Problem in converging stress field at crack tip

[me516]

Hi,

I am currently modeling a stationary crack in a single edge cracked plate of hyperelastic material under mode-I loading with contour integral approach. I'm using quadratic elements without singularity control at crack front. The plate is loaded with prescribed displacements at plate boundaries such that J=1KJ/m2. Each time I run the analysis on Abaqus/CAE with a more refined mesh at crack tip, maximum principal stress increases with mesh density at crack tip. I've found the maximum principal stress at crack tip ranging from 1MPa to 45MPa till now (in different runs) with sufficiently refined mesh at crack tip each time and suspect it to increase further, if my computing resources allowed. This suggests that solution is not converging at crack tip. Please suggest something to fix this.
Note that the calculation of J-integral works fine in all runs.

Regards

 

[ESPcomposites]

I don't think there is anything to "fix". This is the expected behavior and also why the concept of a stress intensity factor was introduced. The point being is that the stress is theoretically infinite at the crack tip and also why fracture mechanics solutions consider results behind the crack tip to quantify the severity (as opposed to the value at the crack tip itself).

Brian

http://www.espcomposites.com

 

[me516]

Thanks for your comment Brian,

It is true that theoretically stress at crack tip should be infinite, however, numerical solutions do not incorporate (1/r) or (1/sqrt(r)) singularity and therefore should converge to a finite value... Consider the attachment. In this attachment abaqus shows maximum von mises stress to be 2.95MPa. I got even 45MPa for the same problem with extremely fine mesh at crack tip.
If it has to keep increasing with further refinement of the mesh then how should I interpret this stress field? And what inferences can I draw?

Wasim

 

[ESPcomposites]

Wasim,

No, FEM will always yield a finite value, but will not converge to a value at the crack tip. The key being that though the very tip will never converge, the area behind the tip will. Look at some finite distanced from the crack tip and compare your various models. If converged, they will yield the same value away from the tip. These finite values are then used to calculate SIF's, along with the basic fracture mechanics equations.

As far as references, a review of fracture mechanics may be in order. The concept of fracture mechanics is to consider a region of high stress intensity. It is nebulous by design. Failure occurs not by the infinite stress at the tip, but rather due to the overall intensity in the region. Though the tip is infinite, the area around it is not. By quantifying that area, we can define the area of high stress intensity. Not sure if that make sense, but I think that is where your breakdown may be.

Brian

http://www.espcomposites.com

 

[SWComposites]

You need to stop looking at stresses at a singularity and use a fracture mechanics based approach to determining crack growth.