My problem concerns a compact tension specimen in which there are weld induced residual stresses. The attached figure shows 2 residual stress profiles in the specimen ligament (specimen uncracked and specimen with a 10 mm fatigue crack extension).
The route I'd recommend would be to set up a Finite Element model of the specimen with residual stresses that correspond to the uncracked (as-machined) specimen; then introduce the cut that represents the fatigue crack, and extract information about the crack opening profile. This can be interpreted in a straighforward LEFM way to extract the K_res that I think you are trying to determine. You can also check for consistency between fatigue cracked sample RS and simulation - the difference _might_ tell you about the effects of crack tip (cyclic) plastic zone (alternatively, you might find that the resolution of your method is insufficient to pick it up).
If you know the residual stress in the CT specimen (I can't see your figure very well except to note that it is a CT sample) then you can select any path that enclosed the crack tip and evaluate the J integral on that path. Knowing J you have the crack tip K value.
A second method is to evaluate the strain energy in the CT specimen due to residual stress with no crack advance and then evaluate the strain energy again due to residual stress after the crack has slightly advanced. The difference in these energies when divided by the crack area of advance is the negative of the strain energy release rate, G. From G you have K residual.
If I had a high quality image of your figure then there may be additional ways to approximate the residual stress intensity factor.
Thank you both for your answers. M. Burns, if you click on the image, you are supposed to be able to see it zoomed. If it does not work, I would be happy to send it to you. Thank you.
You will need a numerical model no matter what - you can't compute the J-integral or strain energy from just the stresses on one line!
I see. Wouldn't the weight function method work for a known stress distribution?
You should use the Green's function for the C(T) recently published by Newman, et al in Engineering Fracture Mechanics. I have verified the accuracy of that work, and highly recommend it.
Residual stress intensity factors were computed from measured residual stress using a Green’s function for the C(T) coupon recently published by Newman, et al and numerical integration, paying careful attention to the singularity of the Green’s function .
I offer you to study these article:
Michael R. Hill,John E. VanDalen ,Michael B. Prime, "Measurements of Residual Stress in Fracture MechanicsCoupons"
Newman, J.C., Yamada, Y., James, M.A., “Stress-intensity-factor equations for compact specimen subjected to concentrated forces"
Wu, X.-R. and Carlsson, A.J., "Weight function and stress intensity factor solutions"
Bao, that's a nice paper. I am glad you suggested it, as I'd not seen it before. The good agreement you show between FE and WF methods is consistent with our work. However, we find that not all WF from the literature give good results for residual stress cases, even though they do give good results for the reference stress fields from which they were derived. For a basic residual stress field and a single-edge cracked plate, we find the Wu and Carlsson WF to be very good to crack size of about a = 0.8W. For the C(T), the Green's function from Newman, which I mentioned earlier and also referenced by Ali, above, is very accurate even for long cracks a/W = 0.9; you have shown fairly good results with the Fett and Munz WF for the C(T), and I am glad to see that; W&C's WF for the C(T) does not allow stress over then entire crack face, so we have never tried to use that one. We have not evaluated the center crack geometry, but I am glad to see your work on that.
There is one point raised in your paper with which I don't agree. You state that the disagreement in SIF for long cracks is a "limitation on the WF method", but I think that is not correct. In our work, we generally have found that errors at long crack sizes are due accuracies of the specific WF employed. I think it is better to acknowledge these as errors of implementation, and not limitations of the WF method; at the same time, developing a very accurate WF for a large range of crack size is difficult.
Again, thanks for pointing to your earlier paper; very nice work.
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