bone structure and mechanical properties

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The Influence of Applied Forces on Different Materials
Background
External forces applied to a solid object may compress, stretch, twist, or bend it out of shape. The ability of an object to return to its original form when the external forces are removed is called the elasticity of the solid. If too much deformation occurs, the object will not return to its original shape - its elastic limit has been exceeded. The study of the elastic properties of materials is an important area of physics. This shouldn't scare you because all of us have experience with bending, twisting, smashing, and stretching different materials almost every day of our lives. In fact, every time we walk or run, our bones are being "smashed" down to some extent constantly. And if any of you have ever broken a bone, you might have done so because the bone was twisted. In this exercise we will first learn a little about how different forces affect different materials and then we will actually apply different forces to things and observe how they are affected. That's right, you will actually be designing an experiment where you will be able to smash, bend, twist, stretch, and break different things, in a way that you will define! But let's begin with some background information to understand how different forces affect different materials.
Essentially all materials yield to some extent under the influence of applied forces, including bone. Ultimately, the change in shape or volume of a body when outside forces act on it is determined by the strength of the material. The strength of a material depends largely on three main factors:

the kind of material, or what it is made of;
the physical characteristics of the material receiving the force, including cross sectional area, geometry (shape), and density (how close together the molecules are); and,
the molecular forces holding the material together (either electrochemical forces, or physical binding forces).Of course, the ability of the material to withstand forces also depends on the kinds of forces that are being applied.
Figure 12.


Let's examine the electrochemical and binding nature of the molecular forces in bone. Compact bone is composed of repeating segments of collagen fibers that appear every 680 Angstroms (the angstrom (A) is a unit of length and is equal to 10 cm) along its length; hydroxyapatite crystals lie within to each segment of the fiber, bound tightly to it (Figure 12). This intimate bonding prevents shear in the bone; that is, it prevents the crystals and collagen fibers from slipping out of place. Such stability is essential in providing strength to the bone. In addition, the segments of adjacent collagen fibers overlap each other, also causing hydroxyapatite crystals to be overlapped like bricks keyed to each other in a brick wall. This produces a very orderly 3-dimensional collagen/crystal composite. The hydroxyapatite crystals (Ca10[PO4]6[OH]2) themselves contain electrochemical forces that keep the calcium, phosphate, and hydroxide molecules together in the right combination.

As mentioned earlier in the chapter:

collagen fibers of bone have great tensile strength (the strength to endure being pulled apart);
calcium salts have great compressional strength (the strength to endure being squeezed).
These combined properties, plus the degree of bonding between the collagen fibers and the crystals, provide a bony structure that has both extreme tensile and compressional strength. In fact, bones are constructed in exactly the same way that reinforced concrete is constructed. The steel of reinforced concrete provides the tensile strength, while the cement, sand, and rock provide the compressional strength. Bone, on a weight basis, is stronger than concrete.
Figure 13. Uniform compressional and tensile forces applied to materials that we understand create predictable stresses. On the other hand, torsional forces are much more difficult to control and Often create more damage.


The direction and magnitude of applied forces will also influence how well a material can withstand those forces. Uniform forces are those that are applied evenly to a material, while non-uniform forces are those that are applied unevenly and can create the most damage. A uniform compressional force and a uniform tensile force are shown in Figure 13. These forces create predictable stresses on materials that are familiar to us. If we are familiar with a material, this means that the molecular forces within the material and the nature of the material is known. Normal human bone is fairly well understood, but a number of factors (e.g., age, gender, state of health including the presence of osteoporosis, etc.) can alter the molecular strength of a bone. Therefore, it is often difficult to determine how any particular bone that is not normal will behave under great stress.

The other force that is shown in Figure 13 is the torsional, or twisting force. It is much more difficult to predict how a material will respond to this kind of force because it is very difficult to produce a uniform twisting effect. Therefore, even with their great compressional and tensile strengths, neither bone nor concrete has a very high level of torsional strength (the strength to endure being twisted).

The term strain refers to the relative change in dimensions or shape of a material which is subjected to stress. That is, strain is the amount of deformation that occurs to a material under stress. Associated with each type of stress, or force, is a corresponding strain. If the stress or applied forces are uniform, the strain on a material can be calculated. In order to define tensile and compressional strains, let's consider an example where uniform stresses are being applied to a one-dimensional metal bar (Figure 14).



Figure 14. (a) A metal bar increases in length due to uniform tensile stress. (b) The bar decreases in length due to uniform compressional stress.


The tensile strain on a body is defined as the ratio of the increase in length of the body to the original length.
Tensile strain = l - lo

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lo

The compressional strain of a body is defined as the ratio of the decrease in length of the body to the original length.
Compressional strain = lo - l

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lo

We will not define torsional strain because twisting is more complicated to represent in a simple way, and our one-dimensional example of a metal bar is not an appropriate model to demonstrate torsional stress and strain. You have probably experimented with such forces without even knowing it by twisting an empty soda can, producing a torsional strain on the can.

Figure 15. A typical stress-strain diagram for a ductile metal undergoing tension.

Finally, when any stress is plotted on a graph against the resulting strain for a material, the resulting stress-strain diagram is found to have several different shapes, depending on the kind of material. As an example of a stress-strain diagram, Figure 15 illustrates the behavior of a particular metal when subjected to increasing tensile (stretching) stress. Let's examine the different sections of the graph.

(1) During the first portion of the curve (up to a strain of less than 1%), the stress and strain are proportional. This holds until the point a, the proportional limit, is reached. We know stress and strain are proportional because this segment of the line is straight. The fact that there is a region in which stress and strain are proportional is called Hooke's Law, named after a physicist named Robert Hooke (1635-1703). The ratio of stress to strain, or the stress per unit strain, is called an elastic modulus or Young's modulus. This relationship can be written as:

Young抯 modulus (Y) = Stress

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Strain

and is essentially the slope of the straight line on the stress-strain diagram. Every material has a unique Young's modulus value. That is, the stress required to produce a given strain depends on the nature of the material under stress. The larger the Young's (electric) modulus for a material, the greater stress needed for a given strain. That is, the greater the Young's modulus for a material, the better it can withstand greater forces.

(2) From a to b on the diagram, stress and strain are not proportional, but nevertheless, if the stress is removed at any point between O and b, the curve will be retraced in the opposite direction and the material will return to its original shape and length. In other words, the material will spring back into shape in a reverse order to the way it sprung out of shape to begin with. In the region Ob, then, the material is said to be elastic or to exhibit elastic behavior and the point b is called the elastic limit.

(3) If the material is stressed further, the strain increases rapidly, but when the stress is removed at some point beyond b, say c, the material does not come back to its original shape or length but returns along a different path to a different point, shown along the dashed line in Figure 15. The length of the material at zero stress is now greater than the original length and the material is said to have a permanent set.

(4) Further increase of stress beyond c produces a large increase in strain until point d is reached at which fracture takes place. From b to d, the metal is said to undergo plastic deformation. If large plastic deformation takes place between the elastic limit and the fracture point, the metal is said to be ductile. Such materials are capable of being drawn out like a wire or hammered thin like gold leaf. If, however, fracture occurs soon after the elastic limit is passed, the metal is said to be brittle.

In this section, you have been exposed to many new terms as we've reviewed different points related to the strength and elasticity of materials. Now it is time to apply this knowledge in a demonstration of how various kinds of stresses, or forces, will affect various kinds of materials. Your entire class will design the experiment in a way that will demonstrate many of the concepts described in this section. Then your class will be broken into small groups and, within each group, you will perform the experiment. Follow the guidelines for this activity that are provided by your teacher as well as the steps provided in the "Procedure" section below. And above all, read everything before you begin.


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Materials
Various materials differing in:
kinds of material,
cross-sectional area,
density, and
geometry (shape).
Various instruments to produce forces such as:
small household hammer,
large rubber hammer,
mortar and pestle,
some kind of a stretching mechanism.
Procedure
Step 1
Before breaking into groups based on your teacher's direction, discuss as a class the different kinds of materials that you plan to use in your demonstration. The class should select items that will demonstrate three different levels of response (no response, partial response, and total fracture) to: (1) a compressional stress, (2) a tensile stress, and (3) a torsional stress. Think of things that would represent a variety of kinds of materials. And then think of things that vary in cross-sectional area, shape, density, and elasticity. Each student should make a list of these items, puffing them in categories similar to that shown in Table 2.
Your teacher will provide you with a separate copy of Table 2 for you to write on. Work with your teacher to help collect enough of each item for each group.

Step 2
Break into your groups and assign one or two students as the "stressors." These are the individuals who will be applying the forces to the various materials. Before they begin to apply forces to the first item, allow the other members of the group to predict, or rate, how the material will respond. Then the stressors can begin their demonstration, using either a compressional, tensile, or torsional stress. The stresses can be applied in a uniform or non- uniform manner to compare the responses of the various materials. Each student in the group, including the stressors, should make notes about each demonstration regarding the following points:
the kind of material something is made of;
the physical characteristics of the material (density, cross-sectional area, and geometry);
the forces between the molecules in the material;
the kind of forces that are applied; and
the direction, relative magnitude, and uniformity of the applied forces.
Finally, it is important for your class to come up with a rating system so that you can rate each material in terms of its:
elasticity;
plasticity;
fracture point, indicating how brittle the material is.
Step 3
Each student should write a report that includes his/her comments and observations about each material and each demonstration. Include at the end of this report the answers (in complete sentences) to the following questions:
Which material that you tested was the most elastic and which was the least elastic of all the materials? What is the main difference between the two materials that makes them respond differently?
Which material that you tested was the most brittle and which was the least brittle of all the materials? What is the main difference between the two materials that makes them respond differently?
Do your answers to Questions 1 and 2 seem similar? Explain.
Draw a hypothetical stress/strain diagram comparing the two materials mentioned in Question 1.
Which material that you tested performed most similarly to how you understand a human bone would perform? What physical properties do the bone and this material have in common?
Well, we are finished with our "Student Investigations." Now that you more fully understand the concepts of bone growth and bone strength, let's move on to examine Dr. Holton's examination of how space flight affects these two bone properties.
Table 2. Example table of the physical characteristics of materials. Demonstration 1 2 3 4 5 Test at least 10 materials
Kind of Material
Cross-sectional area (large-med-small)
Shape (regular-irregular)
Density (high-med-low)
Elasticity (high-med-low)
Brittleness (high-med-low)
Applied Force (compressional, tensile, torsional)
Degree of Aplied force (strong-med-light)
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