Rockwell/Microhardness Reporting

[mrfailure]

A few years ago I asked how everyone reported their hardness results. It seemed like every respondent reported in a different way.

With digital Rockwell testers now the norm, I want to ask: do you report to the 0.1 point or do you round to the nearest integer value. Do you think the wording of ASTM E18 requires you to report Rockwell as integer values? If you round, how do you handle conversions between Rockwell and other scales (Vickers/Knoop/Brinell)?

I'll put out my opinion: I think hardness should be reported to 3 significant digits as this is accurate for properly calibrated modern testers. Rounding to integers degrades the data. Also, using 3 digits generally allows straightforward conversion between Rockwell and Vickers/Knoop/Brinell, which would report to integer values unless the material is really soft.

 

I recommend people read the relevant standards in full, including the commentary. e.g., E92, E384, etc.

"Everyone is entitled to their own opinions, but they are not entitled to their own facts."

 

[Maui]

Mrfailure,

According to ATM E29-13 "Standard Practice for Using Significant Digits in Test Data to Determine Conformance with Specifications" it states in section 7.4,

7.4 Reporting Test Results — A suggested rule relates the significant digits of the test result to the precision of the measurement expressed as the standard deviation σ. The applicable standard deviation is the repeatability standard deviation. The rounding interval for test results should not be greater than 0.5 σ nor less than 0.05 σ, but not greater than the unit in the specification (see 6.2). When only an estimate, s, is available for σ, s may be used in place of σ in the preceding sentence. An alternative statement of the suggested rule is: Write down the standard deviation. Round test results to the place of the first significant digit in the standard deviation if the digit is two or higher, to the next place if it is a one.
Example:
A test result is calculated as 1.45729. The standard deviation of the test method is estimated to be, 0.0052. Round to 1.457 or the nearest 0.001 since this rounding unit, 0.001, is between 0.05 σ = 0.00026 and 0.5σ = 0.0026.

NOTE 3—A rationale for this rule is derived from Sheppard’s adjustment for grouping, which represents the standard deviation of a rounded test result by
[σ2 + w2 / 12]1/2 where σ is the standard deviation of the unrounded test result and w is the rounding interval. The quantity w / [12]1/2 is the standard deviation of an error uniformly distributed over the range w. Rounding so that w is below 0.5 σ ensures that the standard deviation is increased by at most 1 %.
7.4.1 When no estimate of the standard deviation σ is known, then rules for retention of significant digits of computed quantities may be used to derive a number of significant digits to be reported, based on significant digits of test data.

You have no doubt performed Rockwell hardness testing and are familiar with the scatter that is frequently encountered when taking a number of readings from the same test sample in order to determine an average hardness value. Suppose you obtained the following Rockwell B hardness readings from a single test sample: 88.7, 98.2, and 92.5. These are actual values that I measured recently on an incoming sample. The mean is 93.1. The standard deviation is 3.9. What would you report for the representative hardness based on the practice quoted above? I would report the hardness as 93 HRB.

Maui

 

[mrfailure]

Maui,
In the real world, I do not see much scatter in testing the cal block (certainly not the +1.0 tolerance allowed) or in actual test results on a homogeneous material. In your example, I would definitely collect at least 5 values if I saw that degree of scatter, then throw out the high and low values for averaging since sometimes problems occur related to an individual test. If results are really that inconsistent, then you may need to see why (for example, the material may be nonhomogeneous or a type with inherent variability like a casting that needs Brinell rather than Rockwell readings).

 

Here's what I learned in General Engineering 100: Carry all the figures you want in intermediate calculations, but do not report to more significant figures than you can justify. Uncertainty increases at every step of a process.
Hate to sound old-school, but it appears a lot of this basic engineer's tool box, including drawing reading, is no longer taught. Instead, the young engineers I encounter all seem blinded by Tech.

"Everyone is entitled to their own opinions, but they are not entitled to their own facts."

 

[Maui]

mrfailure, that is the point. In the real world you can (and often do) see significant scatter in hardness readings on actual parts. I could have taken a dozen hardness readings on the part that I mentioned above and thrown out the highest and lowest readings, but even if this was done there would still be significant scatter in the results. For that reason alone that third digit in the hardness value should not have been included when reporting the average reading for this component. And if you read the quote from ASTM E29-13 that I posted above, it leads you to the conclusion that two significant digits is the proper way to rep[ort the hardness in this instance.

 

[mrfailure]

Ironic is correct that you need to carry all of the figures through intermediate calculations. As for reporting, you need to report that last digit if the spec limit is to x.x precision. Most but not all Rockwell specs are integer values so it is fine to report that way. For conversions, you need to keep the last digit through the conversion. Microhardness profiles with effective case depths should absolutely report that last digit as you are looking at where the curve crosses 50.0 HRC.

Note that the E29 standard deviation argument Maui is making would also mean that you should be reporting Brinell/Knoop/Vickers to the nearest 10 value.

 

mrfailure,
Not quite. E140 is just a set of best-fit correlations between pairs of hardness scales, for a class of alloy over a wide range of hardness and possibly in a variety of conditions. So there is uncertainty built in to that (on top of everything else).

"Everyone is entitled to their own opinions, but they are not entitled to their own facts."