Investigations Of Anisotropy And Strengthening-toughening Mechanisms Of Cortical Bone

As a kind of natural biological composite material, cortical bone is mainly composed of collagen fibers, hydroxyapatite, water and other amorphous collagen matters. Through untold centuries of evolutionary development, bone possesses high strength, stiffness and fracture toughness. It plays an important role in supporting animal bodies and accomplishing movements. Although the primordial materials and compositions of the bone are not good, the natural evolution makes the optimized combination and distribution of the materials and compositions to form a variety of excellent microstructures. These excellent microstructures make bone possess excellent mechanical properties. The investigation on these excellent microstructures will provide beneficial guidance for synthetic high-performance composite materials.In this dissertation, the relationship between the hierarchical microstructure and the excellent mechanical properties of bone is investigated with the combined method of mechanical tests, observational experiments, model analyses, numerical simulations and biomimetic validations. The aim of the dissertation is to reveal the mechanism of strength and toughness of the bone, and put forward the new idea of the biomimetic preparation of high-performance composite materials. The main work and contributions of this dissertation are listed as follows:① The macro/micro-mechanical properties of a bovine-femora bone in different directions are tested by four-point bending experiment, compact tensile experiments and nano-indentation. The microstructural characteristics and the fracture path are observed by optical microscopy and scanning electron microscope(SEM). It is found that the bone has obvious anisotropic properties. At the macro-scale, it is found that the energy required to generate the fracture surface takes its maximum along the transverse direction of the bone and the fracture energy has its minimum along the radial direction. The fracture energy along the longitudinal direction of the bone is a middle value. At the micro-scale, the hardness and elastic modulus of the bone along its longitudinal direction are larger than those of the bone along its transverse direction. The anisotropic properties of cortical bone are closely related to its hierarchical microstructure. The main reason of the macroscopic anisotropic of the bone is the different crack deflections appear along its different crack-propagation directions, which is caused by the different arrangements of the osteons and cement lines. The main reason of the microscopic anisotropic of the bone is tha different directions of the mineralized collagen fibers in the lamella of the bone.② Based on the SEM photos of the three different fracture surfaces of the bone, it is realized that the paths of the crack propagation of the bone have statistical self-similarity characteristics. The fractal models of the crack deflection of the three fracture directions of the bone are presented. The fracture energies of the three fracture directions are calculated. The calculated results are in good agreement with the tested results. The fractal models of the crack branching and uncrack-ligament bridging of the bone are used to analyze quantitatively the toughening mechanism of crack branching and uncrack-ligament bridging of the bone. It is denoted that this two toughening mechanisms can increase the critical expansion force of the crack and fracture toughness of the bone.③ Based on the experimental results of four-point bending tests, the fractal dimensions and four texture-feature parameters of the fracture surfaces of the bone along its three different directions are calculated by box-counting method and spatial gray level co-occurrence matrix in MATLAB. It is showed that the fractal dimension of the transverse fracture surface of the bone is the largest, the one of the radial fracture surface is the minimal and the one of the longitudinal fracture surface is between them. The fractal dimension can reflect the roughness and complexity of the fracture surface. There is a positive correlation between the fractal dimension and the fracture energy. Four texture feature parameters of the spatial gray-level co-occurrence matrix can describe exactly a certain fracture texture character of the fracture surface and have good texture expression abilities. By combining the fractal dimension with the 2-order statistical parameters of the spatial gray level co-occurrence matrix as a set of feature parameters, the complexity and roughness of the fracture texture of the bone can be described effectively. This method may realize the quantitative analysis and automatic class identification for the fracture texture of the fracture surfaces of the bone.④ A multilevel finite element approach is applied to predict the stress field in the cortical bone of a femur bone when a load is applied to the bone. Analytical results indicate that a stress concentration will occur at the margins of the Haversian canal and in the interstitial tissues of the bone. Since microcracks would occur in the area of the stress concentration, we suppose that the microcracks will occur at the margins of the Haversian canal and in the interstitial tissues. Further, the microcrack propagation in the bone is analyzed using extended finite element method(X-FEM).The result shows that the cement line in bone can raise the fracture resistance of the bone.⑤ A progressive damage approach is used to complete the stress calculation, failure analysis and material degradation of the osteon in the bone based on finite element software, ABAQUS 6.13. The failure criteria and two field variables are inputed to the ABAQUS 6.13 by means of the user subroutine USDFLD(User Defined Field). Comparing three different numerical models of the osteons, we found that the arrangement and shape of the osteocyte lacunae in the osteons is a kind of optimized arrangement. It could determine the initiated location of the cracks and make the microcracks propagate along the circumferential direction of the osteons rather than directely penetrate into the haversian cannal of the osteon.⑥ The effective elastic properties of the bone are analyzed based on Mori-Tanaka method. A step-by-step modeling approach, consisting of successive homogenization steps from nanostructural level up to mesostructural level, is introduced. The analytical results for the elastic modulus of the bone are in good agreement with experimental results.⑦ Through the analyses of the elastic mechanics and finite element simulation, it is revealed that the fiber rounding-hole microstructure of the bone can decrease stress concentration at the edge of the hole and enhance the strength and toughness of the holed composites. Further, based on the experimental observation and model analysis, a kind of biomimetic fiber-rounding-hole composite laminate is fabricated with high-strength glass fibers and epoxy resin. The strength of the biomimetic composite laminate is tested and compared with that of the composite laminate with the drilled-hole structure. The testing result shows that the strength of the rounding-hole composite laminate is markedly larger than that of the drilled-hole composite laminate.⑧ According to the lamellar microstructures of the bone, which are composed of hydroxyapatite and mineralized collagen fibers, a kind of biomimetic fiber-ceramic composite is fabricated. The mechanical properties of the biomimetic fiber-ceramic composite are tested by three-point-bending experiment. It is found that the lamellar structure of the composite is a kind of optimized structure. It can absorb and consume the fracture energy of the composite. The more the fiber layers are, the more fracture energy will be consumed during the composite fractures.