Re-evaluating the toughness of human cortical bone

Abstract

Data for fracture in human humeral cortical bone are re-analyzed to assess the validity for this material of linear-elastic fracture mechanics (LEFM), which is the standard method of analyzing toughness and one basis for analyzing clinical data relating to bone quality. A nonlinear fracture model, which is based on representing the damage zone in the bone by a cohesive model, is calibrated against a number of sets of test data for normal (not diseased or aged) human cortical bone taken from cadavers. The data consist of load vs. load-point displacement measurements from standard compact–tension fracture tests. Conventional LEFM is unable to account for the shape of the load–displacement curves, but the nonlinear model overcomes this deficiency. Calibration of the nonlinear model against one data curve leads to predictions of the peak load and the displacement to peak load for two other data curves that are, for this limited test set, more accurate than those made using LEFM. Furthermore, prior observations of damage mechanisms in bone are incompatible with the modeling assumption of LEFM that all nonlinearity is confined to a zone much smaller than the specimen and the crack length. The predictions of the cohesive model and the prior observations concur that the length of the nonlinear zone in human cortical bone varies in the range 3–10 mm, which is comparable to or larger than naturally-occurring bones and the specimens used to test them. We infer that LEFM is not an accurate model for cortical bone. The fracture toughness of bone deduced via LEFM from test data will not generally be a material constant, but will take different values for different crack lengths and test configurations. The accuracy of using LEFM or single-parameter fracture toughness for analyzing the significance of data from clinical studies is called into question. The nonlinear cohesive zone model is proposed to be a more accurate model of bone and the traction-displacement or cohesive law is hypothesized to be a material property. The cohesive law contains a more complete representation of the mechanics of material failure than the single-parameter fracture toughness and may therefore provide a superior measure of bone quality, e.g., for assessing the efficacy of therapy for osteoporosis.