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Research Papers

# Accounting for Inclusions and Voids Allows the Prediction of Tensile Fatigue Life of Bone Cement

[+] Author and Article Information
Oliver J. Coultrup, Martin Browne

Bioengineering Research Group, School of Engineering Sciences, University of Southampton, Southampton SO17 1BJ, UK

Christopher Hunt

DePuy International Ltd., White Rose Office Park, Millshaw Park Lane, Leeds LS11 0EA, UK

Mark Taylor1

Bioengineering Research Group, School of Engineering Sciences, University of Southampton, Southampton SO17 1BJ, UKmtaylor@soton.ac.uk

1

Corresponding author.

J Biomech Eng 131(5), 051007 (Apr 09, 2009) (8 pages) doi:10.1115/1.3049518 History: Received February 29, 2008; Revised September 25, 2008; Published April 09, 2009

## Abstract

Previous attempts by researchers to predict the fatigue behavior of bone cement have been capable of predicting the location of final failure in complex geometries but incapable of predicting cement fatigue life to the right order of magnitude of loading cycles. This has been attributed to a failure to model the internal defects present in bone cement and their associated stress singularities. In this study, dog-bone-shaped specimens of bone cement were micro-computed-tomography $(μCT)$ scanned to generate computational finite element (FE) models before uniaxial tensile fatigue testing. Acoustic emission (AE) monitoring was used to locate damage events in real time during tensile fatigue tests and to facilitate a comparison with the damage predicted in FE simulations of the same tests. By tracking both acoustic emissions and predicted damage back to $μCT$ scans, barium sulfate $(BaSO4)$ agglomerates were found not to be significant in determining fatigue life $(p=0.0604)$ of specimens. Both the experimental and numerical studies showed that diffuse damage occurred throughout the gauge length. A good linear correlation ($R2=0.70$, $p=0.0252$) was found between the experimental and the predicted tensile fatigue life. Although the FE models were not always able to predict the correct failure location, damage was predicted in simulations at areas identified as experiencing damage using AE monitoring.

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## Figures

Figure 7

A comparison of acoustic emission locations (top), the specimen failure location (second from top), damage locations in the computational simulation of fatigue in the specimen (third from top), and the defect field in the specimen (bottom). In the simulation image, darker areas represent locations of high damage, while the defects seen at the bottom image are all BaSO4 agglomerates. In this specimen, the computational method was not able to successfully locate the failure site, so the computational failure (CF) location and experimental failure (EF) location are both labeled. Condition C was used when modeling the BaSO4 agglomerates.

Figure 1

Specimen geometry (left), highlighting the gauge length (gray area) and position of AE sensors. The width of the gauge length is 12 mm. The test configuration is also shown (right).

Figure 2

Finite element meshes formed in AMIRA 3.1 , showing the relative edge lengths of the cement, pore (P), and BaSO4 agglomerate (A) elements. The finite element boundary conditions are also shown, with a linked elastic foundation at the base of specimens, and loading applied to one node linked to the specimen by nodal ties.

Figure 3

Normalized load-end deflection of specimens with increasing number of fatigue cycles. The failure criterion is highlighted, where a sudden increase in specimen load-end deflection is apparent.

Figure 4

The occurrence of BaSO4 agglomerates and pores in 16 specimens of average volume 2.09×10−6 m3

Figure 5

A comparison of specimen fatigue life from experimental tests and computational simulations. The four different values of Young’s modulus employed for BaSO4 agglomerates in simulations are shown in the key, as are the corresponding trendlines. Experimental tests were terminated at 3×106 cycles: These results are circled in the figure.

Figure 6

A comparison of acoustic emission locations (top), the specimen failure location (second from top), damage locations in the computational simulation of fatigue in the specimen (third from top), and the defect field in the specimen (bottom). In the simulation image, darker areas represent locations of high damage, while the defects seen at the bottom image are all BaSO4 agglomerates. The failure (F) location has been identified between three barium sulfate agglomerates. Damage and AE were also seen at two other locations. Condition C was used when modeling the BaSO4 agglomerates.

Figure 8

Damage (dark areas) in slices through a specimen at given number of loading cycles generated in a computational simulation. Damage takes many cycles to accumulate, occurring at several locations, around pores in this example. Finally, damage rapidly accumulates at one location (the largest pore), leading to failure.

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