Nanoscale Deformation Mechanisms and Yield Prediction of Lamellar Bone

Peruzzi, Cinzia

PhD Tesis (2022)

In nowadays aging societies, pathological fractures such as osteoporotic fractures are bound to increase. This is an issue as it impairs the patients’ quality of life and is also a massive socioeconomic burden. Bone fracture is a multiscale process as not only the quality and quantity of its base constituents but also the hierarchical nature of bone con- tributes to the fracture resistance. Therefore, bone needs to be investigated on all the length scales to then improve the fracture risk assessment. Moreover, bones often frac- ture during traumatic events such as falls, but little high strain rates research has been done on the microscale. The objective of this thesis is therefore to extend the knowledge of the mechanical behavior of bone subjected to high strain rate compressions down to the microscale. To determine the mechanical behavior of bone in conditions that resemble the physi- ological state as close as possible it is important to perform experiments on hydrated rather than dry bone. On the microscale, hydration of the sample is typically achieved by submerging the whole sample into a physiological solution. However, high strain rate experiments cannot be performed in solution due to the fluid drag. Therefore, we de- veloped an indenter setup that performs high strain rate experiments (up to 10mm/s) featuring an experiment chamber that allows to control the relative humidity (5%−95%) and the temperature (up to 60◦C). All the studies conducted during this thesis were performed using this novel indenter setup. A non-destructive method to determine the mineralized collagen fibril orientation was developed based on polarized Raman spectroscopy – quantitative polarized Raman spec- troscopy. The method was calibrated on mineralized turkey leg tendons, a naturally aligned material, and cross-validated using small-angle X-ray scattering. With the cali- brated quantitative polarized Raman spectroscopy method we were able to determine the out-of-plane angle of the mineralized collagen fibrils with an angular certainty of < 10◦. As a next step, we fabricated micropillars of bovine cortical bone with a known miner- alized collagen fibril orientation of 0◦ to 82◦ using the focused ion beam method. The micropillars (5µm in diameter, aspect ratio 1 : 2) were subsequently compressed at room temperature and under hydrated conditions using a quasi-static strain rate. We found a strong dependence of the elastic modulus E and the yield stress σy on the mineralized collagen fibril orientation with an anisotropy of Ea/Et = 3.8 and σy a/σy t = 2.54. Fur- thermore, we found the post-yield behavior to depend on the mineralized collagen fibril orientation as well. More precisely, softening behavior was observed for small out-of- plane angles, while hardening was observed for large out-of-plane angles. The transition from a softening to a hardening post-yield behavior occurs at a region of Θ = 48◦ −54◦. Knowing the information of the mineralized collagen fibril orientation prior to the com- pression experiments helps to reduce the apparent scatter in the gathered data. Subsequently, the strain rate sensitivity of ovine cortical bone was investigated. Bone samples were cut in a way the mineralized collagen fibrils were oriented parallel or per- pendicular to the surface of the sample. Consequently, the micropillars fabricated on the sample surface featured a mineralized collagen fibril orientation perpendicular to the long axis of the micropillars (transverse) or parallel to it (axial). The micropillars were then compressed under humid conditions and with varying strain rates, including the strain rates experienced during traumatic events (10−4s−1 −8 · 102s−1). The anisotropy from the earlier study was confirmed and also a strain rate sensitivity comparable to the strain rate sensitivities reported for other species and higher length scales was found. Thus, we hypothesize that the strain rate sensitivity is an intrinsic property of the or- ganic phase of bones, which is already present at the nanoscale. The compression experiments with varying strain rates (0.1s−1 −100s−1) were repeated on ovine cortical bone micropillars with varying relative humidities (5% − 90%) and temperature (24◦C − 60◦C). They were fabricated so the mineralized collagen fibril orientation is again axial or transverse using a femtosecond pulsed laser ablation. The micropillars fabricated with this new method resulted in larger dimensions (∼ 22µm in diameter and ∼ 64µm in length for the axial and ∼ 78µm for the transverse orientation) and have a bigger taper angle (∼ 19◦ rather than ∼ 2.4◦). To account for the influence of the taper, finite element simulation was performed. We found that the yield stress is highly dependent on the relative humidity. It increases significantly with decreasing relative humidity. Furthermore, we found that the yield stress increases with increasing temperature, which we explain by the drying out of the bone, even when the relative humidity is kept at a constant level of 90%. Furthermore, the strain rate sensitivity and the activation volume were determined during this study and they agree well with values found in earlier studies for different species and different length scales. It was suggested that these small activation volumes are an indication that charge interactions in the extrafibrillar matrix break during deformation. The results from this study support this assumption. Overall, this thesis focused on the micromechanical behavior of bovine and ovine cortical bone at the microscale and under compression. We found an anisotropy of the elastic modulus, yield stress, strain rate sensitivity and post-yield behavior with respect to the mineralized collagen fibril orientation. The strain rate sensitivity was found to be in range with earlier studies conducted on different species and higher length scales. This is an indication that the strain rate sensitivity derives from the organic matrix and is already present at the nanoscale. Furthermore, the activation volumes found in this study also agree well with earlier studies and thus are additional evidence that it is the charge interaction within the extrafibrillar matrix that break during deformation. In addition, we found that the mechanical properties of cortical bone significantly depend on temperature and relative humidity, a dependence that needs to be investigated fur- ther as most mammals have a body temperature of ∼ 37◦, but the temperature is rarely taken into consideration when performing experiments. Concluding, the findings in this thesis help understanding bone a little better and can be incorporated in future fracture risk assessment methods