Mixed-mode fracture of human cortical bone

Although the mode I (tensile opening) fracture toughness has been the focus of most fracture mechanics studies of human cortical bone, bones in vivo are invariably loaded multiaxially. Consequently, an understanding of mixed-mode fracture is necessary to determine whether a mode I fracture toughness test provides the appropriate information to accurately quantify fracture risk. In this study, we examine the mixed-mode fracture of human cortical bone by characterizing the crack-initiation fracture toughness in the transverse (breaking) orientation under combined mode I (tensile opening) plus mode II (shear) loading using samples loaded in symmetric and asymmetric four-point bending. Whereas in most structural materials, the fracture toughness is increased with increasing mode-mixity (i.e., where the shear loading component gets larger), in the transverse orientation of bone the situation is quite different. Indeed, the competition between the maximum applied mechanical mixed-mode driving force and the weakest microstructural paths in bone results in a behavior that is distinctly different to most homogeneous brittle materials. Specifically, in this orientation, the fracture toughness of bone is markedly decreased with increasing mode-mixity.     

Mechanistic aspects of fracture and R-curve behavior in human cortical bone

An understanding of the evolution of toughness is essential for the mechanistic interpretation of the fracture of cortical bone. In the present study, in vitro fracture experiments were conducted on human cortical bone in order to identify and quantitatively assess the salient toughening mechanisms. The fracture toughness was found to rise linearly with crack extension (i.e., rising resistance- or R-curve behavior) with a mean crack-initiation toughness, K0 of approximately 2 MPa square root m for crack growth in the proximal-distal direction. Uncracked ligament bridging, which was observed in the wake of the crack, was identified as the dominant toughening mechanism responsible for the observed R-curve behavior. The extent and nature of the bridging zone was examined quantitatively using multi-cutting compliance experiments in order to assess the bridging zone length and estimate the bridging stress distribution. Additionally, time-dependent cracking behavior was observed at stress intensities well below those required for overload fracture; specifically, slow crack growth occurred at growth rates of approximately 2 x 10(-9) m/s at stress intensities approximately 35% below the crack-initiation toughness. In an attempt to measure slower growth rates, it was found that the behavior switched to a regime dominated by time-dependent crack blunting, similar to that reported for dentin; however, such blunting was apparent over much slower time scales in bone, which permitted subcritical crack growth to readily take place at higher stress intensities.     

天鹅记忆接骨器对实验性骨折愈合中皮质骨血供的影响

目的:观察天鹅记忆接骨器(SMC)对实验性骨折愈合局部血供的影响,探讨SMC促进骨愈合的机理。方法:50只新西兰大白兔双侧肱骨干截骨后,随机选取一侧用SMC固定,对侧用4孔动力加压接骨板(DCP)固定。分别在术后3d,2、4、8、12周时,行微血管碳素墨水造影和放射微球法测定,观察两组固定对骨皮质再血管化过程和局部微循环的影响。结果:SMC组血管再生主要来源于髓内侧,皮质骨再血管化速度明显快于DCP组。SMC组从术后2周开始血流量即开始回升,而DCP组从术后4周才开始回升。术后8周以后,SMC组血供已完全恢复正常,而DCP组一直到术后12周,血供仍未达到正常水平(P<0.05)。结论:SMC具有特殊的空间构型和材质特性,不仅能对骨折形成牢固的固定,而且对骨干血供的损伤较轻,有利于皮质骨的再血管化。     

Fracture mechanics of cortical bone tissue: a hierarchical perspective

The performance of bone tissue in the presence of flaws is a highly remarkable one. Bone tissue is the outcome of an adaptive evolutionary process; thus, insight into the mechanisms by which it fails would provide valuable information not only for development of mechanically superior biomimetic materials but also for development of treatment modalities to prevent debilitating bone fractures. Clinically, fractures of skeletal organs occur as a result of aging, disease, overuse, and trauma. Fracture mechanics, a sub-discipline of solid mechanics that investigates the performance of cracked materials, has been employed extensively in characterizing the mechanisms by which bone tissue fractures. At present the fracture mechanisms at the macroscale are better characterized than at the microscale. On the other hand, a mechanistic understanding of damage evolution at the submicroscopic scale is largely limited to postulations with little experimental insight. The challenge of skeletal fragility will be dealt with more efficiently with deeper understanding of the fracture process at each hierarchical size scale. The most recent review on this subject matter was a decade ago, and there have been numerous developments in the fracture mechanics of bone since then. This review recaps the existing literature with an emphasis on the hierarchical nature of the fracture process in bone, entailing the supramolecular, microscopic, and macroscopic scales.     

Fracture resistance of human cortical bone across multiple length-scales at physiological strain rates

While most fracture-mechanics investigations on bone have been performed at low strain rates, physiological fractures invariably occur at higher loading rates. Here, at strain rates from 10⁻⁵ to 10⁻¹ s⁻¹, we investigate deformation and fracture in bone at small length-scales using in situ small-angle x-ray scattering (SAXS) to study deformation in the mineralized collagen fibrils and at the microstructural level via fracture-mechanics experiments to study toughening mechanisms generating toughness through crack-tip shielding. Our results show diminished bone toughness at increasing strain rates as cracks penetrate through the osteons at higher strain rates instead of deflecting at the cement lines, which is a prime toughening mechanism in bone at low strain rates. The absence of crack deflection mechanisms at higher strain rates is consistent with lower intrinsic bone matrix toughness. In the SAXS experiments, higher fibrillar strains at higher strain rates suggest less inelastic deformation and thus support a lower intrinsic toughness. The increased incidence of fracture induced by high strain rates can be associated with a loss in toughness in the matrix caused by a strain rate induced stiffening of the fibril ductility, i.e., a “locking-up” of the viscous sliding and sacrificial bonding mechanisms, which are the origin of inelastic deformation (and toughness) in bone at small length-scales.     

Cooperation of length scales and orientations in the deformation of bovine bone

Bone has a complex hierarchical structure. Combined wide angle X-ray diffraction and small angle X-ray scattering were used together with in situ tensile testing to investigate the deformation and failure mechanisms of bovine cortical bone at three material levels: (1) the atomic level, corresponding to the mineral crystal phase; (2) the nano level, corresponding to the collagen fibrils; (3) the macroscopic level. It was found that deformation was linear at all three levels up to a strain of 0.2% in the longitudinal tensile direction. At this critical strain a sudden 50% decrease in the fibrillar and mineral strains was observed. This suggests the presence of partial local damage that leads to inhomogeneous strain distributions within the probed gauge volume. This also gives rise to diffraction peak broadening in the mineral phase, as well as strain relaxation at the nanoscale. Above the critical strain the longitudinally oriented strains below the nanoscale remained constant at a reduced level until failure. This suggests that the lateral orientation of the nanostructures toughens the bone, while a higher material level dominated the subsequent deformation process, either by sliding between the lamellar layers or by the growth of microcracks. Analysis of the diffraction data also shows that the bone has compressive residual stress in the crystal phase. A better understanding of the basic mechanics of the hierarchical bone structure could be the basis to enhance research in biomimetics, developing new advanced materials, and to find solutions for orthopedic problems.     

Fracture characterization of human cortical bone under mode II loading using the end-notched flexure test

Fracture characterization of human cortical bone under mode II loading was analyzed using a miniaturized version of the end-notched flexure test. A data reduction scheme based on crack equivalent concept was employed to overcome uncertainties on crack length monitoring during the test. The crack tip shear displacement was experimentally measured using digital image correlation technique to determine the cohesive law that mimics bone fracture behavior under mode II loading. The developed procedure was validated by finite element analysis using cohesive zone modeling considering a trapezoidal with bilinear softening relationship. Experimental load-displacement curves, resistance curves and crack tip shear displacement versus applied displacement were used to validate the numerical procedure. The excellent agreement observed between the numerical and experimental results reveals the appropriateness of the proposed test and procedure to characterize human cortical bone fracture under mode II loading. The proposed methodology can be viewed as a novel valuable tool to be used in parametric and methodical clinical studies regarding features (e.g., age, diseases, drugs) influencing bone shear fracture under mode II loading.     

皮持骨在拉伸型,剪切型和撕裂型加载条件下的断裂韧性——纵向断裂…

对以质骨在拉伸、剪切和撕裂型载荷下的裂纹启裂韧性进行了研究。总数为１３０个紧凑拉式样,紧凑剪切试样和三腿型试样分别用于测量骨的拉伸型、剪切型和撕裂型启裂韧性。多试样柔度法用来测定当ａ／Ｗ＝０．５５（１,裂纹长度,Ｗ,试样宽度）时的临界能量释放率。临界应力强度因子由ａ／Ｗ＝０．５５的试样在试验中得到的临界载荷来计算。为了考察骨力学 各是性对于它的剪切型和撕裂裂纹启裂韧性的影响,对骨试样的裂纹扩展方向     

The effect of strain rate on fracture toughness of human cortical bone: a finite element study

Evaluating the mechanical response of bone under high loading rates is crucial to understanding fractures in traumatic accidents or falls. In the current study, a computational approach based on cohesive finite element modeling was employed to evaluate the effect of strain rate on fracture toughness of human cortical bone. Two-dimensional compact tension specimen models were simulated to evaluate the change in initiation and propagation fracture toughness with increasing strain rate (range: 0.08–18 s⁻¹). In addition, the effect of porosity in combination with strain rate was assessed using three-dimensional models of micro-computed tomography-based compact tension specimens. The simulation results showed that bone’s resistance against the propagation of a crack decreased sharply with increase in strain rates up to 1 s⁻¹ and attained an almost constant value for strain rates larger than 1 s⁻¹. On the other hand, initiation fracture toughness exhibited a more gradual decrease throughout the strain rates. There was a significant positive correlation between the experimentally measured number of microcracks and the fracture toughness found in the simulations. Furthermore, the simulation results showed that the amount of porosity did not affect the way initiation fracture toughness decreased with increasing strain rates, whereas it exacerbated the same strain rate effect when propagation fracture toughness was considered. These results suggest that strain rates associated with falls lead to a dramatic reduction in bone’s resistance against crack propagation. The compromised fracture resistance of bone at loads exceeding normal activities indicates a sharp reduction and/or absence of toughening mechanisms in bone during high strain conditions associated with traumatic fracture.     

Fracture toughening mechanism of cortical bone: an experimental and numerical approach

In this investigation, the crack propagation mechanisms contributing to the toughness of cortical bone were studied using a combination of experimental and numerical approaches. Compact tension (CT) specimens were prepared from bovine cortical bones to achieve crack propagation in the longitudinal and transverse directions. Stable crack extension experiments were conducted to distinguish the crack growth resistance curves, and virtual multidimensional internal bond (VMIB) modeling was adopted to simulate the fracture responses. Results from experiments indicated that cortical bone exhibited rising resistance curves (R-curves) for crack extension parallel and perpendicular to the bone axis; the transverse fracture toughness was significantly larger, indicating that the fracture properties of cortical bone are substantially anisotropic. Microscopic observations showed that the toughening mechanisms in the longitudinal and transverse directions were different. When the crack grew in the transverse direction, the crack deflected significantly, and crack bifurcations were found at the crack wake, while, in the longitudinal direction, the crack was straight and uncracked ligaments were observed. Numerical simulations also revealed that the fracture resistance in the transverse direction was greater than that in the longitudinal direction.     

Quantitative microradiography of cortical bone in disuse osteoporosis following fracture fixation

Stainless steel (elastic modulus 210 GN/m²) and carton fibre reinforced epoxy resin (elastic modulus 65 GN/m²) plates have been attached to intact femora in cats and the development of disuse osteoporosis assessed by microdensitometric methods after 8 months. The bone adjacent to the stainless steel plate showed evidence of considerable demoralization, both uniformly throughout a section and especially at certain focal points. A noticeable, but much smaller amount of osteoporosis developed adjacent to the composite plate. Various methods of presenting quantitative micro-densitometric data are used.     

The fatigue properties of human cortical bone

Rotating cantileverfatigue tests were performed on specimens extracted longitudinally from the cortices of human femora. The usual inverse relationship between stress amplitude and fatigue life was found; the median life was 1·3×10⁴ cycles at a stress amplitude of 12,200 1bf/in² (84·1 MN/m²) and 4·6×10⁶ cycles at 6750 1bf/in² (46·6 MN/m²). Arguments are advanced which suggest that these results are compatible with what is known of the stresses applied in life and the clinical occurrence of fatigue fractures.     

A review of computational models of bone fracture healing

In the process of fracture healing, there are many cellular and molecular events that are regulated by mechanical stimuli and biochemical signals. To explore the unknown mechanisms underlying bone fracture healing, optimal fixation configurations, and the design of new treatment strategies, computational healing models provide a good solution. With the simulation of mechanoregulatory healing models, bioregulatory healing models and coupled mechanobioregulatory healing models, healing outcomes can be predicted. In this review, first, we provide an overview of current computational healing models. Their clinical applications are also presented. Then, the limitations of current models and their corresponding solutions are discussed in this review. Finally, future potentials are presented in this review. Multiscale modeling from the intracellular level to the tissue level is essential, and more clinical applications of computational healing models are required in future research.     

Ultrasonic determination of the elastic modulus of human cortical bone

The elastic modulus (C_ii) of the cortical bones of 19 individuals (14 femurs and 16 tibias, fixed in formalin) was determined ultrasonically. Elastic moduli were measured at four anatomical positions (anterior, posterior, medial and lateral) and in all three planes of orientation (transverse, longitudinal and radial). The mean tibial C_ii (34.11 GPa) was greater than that obtained for femurs (32.52 GPa). The tibial longitudinal plane C_ii (34.1 GPa) was significantly greater than the femoral longitudinal plane C_ii (32.5 GPa). C_ii was significantly higher in the tibia than the femur in both the medial and posterior anatomical positions. The anterior tibia had a significantly lower C₁₁ compared to other positions. C_ii was significantly higher in the longitudinal plane than the transverse or radial planes in both the femur and the tibia. There was no consistent difference in modulus between left and right sides. No age effects were observed. There were no significant differences between males and females, or between African Americans and European Americans.     

Sub-lamellar microcracking and roles of canaliculi in human cortical bone

Bone is a tough biological material. It is generally accepted that bone's toughness arises from its unique hierarchical structure, which in turn facilitates distributed microcracking prior to fracture. Yet, there has been limited progress on the detailed roles of the structural elements in the microcracking process. The present study examines the structure-microcracking relations at the lamellar and sub-lamellar levels of human cortical bone subjected to compressive loading. Laser scanning confocal microscopy revealed a clear influence of the local structure and porosity of the Haversian systems' lamellae on microcrack development. In particular, crack initiation and growth under transverse compression were associated with stress concentration at canaliculi. Later stages of microcracking showed extensive sub-lamellar cracks forming cross-hatched patterns and regularly spaced 0.5-1.7 μm apart. The density, size and regularity of the crack patterns suggest enhanced inelastic deformation capacity through cracking control at the level of mineralized collagen fibril bundles. The present study thus improves the current understanding of the nature of inelastic deformation and microcracking in bone and further suggests that bone's resistance to fracture is achieved through microcrack control at multiple length scales.     

Anisotropy of Young's modulus of human tibial cortical bone

The anisotropy of Young's modulus in human cortical bone was determined for all spatial directions by performing coordinate rotations of a 6 by 6 elastic stiffness matrix. The elastic stiffness coefficients were determined experimentally from ultrasonic velocity measurements on 96 samples of normal cortical bone removed from the right tibia of eight human cadavers. The following measured values were used for our analysis: c ₁₁ =19.5 GPa, c ₂₂ =20.1 GPa, c ₃₃ =30.9 GPa, c ₄₄ =5.72 GPa, c ₅₅ =5.17 GPa, c ₆₆ =4.05 GPa, c ₂₃ =12.5 GPa. The remaining coefficients were determined by assuming that the specimens possessed at least an orthorhombic elastic symmetry, and further assuming that c ₁₃ =c ₂₃ , c ₁₂ =c ₁₁ –2c ₆₆ . Our analysis revealed a substantial anisotropy in Young's modulus in the plane containing the long axis of the tibia, with maxima of 20.9 GPa parallel to the long axis, and minima of 11.8 GPa perpendicular to this axis. A less pronounced anisotropy was observed in the plane perpendicular to the long axis of the tibia. To display our results for the full three-dimensional anisotropy of cortical bone, a closed surface was used to represent Young's modulus in all spatial directions.     

Fractal dimension and mechanical properties of human cortical bone

Fractal dimension (FD) can be used to characterize microstructure of porous media, particularly bone tissue. The porous microstructure of cortical bone is observable in micro-CT (μCT) images. Estimations of fractal dimensions of μCT images of coupons of human cortical bone are obtained. The same samples were tested on a tensile test machine and Young's modulus (YM) and Failure stress were obtained. When both types of measures were compared, a clear correlation was found (R = ?81%, P < 0.01). Young's modulus of each sample and the FD of its μCT images are correlated. From the assumption that cortical bone is approximately a fractal set, a non-linear constitutive relation involving FD is obtained for YM. Experimental results show good agreement with this constitutive relation. Additional parameters in the non-linear relation between YM and FD have been estimated from experimental results and related to physical parameters.