Actual extension rates in the bottle blowing process are much higher then can be obtained on our experimental film stretching machine. Time-temperature superposition was therefore used to extrapolate the obtained stress–strain data to higher extension rates. Time-temperature superposition has been traditionally used in creep, stress relaxation and aging experiments where the desired timescale is too long for experimentation (Ferry, 1970). The method involves shifting curves either horizontally or vertically to give a single master curve covering a large range of data. In a typical application of superposition, experimental data taken at different temperatures are shifted along a logarithmic timescale to obtain a single master curve covering a large scale of time. The amount of horizontal shift along the time axis is called the shift factor. If the Tg is chosen as the reference temperature, the shift factor for most amorphous polymers is given by the Williams-Landel-Ferry (WLF) equation (Williams et al., 1955). The shift factor can be related to the ratio of the relaxation time at temperature T to the relaxation time at the reference temperature.
Ibar (1979a,b, 1984) has investigated in detail the use of superposition to analyze the tensile deformation behavior of amorphous uncrosslinked copolymers of styrene and acrylonitrile. In his work he described a ‘double shift’ procedure to obtain a single master curve from stress–strain data at different temperatures. Gordon et al. (1994) have shown that the true stress versus draw ratio curves of PET can be superimposed in the strain hardening region and concluded that this is evidence that PET behavior could be described by the deformation of a molecular network.
In this work, PET film stress–strain data at three different temperatures (90, 100, 110 °C) and extension speeds (20, 50, 200%/s) were used to extrapolate to higher extension rates of 400, 600 and 800%/s. Superposition was used to generate stress–strain curves which are more characteristic of PET behavior under commercial blow molding conditions. These master curves were then used to extrapolate to the results shown in Fig. 9.7 for 100 °C. For more detail, see Ansari (1998).
9.7. Using superposition to extrapolate the stress–strain behavior at 100 °C for strain rates of 400, 600 and 800%/s for equibiaxial extension.
From these extrapolations we concluded that at 90 °C the higher strain rates have little effect on the stress–strain behavior. At temperatures close to Tg, much less relaxation of the polymer chains occurs during the time of stretching. At higher temperatures such as 110 °C, the effect of extension rate shows a significant increase in the strain hardening region on going from 200 to 600%/s. We find that at higher extension rates the weak strain hardening characteristics at 110 °C are replaced by a strong strain hardening region. Extrapolation of stress–strain curves at 100 °C, as shown in Fig. 9.7, show intermediate results, with some increase in the strength of the strain hardening region at higher extension rates above 200%/s. It also seems that at 400%/s the stress levels almost reach their maximum values, and that even at higher temperatures such as 110 °C, there is no appreciable increase in stress values on going above extension rates of 400 %/s.