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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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References

Burr,  D. B., Forwood,  M. R., Fyhrie,  D. P., Martin,  R. B., Schaffler,  M. B., and Turner,  C. H., 1997, “Bone microdamage and skeletal fragility in osteoporotic and stress fractures,” J. Bone Miner. Res., 12(1), pp. 6–15.
Muir,  P., Johnson,  K. A., and Ruaux-Mason,  C. P., 1999, “In vivo matrix microdamage in a naturally occurring canine fatigue fracture,” Bone (N.Y.), 25(5), pp. 571–576.
Schaffler,  M. B., Choi,  K., and Milgrom,  C., 1995, “Aging and matrix microdamage accumulation in human compact bone,” Bone (N.Y.), 17(6), pp. 521–525.
Freeman,  M. A. R., Todd,  R. C., and Ririe,  C. J., 1974, “The role of fatigue in the pathogenesis of senile femoral neck fractures,” J. Bone Jt. Surg., 56-B(4), pp. 698–702.
Daffner,  R. H., and Pavlov,  H., 1992, “Stress fractures: current concepts,” AJR, Am. J. Roentgenol., 159(8), pp. 245–252.
Egol,  K. A., Koval,  K. J., Kummer,  F., and Frankel,  V. H., 1998, “Stress fractures of the femoral neck,” Clin. Orthop., 348, pp. 72–78.
Mosekilde,  L., 1993, “Vertebral structure and strength in vivo and in vitro,” Calcif. Tissue Int., 53(Suppl 1), pp. S121–S126.
Melton,  L. J., Kan,  S. H., Fyre,  M. A., Wahner,  H. W., O-Fallon,  W. M., and Riggs,  B. L., 1989, “Epidemiology of vertebral fractures in women,” Am. J. Epidemiol., 129(5), pp. 1000–1011.
Carter,  D. R., and Hayes,  W. C., 1976, “Fatigue life of compact bone-I. Effects of stress amplitude, temperature and density,” J. Biomech., 9, pp. 27–34.
Carter,  D. R., and Hayes,  W. C., 1977, “Compact bone fatigue damage—I. residual strength and stiffness,” J. Biomech., 10, pp. 325–337.
Carter,  D. R., and Hayes,  W. C., 1977, “Compact bone fatigue damage: a microscopic examination,” Clin. Orthop., 127, pp. 265–274.
Pattin,  C. A., Caler,  W. E., and Carter,  D. R., 1996, “Cyclic mechanical property degradation during fatigue loading of cortical bone,” J. Biomech., 29(1), pp. 69–79.
Zioupos,  P., Wang,  X. T., and Currey,  J. D., 1996, “Experimental and theoretical quantification of the development of damage in fatigue tests of bone and antler,” J. Biomech., 29(8), pp. 989–1002.
Zioupos,  P., Wang,  X. T., and Currey,  J. D., 1996, “The accumulation of fatigue microdamage in human cortical bone of two different ages in vitro,” Clin. Biomech. (Los Angel. Calif.), 11(7), pp. 365–375.
Guo,  X. E., McMahon,  T. A., Keaveny,  T. M., Hayes,  W. C., and Gibson,  L. J., 1994, “Finite element modeling of damage accumulation in trabecular bone under cyclic loading,” J. Biomech., 27(2), pp. 145–155.
Cheng, D. W., 1995, “Compressive High Cycle at Low Strain Fatigue Behavior of Bovine Trabecular Bone,” SM thesis, Massachusetts Institute of Technology, Cambridge, Massachusetts.
Haddock,  S. M., Yeh,  O. C., Mummaneni,  P. V., Rosenberg,  W. S., and Keaveny,  T. M., 2000, “Fatigue behavior of human vertebral trabecular bone,” Transactions of the Orthopaedic Research Society, 25, pp. 733.
O’Brien, F. J., 2001, “Microcracks and the fatigue behavior of compact bone,” Ph.D. thesis, Trinity College and Royal College of Surgeons in Ireland, Dublin, Ireland.
Caler,  W. E., and Carter,  D. R., 1989, “Bone creep-fatigue damage accumulation,” J. Biomech., 22(6-7), pp. 625–635.
Carter,  D. R., and Caler,  W. E., 1985, “A cumulative damage model for bone fracture,” J. Orthop. Res., 3(1), pp. 84–90.
Guo, X. E., 1993, “Fatigue of Trabecular Bone,” Ph.D. thesis, Harvard University, Cambridge, Massachusetts.
Bowman,  S. M., Guo,  X. E., Cheng,  D. W., Keaveny,  T. M., Gibson,  L. J., Hayes,  W. C., and McMahon,  T. A., 1998, “Creep contributes to the fatigue behavior of bovine trabecular bone,” J. Biomech. Eng., 120(5), pp. 647–654.
Taylor,  D., 1998, “Microcrack growth parameters for compact bone deduced from stiffness variations,” J. Biomech., 31, pp. 587–592.
Schaffner,  G., Guo,  X. E., Silva,  M. J., and Gibson,  L. J., 2000, “Modelling fatigue damage accumulation in two-dimensional Voronoi honeycombs,” International Journal of Mechanical Sciences, 42(4), pp. 645–656.
Makiyama,  A. M., Vajjala,  S., and Gibson,  L. J., 2002, “Analysis of crack growth in a 3D Voronoi structure: A model for fatigue in low density trabecular bone,” J. Biomech. Eng., 124, pp. 512–520.
Burr,  D. B., Turner,  C. H., Naick,  P., Forwood,  M. R., Ambrosius,  W., Hasan,  M. S., and Pidaparti,  R., 1998, “Does microdamage accumulation affect the mechanical properties of bone?,” J. Biomech., 31, pp. 337–345.
Moore, T. L. A., and Gibson, L. J., 2002, “Fatigue microdamage of bovine trabecular bone,” ASME J. Biomech. Eng. (in this issue).
Keaveny,  T. M., Pinilla,  T. P., Crawford,  R. P., Kopperdahl,  D. L., and Lou,  A., 1997, “Systematic and random errors in compression testing of trabecular bone,” J. Orthop. Res., 15(1), pp. 101–110.
Keaveny,  T. M., Guo,  X. E., Wachtel,  E. F., McMahon,  T. A., and Hayes,  W. C., 1994, “Trabecular bone exhibits fully linear elastic behavior and yields at low strains,” J. Biomech., 27(9), pp. 1127–1136.
Lee,  T. C., Arthur,  T. L., Gibson,  L. J., and Hayes,  W. C., 2000, “Sequential labelling of microdamage in bone using chelating agents,” J. Orthop. Res., 18, pp. 322–325.
Moore,  T. L. A., and Gibson,  L. J., 2002, “Microdamage accumulation in bovine trabecular bone in uniaxial compression,” J. Biomech. Eng., 124(1), pp. 63–71.
Keaveny,  T. M., Guo,  X. E., and Wachtel,  E. F., 1993, “Trabecular bone is linearly elastic up to yielding and yields by cracking,” Transactions of the Orthopaedic Research Society, 18, pp. 586.
Seireg,  A., and Kempke,  W., 1969, “Behavior of in vivo bone under cyclic loading,” J. Biomech., 2, pp. 455–461.
Hertzberg, R. W., 1989, Deformation and Fracture Mechanics of Engineering Materials, Wiley, New York.
Guo,  X. E., Gibson,  L. J., McMahon,  T. A., Keaveny,  T. M., and Hayes,  W. C., 1992, “Finite element modeling of fatigue damage accumulation in trabecular bone,” Transactions of the Orthopaedic Research Society, 17, pp. 164.
Bowman,  S. M., Gibson,  L. J., Hayes,  W. C., and McMahon,  T. A., 1999, “Results from demineralized bone creep tests suggest that collagen is responsible for the creep behavior of bone,” J. Biomech., 121(2), pp. 253–258.

Figures

Grahic Jump Location
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.
Grahic Jump Location
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.
Grahic Jump Location
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.
Grahic Jump Location
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%.
Grahic Jump Location
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.
Grahic Jump Location
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%.
Grahic Jump Location
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).
Grahic Jump Location
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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