Biaxial direction

Orientation consists of a controlled system of stretching TP molecules in unioriented [unidirectional (UD)] or bioriented [biaxial direction (BD)]. UD orientation can be in the machine direction (MD) or transverse direction (TD).207 Orientation improves strength, stiffness, optics, electrical, and/or other properties with the usual result that improved product performance-to-cost occur. This technique is used during the processing of many different products such as films, sheets, pipes, fibers, tapes, etc. 

Several more recent variations of the film-to-fiber approach result in direct conversion of film to fabric. The film may be embossed in a controlled pattern and subsequently drawn uniaxiaHy or biaxiaHy to produce a variety of nonwoven products (47). Addition of chemical blowing agents to the film causes fibrillation upon extmsion. Nonwovens can be formed directly from blown film using a unique radial die and control of the biaxial draw ratio (48)... 

Biaxial Orientation. Many polymer films require orientation to achieve commercially acceptable performance (10). Orientation may be uniaxial (generally in the machine direction [MD]) or biaxial where the web is stretched or oriented in the two perpendicular planar axes. The biaxial orientation may be balanced or unbalanced depending on use, but most preferably is balanced. Further, this balance of properties may relate particularly to tensile properties, tear properties, optical birefringence, thermal shrinkage, or a combination of properties. A balanced film should be anisotropic, although this is difficult to achieve across the web of a flat oriented film. 

Disk-shaped molecules based on a metal atom possess discotic Hquid crystal phases. An example is octasubstituted metaHophthalocyanine. FiaaHy, metallomesogens which combine both rod-like and disk-like features iato a single molecule adopt the biaxial nematic phase. In addition to there being a preferred direction for orientation of the longest molecular axis as is tme for the nematic phase, perpendicular to this direction is another preferred direction for orientation of the shortest molecular axis (12). NonmetaHomesogens which combine both rod- and disk-like features iato a single molecule also adopt a biaxial nematic phase, but at least ia one case the amount of biaxiaHty is very small (15). 

In order to develop the proper dow pattern, knowledge of a material s dow properties is essential. Standard test equipment and procedures for evaluating sohds dow properties are available (6). Direct shear tests, mn to measure a material s friction and cohesive properties, allow determination of hopper wall angles for mass dow and the opening size required to prevent arching. Other devices available to evaluate sohds dowabiUty include biaxial and rotary shear testers. 

Biaxial crystals offer the possibiUty of coincidence of the phase matching direction with one of the optic axes. This highly desirable situation, called non-critical phase matching, is quite tolerant of divergence of the incident beam from the most efficient phase matching direction. 

There are four commonly occurring states of stress, shown in Fig. 3.2. The simplest is that of simple tension or compression (as in a tension member loaded by pin joints at its ends or in a pillar supporting a structure in compression). The stress is, of course, the force divided by the section area of the member or pillar. The second common state of stress is that of biaxial tension. If a spherical shell (like a balloon) contains an internal pressure, then the skin of the shell is loaded in two directions, not one, as shown in Fig. 3.2. This state of stress is called biaxial tension (unequal biaxial tension is obviously the state in which the two tensile stresses are unequal). The third common state of stress is that of hydrostatic pressure. This occurs deep in the earth s crust, or deep in the ocean, when a solid is subjected to equal compression on all sides. There is a convention that stresses are positive when they pull, as we have drawn them in earlier figures. Pressure,... 

Deliberately oriented polystyrene is available in two forms filament (mono-axially oriented) and film (biaxially oriented). In both cases the increase in tensile strength in the direction of stretching is offset by a reduction in softening point because of the inherent instability of oriented molecules. 

Structurally the difference between PEN and PET is in the double (naphthenic) ring of the former compared to the single (benzene) ring of the latter. This leads to a stiffer chain so that both and are higher for PEN than for PET (Tg is 124°C for PEN, 75°C for PET is 270-273°C for PEN and 256-265°C for PET). Although PEN crystallises at a slower rate than PET, crystallization is (as with PET) enhanced by biaxial orientation and the barrier properties are much superior to PET with up to a fivefold enhancement in some cases. (As with many crystalline polymers the maximum rate of crystallisation occurs at temperatures about midway between Tg and in the case of both PEN and PET). At the present time PEN is significantly more expensive than PET partly due to the economies of scale and partly due to the fact that the transesterification route used with PEN is inherently more expensive than the direct acid routes now used with PET. This has led to the availability of copolymers and of blends which have intermediate properties. 

Note that the ratio of the ratio of the hoop stress (pR/h) to the axial stress (pR/lh) is only 2. From the data in this question the hoop stress will be 8.12 MN/m. A plastic cylinder or pipe is an interesting situation in that it is an example of creep under biaxial stresses. The material is being stretched in the hoop direction by a stress of 8.12 MN/m but the strain in this direction is restricted by the perpendicular axial stress of 0.5(8.12) MN/m. Reference to any solid mechanics text will show that this situation is normally dealt with by calculating an equivalent stress, Og. For a cylinder under pressure Og is given by 0.5hoop stress. This would permit the above question to be solved using the method outlined earlier. 

If the material is subjected to biaxial stresses in both the x and y directions then the strains will be... 

The preceding biaxial failure criteria suffer from various inadequacies in their representation of experimental data. One obvious way to improve the correlation between a criterion and experiment is to increase the number of terms in the prediction equation. This increase in curvefitting ability plus the added feature of representing the various strengths in tensor form was used by Tsai and Wu [2-26]. In the process, a new strength definition is required to represent the interaction between stresses in two directions. 

Determination of the fourth-rank tensor term F. 2 remains. Basically, F.,2 cannot be found from any uniaxial test in the principal material directions. Instead, a biaxial test must be used. This fact should not be surprising because F-,2 is the coefficient of the product of a. and 02 in the failure criterion. Equation (2.140). Thus, for example, we can impose a state of biaxial tension described by a, = C2 = c and all other stresses are zero. Accordingly, from Equation (2.140),... 

Figure 2. Thermal strain vs temperature curves for VsSi measured along [001] on heating (4.2-60K) and cooling (4.2-1.5K). Curve (a) is for an uniaxial stress (s 0.03o doo)) along [001] (b) and (c) are for biaxial stress applied along [100] and [010] with 0.5o (ioo> and o (ioo>, respectively. The x-ray data of Batterman and Barrett (reference 15) are also plotted for comparison. The insets show the directions of applied stresses and [in case of the curve (a)] the martensite-phase domains. (From reference 5)...

In addition to orientation in one direction (mono-axial orientation), biaxial orientation is possible. This is achieved when sheet is stretched in two directions resulting in layering of the molecules. This can increase the impact strength, tensile strength and solvent cracking resistance of polymers and with crystalline plastics the polymer clarity may also be improved. 

Biaxial load It is a loading condition in which a specimen/product is stressed in two different directions in its plane, i.e., as an example it is a loading condition of a pressure vessel under internal pressure and with unrestrained ends. 

For a biaxially drawn polymer with orthorhombic symmetry, the chain axis is preferentially oriented with respect to the XtX2 plane of the sample, and the direction normal to the chain axis is also preferentially oriented. Infra-red measurements enable the determination of the quantities Pf20 and PL202 and P222, which define these orientation effects as discussed in case (iv) above. 

The determination of biaxially oriented film is comparatively straightforward, as the radiation propagates in the direction normal to the plane of the film and the polarization direction is parallel or perpendicular to the draw direction. theoretical analysis are given in detail in a separate publication 6). 

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