Heterogeneous fracture toughness of human cortical bone tissue

CT-based finite element analysis (FEA) of human bones helps estimate fracture risk in clinical practice by linking bone ash density (\(\rho _{ash}\)) to mechanical parameters. However, phase field models for fracture prediction require the heterogeneous fracture toughness \(G_{Ic}\), which can be derived from the critical stress intensity factor \(K_{Ic}\), determined through various experimental methods. Due to a lack of standards for determining cortical bone’s \(K_{Ic}\), an experimental campaign is presented using 53 cortical specimens from two fresh frozen femurs to investigate whether a correlation exists between \(K_{Ic}\) and \(\rho _{ash}\). We investigated various experimental techniques for correlating \(K_{Ic}\) with \(\rho _{ash}\). We conducted FEAs employing the phase field method (PFM) to determine the most suitable correlation among the five possible ones stemming from the experimental methods. The ASTM standard using displacement at force application point was found to be the recommended experimental method for the estimation of \(K_{Ic}\) perpendicular to osteons’ direction

$$\begin{aligned} K_{Ic} [MPa\sqrt{m}]{=}1.89\left( \rho _{ash} [gr/cc] \right) ^{1.88} \,\, R^2{=}0.5374. \end{aligned}$$

The corresponding statistical critical energy release rate bounds were determined:

$$\begin{aligned} G_{Ic}[N/m]= 321.94 (\rho _{ash}[gr/cc])^{1.69} \times exp(\pm 2SD), \end{aligned}$$

with a standard deviation \(SD= 0.30\) representing a 95.4% confidence interval. The average \(G_{Ic}\) resulted in good correlations between the predicted fracture force by PFM-FEA of four representative specimens and experimental fracture forces. The proposed correlations will be used in CT-based PFM FEA to estimate the risk of hip and humeral fractures.