Stiffness, of materials

Rheology. Determination of mechanical properties can be done in various deformation modes (shearing, compression, extension), leading to different results. Of the parameters to be determined, the modulus or stiffness of materials has been studied and explained best results can give information about structure. 

The commonly-used dynamic mechanical instruments measure the deformation of a material in response to vibrational forces. The dynamic modulus, the loss modulus, and a mechanical damping or internal friction are determined from these measurements. The modulus indicates stiffness of material, and it may be a shear, a tensile, or a flexile modulus, depending upon the experimental equipment. The mechanical damping (internal friction) gives the amount of energy dissipated as heat during the deformation. The internal friction of material is important, not only as a property index, but also for environmental and industrial application. 

The DMA measures the deformation of a material in response to vibration forces or sinusoidal wave. The storage modulus E refers to stiffness of material and tan 5 gives the amount of energy dissipated as heat during deformation (Nielsen Landel 1974). The investigation of dynamic storage modulus and internal friction over a wide range of temperature and frequencies has proven to be... 

It is used to measure the deflection or stiffness of materials under load, and is an important design parameter. It is the structure-insensitive property of a material [30]. The magnitude of the elastic modulus varies widely for different metals for example, E for low-carbon steel is approximately 30 X 10 psi and E for aluminum is 10 X 10 psi. This is only marginally affected by a small variation... 

Polymers containing carbonate units are of great interest for biomedical applications because of their better flexibility and reduced acidity of degradation products (Dobrzynski and Kasperczyk, 2006b). Introduction of TMC units in copolymer chains allows to modify the degradation profile and to decrease the stiffness of materials (Han et ah, 2012a Wach et al., 2013). 

In cases of short-term exposure (e.g., up to a few hours), which would include sterilization by antoclaving (typically 30 min at 134°C/270°C) or paint drying (20 min at 140°C/285°C), decisions made on the basis of maximnm operating tem-peratnre may not be the most appropriate means of selecting candidate materials. For short exposnre times, there may not be any significant level of oxidation or other chemical change in the material that wonld lead to a loss in mechanical or physical properties. However, even short exposnre to high temperatnres can lead to loss of dimensional stability. In some cases, therefore, in which the dimensional stability or stiffness of materials at the maximum use temperature is more important, it may be better to select materials on the basis of the heat distortion temperatnre. 

From table 2.1, it can also be seen that alloying does not significantly change the stiffness of materials. For example. Young s modulus of different aluminium alloys varies only by about 10%, whereas their strength (see chapter 6) can be raised considerably by alloying. 

A complex Young s modulus ( ) reflects the contribution of both storage ( ) and loss ( ") components to the stiffness of material, as follows ... 

No contact with the material, no moving parts to wear out or corrode Unaffected by changes in the tension or stiffness of the conveyor belt Direct readout and adaptabiUty to modem controls... 

Radiation Effects. Polytetrafluoroethylene is attacked by radiation. In the absence of oxygen, stable secondary radicals are produced. An increase in stiffness in material irradiated in vacuum indicates cross-linking (84). Degradation is due to random scission of the chain the relative stabiUty of the radicals in vacuum protects the materials from rapid deterioration. Reactions take place in air or oxygen and accelerated scission and rapid degradation occur. 

Commonly used materials for cable insulation are poly(vinyl chloride) (PVC) compounds, polyamides, polyethylenes, polypropylenes, polyurethanes, and fluoropolymers. PVC compounds possess high dielectric and mechanical strength, flexibiUty, and resistance to flame, water, and abrasion. Polyethylene and polypropylene are used for high speed appHcations that require a low dielectric constant and low loss tangent. At low temperatures, these materials are stiff but bendable without breaking. They are also resistant to moisture, chemical attack, heat, and abrasion. Table 14 gives the mechanical and electrical properties of materials used for cable insulation. 

Reinforcing Resins. Reinforcement and stiffness of a compound can also be achieved with the use of reactive resins. Resins consisting of two-component systems of resorcinol or resorcinol condensation products and a methylene donor such as hexamethoxymethylmel amine (HMMM) or hexamethyltetramine (HMT) are the most popular in tires. These materials can be prereacted and added to the formula, or for more effective results they can react in situ ie, they can be added separately into the formula and react when the tire is vulcanized. 

BeryUium is important as a sensor support material in advanced fire-control and navigation systems for military heflcopters and fighter aircraft utilizing the low weight and high stiffness of the material to isolate instmmentation from vibration. It is also used for scanning mirrors in tank fire-control systems. 

To understand the origin of the modulus, why it has the values it does, why polymers are much less stiff than metals, and what we can do about it, we have to examine the structure of materials, and the nature of the forces holding the atoms together. In the next two chapters we will examine these, and then return to the modulus, and to our bar-chart, with new understanding. 

To conclude, the concept of bond stiffness, based on the energy/distance curves for the various bond types, goes a long way towards explaining the origin of the elastic modulus. But we need to find out how individual atom bonds build up to form whole pieces of material before we can fully explain experimental data for the modulus. The... 

Well, that is the case at the low temperature, when the rubber has a proper modulus of a few GPa. As the rubber warms up to room temperature, the Van der Waals bonds melt. (In fact, the stiffness of the bond is proportional to its melting point that is why diamond, which has the highest melting point of any material, also has the highest modulus.) The rubber remains solid because of the cross-links which form a sort of skeleton but when you load it, the chains now slide over each other in places where there are no cross-linking bonds. This, of course, gives extra strain, and the modulus goes down (remember, E = [Pg.61]

In the last chapter we examined data for the yield strengths exhibited by materials. But what would we expect From our understanding of the structure of solids and the stiffness of the bonds between the atoms, can we estimate what the yield strength should be A simple calculation (given in the next section) overestimates it grossly. This is because real crystals contain defects, dislocations, which move easily. When they move, the crystal deforms the stress needed to move them is the yield strength. Dislocations are the carriers of deformation, much as electrons are the carriers of charge. 

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