Laboratory Analysis: Mechanical Properties of Bone

Lab 7:

Mechanical Properties of Bone

Submitted By

DeAndria Hardy

Date of Experiment: November 13, 2008

Introduction

The purpose of this lab was for students to gain a better understanding of the mechanical properties of bone. To achieve this objective, femur chicken bones were loaded uniaxially until failure, or a break, occurred. By analyzing the bones under three different loading speeds and three different temperature conditions a comprehensive compilation of the bone’s mechanical properties was reached. The speeds used were 5mm/m, 10mm/m and 100mm/m. The temperature conditions were room, hot, and cold.

The properties calculated were: the maximum load the bone withstood the maximum stress the bone withstood, bone toughness, and the modulus of elasticity. These four properties were calculated for each of the 55 bones tested and an average of each parameter taken across all speeds and temperatures. Two-tailed t-tests were used to further evaluate the mechanical properties across the various conditions.

Materials

Raw chicken drumsticks, stripped of flesh and cartilage

Basin of Ice Water

Basin of Hot Water

Methods

This lab was performed as a class. The experiment was broken into four stations: original measurement, load testing, post break measurements, and recording- this allowed each student an opportunity to participate.

The original measurement station involved labeling each bone on both ends with its numerical order, marking a center line, and marking lines three centimeters to either side of the center. After these marks were placed another student measured the total length in centimeters of the bone. These measures were hand recorded. The next station was performed by the lab teaching assistants. After each bone was properly marked the teaching assistant loaded the bones for testing. The first 11 bones were loaded and test at 5mm/m, the second set of 11 bones at 10mm/m and the third set of 11 at 100mm/m. After the first 33 bones were tested at room temperature the fourth and fifth set of 11 bones were tested under other temperature conditions. The fourth set was tested at a speed of 10mm/m after being submerged in hot water. And the fifth set was tested at a speed of 10mm/m after being submerged in an ice bath.

Once the bones reached failure the teaching assistant handed them off to the third, or post break measurements, station. At this station students took six measurements using calibrated calipers. These measurements were the outside diameter perpendicular and parallel to the load point, and four points of measurement of the bone wall’s thickness. These six measurements were taken for each bone and hand recorded.

The final station involved correlating and transferring all measurement taken by hand into a class Excel spreadsheet. The load and extension measurements from the testing performed by the teaching assistants were sent in a separate file.

Results

Table 1- Max Load, Max Stress, Toughness, and Modulus for each test condition

Loading Speed/Treatment Max Load Max Stress Toughness Modulus5mm/m 106.93 1.49E+11 2.18E+07 6.81E+035mm/m 196.855 6.51E+10 5.69E+07 1.14E+035mm/m 188.891 6.97E+10 3.57E+07 1.95E+035mm/m 166.436 8.06E+10 2.28E+07 3.53E+035mm/m 90.333 5.20E+10 1.84E+07 2.83E+035mm/m 248.407 1.05E+11 2.26E+06 4.63E+045mm/m 113.894 3.94E+10 2.13E+07 1.85E+035mm/m 160.406 5.37E+10 3.31E+06 1.62E+045mm/m 124.026 1.11E+11 3.82E+07 2.91E+035mm/m 125.835 8.50E+10 2.96E+07 2.87E+035mm/m 128.376 5.79E+10 4.20E+07 1.38E+0310mm/m 150.328 9.34E+10 7.08E+07 1.32E+0310mm/m 121.361 5.03E+10 1.19E+07 4.22E+0310mm/m 161.997 7.40E+10 8.49E+07 8.72E+0210mm/m 227.238 5.60E+10 1.81E+07 3.09E+0310mm/m 169.395 9.84E+10 9.51E+07 1.03E+0310mm/m 110.302 6.28E+10 9.24E+06 6.80E+0310mm/m 187.768 6.20E+10 5.61E+06 1.11E+0410mm/m 174.398 1.47E+11 7.17E+07 2.05E+0310mm/m 135.621 2.88E+10 6.50E+06 4.43E+0310mm/m 197.779 5.49E+10 1.11E+08 4.93E+0210mm/m 157.752 5.38E+10 6.23E+07 8.64E+02100mm/m 168.904 9.33E+10 2.01E+07 4.65E+03100mm/m 193.831 1.26E+11 2.04E+07 6.18E+03100mm/m 183.574 9.62E+10 6.61E+08 1.45E+02100mm/m 194.028 7.79E+10 2.36E+07 3.30E+03100mm/m 163.592 6.77E+10 2.44E+07 2.77E+03100mm/m 195.903 7.08E+10 1.64E+08 4.31E+02100mm/m 193.289 8.03E+10 1.85E+07 4.34E+03100mm/m 100.547 4.59E+10 1.30E+08 3.54E+02100mm/m 210.272 8.96E+10 4.20E+08 2.13E+02100mm/m 169.233 6.42E+10 2.34E+07 2.75E+03

100mm/m 102.47 4.78E+10 3.67E+06 1.30E+04Hot Water Treatment











10mm/m 127.95 7.66E+10 4.51E+06 1.70E+04Cold Water Treatment











10mm/m 134.691 4.05E+10 2.98E+06 1.36E+04

Table 2-Average Values of Max Load, Max Stress, Toughness, and Modulus

For each condition

Max Load Max Stress Toughness Modulus5 mm/m average 150.035 7.89E+10 2.66E+07 7.99E+03

5mm/m std's 47.133 3.20E+10 1.63E+07 1.34E+04

10mm/m average 163.085 7.10E+10 4.98E+07 3.29E+0310mm/m std's 34.015 3.18E+10 4.01E+07 3.24E+03

100mm/m average 170.513 7.81E+10 1.37E+08 3.47E+03

100mm/m std's 36.863 2.30E+10 2.13E+08 3.77E+03

Hot Water Treatment average 137.667 7.13E+10 6.67E+07 3.89E+03Hot Water std's 39.541 1.39E+10 4.54E+07 6.33E+03

Cold Water Treatment

average 164.462 8.70E+10 4.02E+07 9.28E+03Cold Water std's 59.165 3.16E+10 5.16E+07 8.61E+03

T-Test (5mm/m, 10mm/m) 0.543 0.605 0.115 0.255

T-Test (5mm/m, 100mm/m) 0.228 0.942 0.113 0.348T-Test (10mm/m,100mm/m) 0.656 0.622 0.209 0.915

T-Test (room, hot) 0.188 0.979 0.428 0.796T-Test (room, cold) 0.949 0.149 0.702 0.094T-Test (cold, hot) 0.147 0.172 0.190 0.140

Graph 1-Max Load, speed comparison

Maximum Load (speed comparsion)

0

50

100

150

200

250

1

Speed

Av

era

ge

Ma

xim

um

Lo

ad

(N

)

5mm/m

10mm/m

100mm/m

Graph 2- Max Stress, speed comparison

Maximum Stess (speed comparison)

6.60E+10

6.80E+10

7.00E+10

7.20E+10

7.40E+10

7.60E+10

7.80E+10

8.00E+10

1

Speed

Av

era

ge

Ma

xim

um

Ste

ss

(N/m

^2

)

5mm/m

10mm/m

100mm/m

Graph 3-Toughness, speed comparison

Toughness (speed comparison)

0.00E+00

2.00E+07

4.00E+07

6.00E+07

8.00E+07

1.00E+08

1.20E+08

1.40E+08

1.60E+08

1

Speed

To

ug

hn

es

s (

J/m

^3

)

5mm/m

10mm/m

100mm/m

Graph 4-Modulus of Elasticity, speed comparison

Modulus (speed comparison)

0.00E+00

1.00E+03

2.00E+03

3.00E+03

4.00E+03

5.00E+03

6.00E+03

7.00E+03

8.00E+03

9.00E+03

1

Speed

Mo

du

lus

of

Ela

sti

cit

y (

n/m

^2

)

5mm/m

10mm/m

100mm/m

Graph 5- Max Load, temperature comparison

Maximum Load (temperature comparison)

0

50

100

150

200

250

Temperature

Ave

rage

Ma

xim

um

Lo

ad (N

)

Room Temperature

Hot Water

Cold Water

Graph 6- Max Stress, temperature comparison

Maximum Stress (temperature comparison)

0.00E+00

1.00E+10

2.00E+10

3.00E+10

4.00E+10

5.00E+10

6.00E+10

7.00E+10

8.00E+10

9.00E+10

1.00E+11

1

Temperature

Av

era

ge

Ma

xim

um

Str

es

s

Room Temperature

Hot Water

Cold Water

Graph 7-Toughness, temperature comparison

Toughness (temperature comparison)

0.00E+00

1.00E+07

2.00E+07

3.00E+07

4.00E+07

5.00E+07

6.00E+07

7.00E+07

8.00E+07

1

Temperature

To

ug

hn

es

s (

J/m

^3

)

Room Temperature

Hot Water

Cold Water

Graph 8- Modulus of Elasticity, temperature comparison

Modulus (temperature comparison)

0.00E+00

1.00E+03

2.00E+03

3.00E+03

4.00E+03

5.00E+03

6.00E+03

7.00E+03

8.00E+03

9.00E+03

1.00E+04

1

Temperature

Mo

du

lus

of

Ela

sti

sit

y (

n/m

^2

)

Room Temperature

Hot Water

Cold Water

Graph 9-Yield Stress for Bone 1

Discussion

For each bone the moment at the point of the load, the moment of inertia, stress and modulus of elasticity were calculated. The modulus of elasticity for each bone was calculated only on the portion of the data where the stress-strain curve remained elastic. This was done in accordance with Hooke’s Law. Hooke’s Law suggests, in theory, that if the load were removed at any point during the elastic portion before the yield load was reached the bone should remain intact. This is due to the principle that during the elastic region, the bone retains an amount of

recoil thus it is able to somewhat recover from the load. The closer to the yield point the less elastic the bone properties are. In general if the load was removed approximately midway on the curve through the elastic region the bone would probably only be dented, but still intact. If the load was removed closer to the yield point there’s a higher probability that the bone would crack, but not break completely.

While calculating the modulus of elasticity the yield stress was also analyzed. The yield stress represents the point where Hooke’s Law no longer applies. Once the yield stress is reached the deformation is no longer elastic. At this point on the stress-strain curve the deformation has become plastic and recovery is no longer occurs. In Graph 9, the yield stress occurs approximately at a load of 200 N. The slope of the elastic portion of the graph correlates to the modulus calculated although they are not identical. The modulus calculated is higher than the one observed on the graph. This discrepancy is associated with human error. The calculation of the modulus is based on a chosen point, while the graph and trendline take into account all points. This graph can also be used is estimating toughness. Toughness represents the bones resistance to failure. This like the modulus is calculated only up to the yield point.

Along with calculating the various properties of the chicken bones t-tests were done to compare the results across parameters. Table 2 lists the averages and standard deviations across parameters as well as the t-tests. In general the most significant differences occurred in relation to the hot water conditions with all others. This condition presented the lowest tolerable Max Load yet presented the toughness. This is due to the hot water affecting the bones properties. By submerging the bones it hot water it made them more pliable and this increasing their ability to resist failure. The most noticeable and expected correlation was between the 100mm/m speed and the cold water condition. Across the board these two conditions presented the lower toughness, higher max load, and higher max stress.

In comparison, the chicken bones tested most resemble the mechanical properties found in the bones of a healthy 21 year old male. Graphs like Figure 9 occurred throughout the bone testing. Although the numbers are significantly different these graphs follow the same pattern of bones an average healthy male. Both the bones of a healthy male and those of room temperature bones tested at 10mm/m present high yield strength, a high modulus of elasticity, and high stress. The comparison of this data lends way to comparisons of how conditions like the slow, medium, and fast loading would present themselves in real life situations. Although the loading would occur longitudinally rather than uniaxially the results should still correlate in the same manner. The resulting properties of the slow speed of 5mm/m can be likened to the properties in a human bone during leisurely walking. Likewise the 10mm/m to human bones when doing a leg

press at the gym, the 100mm/n to a human bone during a car crash, the hot water temperature to human bones during exercise in extreme heat and humidity, and the cold water temperature to human bones during extended winter activities like skiing.

Conclusion

Upon completion of the lab students gained a better understanding not only of mechanical properties of bones but also how various conditions affect those properties. The lab experiment involved other calculations, aside from the primary parameters of analysis. The intermediate calculations of moments and inertia allowed a better scope of how the conditions correlated or differed from one another. The student t-test was also a valuable tool in assessing the parameters across all conditions. The t-test showed that the least correlated parameters across conditions existed among the Modulus of Elasticity between the room temperature and cold water bones. Vice versa the greatest correlation existed among the Max Stress between the room temperature and hot water condition. Overall the t-test revealed larger correlations among the temperature conditions than the speed conditions. Through discussion this lab presented the opportunity to see how the conditions simulated in the experiment can be applied to human subjects in real world situations.

Laboratory Analysis: Mechanical Properties of Bone

Education

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