Modeling Fracture in ADINA
In the assessment of possible crack growth in structures such as power plants, heavy machinery and airplanes, the computation of stress intensity factors along 3D cracks using linear elastic fracture mechanics is extremely important.
Traditionally, the J-integral and stress intensity factors are calculated using a virtual shift technique based on nodal point virtual shifts, in which a mapped mesh is required around the crack front. However, for complicated components, it is frequently challenging to construct a mapped mesh around the crack front.
In ADINA System 9.1, 3D fracture mechanics calculations are significantly improved by the introduction of the SVS method of fracture mechanics. The SVS (station virtual shift) method includes the following features:
Because it is not necessary to construct a mapped mesh around the crack front when the SVS method is used, the amount of effort required to perform linear elastic fracture mechanics analysis is considerably reduced.
One fundamental idea used in the SVS method is that virtual shift domains are mesh-independent. As a consequence, when the fracture results are output at equally spaced crack advance stations, these stations are also mesh-independent, thus as the mesh is refined, the fracture results can be expected to become more accurate.
We illustrate the use of the SVS method with a 3D fracture mechanics problem already solved with ADINA Structures in the February 2012 Tech Brief. In the February 2012 Tech Brief, the meshing is somewhat complicated, due to the need to use a mapped mesh on the crack front. In addition, only the J-integral (and not the stress intensity factors) are calculated in the February 2012 Tech Brief.
In the current Tech Brief, we use the SVS method. This allows us to use a free-form mesh everywhere, and to calculate both the J-integral and the stress intensity factors.
Figure 1 shows the nozzle geometry along with a surface crack:
Cracked model definition
The cracked model is constructed as illustrated in the following figures.
Figure 8 Meshes for the nozzle body and crack bodies. The free-form mesh generation features
of the AUI are used for both meshes.
The new CRACK-SVS command of version 9.1 is used to define the SVS virtual shifts. The input for the CRACK-SVS command consists of
Figure 11 shows the SVS virtual shifts created by the CRACK-SVS command and Figure 12 shows the SVS virtual shift symbol.
Figure 13 shows some of the elements near the crack front along with the virtual shifts. The SVS domains are independent of the meshing and the crack advance stations do not coincide with nodes.
The following results are calculated by ADINA Structures:
The results for the first and last virtual shifts are not shown, since these virtual shifts correspond to shifts at the end of an open crack front, and the results from these shifts are not as accurate as the other virtual shifts. One reason for this inaccuracy is that the virtual shift domains for the ends of the open crack front are not entirely contained within the mesh.
The J-integral values are in very good agreement with the results given in the February 2012 Tech Brief.
The stress intensity factor results clearly show that mixed-mode conditions are present on the crack front.
Both the J-integral values and the stress intensity factor values are nearly independent of the radial domain chosen.
Clearly the SVS fracture capabilities of ADINA System 9.1 represent a significant advance.