Haupert Sylvain, Guérard Sandra, Mitton David, Peyrin Françoise, Laugier Pascal
Sorbonne Universités, Université Pierre et Marie Curie, CNRS UMR7371 & INSERM U1146, Laboratoire d'Imagerie Biomédicale, Paris FR-75006, France.
Arts et Métiers ParisTech, LBM, 151 Boulevard de l'Hôpital, Paris, France.
J Mech Behav Biomed Mater. 2015 Aug;48:210-219. doi: 10.1016/j.jmbbm.2015.04.013. Epub 2015 Apr 22.
The objective of this study was to investigate the sensitivity of the nonlinear elastic properties of cortical bone to the presence of a single submillimetric crack. Nonlinear elasticity was measured by nonlinear resonant ultrasound spectroscopy (NRUS) in 14 human cortical bone specimens. The specimens were parallelepiped beams (50×2×2 mm(3)). A central notch of 500 µm was made to control crack initiation and propagation during four-point bending. The nonlinear hysteretic elastic and dissipative parameters αf and αQ, 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 =-5.5±1.5). After crack propagation, the nonlinear elastic coefficient αf increased significantly (p<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<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=0.79, p<0.01) and wet (R=0.84, p<0.005) 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.
本研究的目的是调查皮质骨非线性弹性特性对单个亚毫米级裂纹存在的敏感性。通过非线性共振超声光谱（NRUS）测量了14个人类皮质骨标本的非线性弹性。标本为长方体梁（50×2×2 mm³）。制作了一个500 µm的中心切口，以控制四点弯曲过程中裂纹的萌生和扩展。在干燥条件下对未受损（对照）标本以及在干燥和潮湿条件下对受损标本测量了非线性滞后弹性和耗散参数αf和αQ，以及杨氏模量Eus。使用体素大小为1.4 µm的同步辐射微计算机断层扫描（SR-μCT）评估裂纹长度。在完整标本上测量的αf初始值在所有标本中非常相似（αf = -5.5±1.5）。裂纹扩展后，非线性弹性系数αf显著增加（p<0.006），值范围为-4.0至-296.7。相反，未观察到αQ和Eus有显著变化。在单个亚毫米级裂纹扩展后，与干燥标本相比，在水合标本中观察到更明显的非线性弹性行为（p<0.001）。发现非线性弹性参数αf在干燥（R = 0.79，p<0.01）和潮湿（R = 0.84，p<0.005）条件下均与裂纹长度显著相关。总之，这些结果表明，通过NRUS评估的非线性弹性对机械诱导的单个亚毫米级裂纹敏感，并表明在测量过程中必须严格控制湿度。
