Biaxial tensile flow

The melt bubble is stretched vertically and circumferentially by a factor of 2 or more, so that an initial melt thickness of about 1 mm is reduced to between 250 and 100 pm. In the biaxial tensile flow, the melt stress in the hoop (H) direction can be calculated from the pressure p inside the bubble, the current bubble radius r and thickness t, using Eq. (C.22) of Section C.3. 

The only way to generate data for this type of unsteady biaxial tensile flow is to instrument a blown film machine. The tensile viscosity, defined by Eq. (5.16), hardly changes with the tensile strain rate. Figure 5.15 shows data for the uniaxial stretching of an LDPE and an HDPE. The apparent tensile viscosity increases with strain rate for the more elastic LDPE, in contrast with the non-Newtonian reduction in viscosity in shear flows. 

A few rheometers are available for measurement of equi-biaxial and planar extensional properties polymer melts [62,65,66]. The additional experimental challenges associated with these more complicated flows often preclude their use. In practice, these melt rheological properties are often first estimated from decomposing a shear flow curve into a relaxation spectrum and predicting the properties with a constitutive model appropriate for the extensional flow [54-57]. Predictions may be improved at higher strains with damping factors estimated from either a simple shear or uniaxial extensional flow. The limiting tensile strain or stress at the melt break point are not well predicted by this simple approach. 

Furthermore, when this flow is looked upon as biaxial stretching, it is thought of as being generated by a radial, tensile stress rather than an axial, compressive stress. Thus, the biaxial extensional viscosity is defined as... 

High performance films can be processed from LCPs and blends using shear flow to orient the LCP molecular domains. Biaxial orientation provides high tensile strength and... 

Biaxially self-reinforced HDPE moldings can be produced in a uniaxial shear flow field. The tensile strength in both MD and TD is remarkably enhanced in biaxially self-reinforced samples. The HDPE molded -with the best biaxially self-reinforced effect exhibits a 42% increase in the tensile strength along both MD and TD. 

It should be noted that the properties of oriented films show considerable dependence on the processing conditions (e.g., biaxially oriented films are obtained by blow molding, while extrusion produces uniaxially oriented films). This is important because the mechanical properties of oriented specimens are considerably different in the flow and transverse directions of the films as shown hi Fig. 4.22 (measurements were done by a traditional tensile tester). When the film samples in the form of strips are prepared for TMA measurements, the strips should always be cut from the same orientation (Menczel et al. 1997). When preparing such samples, film widths of >2 mm are recommended in order to minimize edge effects. 

Melt behavior has been studied using uniaxial (also called simple or tensile), biaxial, and planar extensional flows [9, Ch. 6]. However, only the first two of these are in general use and will be discussed here. A uniaxial extensional rheometer is designed to generate a deformation in which either the net tensile stress Tg or the Hencky strain rate e (defined by Eq. 10.89) is maintained constant. The material functions that can, in principle, be determined are the tensile stress growth coefficient / (f, ), the tensile creep compliance, andthetensile... 

Mechanical Properties. Tensile strmgth and modulus were measured according to standard ISO 457-4 procedures. The direction with the higher tmsile strength was designated as the flow axis, and the direction perpmdicular to it as the cross-flow axis. High speed biaxial impact resistance was determined at 6.7 m/sec (15 mph) with a 25.4 mm (1 inch) hemispherical instrumented driven dart at 25°C and -30°C as per ASTM 763-99 and D 5628-99. Results are summarized in Table 2. 

---