Quantification of nonlinear elasticity for the valuation of submillimeter crack length in cortical bone

Abstract

The objective of this study was to investig ate the sensitivity of the nonlinear elastic properties of cortical bon e to the presence of a single submillime tric crac k. Nonli near elasticity was measured by nonlinear resonant ultrasound spectroscopy (NRUS) in 14 human cortical bon e specimen s. The specimen s were parallelepiped beams (50 2 2 mm3). A central notch of 500 mm was made to control crack initiation and propagation during four-point bending. The nonlinear hysteretic elastic and dissipative parameters αf and α Q, and Young's modulus Eus were measured in dry condition for undamaged (control) specimens and in dry and wet conditions for damaged specimens. The length of the crack was assessed using synchrotron radiation micro-computed tomography (SR- μCT) with a voxel size of 1.4 μm. The initial values of αf, measured on the intact specimens, were remarkably similar for all the specimens (αf ¼ 5.57 1.5). After crack propagation, the nonlinear elastic coefficient α f increased significantly (p o 0.006), with values ranging from 4.0 to –296.7. Conversely, no significant variation was observed for αQ and Eus. A more pronounced nonlinear elastic behavior was observed in hydrated specimens compared to dry specimens (p o 0.001) after propagation of a single submillimetric crack. The nonlinear elastic parameter αf was found to be significantly correlated to the crack length both in dry (R ¼0.79, p o0.01) and wet (R ¼0.84, p o0.005) conditions. Altogether these results show that nonlinear elasticity assessed by NRUS is sensitive to a single submillimetric crack induced mechanically and suggest that the humidity must be strictly controlled during measurements.