Fracture Mechanics: Proving Stress Intensity Factor Superposition Principle

[phyo_myatk]

TL;DR Summary

I am calculating Stress Intensity Factors (SIFs) of a flat plate by using the superposition principle (photo attached). Although I have succeded in some FE models, the results are strange for some models. The stress intensity factors are having fluctuations. I would like to know your opinion on this matter. Please have a look at the details. Thank you very much!

I am trying to prove the superposition principle of stress intensity factors (SIFs). The superposition principle states that the stress intensity factors obtained from the boundary loading are equal to those obtained from the crack face traction loading.

I used a flat plate model with the size of (L=124mm, W=50mm, H=22mm). The flat plate has a surface crack at the center (crack length=9mm, crack depth=3.5mm). I used WARP3D open-source code for SIF analysis.

Firstly, the loading is applied at the boundary of the model. And the SIF is calculated under the applied loading. The results (mentioned as case_1 in the figure)obtained for this case are correct compared to the reference solutions.

And then, the same FE model is used for crack face loading. The model is completely the same except for the loading condition. The input is also the same as the previous case. But, the SIF results for this crack face loading are having fluctuations along the crack front (results are mentioned as case_3 in the attached figures).

Firstly, I thought there is an error with the FE modeling. So, I checked the models again, and also tried to regenerate the new models from scratch. The solutions give the same behavior.
Secondly, I checked the functionality of source code, WARP3dD. The codes work fine for the other models.

Thirdly, I also tried other models including flat plates and welded joints. In some cases, the principle is correct. But, in some cases, the solutions for crack face loading conditions are fluctuating.
Finally, I checked if there is any non-uniform stress distribution on the crack face. But, the fluctuations are regardless of loading conditions. Even though the loadings are uniform (in case of flat plate), the SIFs are still fluctuating.

Please let me know your opinion on this matter. I would really appreciate your help.

 

[Illmatic1]

One possible explanation for the fluctuating SIFs could be that the crack face loading is not being accurately modeled. In order to accurately model the crack face loading, it is necessary to account for the details of the crack geometry, such as the angle and depth of the crack. Furthermore, the loading should be applied in a manner that accounts for the stress concentration around the crack tip. It is also possible that the mesh density is not sufficient near the crack tip, which could lead to inaccurate results. Finally, the material properties should also be accurately modeled in order to obtain accurate results. To better understand the cause of the fluctuating SIFs, it may be useful to compare the results obtained from a finite element model with analytical solutions. This would allow you to identify any discrepancies between the two solutions and determine if the fluctuating SIFs are due to modeling errors or numerical inaccuracies.