S.: Please replace the decimal comma used in the graph with decimal point. Decimal comma is the European default setting.

[EOU]

Beautiful Jan and another way to skin the cat! We compared your conclusion to the calculation method proposed by us in our earlier post. We picked the first Vickers/Rockwell C converter we came upon. The conversion calculator we used can be found at this website http://www.tribology-abc.com/calculators/hardness.htm. After finding the Vickers values for Rockwell C 60 and 61 we came up with about a 03.5% increase in hardness from 60 to 61. There is little doubt that these conversion tables are going to vary to some degree. Be it 3.5 or 5% that's a whole lot closer to an informed answer than we've ever seen proposed before. 

Rockwell C 55 to 62? About 28% according to the above linked conversion table. RC 30 - 60? 131%.

[Jan]

Mr. EOU, thanks for sharing the data from the conversion calculator.

My number for HRC 55 to 62 is 34% and for HRC 30 to 60 some 112%.

I would be happy to see that other conversion calculators will show even better numerical compliance.

Jan

[me2]

If I'm not mistaken, Rockwell testing, and hardness testing in general, were devised to estimate strength.  In that light, the Rockwell C scale is close to linear with respect to strength for the range used for most knives, from 55 to 66.    Overall it is not linear.  As the hardness increases, the difference in strength accelerates.

[Jan]

Yes Mr. Me2, you are correct, for metals Rockwell hardness correlates linearly with tensile strength.

Jan

[me2]

So are you trying to quantify the difference between 60 and 61 the same way 50 lbs. is different 51 lbs.? On the surface that sounds easy, but it's likely very difficult, unless you relate it to strength.

[EOU]

Good to hear from you on this thread me2. We went to some effort in the opening post to explain what we were attempting here and that was to put the Rockwell C scale into some meaningful context for the average and even not so average Joe. The difference between 50 and 51 lbs. is 1 can of green beans or one very nice T-bone steak. These are things that we are familiar with and can relate to. Until very recently we had no real idea what the relationship was between Rockwell 50 and 51 other than that they were two reference points on a scale. We still couldn't tell you just off the top of our heads but we have some confidence that we now can calculate the difference and put it into meaningful terms.

[me2]

An interesting point might be that most people can conceptualize what a pound is, but if you hand them a 50 lb then a 51 lb dumbbell, they probably couldn't tell the difference without a scale.  In the same way, a difference of 60 to 61 would be very difficult to detect, other than with a hardness tester.  

1 point of hardness in metal isn't really something we can conceptualize, partly because it changes as you get further up the scale.  Also it's beyond our ability to effect most metals on the C scale without tools.  We can all lift a pound, measure a foot, etc.

[me2]

Interestingly, the 3.5% difference calculated above is quite close to the 3.8% change from 58 to 59 based on tensile strength calculations. 338,000 psi to 351,000 psi. The chart I use stops at 59 w/r to tensile strength conversion.

[Mark Reich]

Well, I'm not surprised I was wrong. I can do that all the time.

I am surprised there is only some insignificant 4% or whatever difference, even calculable by different methods, for an approximable difference of a Rockwell point. 

In thinking more along the lines of the upper limit of workable hardness in blade steel, a difference between 60 and 61 in S30V, for instance, seems much more significant. I reckognize the difference between 56 and 57 in S30V is not nearly as significant.

I suppose that is to be expected, since there is usually less margin for error whenever limits are being pushed. 

It is prudent to consider that one Rockwell point will have much greater influence depending on other factors. I hesitate to assign a single Rockwell point an approximate level of difference, and I'm sure actual performance tests will bear this out.