Multiple methods exist for simulating crack propagation in the finite element method (FEM). Among these, the extended finite element method (XFEM) shows great potential as it allows for the use of larger elements while maintaining accuracy and practicality. Within XFEM, the employment of traction separation laws (TSLs) is a promising approach to capture post-necking effects, which are typically predicted poorly with larger elements. These TSLs are often assumed to be constant along the crack length and are determined by fitting to experimental data.

However, it has been proven that necking and fracture both depend on the state of stress, expressed as stress triaxiality. It is also known that the stress triaxiality within the crack region varies as the crack progresses through a plate due to changing boundary conditions and crack blunting. Consequently, the necking behaviour ahead of the crack tip changes, necessitating multiple stress state-dependent TSLs along the crack length to capture this effect accurately.

In this thesis, a subroutine is developed to enable the use of multiple TSLs along an extending crack in Abaqus based on the stress triaxiality of each element. Additionally, the relationship between TSL parameters and stress triaxiality was determined by minimizing the difference between simulations and experimental data of a large-scale CCT experiment. With this relationship known, it is possible to account for the effect of the changing stress state when determining the TSLs.

The study finds that stress triaxiality-dependent TSLs produce a significantly better match with experimental results compared to a stress triaxiality invariant TSL. This underscores the importance of addressing stress-state dependency in TSL determination. The study also highlights that mesh size and material dependency on TSLs must be addressed so that these TSLs can be applied universally across different conditions.