Shear activation volume

For isotropic glasses, the activation volume tensor has two independent components. These are the bulk activation volume, which is equal to the lattice volume v, and the shear activation volume Q12. The activation volumes in uniaxial tension and compression are found to be [30]... 

Absolute temperature Activation energy Shear activation volume Die exit velocity Distance from die cone apex Geometric factor Die semi-angle Intrinsic thermal expansivity... 

An upper bound analysis of the hydrostatic extrusion of linear polyethylene has been given by Gupta and McCormick This followed the approach outlined above for the flow stress (Eq. (4)) taking results frcnn Coates and Ward to describe the increase in strain rate sensitivity by a reduction in the shear activation volume. Reasonable fits were obtained for experimental data up to comparatively low deformation ratios (R = 9), giving further support for the more extensive treatments presented by Ward and coworkers. 

To obtain information on the actual sizes Of of the relaxation clusters in glassy polymers it is necessary to associate the simulation results with experimental results on shear activation volumes Av that relate directly to the product Qfy. This, together with the simulation results for the transformation shear strain (= 7 ) j offsr a means of estimating the actual values of Of of relaxing clusters and the number of molecular segments n in the clusters that take part in the shear relaxations. Before considering such an evaluation, we first present experimental results on the temperature dependences of the yield stresses of several flexible-chain and stiff-chain glassy polymers. 

We recall two important activation parameters in plastic flow defined in models and experiments the shear activation volume Av and the pressure activation volume Av ... 

Since the product Qfy for each polymer was obtained using room-temperature values of the shear activation volume Av, we consider it as fixed, and substitute it, together with the stress dependence given in eq. (8.11), for Qfy in eq. (8.7), and then, taking this together with eq. (8.6), obtain the activation free energy of... 

We recall that m = Ineo/e, Av is the shear-activation volume at J = 300 K and = 0.012, both of which are listed in Table 8.3 for PC. The only parameter in eq. (8.45) not known a priori is the dilatancy factor at yield where 0, which... 

The shear-activation volumes as determined from the models are given by... 

The specific forms of the shear-activation volumes for the three different modes A, B, and C are... 

Fig. 9.23 Predictions of the stress dependence of the normalized shear-activation volumes of modes A, B, and C of dislocation nucleation, compared with experimental measurements (from Argon et al. (2005) courtesy of Elsevier).

Here Av is the shear-activation volume of the polymer at 293 K, values of which are listed for prominent glassy homo-polymers in Table 8.3, and f(0)/yu(0) is the threshold yield strain in shear at 0 K, which is 0.11 for most glassy polymers, except PS, for which it is 0.12 (Table 8.2). In eqs. (11.46) and (11.51) sq is the preexponential factor that incorporates a frequency factor based on the eigenfre-quency of a plastic relaxation cluster and has typically a magnitude of 1.40 X 10 s for tensile flow in glassy polymers (see Chapter 8). 

The exponent m, as defined by eq. (13.3), typically has a value in the range 21-23 for a glassy thermoplastic or thermoset polymer, for the shear-activation volumes... 

Table 1 Comparison of the shear activation volumes of p- and a-relaxations with the volumes of cooperatively rearranging region (CRR) at Tg (DSC data) and Kuhn segment volumes in glassy...

Putting (V/2 + /3) = V, makes equation (5) exactly identical to equation (1) above. Equation (4) implies that the pressure dependence of the flow stress is given by Of = o2 + yP where y = 2, and for isotropic polymers y is typically > 0.1 - 0.2. V it is reasonable to anticipate that the smaller pressure activation volume Q will change much less with plastic deformation than the shear activation volume V, hence the pressure dependence of the flow stress will increase with increasing plastic strain. 

Previously, the shear activation volume and pressure activation volume Vp were treated as constant parameters for representation of the non-linear viscoelastic part of the Eyring type non-Newtoitian flow in arm (B). This inplies Eyring plots for varying temperature and strain level will be linear and pardlel. However, there is mounting evidence, including results in this work that suggest the presence of multiple activation volumes [8,15-16]. 

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