Allison Roeser

April 25, 2007

Breaking Bones through Torsion

Background

In experiment #4 in which the chicken bones were broken, it was noted that the bones did not break immediately when the force was applied. Rather they bent to some noticeable degree before finally cracking. Seeing that the bones bent in the 3-point-jig setup, led me to wonder how torsion impacted the bending or twisting of bones. Torque is a force that acts tangentially to a cylinder (the bone) (3) and causes rotational rotation of the ends of the cylinder (2). I decided to study the amount of this rotational bending that a bone can withstand before it breaks. Therefore, I have expanded on experiment #4 to study the failure stress (or maximum sheering stress) at which a bone breaks when torsion is applied with a torque wrench. Since torque is a structural property, the amount of torque needed to reach the failure stress will increase as the chicken bone’s diameter increases. In contrast, failure stress is a material property; therefore, it should not change as the diameter of the chicken bone increases. It can be assumed that chicken wings and legs will exhibit the same material properties because they are both composed of collagen and calcium phosphate (1). In experiment #4, we learned that the force will peak at the moment that the bone breaks (Appendix, A). In this experiment, the same peak in torque will occur before the bone breaks, and this peak maximum torque force will be used to calculate the failure stress.

Hypothesis

The central hypothesis for this experiment is that the failure stress will be the same in chicken legs and wings. However, a sub-aim is to study the impact that radius has on the torsion force that is required to break a bone. It is hypothesized the torsion need to reach the failure stress will increase as the radius of the bone increases. Therefore, chicken legs will require a higher torsion force to break than chicken wings will.

Equipment

Major equipment

  • computer

The computer will be used to collect the torque data.

Lab Equipment

  • scalpel
  • scissors
  • tray

These materials will be used to remove the chicken from the bone.

  • calipers

The calipers will be used to measure the exterior an interior diameters of the bones.

Supplies

  • Pacer tech instant adhesive E-5
  • This adhesive is a high quality superglue will be used to glue the bones to the customized sockets. It adheres well to metals.
  • 5 chicken legs per group
  • 5 chicken wings per group

The chicken legs and wings will provide the bones that will be broken.

  • 20 Jumbo Popsicle sticks (3/4” x 6”) per group

The popsicle sticks will be used as a surrogate in order for students to experiment with the torque wrench and data collection software before they actually break the bones. This will aid them in formulating a protocol for breaking the bones.

Newly Purchased Equipment

  • Imada SW-1S data acquisition software

The Imada data acquisition software connects to a digital torque wrench and a computer. It provides a customized Excel spreadsheet that records torque data as the bone is being broken. It works very much like the software used with the Instron. Currently our bioengineering lab does not have anything that can accurately determine the torque that was applied when the bone broke. Therefore, this software is crucial to the experiment.

  • Imada DSW-20 digital torque wrench

A digital torque wrench is required to measure the torque readings with the SW-1S software.

  • 10 custom made sockets per group (Appendix, B)
  • 10 custom made vise attachments per group (Appendix, C)

The students will glue a socket to each end of the chicken bone. One socket will go into the vise and the other will attach to the torque wrench. Therefore, the vise and torque wrench will be able to grip the bone more effectively, reducing the possibility that the bone will detach from the vise or wrench before it actually breaks.

  • Wilton 3in Fixed Clamp-On Vise model # 33150

The vise will be used to hold the bone in place while the torque is applied.

Proposed Methods and Analysis

A. Testing the apparatus with popsicle stick surrogates

1. The jumbo popsicle sticks are provided to simulate the breaking of the chicken bones in order for students to become familiar with the torque wrench and the data acquisition software. Use the popsicle sticks to determine the sampling rate that will be used when breaking the bones. Data does not need to be collected.

2. Tape one end of the popsicle stick into the customized socket and tape the other end into the vise attachment.

3. Place the vise attachment into the vise and tighten. Only the metal vise attachment piece should be in the vise – not the popsicle stick.

4. Break the popsicle stick with the torque wrench. Continue breaking popsicle sticks until the group feels comfortable with the apparatus and the protocol to break the bones. Remove the taped popsicle stick ends from the customized metal pieces because they will be reused when breaking the actual bones.

B. Breaking the bones

1. Remove the meat from the chicken bones. Each wing bone consists of two bones; gently break them apart and discard the smaller of the two.

2. Using the superglue, glue a custom socket to one end of each bone and a custom vise attachment to the other end of each bone. Allow to dry.

3. Place the vise attachment into the vise and tighten. Remember, only the metal vise attachment piece should be in the vise – not the bone.

4. Fit the customized socket into the torque wrench and twist the wrench to apply force to break the bone. Collect the data with the computer software.

5.Once the bone is broken use the calipers to measure its outer and inner diameter at the point in which it broke.

Each group that performs this experiment will have two sample groups – chicken legs and chicken wings. Each sample group will consist of five bones. However, because two groups will perform the experiment on the same day, they may wish to perform the experiment together. If the team performs the experiment together than each sample group will consist of 10 bones.

C. Analyzing the data

The SW-1S software will produce an Excel spreadsheet of data of torque values for each test performed. It will be assumed that the maximum torque value reached is the torque that was required to break the bone.

Failure stress (maximum sheering stress) can be calculated with the equation

Failure stress = T(c) / J

T= maximum torque

c = radius to outer edge of chicken bone

J = π (ro4 - ri4) /2 (polar second moment of inertia of a hollow shaft)

ro4= outer radius of chicken bone(in mm)

ri4 = inner radius of chicken bone (in mm) (4)

A two-tailed unpaired t-test will assuming unequal variance will then be performed on the resulting failure stresses to determine if there is a significant difference between the failure stress in chicken legs and wings.

Potential Pitfalls

As with any experiment there are a variety of things that could adversely impact the data collected. The greatest potential problem would arise if the bone slipped out of the metal attachments before it actually broke. When the bone slipped out of the attachment, it would already be weaker from the torsion applied. Therefore, although the bone could be reglued into the socket, less torque would be required to break it than would initially have been required. Bones should only be attempted to be broken once. The more failed attempts to break a bone that occur, the weaker the bone will become.

Another important attribute that could negatively impact the data is the age of the chicken bones. Younger chickens will probably have bones that are slightly more elastic. Therefore they will rotate further before they break, meaning that more torque will need to be applied to break the bones of younger chickens and that the failure stress will be greater. The “material” of a young chicken is slightly different than the “material” of an old chicken; therefore, a material property like failure stress can vary.

Furthermore, some of the chickens that were used could have been sick or sustained an injury. Even if an injury had healed it could impact the structural integrity of the bone. A chicken bone from a chicken with an illness or injury that impacted its bones would break more easily than a healthy bone.

Another important thing to consider is that the plane that the chicken bone rests in may not be at exactly a ninety degree angle with the plane that the torque wrench moves in. Therefore, the torque value that is acquired will not be a pure torque reading. Instead there will be twisting in directions other than the one that we are attempting to measure. The customized metal pieces will aid in making the plane that the bone rests in and the plane that the wrench moves in as perpendicular as possible.

Also, the torque value that was required to break the bone was assumed to be the highest torque that the SW-1S data acquisition software provided in the Excel spreadsheet it outputed. However, the actual torque value might have been slightly higher. This would have resulted if the bone did not actually break when the highest recorded torque value occurred, but instead broke sometime between that moment and the next time a torque reading was taken. Using a lower torque value would obviously result in a lower failure stress value. Obviously, the higher the sampling rate is that the group uses,the shorter the intervals between torque readings will be and the more accurate the maximum torque values will be.

Finally, the moment of inertia that was used in the calculations was based on a long tube with a constant inner and outer diameter. In reality the shape of a chicken bone is somewhere between a rectangle and a long tube. Also, the inner and outer diameters of the bones vary widely over the entire bone. Therefore, the moment of inertia that is calculated is not completely accurate; instead, it is the closest possible approximation.

Budget

  • Torque data acquisition software SW -1S supplied by Imada $199

Purchased from

  • DSW-20 digital torque wrench supplied by Imada $985

Purchased from

  • 100 chicken wings

Purchased Fresh Grocer (4001 Walnut Street) $1.79/ lb = about $50

  • 100 chicken legs

Purchased from Fresh Grocer $1.49 / lb = about $50

  • 200 customized sockets

Purchased from about $200

  • 200 customized vise attachments

Purchased from about $200

  • Pack of 500 jumbo popsicle sticks item #CS600

purchased from $5.99

  • Wilton 3in Fixed Clamp-On Vise model # 33150

purchased from $21

  • Pacer tech instant adhesive E-5

Purchased from about $5

Total $1715.99

References

1.Bone. (2007). In Encyclopædia Britannica. Retrieved April 25, 2007, from Encyclopædia Britannica Online:

2. John B. Scalzi, "Torsion", in AccessScience@McGraw-Hill, DOI 10.1036/1097-8542.701800, last modified: August 16, 2002.

3. Nelson S. Fisk, “Torque", in AccessScience@McGraw-Hill, DOI 10.1036/1097-8542.701500, last modified: April 10, 2000.

4. Riley, William. Statics and Mechanics of Materials: An Integrated Approach. John Wiley & Sons Inc. 2002. pp.361.

Appendix

A.

Figure 1 Representative Bone Bending Fracture Force Displacement Graph. 1: Force applicator makes contact with bone. 2: End of Linear-Elastic region. 3: Ultimate Strength / Fracture occurs. 4: Fracture Propagation completely through the bone.

B. Each customized socket will be composed of a 3/8” cubed drive that will be attached to a 3/4”long, hollow metal cylinder that has a 1/4” diameter. The attachment will occur between the hole of the cylinder and the side of the cube. The bone will be glued into the hollow cylinder and the torque wrench will attach to the 3/8” drive.

C. Each customized vise attachment will be composed of a 3”x 3/8” x 3/8” metal rectangle that will be attached to a 3/4” long, hollow metal cylinder that has a 1/4” diameter. The attachment will occur between the hole of the cylinder and the 3/8” side of the rectangle. The bone will be glued into the hollow cylinder and the vise will clamp onto the 3/8” side of the metal rectangle .