Auzie5:
To answer your basic question...., you can’t remove a coupon from the pipe without changing the residual stress in it and in the pipe around the coupon hole. And, in fact, if you could measure accurately enough the bend angle in the pipe would change from cutting out the coupon, because you have disrupted the equilibrium stress conditions (the residual stresses) after the bending process. I am aware of the drilling and strain gage method of assessing residual stress, and it pretty much seems to be the standard method today. It machines a std. hole out of the part and measures the strain change around that hole to determine the residual stress. I’ve never used the system you linked and haven’t studied the subject in some years. We didn’t have nearly as nice a set-up as shown in the video, but what they are doing is the same process as we were studying and learning.
Try this thinking on for size, and see if it fits your needs or understanding of your problem. At the same time dig out your Engineering Mechanics, Advanced Strength of Materials and Theory of Elasticity text books and start reviewing them on these topics. Let’s also start out with a simple rectangular beam section, in simple bending, a simple max. bending moment at the center of the beam. We’ve all seen this problem in our early engineering courses, so it may be a slightly simpler example, but the thinking is the same for a cold bent pipe, just a bit more complicated because of shape geometry, etc. The beam is loaded until the top and bot. fibers just start to yield, that’s L1 (load 1). If you continue the loading the locations (the planes) of the yielding fibers move inward toward the N.A. (neutral axis), that’s L2. You are starting to form a plastic hinge, but if you unload the beam, much of its deflection (Δ) will spring back, but not all of the deflection. This residual deflection (residual curvature) is because of the fiber blocks, t&b which have gone beyond yield, have taken a permanent set, and do not (can not) return to zero. And, in fact, material immediately adjacent to these yielded blocks is affected by the block’s yielded condition, and can not return to their initial fiber length either, and the sum of these is residual stress. If you reload the beam to L2, the beam will go back to the deflection which existed before, at L2. If you continue loading now, to L3, the deflection will increase and the two yielded stress blocks will grow, moving further toward to N.A. Now, unload the beam and a greater residual Δ will remain and the residual stresses will be different too, and these stresses will be at a new equilibrium within the member.
Now, look at a typical Stress/Strain curve for most common steels (metals) that we use. They show some linear slope upward as stress and stain increase from zero, that slope is the Modulus of Elasticity (Young’s Modulus), the material follows Hooke’s law; some construction steels have a distinct ‘yield point,’ and then a long plateau with a slight upward slope as stress and strain increase, before they reach a strain hardening region on the curve, at some significant strain. Many steels and other metals don’t have a distinct yield point, so we usually define a yield strength at a .2% strain offset on the curve, and their curves have some straight upward slope from zero stress & strain and then a more continuous upward curved shape, a gradually increasing strain hardening range. You should be able to find the above in some more detail in a good text book. ASM also has some good materials on the subject for various materials. Now, if we think of our beam again, and plot our loadings on the Stress/Strain curve; L1 happens at or near (a little below?) the yield point or yield strength of the material and if we stop just short of L1, the material will unload right back down the slope “E” (the Modulus of Elasticity) slope line. Now, if we reload the beam to L1 and continue on to L2 we will move up the plateau or curve to some higher stress and strain point, and if we unload the beam now, the material will unload from the L2 point on the curve, following a slope of “E” (Hooke’s law) & (parallel to the original “E” slope, to zero load/stress, but with some greater residual strain related to the residual beam Δ or residual stresses. If you reload the beam again, the material will move up the right-shifted “E” sloped line to the L2 point on the curve and then follow the curve up to the L3 load point on the curve. This reloading can basically be repeated on up the curve until the material fails. In fact, this is what you are doing every time you re-bump your pipe with the hydraulic ram, to increase the bend angle a little more.
This yielding and the residual stresses are usually not a problem for our daily design problems because the yielding and residual stresses are nicely aligned (oriented) with the primary stress fields of our loading in the structure/pipe in use. We bend the beam or pipe and release the hydraulic ram (unloading) and the material unloads from L2 or L3 on down the “E” slope to a significantly increased (right shifted) strain. When we apply our design loads to the beam or pipe the material moves up that “E” slope toward the L3 point on the stress/strain curve, never reaching that point if our design stresses stay below yield, or then continues up the curve if our design stresses exceed yield or the L3 stresses, as we apply our design load, and we hardly know the difference. Cold bending is usually not a problem under reasonable conditions, and most of our designs produce stresses below yield, so they are operating on the lower portion of the Stress/Strain curve, with no problem. We are operating below L2 or L3 on the Stress/Strain curve, but starting from a right shifted strain at zero load, and we are still operating well below the ultimate strength of the material. Alternatively, from some situations, you can get poorly arranged (aligned) or very high residual stresses, very stiff/restrained connections, nasty triaxial stress conditions, bad welding and welding details, where this all goes to hell in a hurry.
I think, that rather than testing to find residual stresses at one location for this kind of problem, you might be better off explaining the concept of this residual stress and how it comes to be, as I’ve tried to do above and let it go at that. When we cold bend the beam or pipe we can make reasonable stress calcs. for our bending operation, and then for our unloading operation, and finally for some residual stresses under simple enough conditions. When we reload it under design conditions we don’t allow the stresses to get that high again under normal conditions, and we know it’s starting at some shifted strain level and following the normal Modulus of Elasticity slope, and we know that under normal conditions this is not particularly detrimental to our designs and end uses. To start to actually try to measure these residual stresses and report on them on a regular basis, unless you are addressing a real significant issue or problem, may be starting something that quickly gets out of hand. You’ll never get a string of pipe built for actual use, becuase customers will want you to make 10 tests at every bend, so they can try to prove that they have reason to doubt your analysis and your engineering judgement. This has been working for years with normal pipe diameters, and bend radius’. I’m all for testing if it will prove something, but not just to increase costs, when there is no problem to be evaluated, and nothing to prove.