What Are Some Tips for Automeshing 3D Cracks for Accurate SIF Computation?
When extracting stress intensity factors (SIF’s or K’s) along a crack front that has been automeshed with tetra elements, the recommendation is to have two layers of refinements close to each other to reduce the aspect ratio of the tetras in the region of extraction; this mesh refinement strategy will minimize the mapping effect in the results and is applicable both for SIF and J-integral extractions.
Mesh Refinement Strategy
The innermost layer radius (ri) is typically 0.152 times the characteristic length of the singularity (crack). For example, if the characteristic crack length is 0.1, the innermost layer radius of elements should be ri = 0.152*0.1 = 0.00225. Then, the next layer radius should be 0.152*0.1*2 = 0.0045.
Regarding the rationale for the number 0.15, the optimal grading is actually closer to 0.17 but 0.15 has shown to be sufficient for accurate computation of SIF’s. From “Finite Element Analysis by Drs. Szabo and Babuska, Chapter 6: Regularity and Rates of Convergence”, page 194:
The optimal grading is q = (√ 2 − 1)2 ≈ 0.17, which is independent of the degree of singularity λmin . In practice q = 0.15 can be used.Chapter 6, Regularity and Rates of Convergence, Finite Element Analysis
For additional information, refer to Fracture Mechanics Meshing Strategies.
SIF Computation Strategy
The discussions in Computation of SIFs in StressCheck addresses three important considerations when computing SIFs:
- Approximability of the exact solution,
- Effect of element mapping in the results, and
Assuming the above mesh refinement strategy is utilized, it is recommended to use an extraction radius just outside the first (innermost) layer radius of elements. For example if the first layer of elements is within a radius ri use 1.2*ri for extraction.
Note: in StressCheck v11 and newer, the integration radius available in the Points tab can be computed automatically for K’s and J’s. For additional information, refer to Fracture Mechanics Overview.
For an example of computing accurate SIF’s for 3D cracks, refer to StressCheck Demo: Part-Thru Crack SIFs for Stiffened Lug and StressCheck Tutorial: Crack Front Automeshing/Auto Integration Radius Features.
For additional information on fracture mechanics parameter extractions, refer to Fracture Mechanics Analysis Overview and Numerical Simulation Series: Fracture Mechanics Parameters.