Rate-dependent fracture modes in human femoral cortical bone

Abstract

An accurate understanding of fracture in human bone under complex loading scenarios is critical to predicting fracture risk. Cortical bone, or dense compact bone, is subject to complex loading due to the inherent multi-axial loading conditions, which are also influenced by the anisotropy of the microstructure. When determining critical fracture parameters, bone is traditionally idealized as isotropic. This paper presents a method to examine rate-dependent mode mixity associated with cortical bone crack initiation. Four-point bend experiments have been conducted on cortical femoral bone samples from three human donors at quasi-static (slow), intermediate, and dynamic loading rates. Digital image correlation was used to obtain full-field displacement maps at the crack tip during the experiments. An over-deterministic least squares method is presented and used to evaluate Mode I (opening) and Mode II (shear) stress intensity factors (SIF) for fracture initiation at slow (10$^{-2}$ MPa-m$^{1/2}$s$^{-1}$), intermediate (15 MPa-m$^{1/2}$s$^{-1}$), and high ($4.5^{4}\,\hbox {MPa-m}^{1/2}\,\hbox {s}^{-1}$) stress intensity factor rates. Results show that under dynamic loading, the critical SIF in Mode I assuming material anisotropy is approximately 50 % lower than fracture toughness assuming isotropy. Additionally, critical Mode I and II SIFs had the lowest values at the highest rate of loading examined, decreasing to one third of the values under quasi-static loading. Crack growth in the low and intermediate SIF rates appears to be Mode II dominant, and shows a transition to completely mixed-mode at the high rate of loading. These results suggest that the conventional assumption of isotropy is a conservative estimate at low and intermediate rates, but overestimates fracture strength at dynamic rates.