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TECHNICAL PAPERS

Fatigue of Bovine Trabecular Bone

[+] Author and Article Information
Tara L. A. Moore

Harvard-MIT Division of Health Sciences and Technology, Massachusetts Institute of Technology, Cambridge, MA 02139Orthopedic Biomechanics Lab, Beth Israel Deaconess Medical Center, Boston, MA 02215

Lorna J. Gibson

Department of Materials Science and Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139

J Biomech Eng 125(6), 761-768 (Jan 09, 2004) (8 pages) doi:10.1115/1.1631583 History: Received April 15, 2002; Revised July 02, 2003; Online January 09, 2004
Copyright © 2003 by ASME
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Figures

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Experimental setup, including specimen geometry. An unwaisted cylinder is glued into brass end caps to minimize end effects. The specimen is loaded in compression between two platens (one fixed, one self-aligning) in a servohydraulic testing machine. An extensometer is attached to the specimen endcaps.
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Typical fatigue test. Specimen was loaded at Δσ/E0=0.007 to εmax=−2.5%. The specimen shows both a decrease in normalized secant modulus, Esec/E0, with increasing cycles and an increase in residual or plastic strain with each cycle, Δεpl, to a total residual strain, εres, after N cycles.
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Normalized secant modulus, Esec/E0 (black), and maximum strain, εmax (gray), are plotted as a function of number of cycles, N. Specimens stopped at a given maximum strain will have similar normalized modulus, but those stopped at a preset number of cycles may have different modulus reductions. Each symbol (square, triangle, diamond) represents a different specimen. (a) Δσ/E0=0.008. (b) Δσ/E=0.005.
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Plot of normalized reloading modulus, Er/E0, as a function of maximum strain, εmax. (a) Data plotted by normalized stress. Data at each strain level spread for clarity. (b) Linear regressions for each normalized stress. The regressions intersect the line Er/E0=1 at εmax=−0.42% to εmax=−0.56%.
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Plot of normalized secant modulus, Esec/E0, as a function of maximum strain, εmax. (a) Data plotted by normalized stress. Data at each strain level spread for clarity. (b)- Pooled fatigue data. The data are linearly related (Esec/E0=0.25εmax+1.16,p<0.05,R2=0.34). The regression intersects the line Esec/E0=1 at εmax=−0.64%. Previous data for the reduction in secant modulus with increasing maximum strain for uniaxial monotonic compression are included for comparison.
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Plot of residual strain, εres, as a function of maximum compressive strain, εmax. (a) Data plotted by normalized stress. Data at each strain level spread slightly for clarity. (b) Pooled fatigue data. There is a linear relationship between residual strain and maximimum strain (εres=0.71εmax+0.39,p<0.05,R2=0.76). The regression intersects the axis εres=0 at εmax=−0.55%.
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Normalized stress, Δσ/E0, plotted against number of cycles to reach a maximum strain of −1.3%,Nε max=−1.3%. The data points plotted indicate the cycle number where −1.3% strain was exceeded. There is a power law relationship between normalized stress and number of cycles to εmax=1.3% (Basquin’s law) (N=7.47×10−22(Δσ/E0)−10.4,R2=0.62).
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Bovine trabecular bone follows the Coffin-Manson law at low cycle numbers. There is a power law relationship between the change in the initial change in plastic strain in a single cycle, Δεpl, and number of cycles for specimens tested to less than 100 cycles (filled diamonds) (Δεpl=0.352 N−0.981,R2=0.82). The Basquin law is shown on the plot for N>100. The combined Basquin Coffin-Manson equation suggests that there is a transition in fatigue behavior (from that dominated by elastic deformation at high N to that dominated by plastic deformation at low N) at N∼100 cycles.

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