Norman T L, Vashishth D, Burr D B
Department of Mechanical and Aerospace Engineering, West Virginia University, Morgantown 26505, USA.
J Biomech. 1995 Mar;28(3):309-20. doi: 10.1016/0021-9290(94)00069-g.
The longitudinal fracture toughnesses of human cortical bone were compared to those of bovine cortical bone to test the hypothesis that although human osteonal bone is significantly weaker and more compliant than primary (plexiform) bone, it is not less tough than primary bone. The fracture toughness indices, critical strain energy release rate (Gc) and critical stress intensity factor (Kc), were determined for human Haversian bone and bovine bone under tension (Mode I) loading using the compact tension method. The effects of thickness, crack growth range and anisotropy on fracture indices for slow stable crack growth in cortical bone were determined. Plane strain assumptions required for application of linear elastic fracture mechanics (LEFM) to bone were investigated. Longitudinal oriented fracture toughness tests were used to assess the crack inhibiting effect of human bone microstructure on fracture resistance. Human bone Kc calculated from the stress concentration formula for 2 and 3 mm thick specimens equaled 4.32 and 4.05 MN m-3/2, respectively. Human bone Gc calculated from the compliance method equaled 827 N m-1 for 2 mm thick specimens and 595 N m-1 for 3 mm thick specimens. It was found that crack growth range, thickness and material assumptions affect fracture toughness. Kc calculated from Gc using an anisotropic relation provided the lowest estimate of Kc and equaled 3.31 MN m-3/2 for 2 mm thick specimens and 2.81 MN m-3/2 for 3 mm thick specimens. Both Kc and Gc were significantly reduced after being adjusted to ASTM standard thickness using ratios determined from bovine bone. The fracture toughness of bovine bone relative to human bone ranged from 1.08 to 1.66. This was compared to the longitudinal strength of bovine bone relative to the longitudinal strength of human bone which is approximately equal to 1.5. We found that even though human bone is significantly weaker than bovine bone, relative to its strength, the toughness of human and bovine bone are roughly similar, but the data were not sufficiently definitive to answer the question of which is tougher.
将人类皮质骨的纵向断裂韧性与牛皮质骨的纵向断裂韧性进行比较，以检验以下假设：尽管人类骨单位骨比初级（丛状）骨明显更脆弱且更具柔韧性，但它的韧性并不低于初级骨。使用紧凑拉伸法，测定了人类哈弗斯骨和牛骨在拉伸（I型）载荷下的断裂韧性指数、临界应变能释放率（Gc）和临界应力强度因子（Kc）。确定了厚度、裂纹扩展范围和各向异性对皮质骨中缓慢稳定裂纹扩展的断裂指数的影响。研究了将线性弹性断裂力学（LEFM）应用于骨时所需的平面应变假设。使用纵向取向的断裂韧性试验来评估人类骨微观结构对断裂阻力的裂纹抑制作用。根据应力集中公式计算得出，2毫米厚和3毫米厚试样的人类骨Kc分别为4.32和4.05 MN m-3/2。根据柔度法计算得出，2毫米厚试样的人类骨Gc为827 N m-1，3毫米厚试样的人类骨Gc为595 N m-1。研究发现，裂纹扩展范围、厚度和材料假设会影响断裂韧性。使用各向异性关系从Gc计算得出的Kc提供了最低的Kc估计值，2毫米厚试样的Kc为3.31 MN m-3/2，3毫米厚试样的Kc为2.81 MN m-3/2。使用从牛骨确定的比率将其调整到ASTM标准厚度后，Kc和Gc均显著降低。牛骨相对于人类骨的断裂韧性范围为1.08至1.66。将此与牛骨相对于人类骨纵向强度的纵向强度进行比较，后者约等于1.5。我们发现，尽管人类骨明显比牛骨脆弱，但其相对于自身强度而言，人类骨和牛骨的韧性大致相似，但数据不够确凿，无法回答哪种骨更坚韧的问题。
