Temperature dependence of the plastic resistance

As with amorphous metals and semiconductors, the unit plastic relaxations in glassy polymers are also thermally assisted shear transformations (STs), which control the temperature dependence of the plastic resistance and encompass other phenomena of strain softening and the pressure dependence of the resistance. Moreover, the incremental processes of molecular-segment alignment, resulting 

11 The temperature dependence of shear yield stresses normalized with appropriate temperature-dependent shear moduli of six prominent glassy polymers studied by Argon and Bessonov (1977). 

We start by adopting the same form of the activation free-energy model as in Chapter 7 for the free-energy barrier AG of the shear transformation 

7) Of is the volume of the relaxing ST cluster of segments making up the ST, 7 is the transformation shear strain, r(0) is the threshold shear resistance at 0 K, and g T) = fi T)/fi 0)is the shear modulus at the temperature T of interest normalized by the shear modulus /i(0) at 0 K, represented by the temperature-dependent storage modulus of the polymer. 

Relating the Helmholtz free energy to a cosine potential, as done in Chapter 7, from which the plastic shear resistance r and its particular form are derivable, gives the peak threshold resistance i at the temperature of interest as 

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To = 2550 K, breaks down at about T = 0.62Tg as the temperature dependence of the plastic resistance becomes linear and the resistance vanishes at Jg, as shown in Fig. 7.17, all because of a rapidly decreasing time constant for structural relaxations. 

In determining the temperature dependence of the plastic resistances in uniaxial deformation the temperature dependence of the shear modulus fj. = C55 is needed. Karasawa et al. (1991) provide such information derived from theoretical force-field methods. Their calculated results for C55 appear as the upper curve in Fig. 9.20. However, for a variety of reasons discussed by Argon et al. (2005), including the defected nature of the usual HDPE, the C55 modulus needs to be attenuated by a factor of 0.635. This attenuated modulus is also shown in Fig. 9.20, as the lower curve. 

Thus, with these strain-induced modifications the temperature dependence of the plastic-shear resistance is still given by eq. (7.13), but with the factors in it being appropriately modified by the factor/(yP). This results in a modification of eq. (7.13) to... 

The temperature dependence of the plastic-shear resistance r (or uniaxial resistance a) and the activation volume are both very useful in probing the active mechanism of deformation. 

Correspondingly, eq. (13.2) representing the strain-rate dependence of the plastic resistance is taken to be given by a standard uniaxial reference experiment at a reference strain rate e gf, typically of magnitude 10 s that evokes a reference tensile uniaxial plastic resistance o-j-gf, which in this case would be the tensile yield stress o-q. The form of the idealized power law relating eg to Ug is given by the exponent m of the equivalent stress, which must be temperature-dependent in a form given in Chapter 8 as... 

In air cooled battery packs, pack-to-vehicle resistance is strongly influenced by road contaminants such as dirt and salt, and pack case design must take this into consideration. For water cooled designs, the issue is the resistance of the plastic casing materials to the coolant (e.g. ethylene glycol). There is a strong dependence of the plastic resistance to temperature where a pack isolation resistance of 500 Mil at 20°C may be reduced to 5 Mfl at 65°C. A figure of merit for HEV and EV battery pack isolation is a resistance of 1 to 10 Mil. 

While the kinetics of plastic response in metallic glasses in the low-temperature realm exhibits a remarkable mechanistic universality, where the nucleation of STs occurs in a substantially frozen structure, the steep decrease in the temperature dependence of the yield stress and the stress exponent m of the plastic strain rate above 0.62rg signifies the onset of a fundamental change in the mechanism. Thus, the universal response at low temperature, with the slow decrease of plastic resistance with temperature, extrapolating to a vanishing level at a universal temperature of... 

The above developments then lead to a quite simple dependence of the plastic-shear resistance on temperature in the kinetic-law range of 0.62 Tg >T >Tg. 

To probe the models for nucleation-controlled plastic flow we compare the predicted temperature dependence of the tensile plastic resistance with the tensile-yield-stress experimental results of Brooks and Mukhtar (2000). For comparison the polyethylene PE3 of average molecular weight = 131000 with a crystallinity of only 0.673 and lamella thickness of 34.3 nm is chosen. For the predictions of the temperature dependence, eqs. (9.26)-(9.28) of Section 9.4.3 are used, where we take in the denominator of eq. (9.25) the factor (1 + K), since the experiments were performed in tension. Noting that the lamella thickness of this polymer type is 1 = 34.3 nm, which is thicker than that for mode A of monolithic-screw-dislocation nucleation, we consider only modes B and C involving nucleation of screw-dislocation half loops and edge-dislocation half loops, and, together with the results of Fig. 9.21, we state the expected tensile yield stress Oy to be... 

A hard but brittle finish may break and flake off when the fibers are flexed. The resistance to plastic deformation has to be balanced with sufficient pliability. The temperature dependence of the physical properties and the transition temperatures are important for soil-retardant finishes cured at elevated temperatures. A soil retardant that melts below the cure temperature can spread on the fibers during cure. 

A major property improvement achieved through plasticization is the enormous reduction in the glass transition temperature, T, of PVC so that pliability and impact resistance of the plasticized composition is retained over a wide temperature range. Lowering of T is so important in the free volume theory that it is considered by some synonymous with plasticization. Many essential commercial applications of flexible vinyl depend upon this property modification. Without low-temperature flexibility, some of the... 

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