# Crack propagation and crack coalescence in a multiscale framework

Leaders: | S. Löhnert, P. Wriggers |

Team: | M. Holl |

Year: | 2010 |

Date: | 29-11-11 |

In this project the long life fatigue strength of regenerated components will be simulated within the joint research project SFB 871.

Hence a numerical framework for propagating and intersecting cracks on micro and macro scales is set up. Modeling cracks using the eXtended Finite Element Method (XFEM) provides an accurate and efficient numerical framework to model propagating and intersecting cracks: The new crack geometry can easily be updated without changing the mesh topology.

Capturing micro and macro cracks with either the XFEM or the FEM in a single scale analysis is either inaccurate or numerically inefficient. Assuming large differences in length of macro and micro cracks allows scale separation and thus the application of the so-called multiscale projection method. This method is able, compared to other multiscale methods, to take localization effects on the micro scale into account.

The main goal of this project is the fully adaptive coupling between the XFEM for propagating and intersecting cracks with the multiscale projection method.

To show the benefit of the proposed multiscale method and the need of taking micro localization effects e.g. microcracks into account, a domain as depicted in figure 1 is investigated. The structure contains two macrocracks and about 150 microcracks randomly distributed in the domain.

Figure 1:* Macrocracks (red) and about 150 microcracks (blue).*

Loading the linear elastic structure results in crack propagation and crack coalescence as depicted in figures 2-4. The propagating macro crack interacts with the surrounding microcracks and merges with some of them. Finally the propagating macrocrack intersects the second macrocrack and one of the other two crack tips propagate. The full simulation is available as movie as well.

Figure 2:* **First crack coalescence: Macrocrack intersects with a microcrack (von Mises stress).*

Figure 3:* **Crack coalescence influences crack path significantly (von Mises stress).*

Figure 4:* **Finally both macrocracks intersect (von Mises stress).*

This leads to a decreasing stiffness of the material, as displayed in figure 5. Due to coalescence with other cracks, the load factor is not only decreasing but also increasing. In a singlescale analysis the load factor is only decreasing since no microcracks are assumed. Hence microcracks may have a great impact on the needed external load to perform crack propagation.

Figure 5:* **Load factor diagram for a singlescale and a multiscale analysis. The gray points refer to figure 2-4 before and past crack coalescence.*

Furthermore figure 5 shows that the external load needed for the first crack propagation steps is higher in the singlescale analysis than in the multiscale computation. The reason for this phenomena is the presence of microcracks around the propagating macrocrack tip: A microcrack shields the macrocrack tip and thus leads to lower stresses around the macrocrack tip as displayed in figure 6. Thus the external load needs to increase to perform crack propagation.

Figure 6:* **Microcrack shields propagating macorcrack (von Mises stress).*

Finally the crack paths for a singlescale computation and a multiscale analysis are displayed in figure 7. Even though both computations lead to intersecting macrocracks, the crack paths differ significantly due to the presence of micro cracks in one simulation. Hence the effect of micro cracks cannot be neglected.

Figure 7:* **Singlescale analysis (left) and multiscale analysis (von Mises stress).*