Strain recoverable

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. 

Equations (5.51), (5.52) and (5.53) can be cumbersome if they are to be used regularly so the relationships between swelling ratio and recoverable strain are often presented graphically as shown in Fig. 5.11. 

In addition, if the swelling of the extrudate is measured in each of these two tests then the swelling ratio using the long die will be Bsr and the swelling ratio using the short die will be Ber (see Section 5.6). Using equation (5.44) and (5.47) this enables the shear and tensile components of the recoverable strains to be calculated and from them the shear and tensile moduli. 

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. 

Fig. 21. Recoverable strain as a function of shear stress for polystyrene/toluene solutions with different molar masses at 5 wt%. (+) polyacrylamide/water solutions, ( ) 2 wt%, (x) 2 wt% (with surfactant), (O) 4 wt% and polyethylene melts...

Zuidema, H., Peters, G.W.M. and Meijer, H.E.H. (2002) Development and validation of a recoverable strain based model for flow-induced crystallization of polymers, Macromol. Theory Simul. 10(5), 447-460... 

Fig. 2.3 (a) Variation of the strain with temperature and time.(b) Creep and recoverable strain. (From ref. [5])... 

The measurements reported by Bach (56) apparently were not under constant temperature conditions. Strain recovery after loading in the plasticized state is small. The longer the loading period the smaller the recoverable strain. This suggests plastic flow under load and a conversion of delayed elastic strain into an irreversible deformation. 

Example 12.1 Recoverable Strain Graessley et al. (22) found that, with polystyrene extradate velocities of 1-3 mm/s in the temperature range of 160°-180°C, about 90% of the final D/Dq value was reached at an axial distance of 0.1 cm past the capillary exit. The rest of the swelling was completed in the next three centimeters. We wish to calculate the recoverable strain at 0.1 cm. 

Recoverable strain can also be defined as the tensile strain needed to pull a fully swollen extrudate until its diameter is that of the capillary (22).5 Assuming constant density nD-iL/A = kDqLq/A, or Lq/L = SR = (D/Dq)2. At 0.1 cm past the capillary exit SR = 0.81 (D/Dq)2, and at 3 cm, it is (D/Dq)2. Therefore, at 0.1 cm, 19% of the recoverable tensile strain that the extradate is capable of undergoing is still present. In other words, if no further swelling were allowed, 0.19(D/Dq)2 would he the value of the average frozen-in strain in the extradate. 

Finally, they calculated the recoverable strain of each of the polymers used, and the difference between two adjacent layers, A SR, that is, the difference in their elasticity... 

Elasticity of solids determines their strain response to stress. Small elastic changes produce proportional, recoverable strains. The coefficient of proportionality is the modulus of elasticity, which varies with the mode of deformation. In axial tension, E is Young s modulus for changes in shape, G is the shear modulus for changes in volume, B is the bulk modulus. For isotropic solids, the three moduli are interrelated by Poisson s ratio, the ratio of traverse to longitudinal strain under axial load. 

In this case, one has only two invariants of the internal tensor, which makes the general relations for the tensor functions simpler. However, it does not mean that the final relations will be simpler. We can see later (see Section 9.3.5) that there is a relation between the recoverable strain and the deformation of macromolecular coil (see formula (9.75)), so a transfer from one formalism to the other can be performed and the results of the two approaches can be compared. 

One of the prominent features of polymeric liquids is the property to recover partially the pre-deformation state. Such behaviour is analogous to a rubber band snapping back when released after stretching. This is a consequence of the relaxation of macromolecular coils in the system every deformed macro-molecular coil tends to recover its pre-deformed equilibrium form. In the considered theory, the form and dimensions of the deformed macromolecular coil are connected with the internal variables which have to be considered when the tensor of recoverable strain is to be calculated. Further on, we shall consider the simplest case, when the form and dimensions of macromolecular coils are determined by the only internal tensor. In this case, the behaviour of the polymer liquid is considered to describe by one of the constitutive equations (9.48)-(9.49) or (9.58). 

To determine the tensor of recoverable strains, we have to equate the stress tensor for a deformed polymer network (given in the simplest case by equation (1.43)) with the elastic part of the stress tensor for a polymer liquid, given in the general case by equation (9.19) or, in the simplified case by equation (9.48). The latter case leads to the relation... 

To determine the shear modulus and the tensor of recoverable strains, we calculate the determinants of the left-hand and right-hand sides of equation (9.74). Taking into account the incompressibility of the polymer liquid, i.e. relation AyAjy = 1, we obtain... 

We consider these invariants independent of each other, so that we termine the shear modulus and the tensor of recoverable strains... 

During steady shear flow the strain y(t) is composed of irrecoverable viscous strain, yvis(0 and elastic or recoverable strain, ylec(t) ... 

Table 15.12 gives a survey of the more important rheological equations. Figs. 15.36 and 15.37 (already discussed) show the relationship between swelling ratio and recoverable strain. It is far beyond the scope of this book to go into detail of this subject. The interested reader is referred to, e.g. Collyer (1993), Collyer and Clegg (1998) and Denys (2003). 

Superelasticity refers to the ability of certain materials to undergo unusually large elastic deformations over a certain temperature range. In the most well-known superelastic material, nitinol (NiTi 51% Ni), up to 11 percent recoverable strain is observed (as much as 25 percent in specific directions in single crystals ). As a comparison, only... 

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