Deformation and recoverability

Shape memory polymers are here to stay, not only because of their unique ability to display double existence under the influence of a triggering mechanism, but also because, unlike shape memory alloys, their elastic deformation and recoverable strains are huge, and their transition dependence can be tailored to fit specific requirements as well as having excellent biocompatibility, nontoxicity, ease of manufacture, and, perhaps most importantly, low cost of manufacture. 

The phenomenon that a rubber or a mbberlike material can be stretched is termed deformation and the ability of it to recover and return to its original conformation is termed recoverability. Thus, the basic properties of rubber and rubberlike materials are deformation and recoverability, which are parallel to the properties of liquid crystals, namely, order and mobility. 

The unique feamre of rubber is its network. It is the network that can sustain its stretching and its ability to recover. Once a linear polymer chain is stretched or deformed, it cannot recover. Natural rubber obtained from the rubber tree does not have practical uses because there are no cross-links in the molecules. Only when the cross-links between the chain segments are introduced to form a three-dimensional network do deformation and recoverability become intrinsic properties of the material. Figure 7.1 shows a statistical model of the network structure of rubber. 

There are four regions of different stress-strain behavior. In region 1, the polymer experiences elastic deformation and recoverable strain. In this region the molecules are deformed in shape as much as the available molecular motions... 

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. 

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. 

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... 

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),... 

We also compared two sets of specimens that had been drawn to the same extent. Both were allowed to relax for 48 h after stretching, one set clamped at its specified elongation, the other allowed to relax freely, undamped. The dichroism results show a large difference between the recoverable (elastic+anelastic) deformation and the total deformation for both XL and NXL phases (see Ligures 3 and 4 of Davidson and Gounder ). 

The rheology of lubricated polytetrafluoroethylene compositions was studied by Lewis and Winchester. The mechanism appeared to be a combination of permanent and elastic deformations in the region just before the orifice of the die in the extruder. As a result of permanent deformation, the polymer particles are partially transformed into long fibers. The relative amounts of permanent and recoverable deformation were related to the rate and temperature of extrusion and the geometry of the extruder. Plastic deformation is favored by extruding at temperatures above the 19 and 30° transitions (Snelling and Lontz). 

The parallel arrangement, also shown in Figure 2.49, is called the Voigt model. It is used to model the behavior of a cross-linked but sluggish polymer, such as one of the polyacrylates. Since the spring and dashpot must move in parallel, both the deformation and the recoverability are retarded. 

For common liquids, the viscosity is a material constant which is only dependent on temperature and pressure but not on rate of deformation and time. For polymeric liquids, the situation is much more complicated viscosities and normal stress coefficients differ with deformation conditions. Because polymer melts are viscoelastic their flow is accompanied by elastic effects, due to which part of the energy exerted on the system is stored in the form of recoverable energy. For this reason the viscosities are time and rate dependent polymer melts are viscoelastic. 

FIG. 15.11 Total, viscous and recoverable (i.e. elastic) deformations, y, yvis and yrec, respectively, during steady shear flow and recovery after cessation of flow at time f,. 

At small strains, polymers (both amorphous and crystalline) show essentially linear elastic behavior. The strain observed in this phase arises from bond angle deformation and bond stretching it is recoverable on removing the applied stress. The slope of this initial portion of the stress-strain curve is the elastic modulus. With further increase in strain, strain-induced softening occurs, resulting in a reduction of the instantaneous modulus (i.e., slope decreases). Strain-softening phenomenon is attributed to uncoiling... 

Immediate elastic recovery (ASTM D 4848), Recoverable deformation that is essentially independent of time, that is, occurring in (a time approaching) zero time after removal of the applied force. (See Delayed deformation and compare with (delayed) elastic recovery.)... 

Up to point 1 in Figure 3.2a, the material behaves as an elastic solid, and the deformation is recoverable. This deformation, which is small, is associated with the bending or stretching of the interatomic bonds between atoms of the polymer molecules (see Figure 3.4a). This type of deformation is nearly instantaneous and recoverable. There is no permanent displacement of the molecules relative to each other. 

The biomechanical response of the body has three components, (1) inertial resistance by acceleration of body masses, (2) elastic resistance by compression of stiff structures and tissues, and (3) viscous resistance by rate-dependent properties of tissue. For low-impact speeds, the elastic stiffness protects from crush injuries whereas, for high rates of body deformation, the inertial and viscous properties determine the force developed and limit deformation. The risk of skeletal and internal organ injury relates to energy stored or absorbed by the elastic and viscous properties. The reaction load is related to these responses and inertial resistance of body masses, which combine to resist deformation and prevent injury. When tissues are deformed beyond their recoverable limit, injuries occur. 

Given a sufficiently long time of creep, the velocity of creep will decelerate to zero and y t) attains an equilibrium limit if a viscoelastic solid is being measured. On the other hand, if the material is a viscoelastic liquid, the velocity of creep will decelerate to a finite constant value. Viscoelastic steady state is achieved, and y t) increases indefinitely. The creep experiment has a second part when the stress is set to zero after a period of creeping. A portion or all of the strain accumulated during creeping is then recovered as a function of time for a viscoelastic liquid or solid, respectively.For a viscoelastic liquid, the portion that is permanent deformation and irrecoverable reflects the contribution of viscous flow to the total deformation accumulated during creep. Since a viscoelastic solid does not flow, all of its creep deformation is recoverable. 

For the purpose of considering both rubbers with fully recoverable deformation and glassy polymers that exhibit rubbery behavior above their Tg through the presence of entanglement networks, we distinguish two separate families of material (a) rubbers that have been cross linked through vulcanization and (b) some glassy polymers that show prominent rubbery behavior in their mechanical responses above their Tg for short periods. 

Well characterized copolymers have been commercially available since the mid 1960 s when Shell manufactured, by anionic polymerization, SBS and SIS copolymers. Both block and graft copolymers will chain segregate due both to low entropy contributions and to lack of interactions which would favour miscibility (1). The combination of melt processability, high strength and recoverable high deformability made these and related polymers attractive alternatives to elastomers which require chemical cross-linking. A key to the behaviour of the thermoplastic elastomers is the thennally reversible association of similar chain segments into domains, which for chains below the Tg can act as cross-links. 

As a melt is subjected to a fixed stress (or strain), the deformation vs. time curve will show an initial rapid deformation followed by a continuous flow (Fig. 1-6). The relative importance of elasticity (deformation) and viscosity (flow) depends on the time scale of the deformation. For a short time, elasticity dominates over a long time, the flow becomes purely viscous. This behavior influences processes when a part is annealed, it will change its shape or, with post-extrusion (Chapter 5), swelling occurs. Deformation contributes significantly to process flow defects. Melts with 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. 

Particularly, although the repetitive compressive load applied is a haversine and is applied along the vertical diametral plane of a specimen, the resilient Poisson ratio, p, is first calculated using the recoverable vertical and horizontal deformations, and subsequently two separate resilient moduli, Mr, are determined the instantaneous resilient modulus and the total resilient modulus. 

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