Journal of Undergraduate Research
Volume 4, Issue 12 - September 2003

Fractographic Analysis of Manatee Rib Bone

Sara Shmalo

ABSTRACT

Image 1. Manatee. This photo was borrowed from the U.S. Fish and Wildlife Services Webpage
Image 1. Manatee. This photo was borrowed from the U.S. Fish and Wildlife Services Webpage

The Florida manatee (Trichechus manatus latirostris), an endangered specie, is considered to be one of the most threatened marine mammals found in United States waters. Approximately, one-fourth of all manatee deaths, from 1976-2001, can be attributed to watercraft-related accidents [1]. By reducing watercraft-related mortality, the Florida manatee can be saved. Usually when a manatee hears a boat approaching it comes to the surface. This makes it easy for a boat to strike a manatee. Impact by a boat’s propeller or hull can lead to the fracture of a manatee’s ribs [2,3]. In order to establish safe boat speeds for manatee protection, an estimate of the forces required to fracture manatee bone is needed. An understanding of manatee rib fracture can be used in the prediction of critical impact loads, thereby providing the basis for scientifically valid wake zone speeds.

This project involves identifying a technique to measure the toughness of manatee ribs by applying the principles of fracture mechanics. The objectives of this project are to accurately locate and record the size of the crack origin, determine the geometric factor from the crack origin, and calculate the fracture toughness in terms of KIC.

This study shows that the average toughness of manatee ribs is 2.2 MPa*m^(1/2) with a standard deviation of .5 MPa*m^(1/2). This data forms a normalized Gaussian distribution and helps to explain the complex microstructure of manatee ribs.

INTRODUCTION

Attempts have been made to regulate boating activities by establishing speed zones in areas where manatees and boats coexist [7]. Often, the creation of these boat speed zones is a highly subjective process that utilizes arbitrary standards. These zones are not based on what actually happens when a boat impacts a manatee. When a manatee senses a boat is approaching it rises to the surface of the water. The propeller wounds the flesh of a manatee, while the hull actually fractures the ribs [4]. The broken ribs can then puncture the manatee’s lungs and result in their death. In order to establish safe boat speeds for manatee protection, an estimate of the forces required to fracture manatee bone is needed. An understanding of manatee rib fracture can be used in the prediction of critical impact loads, thereby providing the basis for scientifically valid wake zone speeds. This will be a more objective approach for establishing boat speed zones to reduce watercraft-related mortality.

The fractography method is applicable in this procedure because unlike most bones, manatee bones are highly mineralized. Therefore, fracture of the ribs is very similar to the ceramic fracture process. We can then apply established fracture analysis techniques used for ceramics to manatee ribs.

Fracture toughness is the ability to resist fracture, measured as the critical stress intensity factor (KC). This factor is an estimate of a materials ability to resist cracking which can lead to breakage. By applying the principles of fracture mechanics to manatee ribs, the fracture toughness can be calculated.

Finding the crack origin involves identifying characteristic fracture surface features using the principles of fractography, which have been developed over the last 50 years. The ease of this task is determined by the porosity and homogeneity of the material. For example, glass is a homogeneous material where one is easily able to identify the crack origin. Bone is substantially more difficult because of varying degrees of porosity, uneven fracture surfaces, and its compositional variations.

Manatee ribs are composed mostly of plexiform bone, a type of compact bone [8]. Based strictly on observation, manatee calves have between 30-50% porosity and adults have 1-2% porosity. Plexiform bone becomes more condensed as a manatee ages and the bone increases in strength and toughness. In the adult manatees the porosity is filled in and the bone becomes denser, but some porosity is still visible in the outer edges of the rib. The adult ribs form an elliptical shape. As manatee bones develop, the bone grows and creates voids. Simultaneously, marrow is deposited between the empty spaces to make the bones more dense, less porous, and stronger. The pores in the bone are not always uniformly distributed. There is greater toughness in the bones closer to the spine of the manatee and lesser strength towards the dorsal end of the animal [9].

The adult manatees have uniform strength from the head to tail. The sub-adults lack this uniformity. A cross-section taken from a sub-adult shows that one side of a rib can be more porous while the other side of the cross-section is denser and has more marrow content.

<p class="paper">&nbsp;</p> <p class="paper"><span class="papertitle">INTRODUCTION</span></p> <p class="paper"><br />

Image 2. Manatee. This image was borrowed from the Save the Manatee webpage.

MATERIALS AND METHODS

The manatee ribs were obtained from whole manatees of known length and cause of death. The manatee ribs were cut into cross-sectional areas, divided into rectangular bars with dimensions 3mm x 3mm x 50mm, and subjected to loading in 3 point flexure until fracture.

Figure 1. This is a model that depicts a 3 point flexure test.

Figure 1. This is a model that depicts a 3 point flexure test. The span is 40 mm, and is the distance between the bottom two points. The force on the compressive side is centered directly in the middle of the sample. The length of the specimen is 50 mm and its width and height are 3 mm each.

When the rectangular bars are loaded in 3 point flexure tests, fracture usually occurs on the tensile side of the material where the largest flaw is located. Fractography is then used to measure the flaw size so we can determine the critical stress intensity factor, KC. Using the size of the flaw or crack at the origin, the stress at fracture, and the geometric factor, the fracture toughness can be calculated. The fracture toughness formula is shown below:

Equation 1 This is the fracture toughness equation where KC, is the critical stress intensity factor, Y, is the geometric factor, s, is the stress at fracture, and c, is the flaw size. The geometric factor, Y, is a value related to the shape and position of the crack origin (YP) and is also a function of crack length (c) and width of specimen (W) [9].

Therefore, Y can be expressed as [9]:

Equation 2 This formula is used to calculate the geometric factor, Y, and accounts for the shape and position of the fracture origin.

Equation 2 This formula is used to calculate the geometric factor, Y, and accounts for the shape and position of the fracture origin.

There are three types of cracks that can be detected in manatee rib bones: corner, side and internal. For each crack type there are different geometrical factors. For corner cracks, YP = 1.4, for edge circular cracks YP = 1.24, and for circular internal cracks, YP = 1.12 [9]. Y(c/W) is the finite width correction factor expressed by [9]:

Equation 3 This formula represents the finite width correction factor.

Equation 3 This formula represents the finite width correction factor.

This correction factor is needed when the crack sizes of the specimen are relatively larger than the width of the sample. The stress at failure, s, was determined from the 3 point flexure test. This value gives the maximum stress at failure and sometimes needs to be adjusted. If the flaw is not located directly at the center of the specimen, the failure did not occur at the maximum stress and needs to be corrected [9].
The flaw size, c, is based on the dimensions of the flaw. In this case c forms elliptical or semi-circular shaped cracks and Formulawhere the major axes of the flaw are 2a and 2b.

The way to detect the proper fracture origin is to look at the fracture surface under the optical microscope and identify the characteristic markings. These regions radiate from the flaw and help to identify the origin of the crack. There are markings called twist hackle (river markings) which can be seen on the fracture surface and can be traced back to the fracture origin.

Also, the Gaussian probability distribution will be used. The Gaussian probability distribution has a mean m and standard deviation s. This is a normalized Gaussian function of the form:

Equation 4 This equation with be used to represent the probability of obtaining a certain toughness value.
Equation 4 This equation with be used to represent the probability of obtaining a certain toughness value.

RESULTS

The results I obtained from my research are shown in the graphs below. Also, attached as appendix A is a table containing all my measurements.

Figure 2 This graph shows strength increases with decreasing crack size
Figure 2 This graph shows strength increases with decreasing crack size. These results are not unreasonable because manatee ribs are not a homogenous material. Different cross sections of the rib are more porous give rise to ultimately more than one material.

Figure 3. This graph represents Toughness vs. Crack Size
Figure 3. This graph represents Toughness vs. Crack Size. It shows that the toughness of manatee ribs increases with flaw size and follows R-curve behavior.

Figure 4 This Gaussian distribution shows Probability vs. Toughness
Figure 4 This Gaussian distribution shows Probability vs. Toughness. It has an average toughness value of 2.2 MPa*m^(1/2) and a standard deviation of .5 MPa*m^(1/2).

DISCUSSION

This Fractography analysis relies on a straightforward methodology. Its procedure is to observe a fracture surface, locate fracture markings, and follow them to the origin. However, these steps tend to become more difficult tasks when looking at more complex microstructures. In the case of manatee ribs, it required just learning about the microstructure and becoming familiar with its pattern. The microstructure of the bone changed depending upon the structures porosity. Since the material is not homogonous like glass, it becomes very difficult to determine the boundaries of the crack.

The problems I encountered when studying the fracture surfaces of the bone was accurately measuring the crack size. I was easily able to identify crack origins, but I had difficulty measuring the crack boundary. Also, the cracks usually were on many planes and it required changing focus to determine the exact dimensions of the crack. I think that it is difficult to obtain an accurate reading as to the dimensions of the crack, but everyone will be in agreement as to where the crack originated.

The results obtained are all in agreement with one another. Figure 2 shows that strength increases with decreasing crack size. At first glance this graph seems to be confusing and there could have possibly been an error in the experiment. This graph was expected to show a linear line that increases. Noting where the data is located, it appears this way because we are observing at least two different populations. Although we are only looking at manatee ribs, the material is not homogenous throughout and some regions of bone are more porous than other regions.

Figure 3 depicts that fracture toughness increases with increasing flaw size. This set of data follow R-curve behavior. R stands for crack resistance and indicates that the fracture toughness is not a constant value and it can increase with increasing crack length [5].

Finally, figure 4 is a plot of a normalized probability distribution, which gives a “bell shaped curve.” This graph gives a mean toughness of 2.2 MPa*m^(1/2) and a standard deviation of .5 MPa*m^(1/2). From the toughness value of these manatee ribs, the strength of a fractured rib from a dead manatee can be determined from the examination of the fracture surface and determination of the critical crack size using Equation 1. Once the strength is known, then an estimate of the impact force can be determined using standard physics and mechanics principles. Once the impact force is known, an estimate of boat speeds for different weight boats can be determined.

CONCLUSION

Developing scientifically valid standards ensures that greater protection can be afforded the manatee without capriciously regulating human activity.

ACKNOWLEDGEMENTS

I would like to thank Dr. Mecholsky for being my mentor and advising me with the University Scholar’s Program. I also want to thank Bratt Yan for taking me under his wing and exposing me to the world of manatees. With his help, I became able to look at a rib sample and detect the fracture origin. Throughout the entire summer he supported me and provided me with all the tools I needed to obtain data and conduct meaningful research. Bratt has instilled me with many skills and Dr. Mecholsky exposed me to the world of fracture and its many applications; to both of them I am very thankful.

REFERENCES

  1. Manatee Mortality 1976-2001. http://www.savethemanatee.org/mortalitychart.htm
  2. Manatee Mortality Statistics. http://www.savethemanatee.org/mort.com.
  3. Florida Marine Research Institute. http://www.floridamarine.org/features/view_article.ask?id=6780.
  4. Making Sense of Manatees. http://rgp.ufl.edu/explore/v07n2/manatees.html.
  5. Greene, David. An Introduction to the Mechanical properties of Ceramics.Cambridge University Press. 1998.
  6. Gaussian Distribution from MathWorld. http://mathworld.wolfram.com/GaussianDistribution.html.
  7. Clifton, K.B. Fractographic Analysis of Manatee Rib Bone. http://www.vetmed.ufl.edu/flmmhc/PDF%20files/PosterPDFs/Rehabilitation%20Postser%20Clifton%20et%20al.pdf.
  8. Martin, R. B., Burr, D. B., and Sharkey N. A. (1998). “Skeletal Tissue Mechanics”. Springer-Verlag, New York, 31-38 p.
  9. Yan, Jia-Hau (Bratt). Biomechanical Properties of Manatee Rib Bone and Analytical Study By Using Finite Element Analysis. University of Florida, 2002.

--top--

Back to the Journal of Undergraduate Research