Deformation, biaxial

R. Keshavaraj, R. W. Tock, and D. Haycook, Feedforward Neural Network Modeling of Biaxial Deformation of Airbag Fabrics ANTEC 95 Proceedings, SPE Technical Papers, Modeling of Polymer Properties and Processes, Boston (May 1995). 

Uniaxial deformations give prolate (needle-shaped) ellipsoids, and biaxial deformations give oblate (disc-shaped) ellipsoids [220,221], Prolate particles can be thought of as a conceptual bridge between the roughly spherical particles used to reinforce elastomers and the long fibers frequently used for this purpose in thermoplastics and thermosets. Similarly, oblate particles can be considered as analogues of the much-studied clay platelets used to reinforce a variety of materials [70-73], but with dimensions that are controllable. In the case of non-spherical particles, their orientations are also of considerable importance. One interest here is the anisotropic reinforcements such particles provide, and there have been simulations to better understand the mechanical properties of such composites [86,222],... 

Elliott and co-workers performed a detailed SAXS investigation of the morphology of Nafion membranes that were subjected to uniaxial and biaxial deformation. For as-received membranes, manufactured by Du Pont using an extrusion process, the cluster reflection was shown to exhibit a limited degree of arching in the direction perpendicular to the machine direction. Upon uniaxial extension, this arching was observed to increase in a manner consistent with previous studies. This arching was rationalized on... 

Our own experience, as well as that of other authors, has shown that very precise measurement for the stress-strain relationship under general biaxial deformation is required to investigate the behavior of the strain energy density function of rubber vulcanizates. Unfortunately, available biaxial extension data are still too meager to deduce the general form of the strain energy density function of rubber-like substances. We wish to take this opportunity to summarize the principal results from our recent efforts, in the hope that they may serve to illustrate the interesting and complex nature of the derivatives 31V/9/,- of such substances. 

Fig. 24 B. Time dependence of BJV/B/j and 2 f°r carbon-filled SBR at various strip biaxial deformations Sj (/ j = 3.405,...

PET film. The overall improvement in barrier properties of PET upon biaxial deformation, followed by heat-setting, is the combined result of higher deformation-induced crystallization and orientation. The role of crystallinity may be more significant than that of orientation, because it reduces both the diffusion rate (increasing the permeant s path tortuosity ) as well as its solubility, while orientation reduces only the diffusion rate. 

It should be pointed out that under service conditions materials naturally experience biaxial deformations. Work is currently underway in our laboratory employing a variety of different biaxial stress histories. 

It is not evident, without the proper biaxial data, that materials which show this instability in uniaxial extension, will also show a similar Instability in biaxial deformation. 

From experiments in our laboratory on biaxial deformations of thin sheets, it is found that in some materials cracks are formed without any evidence of necking, while at the same levels of strain in uniaxial extension necking had already occurred. This is not surprising since the potential function w depends on the strain Invariants and for biaxial experiments, the solution given in section III has to be modified because the strain potential now has to be differentiated with respect to the first and second strain invariants. More work in biaxial deformations will lead to a better description of the failure mechanism In general. 

Because of biaxial deformations in the blowing process, the tensile modulus is usually determined in both the machine direction (MD) and TD. Results obtained from... 

Figure 14 13 Schematic represemation of isotropic and biaxial deformation processes in latex films. (Taken from ref. [12c].)...

Saikrasun S, Bualek Limcharoen S, Kohjiya S, Urayama K. 2005. Anisotropic mechanical properties of thermoplastic elastomers in situ reinforced with thermotropic liquid crystalline polymer fibers revealed by biaxial deformations. J Polym Sci Part B Polym Phys 43 135 144. 

The molecular orientation in the film occurs when the relaxation time of the solution becomes longer than the characteristic time for the biaxial deformation applied by the compressional stress due to the solvent evaporation, which was quantitatively calculated by Croll [13]. Therefore, the evaporation rate has to be considered to discuss the birefringence in a solution-cast film. 

In conclusion the usefulness of the sonic technique has found merit when applied to uniaxially deformed materials that can be fabricated to give rodlike geometry. It seems that its application to biaxially deformed material, however, hardly has desirability, particularly if one is attempting to determine planar orientation. 

IR and V denote infra-red and visible respectively. (U) and (B) denote uniaxial and biaxial deformation, respectively. 

Here, as in all following sub-sections, except for equi-biaxial deformation, the principal direction of stretch is the 2-direction, and constancy of volume given by eq. (6.27) applies. 

Nevertheless, in outline, the theory is well supported eiqteriment at values A < 1.2. For trample, the predicted dependence of the shear modulus (eqn 3.30) on both T and N is dosel obeyed. The theory is also independent of chemical corrqxisition (as is the kinetic theory of gases) and this is supported by experiment. Note that although we have used eqn 3.29 to predict the results of a tensile experiment it may also be used for more complex situations, such as a pressurized tube (Problem 3.16) or a sheet subject to biaxial deformation (Problem 3.1S). 

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