An analysis of fracture in staggered mineralized collagen fibril arrays

Abstract

Fracture resistance of bone arises from various toughening mechanisms at multiple hierarchical levels. Despite considerable effort devoted to identification of fracture mechanisms associated with the ingenious hierarchical structure of bone, how the structural elements at the submicroscale contribute to the toughness of bone is largely unknown. In this study, the calculations are carried out for a biological composite consisting of mineralized collagen fibrils (MCFs) embedded in an extrafibrillar matrix (EFM), and the individual effects of the parameters associated with energy dissipation in the EFM are elucidated. The intrafibrillar plasticity through mineral/collagen sliding, the interfibrillar sliding and the mechanism of energy dissipation of the EFM are incorporated in the computational model. Furthermore, the staggered arrangement of MCFs and the fracture of the interfaces between MCFs and the EFM are accounted for. It is found that high stiffness of the EFM gives rise to enhanced energy dissipation in the EFM and reduced damage of the MCF/EFM interface. In addition, plastic deformation in MCFs is activated by the high stiffness of the EFM, which promotes energy dissipation, thereby enhancing toughness of the MCF arrays. The low initial yield stress of the EFM plays the roles in increasing energy dissipation in the EFM, promoting plastic deformation in MCFs and mitigating fracture of the MCF/EFM interface. The fracture behavior of MCF arrays is also influenced by the post-yield strain hardening behavior of the EFM; strong strain hardening enables diffuse damage of the MCF/EFM interface. We further reveal that strong post-yield strain hardening of MCFs increases the propensity of damage of the MCF/EFM interface and delays plastic deformation in MCFs. The findings of this study can not only shed new light on the fracture mechanisms of the staggered MCF arrays, but also provide mechanistic insights into bioinspired materials design.