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Understanding bone strength is important when assessing bone diseases and their treatment. Bending experiments are often used to determine strength. Then, flexural stresses are calculated from elastic bending theory. With a brittle failure criterion, the maximum flexural tensile stress is equated to (nominal) strength. However, bone is not a perfectly brittle material. A quasi-brittle failure criterion is more appropriate. Such an approach allows for material failure to occur before full fracture. The extent of the subcritical damage domain then introduces a length scale. The intrinsic strength of the bone is calculated from the critical load at fracture and the failure process zone dimensions relative to the specimen size. We apply this approach to human cortical bone specimens extracted from a femur. We determine strength measures in the untreated reference state and after treatment with the selective estrogen receptor modulator raloxifene. We find that the common nominal strength measure does not distinguish between treatments. However, the dimensions of the failure process zone differ between treatments. Intrinsic strength measures then are demonstrated as descriptors of bone strength sensitive to treatment. An extrapolation of laboratory data to whole bone is demonstrated. 

This publication documents measurement data for two in-situ loaded fracture mechanics specimens observed with 3D X-ray microscopy. Materials The diaphysis of a human (92-year-old, male) cadaveric femur was obtained through the Indiana University School of Medicine Anatomical Donation Program. Bars (nominally 4.0 mm x 4.0 mm cross section) were extracted from the diaphysis as demonstrated in Figure-samplelocation. Two single Edge Notch Bend, SEN(B), specimens for a load span s=20 mm were machined for a three-point bend fixture for crack growth in the transverse direction. SEN(B) specimens had the following dimensions (height d, depth b, initial crack length a0): beam 1 d=4.0 mm, b=4.0 mm, a0=1.8 mm, beam 2 d=4.1 mm, b=3.9 mm, a0=1.7 mm). Osteon diameter was measured was measured on polished sections by using backscatter SEM images following Britz (2009), Figure samplelocation.jpg. Using ImageJ, a grid is imposed on the images and On.Dm is determined as the Feret Diameter for at least 40 On.Dm measures. For beam 1 mean On.Dm is 242 micrometer and for beam 2 284 micrometer. Experiments and Data Fracture experiments were conducted with a Deben 5000 load rig in a Zeiss XRADIA 3D microscope. For system details see https://www.physics.purdue.edu/xrm/about-our-instruments/index.html. Data for these experiments is given in the two csv files of this project data set. In these experiments force F (load cell) data and image frame data are obtained as machine output. Crack mouth opening displacement (CMOD) is obtained from 3D X-ray images at frame numbers synchronized to force readings. Fracture process zone (FPZ) length L. FPZ length data is obtained from 3D image data in Gallaway, G. E.; Allen, M. R.; Surowiec, R. K.; Siegmund, T. H. (2025). 3D Image Data from In-situ X-ray Imaging Transverse Crack Growth Experiments in Human Cortical Bone. Purdue University Research Repository. doi:10.4231/94PZ-AB06 Code Code (Analysis_Main.m, Analysis_Func.m) takes data from the .csv files and determines the linear elastic fracture mechanics quantities (LEFM toughness), the quasi-brittle fracture mechanics quantities (QBFM toughness), and the tissue intrinsic (size-independent) fracture properties (tissue toughness, tissue strength, tissue lengthscale). Output is depicted as force-CMOD and fracture process zone length - CMOD records, and as crack growth resistance curves (quasibrittle energy release rate vs. fracture process zone length). In addition, the microstructure constant eta is obtained as the ratio between the tissue intrinsic lengthscale and the mean osteon diameter. Code (P_star.m) is provided to determine maximum sustainable load of a femoral shaft in three-point bending. It is assumed that the beam is a pipe with a surface crack of depth equal to the mean osteon diameter. This code can be used for sensitivity studies of the dependence of whole bone maximum sustainable load on cortical thickness, tissue intrinsic strength and microstructure constant eta. Example calculations are depicted in two relevant figures. 

This publication documents 3D image stacks for two in-situ loaded fracture mechanics specimens observed with 3D X-ray microscopy, 2D image stacks of the crack mouth opening displacement during said loading, and analysis codes which supported the publication. Materials: The diaphysis of a human (75-year-old, male) cadaveric femur was obtained through the Indiana University School of Medicine Anatomical Donation Program. Nominal 4 mm x 4 mm x 24 mm beams were sectioned from the femur diaphysis. Experiments were conducted on 12 beams. Beams were assigned to 2 groups: treated with Raloxifene (RAL), treated with a vehicle (VEH) control. Image data are provided for one beam from the RAL group and one beam from the VEH group. Additional images can be made available upon request to the corresponding author. Imaging: ;For in-situ fracture mechanics experiments: 2D and 3D scans were acquired by Glynn Gallaway using a 4-point bending rig for single edged notched bend specimens in a water bath with a Deben CT5000N load cell (Deben, Bury St. Edmunds, UK) in a Zeiss XRADIA 510 Versa 3D X-Ray microscope (Carl Zeiss AG, Baden-Wuerttemberg, Germany) at Purdue University. The 4-point bending frame had a span 16 mm with X-ray transparent, glassy carbon supports. To maintain hydration, bending frame was situated in a waterbath filled with DI water. Displacements were applied at 0.1 mm/min. Load cell outputs were monitored and recorded. During loading 2D images were obtained every 1 second. 3D X-ray images were acquired with a resolution of 4.5 um, exposure time 6 sec., 2401 projections, 120 kV, 10 W, 4 x objective, and a LE2 filter. X-ray projections were processed through XRADIA Scout-and-Scan Reconstructor. A recursive Gaussian smoothing filter (1 pixel) was applied to reduce image artifacts. Image stacks are exported as tiff files and provided for each specimen. Images are provided for one RAL treated sample and one VEH treated sample. 

Abstract Fluids with different densities often coexist in subsurface fractures and lead to variable‐density flows that control subsurface processes such as seawater intrusion, contaminant transport, and geologic carbon sequestration. In nature, fractures have dip angles relative to gravity, and density effects are maximized in vertical fractures. However, most studies on flow and transport through fractures are often limited to horizontal fractures. Here, we study the mixing and transport of variable‐density fluids in vertical fractures by combining three‐dimensional (3D) pore‐scale numerical simulations and visual laboratory experiments. Two miscible fluids with different densities are injected through two inlets at the bottom of a fracture and exit from an outlet at the top of the fracture. Laboratory experiments show the emergence of an unstable focused flow path, which we term a “runlet.” We successfully reproduce the unstable runlet using 3D numerical simulations and elucidate the underlying mechanisms triggering the runlet. Dimensionless number analysis shows that the runlet instability arises due to the Rayleigh‐Taylor instability (RTI), and flow topology analysis is applied to identify 3D vortices that are caused by the RTI. Even under laminar flow regimes, fluid inertia is shown to control the runlet instability by affecting the size and movement of vortices. Finally, we confirm the emergence of a runlet in rough‐walled fractures. Since a runlet dramatically affects fluid distribution, residence time, and mixing, the findings in this study have direct implications for the management of groundwater resources and subsurface applications. 

contain conspicuous acknowledgement of where and by whom the paper was presented. ABSTRACT: Shear strength along discontinuities plays a crucial role in the stability of rock structures. The development of geophysical methods to remotely monitor and assess changes in shear strength is essential to the identification of rock hazards that can lead to the loss of life and failure of civilian infrastructure. In this study, compressional and shear ultrasonic waves were used to monitor slip along discontinuities (with different surface profiles) during shearing. A series of laboratory direct shear experiments were performed on two gypsum blocks separated by a frictional discontinuity. The gypsum blocks had perfectly matched contact surfaces with a half-cycle sine wave profile that spanned the central third of the discontinuity, surrounded by planar surfaces. The amplitude of the half-cycle sine wave was varied and ranged between 2 to 10 times the height of the asperities. Compressional, P, and shear, S, ultrasonic waves were continuously transmitted and recorded throughout the shearing process, while Digital Image Correlation (DIC) was used to capture surface displacements. At low normal stresses, distinct maxima in the normalized P and S wave transmitted amplitudes occurred before shear failure in regions where dilation was observed. Where dilation was not detected, an increase in transmitted wave amplitude was observed, even after the peak shear stress was achieved. At high normal stresses, dilation was suppressed, which was associated with an increase in wave amplitude with shear stress until the peak, and then a decrease in amplitude. Monitoring changes in transmitted wave amplitude is a potential method for the detection of dilation along rock discontinuities.