Load Data and Code for Analysis of In-situ X-ray Transverse Crack Growth Experiments in Specimens of a Human Cortical Bone

<p>This publication documents measurement data for two in-situ loaded fracture mechanics specimens observed with 3D X-ray microscopy.</p>

<p><strong>Materials</strong></p>

<p>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 <a class="preview file:samplelocation.jpg" href="https://purr.purdue.edu/projects/bonehydration/files/download?subdir=IN-SITU-CRACK-GROWTH&asset=samplelocation.jpg">samplelocation.jpg</a>. 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.</p>

<p><strong>Experiments and Data</strong></p>

<p>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). <b><a class="citation-title" href="https://doi.org/10.4231/94PZ-AB06" rel="external" target="_blank">3D Image Data from In-situ X-ray Imaging Transverse Crack Growth Experiments in Human Cortical Bone</a></b>. Purdue University Research Repository. <a href="https://doi.org/10.4231/94PZ-AB06" rel="external" target="_blank">doi:10.4231/94PZ-AB06</a><br />
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<strong>Code </strong></p>

<p>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.<br />
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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.</p>