Add a J-integral subnode under a Crack node in order to compute the J-integral along a certain integration path. When a J-integral has been computed, stress intensity factors will also be available.

An alternative to using J-integral evaluation is to use the Virtual Crack Extension method.

Enter the Radius of contour integral, rΓ. The default value is an expression of the form solid.<crack_tag>.crackSize*0.5. The variable crackSize is estimated from the crack geometry. For common cases, in particular in 2D, this is exactly the length of the crack. For more complex cases, in particular for branched cracks, there is no well-defined crack length, and the value of the variable must be considered only as being of the right order of magnitude.

When computing stress intensity factors from the scalar-valued J-integral, an additional relation is needed in order to separate KI, KII, and (in 3D) KIII from each other. To perform this separation, the ratios between the displacement jumps in different directions across the crack surface are computed. The location for sampling the displacements should ideally be close enough to the crack tip, so that the field is governed by the crack tip singularity. On the other hand, it is not possible to evaluate too close to the crack tip, since the local solution is then not accurate as an effect of that same singularity. Rather than sampling displacements at a certain point, the ratios are averaged over a certain region. The default averaging region starts at 20% of the crack length, and ends at 50% of the crack length.

To change the size of the averaging region, enter the lower bound, b, and upper bound, c. If you are using a fine mesh around the crack tip, it is possible to use values significantly smaller than the default ones. Having the lower bound at a distance of two elements from the crack tip is sufficient.

Select Number of integration points — Fixed number or Relative to path length.

When Fixed number is selected, enter the total number of points along the integration path, NΓ.

When Relative to path length is selected, enter a relative number of points along the integration path, nΓ. The total number of integration points is computed as

where rΓ is the radius of the integration path, and Lcrack is the crack length (as represented by the variable solid.<crack_tag>.crackSize).

Select Number of integration points — Fixed number or Relative to enclosed area.

When Fixed number is selected, enter the total number of integration points on the enclosed surface, NA.

When Relative to enclosed area is selected, enter a relative number of points on the enclosed surface, nA. The total number of integration points is computed as

where rΓ is the radius of the integration path, and Lcrack is the crack length (as represented by the variable solid.<crack_tag>.crackSize).

The default is that the region used for the evaluation starts at a distance of 20% of the crack length from the tip, and extends to half the crack length. You can modify these values by entering a Lower bound, b, and an Upper bound, c.

Physics tab with Crack node selected in the model tree: