Introduction

The optimal meshing strategy for the computation of accurate fracture mechanics parameters at crack tips or along crack fronts depends on 1) the reference (e.g. Planar, 3D), 2) the crack shape (e.g. straight, elliptical), and 3) the element topology (e.g. hexahedra, quadratically mapped tetrahedra).

The following provides tips on the optimal methodologies for meshing crack geometries in 2D and 3D, as well as extracting high-quality SIFs and J-integrals at crack tips/along crack fronts. For more details on fracture mechanics parameter computation, refer to the Fracture Mechanics Analysis Overview.

Planar and Axisymmetric Analysis

It is possible to use coarse meshes for the computation of the fracture mechanics parameters for two-dimensional (Planar) and axisymmetric problems. Care should be exercised in such cases because the dependence of the results on the size of the integration circle can be more significant.

• Numerical evidence indicates that for most practical cases in two-dimensions, the coarse mesh approach should give results which will not differ by more than 4 or 5% from those obtained with two (2) layers of graded elements.

The following guidelines should be followed when designing a coarse mesh near crack tips for planar and axisymmetric analyses:

• Avoid very distorted elements near the crack tip.
• Keep the size of the elements near the crack tip about the same.
• If hand-meshing the model, use quadrilateral elements around the crack tip and select the product space.

When computing SIF or J-integral, select the radius of the integration path such that it runs roughly through the middle of the smallest element around the crack tip.

• Theoretically the extraction should be path independent.
• The size of the integration path can be chosen arbitrarily, provided it remains inside the domain.

For an example of a meshing strategy for a 2D thru crack at a hole edge, refer to StressCheck Demo: 2D Fracture Mechanics Analysis.

3D Analysis

As discussed in the “Note About the CIM in 3D” in the Fracture Mechanics Analysis Overview and well as in Computation of SIFs in StressCheck, it is recommended to use the following guidelines when designing meshes for the computation of fracture mechanics parameters in 3D:

Hand Meshing

For geometries/cracks in which the model domain is to be hand meshed with hexahedral and pentahedral elements, it is recommended to incorporate at least two layers of geometrically graded elements towards the crack tip with a common factor of 0.15. An example of two layers of geometrically graded hexas/pentas around a 3D crack front at a symmetry plane is shown above in Figure 2.

For a detailed example of hand-meshing a part-thru crack, refer to Part-Thru Crack Hand Mesh Best Practices.

Automeshing

For geometries/cracks in which the model domain is to be automatically meshed with quadratically mapped elements, it is recommended to use the automatically generated parameters for the Crack Front automesh method. The default parameters will produce a mesh with 4 geometrically graded layers of pentahedral and hexahedral elements plus an additional integration layer.

• The integration layer is added around the innermost layer where the integration path for fracture extractions lies (Figure 4).
• This helps keep the aspect ratio of the elements where extractions occur near 1 and reducing the stress gradient on the elements where the extraction is performed, which increases solution quality without significantly impacting overall element count.

The Ratio and Radius values are selected based on the crack size to provide an optimal aspect ratio of elements in the innermost layer. The D/H value will provide minimal deviation of element edges to the underlying geometry and allow the mesh to refine more in areas of high curvature for irregularly shaped cracks (Figure 5).

There is also an additional option to geometrically grade the mesh toward the ends of the crack. This feature is particularly useful if the singularities at the free surfaces are having a particularly strong effect on the distribution of stress intensity factors (Figure 6).

• This is usually observed in the form of oscillations near either end of the crack.
• Similar to the layers around the crack front, the ends are graded geometrically with a factor of 0.15.
• Two layers are used on each end and their size is calculated based on the length of the selected crack curve. The first layer is sized at 0.15³ times the curve length and the second layer is 0.15² times the curve length.

The above examples have all shown the Crack Front mesh with the “Mixed Mesh” option on. In general, this is the best approach for obtaining the most accurate fracture mechanics values with the least computational investment.

• If the toggle is switched off, the mesh will be generated using all tetrahedrons.
• Since tetrahedral elements are much more sensitive to high aspect ratios, the default settings will change to produce a mesh with only 2 geometrically graded layers rather than 4.
• The integration layer may still be used to add a 3^rd layer to aid in extractions but, in general the mixed mesh will produce the best results.

An example distribution of Mode I stress intensity factor along a through crack in a large plate is shown in Figure 7 below. Note how the oscillations close to the ends disappear with the introduction of the end gradation option:

• For elliptical or semi-elliptical cracks, refer to Helpful Hints and Tips: Elliptical Crack Automeshing Guidelines.
• For tips on generating boundary layer automeshes at crack fronts, refer to MeshSim Automesh Generation Methods.

When extracting fracture mechanics parameters for hand-meshed or automeshed domains, the integration radius should be just outside the innermost layer. This applies to both Points and Fracture tab extractions. Note that when “AUTO” is selected for the integration radius (available in StressCheck v11 and newer), StressCheck will automatically compute the appropriately-sized integration radius following this guideline.

For examples of automeshing strategies for 3D part-thru cracks, refer to StressCheck Demo: Part-Thru Crack SIFs for Stiffened Lug and StressCheck Tutorial: 3D Crack with Curve Refinement.