Application of Elastic-Plastic Fracture Mechanics to Determine the Locational Variation in Fracture Properties of Cortical Bone

Abstract

The complex nature of bone material results in a locational variation of fracture and mechanical properties. The heterogeneity associated with bone material and complex hierarchical assembly results in several toughening mechanisms, such as plasticity, micro-cracking, viscoplasticity, etc. These toughening mechanisms and presence of water in bone material makes the linear elastic fracture mechanics (LEFM) inapplicable in such materials. The present work is focused on the elastic-plastic fracture mechanics (EPFM) approach to estimate the locational variation in fracture properties of buffalo cortical bone for longitudinal, as well as transverse orientation of cracking. Samples from upper, middle, and lower locations of bone diaphysis were tested using compact tension and single-edge notch-bending testing methods for longitudinal and transverse orientation of cracking, respectively. The crack-tip opening displacement (CTOD) approach was applied to determine fracture properties, such as CTOD toughness (δc), J integral (Jcδ), and equivalent fracture toughness (Kδc) at different locations of bone diaphysis. The effect of orientation and location on mechanical properties of cortical bone, such as elastic modulus (E) and yield strength (σys), was also analyzed with the help of tensile testing. The equivalent fracture toughness values (Kδc) obtained in the present work were found to be three times higher than the corresponding values reported in the previous reports where the LEFM approach was applied favoring the application of EPFM for bone materials. The mechanical properties, as well as the fracture properties, were found to be maximum at middle location and minimum at lower location of bone diaphysis. The locational variation in fracture and mechanical properties observed in the present work are considered to be because of locational distribution of collagen fibrils, minerals, porosity, and density at different locations of bone diaphysis.