Recoverable deformation

The various elastic and viscoelastic phenomena we discuss in this chapter will be developed in stages. We begin with the simplest the case of a sample that displays a purely elastic response when deformed by simple elongation. On the basis of Hooke s law, we expect that the force of deformation—the stress—and the distortion that results-the strain-will be directly proportional, at least for small deformations. In addition, the energy spent to produce the deformation is recoverable The material snaps back when the force is released. We are interested in the molecular origin of this property for polymeric materials but, before we can get to that, we need to define the variables more quantitatively. 

Deformation is the relative displacement of points of a body. It can be divided into two types flow and elasticity. Flow is irreversible deformation when the stress is removed, the material does not revert to its original form. This means that work is converted to heat. Elasticity is reversible deformation the deformed body recovers its original shape, and the appHed work is largely recoverable. Viscoelastic materials show both flow and elasticity. A good example is SiEy Putty, which bounces like a mbber ball when dropped, but slowly flows when allowed to stand. Viscoelastic materials provide special challenges in terms of modeling behavior and devising measurement techniques. 

Another property pecuHar to SMAs is the abiUty under certain conditions to exhibit superelastic behavior, also given the name linear superelasticity. This is distinguished from the pseudoelastic behavior, SIM. Many of the martensitic alloys, when deformed well beyond the point where the initial single coalesced martensite has formed, exhibit a stress-induced martensite-to-martensite transformation. In this mode of deformation, strain recovery occurs through the release of stress, not by a temperature-induced phase change, and recoverable strains in excess of 15% have been observed. This behavior has been exploited for medical devices. 

When a fiber is stressed, the instantaneous elongation that occurs is defined as instantaneous elastic deformation. The subsequent delayed additional elongation that occurs with increasing time is creep deformation. Upon stress removal, the instantaneous recovery that occurs is called instantaneous elastic recovery and is approximately equal to the instantaneous elastic deformation. If the subsequent creep recovery is 100%, ie, equal to the creep deformation, the specimen exhibits primary creep only and is thus completely elastic. In such a case, the specimen has probably not been extended beyond its yield point. If after loading and load removal, the specimen fails to recover to its original length, the portion of creep deformation that is recoverable is still called primary creep the portion that is nonrecoverable is called secondary creep. This nonrecoverable elongation is typically called permanent set. 

Deformation Under Loa.d. The mechanical behavior of coal is strongly affected by the presence of cracks, as shown by the lack of proportionahty between stress and strain in compression tests or between strength and rank. However, tests in triaxial compression indicate that as the confirming pressure is increased different coals tend to exhibit similar values of compressive strength perpendicular to the directions of these confining pressures. Except for anthracites, different coals exhibit small amounts of recoverable and irrecoverable strain underload. 

Linear-elasticity, of course, is limited to small strains (5% or less). Elastomeric foams can be compressed far more than this. The deformation is still recoverable (and thus elastic) but is non-linear, giving the plateau on Fig. 25.9. It is caused by the elastic... 

It is somewhat difficult conceptually to explain the recoverable high elasticity of these materials in terms of flexible polymer chains cross-linked into an open network structure as commonly envisaged for conventionally vulcanised rubbers. It is probably better to consider the deformation behaviour on a macro, rather than molecular, scale. One such model would envisage a three-dimensional mesh of polypropylene with elastomeric domains embedded within. On application of a stress both the open network of the hard phase and the elastomeric domains will be capable of deformation. On release of the stress, the cross-linked rubbery domains will try to recover their original shape and hence result in recovery from deformation of the blended object. 

In the region where the relationship between stress and strain is nonlinear, the material is said to be plastic. Elastic deformation is recoverable upon removal of the load, whereas plastic deformation is permanent. The stress at which the transition occurs, o, is called the yield strength or yield point of the material, and the maximum... 

As reviewed thermoplastics (TPs) being viscoelastic materials respond to induced stress by two mechanisms viscous flow and elastic deformation. Viscous flow ultimately dissipates the applied mechanical energy as frictional heat and results in permanent material deformation. Elastic deformation stores the applied mechanical energy as completely recoverable material deformation. The extent to which one or the other of these mechanisms dominates the overall response of the material is determined by the temperature and by the duration and magnitude of the stress or strain. The higher the temperature, the most freedom of movement of the individual plastic molecules that comprise the... 

Deformation contributes significantly to process-flow defects. Melts with only small deformation have proportional stress-strain behavior. As the stress on a melt is increased, the recoverable strain tends to reach a limiting value. It is in the high stress range, near the elastic limit, that processes operate. 

In ordinary solids such as crystalline or amorphous glassy materials, an externally applied force changes the distance between neighboring atoms, resulting in interatomic or intermolecular forces. In these materials, the distance between two atoms should only be altered by no more than a fraction of an angstrom if the deformation is to be recoverable. At higher deformations, the atoms slide past each other, and either flow takes place or the material fractures. The response of rubbers on the other hand is almost entirely intramolecular [4,5]. 

Clarity requires that a distinction be made between elastic strain and plastic deformation. They both have units of length/length, but they are physically different entities. Elastic strain is recoverable (conservative) plastic deformation is not (non-conservative). At a dislocation core, where atoms exchange places via shear, the plastic displacement gradient is a maximum as it passes from zero some distance ahead of the core, up to the maximum, and then back to zero some distance back of the core. In crystals with distinct bonds, the gradient becomes indefinite (infinite) at the core center. 

The volume deformations of concrete are shrinkage, which occurs under drying conditions, and creep, which is the additional deformation obtained under an applied stress. Creep does occur under saturated conditions (basic creep) but increases considerably under conditions of moisture loss. The picture is rather complicated in that creep is made up of a recoverable and irrecoverable portion on removal of the applied stress. 

It should make sense then, that as we attempt to pull atoms apart or force them further together through an applied stress, we can, at least in principle, relate how relatively difficult or easy this is to the potential energy function. We can develop a quantitative description of this process of pulling atoms apart, provided that we do so over small deformations, in which the deformation is wholly recoverable that is, the atoms can return back to their original, undeformed positions with no permanent displacement relative to one another. This is called an elastic response. The term elastic here does not imply anything specific to polymers in the same way that the more everyday use of the term does. It is used in the same sense that it is in physics and chemistry—a completely recoverable deformation. 

To this point, we have limited the discussion to small strains—that is, small deviations from the equilibrium bond distance, such that all imposed deformations are completely recoverable. This is the elastic response region, one that virtually all materials possess (see Figure 5.8). What happens at larger deformations, however, is dependent to some... 

As the term implies, viscoelasticity is the response of a material to an applied stress that has both a viscous and an elastic component. In addition to a recoverable elastic response to an applied force, polymers can undergo permanent deformation at high strains, just as was the case for metals and some glasses, as described previously. The mechanism of permanent deformation is different in polymers, however, and can resemble liquid-like, or viscous flow, just like we described in Chapter 4. Let us first develop two important theoretical models to describe viscoelasticity, then describe how certain polymers exhibit this important property. 

The total deformation in the four-element model consists of an instantaneous elastic deformation, delayed or retarded elastic deformation, and viscous flow. The first two deformations are recoverable upon removal of the load, and the third results in a permanent deformation in the material. Instantaneous elastic deformation is little affected by temperature as compared to retarded elastic deformation and viscous deformation, which are highly temperature-dependent. In Figure 5.62b, the total viscoelastic deformation is given by the curve OABDC. Upon unloading (dashed curve DFFG),... 

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