Engineering | Finite Element Analysis | Stress
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Most FE solutions are loosely based around contour integral approaches, as they include
the influence of significant plastic deformation accompanying the initiation and
stable growth of cracks.
The J-Integral uses a path independent contour integral
that encloses the crack tip. Mathematically it is a line integral in 2D where an
arbitrary chosen path for the line integral is required. Failure by initiation &
growth of a crack is associated with a critical value of J. Once it is found, the
critical stress intensity factor can be determined. In order to ensure that the path
used in the FE model is independent, multiple contours around the crack tip are usually
extracted automatically.
It is usual to use 8 noded quadrilaterals in such an analyses,
with one edge collapsed to zero length at the crack tip. The midside nodes of the
remaining non-zero length sides are usually placed at quarter the distance to the
edge not in contact with the crack tip. The reason being that it produces a singularity
at the crack tip & hence a solution is guaranteed.
Fracture - fe
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