Experimental evaluation of fracture properties of bovine hip cortical bone using elastic–plastic fracture mechanics

BACKGROUND: Understanding the fracture mechanics of bone is very important in both the medical and bioengineering field. Bone is a hierarchical natural composite material of nanoscale collagen fibers and inorganic material. OBJECTIVE: This study investigates and presents the fracture toughness of bovine cortical bone by using elastic plastic fracture mechanics. METHODS: The J-integral was used as a parameter to calculate the energies utilized in both elastic deformation (Jel) and plastic deformation (Jpl) of the hipbone fracture. Twenty four different types of specimens, i.e. longitudinal compact tension (CT) specimens, transverse CT specimens, and also rectangular unnotched specimens for tension in longitudinal and transverse orientation, were cut from the bovine hip bone of the middle diaphysis. All CT specimens were prepared according to the American Society for Testing and Materials (ASTM) E1820 standard and were tested at room temperature. RESULTS: The results showed that the average total J-integral in transverse CT fracture specimens is 26% greater than that of longitudinal CT fracture specimens. For longitudinal-fractured and transverse-fractured cortical specimens, the energy used in the elastic deformation was found to be 2.8–3 times less than the energy used in the plastic deformation. CONCLUSION: The findings indicate that the overall fracture toughness measured using the J-integral is significantly higher than the toughness calculated by the stress intensity factor. Therefore, J-integral should be employ to compute the fracture toughness of cortical bone.

Upper and Lower Bounds for the Parameters of One-Dimensional Theories for Sandwich Fracture Specimens

Upper and lower bounds for the parameters of one-dimensional theories used in the analysis of sandwich fracture specimens are derived by matching the energy release rate with two-dimensional elasticity solutions. The theory of a beam on an elastic foundation and modified beam theory are considered. Bounds are derived analytically for foundation modulus and crack length correction in single cantilever beam (SCB) sandwich specimens and verified using accurate finite element results and experimental data from the literature. Foundation modulus and crack length correction depend on the elastic mismatch between face sheets and core and are independent of the core thickness if this is above a limit value, which also depends on the elastic mismatch. The results in this paper clarify conflicting results in the literature, explain the approximate solutions, and highlight their limitations. The bounds of the model parameters can be applied directly to specimens satisfying specific geometrical/material ratios, which are given in the paper, or used to support and validate numerical calculations and define asymptotic limits.

Analysis of Notch Effect in 3D-Printed ABS Fracture Specimens Containing U-Notches

In this paper a fracture assessment in additive manufactured acrylonitrile butadiene styrene (ABS) fracture specimens containing U-notches is performed. We performed 33 fracture tests and 9 tensile tests, combining five different notch radii (0 mm, 0.25 mm, 0.50 mm, 1 mm and 2 mm) and three different raster orientations: 0/90, 30/−60 and 45/−45. The theory of critical distances (TCD) was then used in the analysis of fracture test results, obtaining additional validation of this theoretical framework. Different versions of TCD provided suitable results contrasting with the experimental tests performed. Moreover, the fracture mechanisms were evaluated using scanning electron microscopy in order to establish relationships with the behaviour observed. It was demonstrated that 3D-printed ABS material presents a clear notch effect, and also that the TCD, through both the point method and the line method, captured the physics of the notch effect in 3D-printed ABS. Finally, it was observed that the change in the fracture mechanisms when introducing a finite notch radius was limited to a narrow band behind the original defect, which appeared in cracked specimens but not in notched specimens.

Comparison of Methods to Find the Weibull Stress Parameters

The Weibull stress (Beremin, 1983) relates the local first principal stress and plastically strained volume to the probability of fracture. It requires two constants (m, σu) as input, which are generally regarded as material parameters. As the Beremin approach is used in the background to structural analysis rules, the Beremin parameters are now being used in other situations, including engineering analysis. However, the currently accepted way to find the Beremin constants requires twenty tests, which is considered to be unacceptably expensive for industrial application. Less expensive ways of finding the Beremin parameters have been published in the literature, but they have never been compared to the de facto standard. In this paper, the Beremin parameters were found by the de facto standard method and two other ways, and a comparison is made. It was found that the Beremin parameters can be estimated with reasonable accuracy with a method that uses on just two sets (six specimens) of fracture specimens by careful application of the method of Andrieu (2012). Also, a proposal is made for another method which is based only on the Master Curve temperature T0.

Shear and foundation effects on crack root rotation and mode-mixity in moment- and force-loaded single cantilever beam sandwich specimen

Foundation effects play a crucial role in sandwich fracture specimens with a soft core. Accurate estimation of deformation characteristics at the crack front is vital in understanding compliance, energy release rate and mode-mixity in fracture test specimens. Beam on elastic foundation analysis of moment- and force-loaded single cantilever beam sandwich fracture specimens is presented here. In addition, finite element analysis of the single cantilever beam specimen is conducted to determine displacements, rotations, energy release rate and mode-mixity. Based on finite element analysis, a foundation modulus is proposed that closely agrees with the numerical compliance and energy release rate results for all cases considered. An analytical expression for crack root rotation of the loaded upper face sheet provides consistent results for both loading configurations. For the force-loaded single cantilever beam specimen (in contrast to the moment-loaded case), it was found that the crack length normalized energy release rate and the mode-mixity phase angle increase strongly as the crack length decreases, a result of increased dominance of shear loading.

Fabrication of micro-scale fracture specimens for nuclear applications by direct laser writing

ABSTRACTThe structural integrity of nuclear fission and fusion power plant components is the focus of this research. The state of the art is using micro scale specimens milled with a focussed ion beam (FIB). Because of their very low volume such specimens can be lab tested, even when irradiated to low or medium level of activity. This offers a possibility of testing multiple specimens to investigate stochastic effects, e.g. effects of irradiation on the shift of the ductile to brittle transition. However, FIB milled specimens suffer from Ga contamination, to the degree that the validity of fracture data obtained on such specimens is questionable. We propose to use nano-additive manufacturing as an alternative to FIB for making micro scale fracture specimens. A combination of two-photon polymerization and electrodeposition and sputtering was used to manufacture micro-scale Brazilian disk fracture specimens (CBD), which are free from Ga and thus better suited for the study of irradiation effects on structural integrity. In this study Ni CBD specimens were made with 30 µm diameter and up to 13 µm thickness. The slot width varied between 1 µm to 2.9 µm width the corresponding slot length of between 7.5 µm and 8 µm. Consecutive FIB characterization shows that the specimens have polycrystalline microstructure with sub-µm grains. The work is ongoing making W CBD specimens and on reducing the slot width and using chemical vapor deposition fabrication.