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I've been studying the contour method for measuring residual stress. See https://www.lanl.gov/contour/ if you are not familiar.

In the contour method, a single cut is made all the way through the workpiece.

What if the cut was made only part of the way through the workpiece? Would such a cut be sufficient to estimate the component of stress normal to the cutting plane?

Has anyone ever tried this or seen any work which tries to do this?

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It depends what you mean by normal stress. Mean value of normal stress across a full section should be 0 if the specimen is not loaded in any way. So I presume you are interested in actual distribution of normal stress across the section.

I don't think partial cut would "cut it" in general case. You need to make the cut all the way through, so the newly created surface can fully relax and take a new shape due to residual stress.

If you do just a partial cut, there are infinitely many possibilities for residual stress in the uncut part of the cutting plane and also the cut section may not have free space to relax if there were local compressive stresses.

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