Mesh Refinement Strategy

The innermost layer radius (r_i) 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 r_i = 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 [25]. 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
• Path-independence

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 r_i use 1.2*r_i 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.