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Quasi-brittle fracture mechanics is used to evaluate fracture of human cortical bone in aging. The approach is demonstrated using cortical bone bars extracted from one 92-year-old human male cadaver. In-situ fracture mechanics experiments in a 3D X-ray microscope are conducted. The evolution of the fracture process zone is documented. Fully developed fracture process zone lengths at peak load are found to span about three osteon diameters. Crack deflection and arrest at cement lines is a key process to build extrinsic toughness. Strength and toughness are found as size-dependent, not only for laboratory-scale experimental specimens but also for the whole femur. A scaling law for the length fracture process zone is used. Then, size-independent, tissue fracture properties are calculated. Linear elastic fracture mechanics applied to laboratory beam specimens underestimates the tissue toughness by 60%. Tissue fracture properties are used to predict the load capacity of the femur in bending within the range of documented data. The quasi-brittle fracture mechanics approach allows for the assessment of the combined effect of bone quantity and bone quality on fracture risk. However, further work is needed considering a larger range of subjects and in the model validation at the organ length scale.
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Load Data and Code for Analysis of In-situ X-ray Transverse Crack Growth Experiments in Specimens of a Human Cortical Bone
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.
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- Award ID(s):
- 1952993
- PAR ID:
- 10531684
- Publisher / Repository:
- Purdue University Research Repository
- Date Published:
- Subject(s) / Keyword(s):
- Bone Matlab Fracture Mechanics Mechanical Engineering FOS: Mechanical engineering Mechanical Engineering (Dept) Mechanical engineering (FOS)
- Format(s):
- Medium: X Size: 12 files; 2 MB Other: text/x-fortran; text/plain; image/jpeg
- Size(s):
- 12 files 2 MB
- Location:
- Purdue University Research Repository
- Right(s):
- Creative Commons Zero v1.0 Universal
- Institution:
- Purdue University
- Sponsoring Org:
- National Science Foundation
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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.more » « less
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This publication documents 3D image stacks from HR-pQCT imaging of a femur diaphysis, as well as image stacks for two in-situ loaded fracture mechanics specimens observed with 3D X-ray microscopy. Imaging For HR-qQCT: HR-pQCT scans were acquired by Rachel Surowiec using an XtremeCT II scanner (SCANCO Medical AG, Bruttisellen, Switzerland) within the Musculoskeletal Function, Imaging and Tissue (MSK-FIT) Resource Core of the Indiana Center for Musculoskeletal Health’s Clinical Research Center (Indiana University, Indianapolis, IN). Scans are performed at 60.7 um resolution, a 68 kV, 1467 uA, 43 ms integration time, 1 frame averaging. Raw scans are ‘.RSQ’ file types. The ISQ file type were read into ImageJ using the Import-KHKs Scanco uCT ISQ file reader plug-in, and exported as bmp image stacks, image stacks are provided in two parts. Reconstructed images are rotated in dataviewer so that all bones are in the same orientation (prox/distal/anterior/posterior for the Femur). For in-situ fracture mechanics experiments: 3D scans were acquired by Glynn Gallaway using a 3-point bending rig for single edged notched bend specimens 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-Württemberg, Germany) at Purdue University. The 3-point bending frame had a span 20 mm with X-ray transparent, glassy carbon supports. To maintain hydration, the beam was wrapped in a plastic film slit at the notch. Displacements were applied at 0.1 mm/min. Load cell outputs were monitored and recorded. Displacements are held constant during image acquisitions. The first 3D image was obtained at the onset of non-linearity. Subsequently, the displacement was increased until a load increase of 10 N was observed, and another image was obtained. This sequence was repeated 6-times until peak load. 3D X-ray images were acquired with a resolution of 4.5 um, exposure time 5 sec., 801 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 (s=1 pixel) was applied to reduce image artifacts. Image stacks are exported as tiff files and provided individually for each load step and specimen. Two experiments are documented (beam 1 and beam 2). MaterialstThe diaphysis of a human (92-year-old, male) cadaveric femur was obtained through the Indiana University School of Medicine Anatomical Donation Program.more » « less
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