Modulus and stiffness

Table 5.2 lists polymers and their tendency toward crystallinity. Yield stress and strength, and hardness increase with an increase in crystallinity as does elastic modulus and stiffness. Physical factors that increase crystallinity, such as slower cooling and annealing, also tend to increase the stiffness, hardness, and modulus of a polymeric material. Thus polymers with at least some degree of crystallinity are denser, stiffer, and stronger than amorphous polymers. However, the amorphous region contributes to the toughness and flexibility of polymers. 

Modulus and stiffness, presumably due to the thicker cell walls. 

Carbon nanotubes and carbon nanofibers have been sfudied lately as reinforcement materials for several different polymers because their high modulus and stiffness bear the promise of levels of reinforcement not found with micron-size particles or fibers. This performance can be achieved wifh concentrations... 

The interface between fiber (or whisker) and matrix is the key to the overall mechanical properties of a composite. A weak interface allows a propagating crack to be deflected, which increases the toughness of the composite. A strong interface allows transfer of the load from the matrix to the fiber and produces an increase in modulus and stiffness of the composite. In CMCs we are usually more interested in producing a weak interface so that debonding occurs, which often leads to fiber pull-out by frictional sliding and substantial absorption of energy. 

The subject of filler reinforcement on vulcanized rubber is very wide and complex. Fillers can be classified as reinforcing, semi-reinforcing and non-reinforcing. All fillers increase the hardness, modulus and stiffness of vulcanized rubber whether or not they are reinforcing or non-reinforcing. It has been established for a very long time that the term reinforcement has been widely used by the rubber technologist to denote the enhancement in the tensile... 

Polystyrene and polybutadiene are glassy and rubbery, respectively. They are substantially immiscible over their entire composition range. Show how both soft (low modulus) and stiff (high modulus) materials may be made from a 50/50 composition. 

Modulus and stiffness It is a measure of modulus with its relationship of load to deformation or the ratio between the applied stress and resulting strain. It is identified as stiffiiess (El) = modulus (E) times moment of inertia (I). The term stifihess is often used when the relationship of stress-strain does not follow the modulus of elasticity s straight-line ratio. 

Moment of inertia Also called rotational inertia or El. El is the sum of the products formed by multiplying the mass (or sometimes the area) of each element of a figure by the square of its distance from a specified line. See Modulus and stiffness. 

Sometimes cemented carbide tools are used not only for hardness and wear resistance but also for high modulus or stiffness. For example, in end mills used in high speed machining of aluminum alloys, the deflection of the tool can affect the performance of the tool considerably. This includes chatter... 

In the manufacture of highly resident flexible foams and thermoset RIM elastomers, graft or polymer polyols are used. Graft polyols are dispersions of free-radical-polymerized mixtures of acrylonitrile and styrene partially grafted to a polyol. Polymer polyols are available from BASF, Dow, and Union Carbide. In situ polyaddition reaction of isocyanates with amines in a polyol substrate produces PHD (polyhamstoff dispersion) polyols, which are marketed by Bayer (21). In addition, blending of polyether polyols with diethanolamine, followed by reaction with TDI, also affords a urethane/urea dispersion. The polymer or PHD-type polyols increase the load bearing properties and stiffness of flexible foams. Interreactive dispersion polyols are also used in RIM appHcations where elastomers of high modulus, low thermal coefficient of expansion, and improved paintabiUty are needed. 

Ultem PEI resins are amber and amorphous, with heat-distortion temperatures similar to polyethersulfone resins. Ultem resins exhibit high modulus and ate stiff yet ductile. Light transmission is low. In spite of the high use temperature, they are processible by injection mol ding, stmctural foam mol ding, or extmsion techniques at moderate pressures between 340 and 425°C. They are inherently flame retardant and generate Httie smoke dimensional stabiUties are excellent. Large flat parts such as circuit boards or hard disks for computers can be injection-molded to maintain critical dimensions. 

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. 

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