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Suppose I have a piece of metal (of arbitrary geometry) with some residual stress profile. I then remove a chunk of the metal and the piece of metal deforms (due to the residual stress). For simplicity, assume that the material removal process does not introduce residual stress (due to the metal heating up and cooling down, etc.)

I would like to quantify how the residual stress field of the piece of metal changes due to the material removal.

I have done some experiments in FEA to get some intuition, but I'm struggling to quantify/formalize what I'm observing.

This screenshot shows the Von Mises Stress of a rectangular metal bar before material removal: enter image description here

This screenshot shows the Von Mises Stress of the same rectangular metal bar after material removal. As you can see, the bar has bent due to the residual stress. enter image description here

When I probed the stress tensors of various elements, I noticed that the stress tensor entries change (across the material removal) for elements which are both close to the region of material removal and far from the region of material removal. Is this expected behavior? Will it always be the case that the stress tensors which are close to the region of material removal will change more than the stress tensors which are far away from the region of material removal?

If folks know about any relevant literature, please point me to it. Thank you!

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    $\begingroup$ If parts are modeled as nodes connected by springs, energy stored within would be loaded springs. Cutting other springs that were preventing loaded springs should release some loaded springs and reduce internal stress. Expect your FEA to show some fishy stress values due to what node locations it considers to be 0 stress. $\endgroup$
    – Abel
    Nov 30, 2023 at 6:55

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I would like to quantify how the residual stress field of the piece of metal changes due to the material removal.

For this, I would recommend analysing relatively simple beam bending of a bimetallic beam loaded by temperature. It can have rectangular section, each half from one of the metals. When the temperature changes from initial state without stresses, there are thermal stresses in the beam due to different thermal expansions of each metal, so the beam bends and there will also be some residual stresses. If there are no other external loads, you can calculate the stresses from condition of zero axial force in the whole section (sum of axial stresses) and zero bending moment caused by axial stress distribution in the section.

You can also "remove" part of the section and recalculate resulting stress distribution and deformation.

Will it always be the case that the stress tensors which are close to the region of material removal will change more than the stress tensors which are far away from the region of material removal?

If there is just residual stress and the structure is not subjected to any external loads, it might be the case. There can also be no change whatsoever, if the removed part had zero stress.

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