Extension biaxial

The elongation viscosity defined by Equation (1.19) represents a uni-axial extension. Elongational flows based on biaxial extensions can also be considered. In an equi-biaxial extension the rate of deformation tensor is defined as... 

A method for measuring the uniaxial extensional viscosity of polymer soHds and melts uses a tensile tester in a Hquid oil bath to remove effects of gravity and provide temperature control cylindrical rods are used as specimens (218,219). The rod extmder may be part of the apparatus and may be combined with a device for clamping the extmded material (220). However, most of the mote recent versions use prepared rods, which are placed in the apparatus and heated to soften or melt the polymer (103,111,221—223). A constant stress or a constant strain rate is appHed, and the resultant extensional strain rate or stress, respectively, is measured. Similar techniques are used to study biaxial extension (101). 

Kawabata, S. and Kawai, H. Strain Energy Density Functions of Rubber Vulcanizates from Biaxial Extension. Vol. 24, pp. 89 — 124. 

Equi-biaxial extension results have been obtained by inflating sheets of unimodal and bimodal networks of PDMS [114,115]. Upturns in the modulus were found to occur at high biaxial extensions, as expected. Also of interest, however, are pronounced maxima preceding the upturns. Such dependences represent a challenging feature to be explained by molecular theories addressed to bimodal elastomeric networks in general. 

When low density foams are produced, the polymer melt must undergo high biaxial extension in order to... 

If tan 5 is high, so are the tensile stresses when the foam face polymer is subjected to biaxial extension. The foam faces may fracture if the tensile stress exceeds a critical level. The consequence of such fractures is the growth of abnormally large cells, with more than the usual 14 or 15 faces (Figure 5). 

For the biaxial extension of partly crosslinked PE melt, the tensile stress is given by ... 

A simple bubble machine is devised and successfully applied in characterising lightly crosslinked PE resins for foam expansion. The biaxial stress-strain relationship is deduced from the air injection rate and pressure. The effects of strain rate, temperatnre and crosslinker level on the stress-strain behavionr are investigated. Uniaxial extension experiments are also performed and compared with biaxial extension data. 5 refs. 

V. Summary of Results from the Authors Biaxial Extension Experiments. 106... 

In the present article, we summarize typical approaches to the evaluation of the strain energy density function from biaxial extension experiments and illustrate some intportant data. This article is not a review in the ordinary sense, as it deals to a large extent with a series of experiments carried out in our laboratory. By this we do not mean to bias or ignore any of the many important contributions by other authors. 

Strain Energy Density Functions of Rubber Vuicanizates from Biaxial Extension... 

The stress-strain relations for some special cases of biaxial defonnation are derived from Eqs. (13) to (15) in the following way. Strip biaxial extension of incompressible material is defined as the mode of deformation in which one of the Xj, say X2, is kept at unity, while the other, Xt, varies. This deformation is also called pure shear . We have for it ... 

C. Determination of 9 W/bl ( and bWlbl2 from Biaxial Extension Experiments... 

For incompressible material, the stress-strain relations for biaxial extension are given by Eqs. (13) and (14), which may be solved for bW/bli and bWjbI2 to give... 

Fig. 3. Treloar s biaxial extension experiment lower figure shows undeformed specimen. (Reproduced from Treloar,...

Fig. 4. Rivlin-Saunders apparatus for biaxial extension. Specimen is 8 cm x 8 cm and 0.7 mm thick. [Reproduced from Rivlin, R. S., Saunders PhiL Trans. Roy. Soc. A243, 251 (1951), Fig. 3.J...

Fig. 5. Blatz-Ko s apparatus for equal biaxial extension. Specimen in undeformed state is 3 in x 3 in and 0.0187, in thick...

Blatz and Ko19) also devised an apparatus which allows strip-biaxial extension testing to be performed (Fig. 6). Here one of the stretch ratios, say X2, is held at unity while the sample sheet is extended in the direction of the stretch ratio Xj. 

Becker25 improved the biaxial extension apparatus of Blatz and Ko in such a way that pairs of different values of Xj and X2, i.e., general biaxial extensions, can be obtained. Here, pairs of two rectangular tracks are connected to the pulling rods in asymmetric fashion, as shown in Fig. 7. With the use of this apparatus he obtained valuable information about the behavior of dW/d/j and dW/d/2 for natural rubber vulcanizate. His principal results are presented in Section V. 

Another apparatus for general biaxial extension testing, illustrated in Fig. 8, was built at our laboratory27). A square sheet of rubber, 11.5 cm long and 1 mm thick, is clamped at the edges by several pieces of movable chucks and stretched biaxially by means of the two bars that can be displaced separately bade and forth by a servo-meachnism. Tensile forces acting on the sheet in the stretching directions are transmitted to the bars and measured by two transducers mounted at the ends of each bar. After many modifications and improvements on the mechanical and electric parts,... 

Fig. 7. Becker s apparatus for biaxial extension. Specimen is 2.5 in x 2.5 in and 1 mm thick...

Rivlin and Saunders11 suggested from their biaxial extension experiments on vulcanized natural rubber that the form of W for rubber-like material would be... 

---