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If engineers use viscoelastic materials in their designs or if their devices are intended to operate in environments with viscoelastic materials, it is imperative that they understand how viscoelastic materials behave. As an example, during the construction of the Fort Point Channel Tunnel in Boston, concrete ceiling panels were hung using bolts embedded in epoxy a type of polymer.

Over time, the bolts pulled out of the epoxy causing a three-ton panel to crash on the roadway below. The panel landed on a car carrying a young couple, killing the female passenger and injuring the male driver. The epoxy used was a viscoelastic material that deforms over time when a force is applied to it until it reaches an equilibrium state creep.

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In this case, the concrete panel weighed too much for the epoxy and caused it to deform to the point of failure. The failure of this panel set off a chain reaction that eventually led to 12 tons of concrete falling to the roadway below see Figure 1. After inspection of the tunnel, unsafe bolts were identified. Had engineers fully understood viscoelasticity, this incident might have been avoided.

You can see that it is important for all types of engineers to fully understand viscoelasticity if they are going to design devices that use or interact with polymers or biological materials. Present the following information to students, with or without the attached PowerPoint presentation.

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Viscoelasticity: Viscoelastic materials exhibit both viscous and elastic characteristics when undergoing deformation. This results in time-dependent behavior, which means that a material's response to deformation or force may change over time. Think of the Using Hooke's Law to Understand Materials activity: When you hang a weight on a spring it stretches to a certain displacement.

If you take the weight off and put it back on it goes to the same displacement. If you let the weight hang from the spring for an hour, it does not change its displacement.

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If you slowly or quickly hang the weight on the spring, it still goes to the same displacement. This is not the case for viscoelastic materials; all of these factors can change how the material responds. The following material introduces some typical behaviors of viscoelastic materials. Strain Rate Dependence: Viscoelastic materials respond differently depending on how fast they are stretched.

Remember that displacement or stretch is related to strain, so the strain rate defines how fast the material is stretched. Therefore, viscoelastic materials are said to be strain rate-dependent. This can be demonstrated easily with silly putty. Encourage students to stretch their silly putty at different rates and observe the behavior.

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If you slowly stretch silly putty slow strain rate , the material seems to stretch forever, is very pliable, and behaves more like a highly viscous fluid. If you quickly stretch the silly putty fast strain rate , then it breaks immediately without much displacement, seems stiff, and behaves more like a solid with little elasticity. The same material has two very different responses to a force depending on how fast the force was applied!

It seems that faster strain rates cause more elastic responses and the material behaves more like a solid stiffer , whereas slower strain rates cause more fluid-like behavior. This is a common characteristic of viscoelastic materials. Figure 2. Stress-strain diagram of a biological material that was exposed to two different strain rates. Figure 2 shows the difference in response of a biological material when it is stretched fast compared to slow.

Both tests produced an initially curved response followed by a linear region, which is a typical stress-strain curve of viscoelastic materials. The fast strain rate produced a smaller curved region, in which the radius of curvature is small. The slow strain rate produced a very large curved region with a large radius of curvature. The linear region of the fast strain rate has a larger slope than the slow strain rate.

This graph supports qualitative observations of silly putty.

The curved region represents the viscous response of the material; a larger curved region suggests a more viscous response. The linear region represents the elastic response of the material; a larger slope represents a stiffer material. Stress Relaxation: If you apply a constant displacement to a viscoelastic material, then the force to hold the material in this configuration decreases over time.

An example of stress relaxation is when a rubber band, which is a polymer, is wrapped around a newspaper for an extended period of time. The rubber band is held at a constant displacement, however the force that it is applying to the newspaper decreases over time and it loses its integrity. The force continues to decrease until the material reaches an equilibrium in which the force becomes constant. Figure 3. Stress vs. This response is termed stress relaxation. Figure 3 shows a stress vs. The initial vertical line represents the amount of force or stress it took to displace the material.

As the material is held at that displacement, the stress in the material or force it takes to hold the material at that displacement decreases over time. Towards the end of the graph, the line becomes horizontal, indicating that the stress is no longer changing and the material has reached equilibrium. Creep: If you apply a constant force to a viscoelastic material, then the displacement increases over time.

When this force is released, it takes time for the material to recover to its initial configuration. An example of creep is when a bungee cord a polymer is used to hang a bike from the ceiling to save floor space. The bike is the constant force, so the bungee cord lengthens over time.

Similar to stress relaxation, the displacement increases until the material reaches an equilibrium in which the displacement becomes constant. This was the cause of failure of the epoxy holding the concrete ceiling panels in the Fort Point Channel Tunnel see Figure 1. The epoxy that held the bolts underwent creep and never reached equilibrium before the panels fell.

Figure 4. Strain vs. This response is termed creep. Figure 4 shows a strain vs. The initial vertical line represents the initial strain that the material experienced due to the force. This is similar to springs that immediately stretch when a force is applied. With the force constantly applied, the material continues to strain or displace over time.

Eventually the material reaches equilibrium, which is seen by the horizontal line.

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When the force is removed, the initial decrease in strain is equal to the amount of strain the material instantaneously experienced when it first had the force applied. Over time, the material returns to its original configuration and its strain becomes zero. Hysteresis : When a weight is applied to a spring, the spring stores energy to be able to return to its original configuration once the weight is removed.

The amount of energy stored is equal to the amount of energy it took to displace the spring. When viscoelastic materials have a force applied to them and then removed, it takes more energy to displace the material than it does to return the material to its original configuration. In other words, it consumes more energy during the loading phase applying a load and stretching the material compared to the unloading phase taking the load away and allowing the material to return to its original state.

This energy difference is caused by the material losing energy during the loading phase, due to heat dissipation or molecular rearrangement within the material. Engineers calculate the amount of energy that was lost by analyzing the stress-strain diagram generated while stretching loading and unstretching unloading the material. The area between the loading and unloading curve represents the energy lost. Figure 5: Stress-strain diagram of a biological material that was loaded and then unloaded.

The area between the two lines is equal to the energy lost during this process. This is termed hysteresis. Figure 5 shows a stress-strain curve that was generated by loading and unloading a biological material.

The loading portion is the top curve and the unloading region is the bottom curve. Figure 6. Force vs. The peak force and hysteresis decrease with each cycle. This is termed preconditioning. Preconditioning: If the viscoelastic material is continued through this loading and unloading process, then the amount of energy lost in a cycle decreases until it reaches equilibrium close to zero energy lost. The amount of force it takes to displace the material also decreases with more cycles until the equilibrium point is reached. Exposing a viscoelastic material to this type of cyclic loading allows the viscous part of the material response to be dissipated and only the elastic portion remains.

This is why the material is able to reach equilibrium. The viscous part of a material response can be difficult to fully characterize and understand, but the elastic behavior is easily understood and repeatable, making preconditioning useful to engineering researchers who need to compare elastic solids to viscoelastic materials.