Role of strain rate sensitivity of extrafibrillar matrix on fracture in mineralized collagen fibril arrays

Bone is a biological composite possessing complex hierarchical structure, which endows it with extraordinary damage tolerance. Despite the progress on the relationship between fracture behavior and the hierarchical structure of bone, contributions of the submicroscale constituents to fracture resistance of bone remain elusive. In this study, the calculations are carried out for fracture in staggered mineralized collagen fibril (MCF) arrays using the cohesive zone framework. The strain rate hardening of extrafibrillar matrix (EFM), post-yield strain hardening of the EFM, plastic deformation of the MCF caused by mineral/collagen sliding, and debonding of the interface between MCF and EFM are accounted for in the analyses; the individual and combined effects of strain rate sensitivity of the EFM and fracture properties of the EFM-MCF interface are revealed. It is found that for the strong EFM-MCF interface, high degree of strain rate sensitivity of EFM gives rise to low toughness of MCF arrays. Compared with plastic deformations in MCFs and EFM, interfacial debonding provides smaller contribution to toughness of MCF arrays, and plastic dissipation of MCFs is the major source of toughening. For the tough EFM-MCF interface, the toughness of MCF arrays increases with increasing degree of strain rate sensitivity of EFM, and the EFM with high degree of strain rate sensitivity promotes spreading of plastic deformation, leading to amplified damage energy dissipation in interfaces. We have further identified that strain rate sensitivity of the EFM has negligible influence on toughness of MCF arrays in the case of weak EFM-MCF interface, where interfacial debonding serves as the major toughening mechanism. However, the strain rate sensitive EFM can still activate the mechanism of spreading plastic deformation in this case, giving rise to the increase in relative contribution of plastic dissipation in MCFs with increasing strain rate sensitivity of the EFM.