Cohesive zone models of localization and fracture in bone

Abstract

Previously published experimental data for the fracture of bone are analysed using cohesive zone models to deal with the non-linear processes of material failure. Non-linear effects dominate tests; linear-elastic fracture mechanics cannot give an internally consistent account of the data. In contrast, the same cohesive traction law can account accurately for substantial differences in the fracture data for normal (non-diseased or aged) adult human humeral cortical bone taken at two laboratories, where different specimen configurations were used. Further model calculations illustrate more general characteristics of the non-linear fracture of bone and demonstrate in particular that the fracture toughness of bone deduced via LEFM from test data is not a material constant, but will take different values for different crack lengths and test configurations. LEFM can be valid only when the crack is much longer than a certain length scale, representative of the length of the process zone in the cohesive model, which for human cortical bone ranges from 3 to 10 mm. Naturally-occurring bones and the specimens used to test them are not much larger than this dimension for most relevant orientations, implying the necessity of non-linear fracture models. The analysis of fracture data also requires proper representation of the approximately orthotropic elasticity of the bone specimen. The fracture test data show that human humeral cortical bone is much more compliant in shear in the plane of the test specimen than would be inferred from the relevant Young’s moduli, if the material were isotropic in that plane, as is often assumed. If the specimen is incorrectly assumed to be isotropic in that plane, the initial measured compliance cannot be reproduced to within a factor of four and the fracture toughness deduced from the measured work of fracture will be overestimated by ∼30%.