Damage Rate is a Predictor of Fatigue Life and Creep Strain Rate in Tensile Fatigue of Human Cortical Bone Samples

[+] Author and Article Information
John R. Cotton1

 Department of Engineering Science and Mechanics and Virginia Tech–Wake Forest School of Biomedical Engineering and Science, Virginia Tech, Mail code 0219, Blacksburg, VA 24061 jcotton@vt.edu

Keith Winwood

 Institute for Biophysical and Clinical Research into Human Movement, Manchester Metropolitian University, Alsager, UK

Peter Zioupos

 Center for Materials Science and Engineering, Cranfield Postgraduate Medical School, Cranfield University, Shrivenham, UK

Mark Taylor

 Bioengineering Science Research Group, School of Engineering Science, University of Southampton, Southampton, UK


Corresponding author.

J Biomech Eng 127(2), 213-219 (Sep 28, 2004) (7 pages) doi:10.1115/1.1865188 History: Received August 07, 2003; Revised September 28, 2004

We present results on the growth of damage in 29 fatigue tests of human femoral cortical bone from four individuals, aged 53–79. In these tests we examine the interdependency of stress, cycles to failure, rate of creep strain, and rate of modulus loss. The behavior of creep rates has been reported recently for the same donors as an effect of stress and cycles (Cotton, J. R., Zioupos, P., Winwood, K., and Taylor, M., 2003, “Analysis of Creep Strain During Tensile Fatigue of Cortical Bone  ,” J. Biomech.36, pp. 943–949). In the present paper we first examine how the evolution of damage (drop in modulus per cycle) is associated with the stress level or the “normalized stress” level (stress divided by specimen modulus), and results show the rate of modulus loss fits better as a function of normalized stress. However, we find here that even better correlations can be established between either the cycles to failure or creep rates versus rates of damage than any of these three measures versus normalized stress. The data indicate that damage rates can be excellent predictors of fatigue life and creep strain rates in tensile fatigue of human cortical bone for use in practical problems and computer simulations.

Copyright © 2005 by American Society of Mechanical Engineers
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Figure 1

Results of fatigue test showing material damage plotted against cycles. This sample was taken from a 53-year-old female, had a maximum stress of 72MPa, and failed at 2626 cycles. Dashed lines demonstrate the limits of 10% and 90% of the life. A linear fit (solid line) was performed over the large middle portion of the life where damage accumulation is reasonably constant. The slope of this line is the damage per cycle value.

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Figure 2

Plots of stress and normalized stress for (a) cycles to failure Nf, (b) damage rates ΔD∕ΔN, and (c) creep rates Δεc∕ΔN

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Figure 3

Behavior of (a) cycles to failure as a function of the rate of damage, (b) cycles to failure as a function of the creep rate, and (c) creep rates as a function of the rate of damage

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Figure 4

Collated data of the damage rates as a function of normalized stress level and age by using the present data (solid symbols) and from a previous study (2) (open symbols). (Data points for females only and for the parameters identified from the regression analysis from each individual.)

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Figure 5

Previous relationships for fatigue effects on bone are compared to results shown here. Previously, stress drives material damage (measured as a loss in modulus), creep strain, and the number of cycles to failure (a). We also note that as stress is applied, damage occurs but that damage better predicts life and creep rates (b). Alternatively, (c) stress could drive creep rates which then can be studied to predict failure or damage. One advantage of this finding is that measuring damage rates or creep rates, early in the test, will give a better prediction than stress. Correlations between parameters are all from this work.




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