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TECHNICAL PAPERS: Bone/Orthopedics

# Application of Fracture Mechanics to Failure in Manatee Rib Bone

[+] Author and Article Information
Jiahau Yan

Department of Materials Science and Engineering,  University of Florida, P.O. Box 116400, Gainesville, FL 32611bratt@ufl.edu

Kari B. Clifton

Department of Physiological Sciences,  University of Florida, P.O. Box 100144, Gainesville, FL 32610CliftonK@mail.vetmed.ufl.edu

Roger L. Reep

Department of Physiological Sciences,  University of Florida, P.O. Box 100144, Gainesville, FL 32610reep@ufbi.ufl.edu

John J. Mecholsky

Department of Materials Science and Engineering,  University of Florida, P.O. Box 116400, Gainesville, FL 32611jmech@mse.ufl.edu

$GC=KC2∕E′$ where $E′=E$ for plane stress and $E′=E∕(1−ν2)$ for plane strain, for $ν=Poission$’s ratio.

J Biomech Eng 128(3), 281-289 (Dec 05, 2005) (9 pages) doi:10.1115/1.2187044 History: Received November 19, 2004; Revised December 05, 2005

## Abstract

Background. The Florida manatee (Trichechus manatus latirostris) is listed as endangered by the U.S. Department of the Interior. Manatee ribs have different microstructure from the compact bone of other mammals. Biomechanical properties of the manatee ribs need to be better understood. Fracture toughness $(KC)$ has been shown to be a good index to assess the mechanical performance of bone. Quantitative fractography can be used in concert with fracture mechanics equations to identify fracture initiating defects∕cracks and to calculate the fracture toughness of bone materials. Method of approach. Fractography is a standard technique for analyzing fracture behavior of brittle and quasi-brittle materials. Manatee ribs are highly mineralized and fracture in a manner similar to quasi-brittle materials. Therefore, quantitative fractography was applied to determine the fracture toughness of manatee ribs. Results. Average fracture toughness values of small flexure specimens from six different sizes of manatees ranged from $1.3to2.6MPa(m)1∕2$. Scanning electron microscope (SEM) images show most of the fracture origins were at openings for blood vessels and interlayer spaces. Conclusions. Quantitative fractography and fracture mechanics can be combined to estimate the fracture toughness of the material in manatee rib bone. Fracture toughness of subadult and calf manatees appears to increase as the size of the manatee increases. Average fracture toughness of the manatee rib bone materials is less than the transverse fracture toughness of human and bovine tibia and femur.

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## Figures

Figure 1

Skeleton of a manatee. Manatee ribs cover most of the body and protect the internal organs. Bending specimens were cut from three ribs, one from the cranial, one from the central, and one from the caudal thoracic region. For each rib, specimens were taken from the three segments shown in the figure.

Figure 2

A typical force-displacement curve of the manatee rib specimens loaded under three-point flexure. It shows a quasi-brittle failure, i.e., the force-displacement curve is mostly linear for a large portion of the deformation with little, if any, nonlinearity near fracture.

Figure 3

Fracture surface of a whole rib. Apparent twist hackle markings point toward the fracture origin, which was located on the tensile side when the rib was loaded from the opposite side. Twist hackle markings are fracture steps in the approximate direction of crack propagation due to a slight local shear stress in addition to the main tensile stress controlling the overall direction of crack propagation (length of the caliper: 22cm).

Figure 4

An apparent hole near the tensile side of a flexure specimen was identified as the source of the fracture origin. The arrows in inset indicate the boundary of the critical crack. (Note: the scale bar in inset is smaller than the one on the main image.)

Figure 5

Average values of the critical stress intensity factor, KC, of all the manatees are shown in the figure. I-bars show standard deviations. Using a one-way ANOVA with α=0.05, animals with the same Roman numeral are not significantly different.

Figure 9

Stress distribution of a bending specimen and the determination of critical stress. (a) Magnitude of stress along the x-axis of a three-point flexure. (b) Stress distribution along the y-axis. (c) An example of internal crack origin. The critical stress at fracture is 147.9MPa.

Figure 7

Relationships between fracture toughness and porosity (a), and critical stress and porosity (b). Porosity measurements were done on 14 specimens: 3 of them were from the adult, 9 were from the four subadults, and 2 were from the calf. Trendlines with a natural log-regression along with R-squared values are shown in the figures.

Figure 6

SEM images show different porosity and pore structures in different specimens. Fracture toughness of each specimen is also listed. The arrows on top of each image show the crack origins. (Scale bars are 2mm in (a) and (b), and 1mm in (c) and (d).)

Figure 8

The crack origins can be classified into three types according to where the origins are: corner crack, surface crack, and internal crack. The stress intensity factor coefficient and the determination of lengths a and b in the three types are shown in the figure. Critical crack size (c) is the square root of a times b.

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