The Slitting Method for Residual Stress Measurement         : FAQ

# Frequently Asked Questions on Slitting (Crack Compliance) Measurement of Residual Stress

I want this FAQ to be helpful. Please email me (Mike Prime) if you find these answers to be unclear or incomplete or if you have a suggestion for improvement.

## See Resources and Help for getting free data reduction or the quickest way to do it yourself.

M. B. Prime, "Experimental Procedure for Crack Compliance (Slitting) Measurements of Residual Stress," LA-UR-03-8629, Los Alamos National Laboratory Report, 2003. pdf document

## Questions:

Calculations:
"Calculations" refers to the process of determining residual stress profiles from the measured strain data.
- When should I use plane stress or plane strain compliances?
-Is there commercial software for doing compliance calculations?
-How does one calculate the stresses?
-What is the best way to calculate or obtain calibration coefficients (compliance functions)?
-My top gage and back gage disagree or give different results, why?
-What if I can't fit the data well with a series expansion?

Can I measure my material (e.g. various metals, alloys, hard steel, polymers, composites, non-crystalline materials, etc.) ?
Probably. Really you just need to be able to put on a strain gage and find some way to make a cut. The only other consideration is that the material behave mostly elastically as the residual stresses relax during cutting. See the literature page for the vast variety of materials slitting has been successfully applied to: steel, aluminum alloys, titanium alloys, polycarbonate, PMMA, stellite, copper, metal matrix composites, polymer composites, bulk metallic glasses, functionally graded materials, etc. As far as hard materials, EDM works just fine (no introduced stresses), for example the hardened steel in the ring test. Back to top

Can one measure parts with unusual or complex geometries?
Yes. Because you can calculate the calibration coefficients using a fairly simple elastic finite element model, geometric complexity is not a problem. A paper by Rankin et al. (reference) has a good explanation of FEM calculations of the calibration coefficients. The other consideration for complex geometries is that you have to be able to assume that on the plane of the cut. the stresses only vary with cut depth, not in the transverse direction. If the stresses vary in both directions of the plane of the cut, then consider using the contour method. Back to top

How big or small of a part can one measure?
There is almost no limit when you are measuring through-thickness stresses. For big examples, stresses have been measured in 166 mm (6.5 inch) thick plate (reference 22) and 140 mm (5.5 inch) diameter solid cylinders (reference 29). For small examples, I have measured stress profiles through the thickness of 2.9 mm thick (0.1 inch) thick plate (unpublished). Measuring near-surface stresses in regions of less than 0.5 mm depth is tricky, but shot peening stresses varying in a a depth of 0.2 mm have been measured (reference 24). Stress measurements in layers 1 mm thick or more is straightforward, see these results on a surface hardened ring. Back to top

Can one measure low magnitude residual stresses with good precision?
Definitely, that is one of the strengths of slitting measurements. See the measurement results in the stress relieved aluminum for a good example. There the stress magnitudes are under 20 MPa (3 ksi, σ/E < 0.0003) and the uncertainty was about ± 1-2 MPa. See also the paper by Aydiner at al. (reference) where the stress magnitudes in a bulk metallic glass were less than 15 MPa (2 ksi , σ/E < 0.0002) and the uncertainty was about ± 1-2 MPa. Back to top

Will there be yielding problems if the stresses are large?
In most applications*, back gage (opposite the cut) data is generally not significantly affected by plasticity for residual stresses up to at least 80% of the yield stress. Top gage data is more affected. If you do you have yielding affects, you will measure greater strains and then calculate unrealistically large stresses, so you can see the affect. If you calculate stresses greater than yield, beware. See Lee and Hill 2007 paper in new papers page for a simulation showing minimal plasticity effects even for large stresses. *In rings/cylinders, cutting through the thickness of the ring can release a bending moment and cause early yielding. In such cases, cut through the ring and measure the released bending moment. Then cut through the thickness of the severed ring to measure the non-bending part of residual stresses. Back to top

Are there commercial labs that perform measurements?
Yes. (See disclaimer , for information purposes this answer lists all known labs that do these measurements, and LANL does not endorse any of these). Weili Cheng, a pioneer in crack compliance does measurements through BEAR, inc. Hill Engineering does commercial measurements and has a nice page on the technique. In Europe, Mat-Tec does measurements. Back to top

Can I measure shot peening or other near-surface stresses?
See shot peening page for an example and a discussion. There are limits on how thin a layer. Machining stresses would be difficult but possible with care. Also see answer for micro/nano size applications. Back to top

Does it matter how you make the cut? I want to use a saw or a milling cutter, not EDM.
A back gage (opposite the cut) is relatively insensitive to cutting stresses, so a milling cutter with care should be fine. A top gage is much more sensitive to cutting induced stresses, so it can make a bigger difference if you are trying to measure near-surface stresses. See the next answer for more on top and back gages. Back to top

Do I need a gage on the top (near the beginning of the cut) as well as the back (opposite the cut)?
An additional gage on the top face close to the cut (several top gages visible in pictures on home page) can improve the results, but it is more difficult to work with because you will cut very close to it. What the top gage will do, if you use one, is improve the results for the first 5-10% of the cut depth. The back gage all by itself can get very good results for stresses from about 5% of the thickness to 95%. Back to top

Are the strain measurements taken at intervals or in real-time as the cut is being made?
Intervals. We stop cutting, wait for the strain gage to stabilize, and take a reading. Some researchers have use real-time readings, but special care is required. Back to top

Do you measure the temperature to ensure it does not have an effect on strain readings?
We usually try to do EDM cutting underwater, and the temperature is extremely stable. Also, we use thermally compensated strain gages and a 3-wire quarter bridge setup to minimize temperature effects. Still, when we use mechanical cutting (e.g., sawing) we wait long enough for any temperature effects to settle out before taking a reading. Back to top

How many cuts should I make?
This conference paper shows that a minimum of 25 cuts for a through-thickness measurement reduces errors quite a bit. I usually try to make 30 to 40. Back to top

What strain gage coating do you use?
Professor Mike Hill at U.C. Davis has studied different coating for use with slitting. He uses an acrylic coating and then paraffin wax on top of that. Each layer should overlap the previous layer by a reasonable amount. For cases with very large strains, a more ductile coating (silicone rubber instead of acrylic) may be necessary. Back to top

Do you trim the gages so you can cut closer?
When performing a near-surface stress measurement with a "top" gage (several top gages visible in pictures on home page or see figure 1 in literature review pdf for terminology) we will trim the foil backing on the strain gage so that the cut can be closer to the gage for better sensitivity. We will not trim all the way up the the grid. For example, on this Micromeasurments gage , we would trim away most of the alignment arrow in front of the gage, but no more than that. Back to top

Is it important how I hold (clamp) the part during cutting?
Yes, the part must be free to deform correctly so the strain readings are correct. The part should be clamped away from the cut and strain gages. It should be clamped on just one side of the part, with the other side free to move. See EDM page for a sketch of a clamping arrangement that won't affect the strain readings. Back to top

Can the cut close on itself? If it does close, what should one do?
Yes it can if you cut into a highly compressive stress field (the top and back gages will be reading tensile strain). You don't want closure to happen, because the strain readings will be "wrong." While cutting is stopped for strain readings, use a feeler gauge to see if the cut is closed. If it is about to close, you need to open up the cut. With EDM, you can cut back out from the cut tip, but sometimes it works better to cut back in from the beginning of the cut. Beware if you have a top gage: cutting back out can remove material and change the cut face to top gage distance, which you need to measure accurately and you usually measure after the test is done. Do your best to measure this distance (maybe take a high-res photo) before you change it. Back to top

Is there any information available about the most appropriate EDM parameters to make the cut?
There really is not information on specific parameters, but you probably don't want to worry about specific settings for each parameter on an EDM machine. I use settings provided by the manufacturer that are called "skim cut" or "finishing cut" settings. Most machines have similar settings, but the terminology differs by manufacturer. In order to get the best surface finish, most machines have settings for 4 or so successive cuts, where each successive cut has decreasing power. You probably want to use the settings for the 2nd or 3rd of these cuts. Practice on your material and see what cuts slowly without being too slow and without the wire breaking. Back to top

Can slitting be applied to micro/nano sized applications?
Yes. See the 2004 paper by K.J. Kang et al. Using focused ion beam (FIB) machining, one can make a sub-micron sized slit. SEM imaging can then get nanometer-scale displacements. Back to top

Is there commercial software for doing compliance calculations?
Unfortunately, no. See Resources and Help for a MATLAB script you can use. Or you can email me (Mike Prime) and I can email some other MATLAB scripts to you once you state you agree to the disclaimer. But be warned that this is not automatic software, you will need to spend some time and effort to learn to use it correctly. Back to top

How does one calculate the stresses?
See the theory page for a illustrated explanation and a paper you can download. We use a set of calibration coefficients that are least squares fit to the measured strain. The result is the residual stress profile (stress as a function of depth) expressed as a series expansion in polynomials. It a very robust way to reduce the data and is tolerant of experimental noise in the measured strains. Back to top

What is the best way to calculate or obtain calibration coefficients (compliance functions)?
Lee, MJ ; Hill, MR, 2007, "Effect of strain gage length when determining residual stress by slitting," Journal of Engineering Materials and Technology, 129(1), 375-382. Has a table of compliances for the back face gauge on a beam. Ready to use! Back to top

In the scripts I provide (see previous answer) there are FORTRAN programs for a couple simple geometries (back gage or top gage on a beam). This most versatile way is to use a finite element model, and it really is not that difficult. A paper by Rankin et al. (reference) has a good explanation of FEM calculations of the calibration coefficients. I can provide a couple sample ABAQUS input decks if you email me (Mike Prime). Back to top

My top gage and back gage disagree or give different results, why?
In such cases, the top gage results are often in error. Because it is so close to the cut, the top gage results can be affected by yielding as the stresses relax during cutting. Similarly, the top gage can be affected by stress introduced by the cutting process. For these reasons, the back gage results are often more reliable. A top gage will also be affected by shear stresses if they are present (see MMC example of significant shear stresses). (Using top gages on either side of the cut can let you measure the shear stresses). Also, the top and bottom gages can give different results of the stresses vary in the out-of-plane direction (which would be contrary to the assumption that on the plane of the cut, the stresses only vary in the direction of cut depth extension). Back to top

What if I can't fit the data well with a series expansion?
Use the pulse method. See shot peening page for an example and a brief discussion. Pulse method: Schajer, G. S., and Prime, M. B., 2006, "Use of Inverse Solutions for Residual Stress Measurements," Journal of Engineering Materials and Technology, 128(3), 375-382. preprint (pdf). (LA-UR-04-5890) Back to top

When should I use plane stress or plane strain compliances?
The 3D paper gives a simple correction to compliances for 3D effects. See the summary in the 2nd paragrapn of the conclusions. With slightly less accuracy, just use plane stress when the width of a beam is less than 0.7 times the thickness, and plane strain when it is more.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.
<p class="location">.
<p class="location">.
<p class="location">.
<p class="location">.
<p class="location">.
<p class="location">.