A new method of crack propagation X-FEM reliable, robust and powerful

26 March 2012

by D. Colombo, University of Manchester

A new method for crack growth simulation, based on the X-FEM which avoids to explicitly mesh the crack, is available in PROPA_FISS. This method, called "geometrical", is based on an implicit representation of the crack by means of two level set functions, as in the case of the "upwind" and "simplex" methods already available. However, unlike these ones, the update of the level sets consequent to the propagation is based on a geometric calculation and not on the resolution of Hamilton-Jacobi partial differential equations. The new method differs also from the "maillage" method available in PROPA_FISS, which calculates the two level set functions locating the crack by means of a mesh representing the crack surface and independent from the structural mesh.

Figure 1 : 3-points bending specimen containing an initially planar crack with a straight front inclined by 45 °, subjected to a fatigue mixed mode I + II + III condition by the effect of the cyclic loading F.

With this new method, crack propagation simulation gets more stabile, more robuste and much faster. In the 3D mixed mode I + II + III propagation test shown in figures 1 to 3, the geometrical method is 2 to 7 times faster than the "maillage" method. Unlike this one, the calculation time for the geometrical method is independent of crack extension and is constant throughout the whole propagation simulation. It is also 3 to 5 times faster than the "upwind" method with calculated crack fronts, and crack surfaces that are much smoother. In this case, the "simplex" method, second available method based on the integration of Hamilton-Jacobi equations to obtain the level sets evolution, fails to converge.

Figure 2 : View of the crack propagation on the surface of the specimen.
Figure 3 : View of the crackfronts and surface during propagation. The change in the orientation of the initially planar crack surface is clearly shown.

The localisation of the computational domain where the the crack level sets are updated, which was introduced for the “simplex” and “upwind” methods, is not recommended with this new method because it can be time consuming, except for very large meshes. Finally, the regular auxiliary grid used to solve Hamilton-Jacobi update equations is no longer necessary, which greatly simplifies the implementation of the propagation process.

Finally cases of crack front splitting and merging during the propagation are automatically taken into account by this new method, without any intervention from the user, as for the other methods of crack propagation.

Figure 4 : View of a mode I propagation of an initially semicircular crack. The crack front splits in two fronts which merge later during the propagation due to the presence of the hole.
Figure 5 : Top view of figure 4 showing the crack front evolution. The initially semicircular crack is located at the bottom, in the middle of the section.

This work is the subject of a publication: D. Colombo. An implicit geometrical approach to level sets update for 3D non planar X-FEM crack propagation. Computer Methods in Applied Mechanics and Engineering, published online.