The Investigation of Crack Propagation in Cortical Bone using a Phase Field Fracture Approach

Sammanfattning: Human cortical bone tissue is a complex and strong composite material, with the ability to resist damage via slowing, stopping or redirecting propagating cracks. However, the ability is impaired with age. At the microscale, changes are seen both in terms of increased porosity and as changes in local material parameters. The microstructure is based on circular concentric layers of bone tissue, called osteons, which surround the Haversian canals. The osteons are embedded in an interstitial matrix, and are separated by weak interfaces called cement lines. Both local material parameters and the effect of local toughening mechanisms are difficult to evaluate experimentally. Thus, computational models can be used as a complement. The aim of this thesis was to investigate crack propagation in the microstructure in cortical bone using a phase field fracture approach. The phase field method is a continuous damage model in which the crack is allowed to advance if the energy release rate exceeds a critical limit. The crack is described by a crack density function which is dependent on a diffuse damage field. In this thesis, a phase field framework based on open source codes was implemented as a user-defined element subroutine in Abaqus. The framework was evaluated using typical benchmarks tests commonly used in the literature. Realistic cortical bone models in 2D were created from microscopy images. The crack propagation was investigated for different material parameters, geometries and levels of porosity. The critical energy release rate of the cement lines and the osteons affected the crack propagation. With a lower value for the cement lines and a higher value for the osteons compared to the interstitial matrix protected the osteons from damage and redirected the crack into the cement lines. The ability to deflect advancing cracks decreased with increasing porosity, which is in line with both numerical and experimental studies in literature. The phase field framework implemented in this work is a great tool for studying crack propagation in cortical bone. It could be used to further analyze the local mechanical properties and give additional insights in how the bone tissue is designed to resist fracture.