Fatigue Energy Dissipation in Trabecular Bone Samples with Stepwise-Increasing Amplitude Loading*

Tomasz Topoliński; Artur Cichański; Adam Mazurkiewicz; Krzysztof Nowicki

doi:10.3139/120.110235

Article

Fatigue Energy Dissipation in Trabecular Bone Samples with Stepwise-Increasing Amplitude Loading*

Tomasz Topoliński , Artur Cichański , Adam Mazurkiewicz and Krzysztof Nowicki

Published/Copyright: May 28, 2013

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From the journal Materials Testing Volume 53 Issue 6

Abstract

The research method proposed in the paper assumes multi-level loads of trabecular bone, which are similar to the real ones and demonstrate a step-wise amplitude increase. Throughout the study, such loadings were applied to bone structures sampled from 61 donors. The samples were obtained after hip arthroplasty from the neck fragment of femur heads. All the samples were scanned with a desktop microtomographer. The fatigue damage of the sample structures throughout the experiments was seen in changes in the form of the hysteresis loop recorded in the stress-strain system. The dissipation energy, which is calculated based on the hysteresis loop, is present in the fatigue life function. A three-stage sample fatigue damage pattern was demonstrated. The sum of the dissipation energies was calculated for all the hysteresis loops, and thus we obtain the accumulated dissipation energy, which is referred to as the total fatigue life for all the samples. The calculation results were determined to have an exponential-like curve and reported a high value of the coefficient of determinacy. The accumulated dissipation energy is also related to the value of the compressive stress levels applied. Referring the calculated results of the accumulated energy to the structure index BV/TV, we identified the existence of a strong relationship between the quantities.

Kurzfassung

Die physiologische Beanspruchung von Knochen ist eine Art von wahllos variierenden Lasten, die im Labor als Einstufenversuch bedeutend vereinfacht werden können. Das in diesem Beitrag propagierte Verfahren geht von mehrstufigen Beanspruchungen aus, die den realen Beanspruchungen nahekommen und eine stufenweise Anhebung der Amplitude aufweisen. In dieser Studie wurden solche Beanspruchungen an Knochenstrukturen, die von 61 verschiedenen Personen stammten, aufgebracht. Alle Proben wurden mit einem Tisch-Mikro-CT gescannt. Dieser Test ergab die Werte von elf Basisknochenstrukturindizes. Die Knochenproben wurden in einer hydraulischen Prüfmaschine getestet. Die schrittweise erhöhte Druckbeanspruchung hatte eine sinusförmige Form. Die Ermüdungsschädigung der Strukturproben während der Versuche konnte anhand der Form der Hysteresisschleife erkannt werden, die in dem Spannung-Dehnungs-System aufgezeichnet wurde. Die Energiedissipation, die anhand der Hyseresisschleife berechnet wurde, ist in der Lebensdauerfunktion enthalten. Die Summe der Energiedissipationen wurde für alle Hystereseschleifen berechnet und ergibt die akkumulierte Energiedissipation, auf die für alle Proben als Gesamtlebensdauer Bezug genommen wurde. Die Berechnungsergebnisse wurden ermittelt, um eine Exponentialkurve zu erhalten und ergaben eine hohen Wert des Koeffizienten R2. Die akkumulierte Energiedissipation wird auch auf die Werte der Druckspannungsniveaus bezogen. Eine Analyse dieser Beziehung in normalisierten relativen Koordinaten beim Maximalwert zeigte eine Ähnlichkeit zur Prozessdynamik der Ermüdung der Proben, unabhängig von der Knochenstruktur. Unter Bezug der berechneten Ergebnisse der akkumulierten Energie auf den Strukturindex BV/TV wurde eine strenge Abhängigkeit zwischen den Größen festgestellt. Der in diesem Beitrag propagierte Versuch lässt sich schnell durchführen und ermöglicht es, Ergebnisse zu gewinnen, die auf die Knochenstrktur bezogen werden können, wenn als Kriterium die Energiedissipation gewählt wird.

Extended version of the contribution for the Symposium on Fatigue Failure and Fracture Mechanics

Tomasz Topoliński is a professor at the Department of Basics Mechanical Engineering and Mechatronics at the University of Technology and Life Sciences in Bydgoszcz, Poland. He deals with biomechanical engineering, trabecular bone structure investigation, and fatigue research of plastics.

Artur Cichański is a lecturer at the Department of Machinery Design and Control at the University of Technology and Life Sciences in Bydgoszcz, Poland. His research focuses on fatigue problems in conditions of multiaxial loading, Computer Aided Design, and finite element method.

Adam Mazurkiewicz is a lecturer at the Department of Basics Mechanical Engineering and Mechatronics at the University of Technology and Life Sciences in Bydgoszcz, Poland. He deals with changes of trabecular bone structure during bone illnesses e. g. osteoporosis or coxarthrosis, strength of trabecular bone dependend on the degree of advanced bone illnesses, and remodeling of trabecular bone.

Krzysztof Nowicki is a lecturer at the Department of Machinery Design and Control and Mechatronics at the University of Technology and Life Sciences in Bydgoszcz, Poland. His area of scientific interest includes fatigue of materials and structural components, computational methods in machinery design, and artificial intelligence.

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Published Online: 2013-05-28

Published in Print: 2011-06-01

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https://doi.org/10.3139/120.110235