J-Integral
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.
The J-integral node is only available with some COMSOL products (see https://www.comsol.com/products/specifications/).
J-integral
The J-Integral is computed along a circular path centered at the crack front.
For 2D components, the integration path for the J-integral can be described either by a sequence of boundaries, or as a circular path around the crack tip. Select Integration path — Circular or On edges.
If On edges is selected, a new section, Integration path is shown. In that section, select the boundaries that define the integration path. The boundaries much be selected so that they form a contiguous path from one side of the crack surface to the other. In case the crack is located on a symmetry plane, the path should go from that plane to the crack surface.
For the case Circular, see below.
Circular Integration Path
Enter the Radius of contour integral, . 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.
The integration path must not intersect any external boundaries or internal slits, such as other cracks. There should also not be any holes or applied loads inside the integration path. Integration paths with a very small radius compared to the crack length will in general give low accuracy, since they will pass through the singular stress field in the vicinity of the crack tip. It is good practice to evaluate the J-integral along several paths, to assess the accuracy.
In 3D, the J-integral will vary along the crack front. It will be computed along several circular paths, centered at different locations along the crack front.
Stress Intensity Factors
When computing stress intensity factors from the J-integral, the
Integration
In this section, you can adjust the accuracy of the numerical evaluation of the J-integral. The section is only shown when circular integration paths are used.
Integration on Contour
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, .
When Relative to path length is selected, enter a relative number of points along the integration path, . The total number of integration points is computed as
where is the radius of the integration path, and Lcrack is the crack length (as represented by the variable solid.<crack_tag>.crackSize).
Integration on Surface
In 3D and 2D axisymmetry, the J-integral also has contributions from the surface enclosed by the integration contour.
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 is the radius of the integration path, and Lcrack is the crack length (as represented by the variable solid.<crack_tag>.crackSize).
Stress Intensity Factors
In order to separate the stress intensity factors for the different crack modes, the displacements on the crack surfaces are analyzed. In order to get a good value, this analysis should be performed in a region where the theoretical solution for the fields around a crack tip is valid. Ideally, this is close to the crack tip. It is, however, not possible to get an accurate numerical evaluation very close to the crack tip, due to the singularity of the fields.
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.
See also J-integral Theory in the Structural Mechanics Theory Chapter.
Location in User Interface
Context Menus
Solid Mechanics>Crack>J-Integral
Ribbon
Physics tab with Crack node selected in the model tree:
Attributes>J-Integral