Cross-section rigid

Textile fibers must be flexible to be useful. The flexural rigidity or stiffness of a fiber is defined as the couple required to bend the fiber to unit curvature (3). The stiffness of an ideal cylindrical rod is proportional to the square of the linear density. Because the linear density is proportional to the square of the diameter, stiffness increases in proportion to the fourth power of the filament diameter. In addition, the shape of the filament cross-section must be considered also. For textile purposes and when flexibiUty is requisite, shear and torsional stresses are relatively minor factors compared to tensile stresses. Techniques for measuring flexural rigidity of fibers have been given in the Hterature (67—73). 

Figure 2.3. A rigid piston drives a shock wave into compressible fluid in an imaginary flow tube with unit cross-sectional area. The shock wave moves at velocity U into fluid with initial state 0, which changes discontinuously to state 1 behind the shock wave. Particle velocity u is identical to the piston velocity.

However when the SF cross-section is analyzed, its composite nature still results in a twofold increase in rigidity, compared to an equivalent amount of solid plastic, since rigidity is a cubic function of wall thickness. This increased rigidity allows large structural products to be designed with only minimal distortion and deflection when stressed within the recommended values for a particular foamable plastic. 

When a mbber block of rectangular cross-section, bonded between two rigid parallel plates, is deformed by a displacement of one of the bonded plates in the length direction, the rubber is placed in a state of simple shear (Figure 1.1). To maintain such a deformation throughout the block, compressive and shear stresses would be needed on the end surfaces, as well as on the bonded plates [1,2]. However, the end surfaces are generally stress-free, and therefore the stress system necessary... 

The facility, methods of procedure, and materials employed in this study have been discussed in detail elsewhere O9O 9 and are only briefly described here. The outdoor reaction chamber employed in this study consists of a 309000-liter FEP-type Teflon bag of triangular cross section held semi-rigidly by a framework of steel pipes. The chamber houses a set of multiple-reflection optics (capable of pathlengths in excess of 1 km) which is interfaced to a Midac interferometer and associated data system. 

Figure 5.7 The role of stress caused by lattice mismatch between SAM and substrate illustrated in (a) and (b) by a cross-section of a SAM (x-z plane), indicated adsorption sides (x-y plane) and the molecule-substrate interaction potential V where the solid circles indicate the energy of an adsorption site for a particular SAM molecule, (a) For rigid molecules, stress is mainly released by defect formation in SAM, which results in a layer of rather low crystallinity and small domains, (b) Molecules...

To illustrate the point, we present Figure 20.3, a schematic cross section of a thin-fihn hard disk. The Ni-P layer, whose purpose is to render a nearly perfectly smooth, rigid. 

---