Intensification factor

Fracture Mechanics. Linear elastic fracture mechanics (qv) (LEFM) can be appHed only to the propagation and fracture stages of fatigue failure. LEFM is based on a definition of the stress close to a crack tip in terms of a stress intensification factor K, for which the simplest general relationship is... 

The concepts behind the analysis are not difficult. The piping system is simply a stmcture composed of numerous straight and curved sections of pipe. Although, for straight pipe, elementary beam theory is sufficient for the solution of the problem, it is not adequate for curved pipe. However, by the iatroduction of a flexibiUty factor, to account for iacreased flexibiUty of curved pipe over straight pipe, and a stress intensification factor, /, to account for... 

Flexibility and Stress-Intensification Factors. The flexibihty factor k (>1.0) is defined as the ratio between the rotation per unit length of the part in question produced by a given moment to the rotation of a straight pipe (of the same size and schedule) produced by the same moment. A close approximation of the flexibiUty factor that agrees quite well with theory and experiment for bends is as follows ... 

In the absence of more direc tly applicable data, the flexibility factor k and stress-intensification factor i shown in Table 10-54 may be used in flexibihty calculations in Eq. (10-101). For piping components or attachments (such as valves, strainers, anchor rings, and bands) not covered in the table, suitable stress-intensification factors may be assumed by comparison of their significant geometry with that of the components shown. 

Comprehensive analysis shall take into account stress-intensification factors for any component other than straight pipe. Credit may be taken for the extra flexibility of such a component. 

TABLE 10-54 Flexibility Factor kand Stress-Intensification Factor i ... 

The flexibility factor k applies to bending in any plane. The flexibility factors k and stress intensification factors shall not be less than unity factors for torsion equal unity. Both factors apply over the effective arc length (shown by heavy centerlines in the sketches) for curved and miter bends and to the intersection point for tees. 

A single intensification factor equal to 0.9/h may be used for both and if desired. 

Sweepolet is a contoured, integral r r, rr butt-weld branch connection with a low intensification factor for low stresses -fatigue life. The attachment weld is easily amined by radiography, ultrasound and other standard non-destructive techniques. 

Land-use intensification factor 10 To within 1 order or magnitude... 

The stress intensification factors in Appendix D of ASME B31.3 have been developed from fatigue tests of representative piping components and assemblies manufactured from ductile ferrous materials. The allowable displacement stress range is based on tests of carbon and austenitic stainless steels. Caution should be exercised when using eqs. (la) and (lb) (para. IP-2.2.10) for allowable displacement stress range for some nonferrous materials (e.g., certain copper and aluminum alloys) for other than low-cycle applications. 

Standard Test Method for Determining Stress Intensification Factors (/-Factors) for Metallic Piping Components.B31J-2008... 

Figure 10.35 The effect of hydraulic pressure on injectate temperature and specific rate. The data are for a 125 mm diameter screw and an intensification factor of 10 for a molding machine running a HIPS resin at a screw speed of 100 rpm...

The pressure at the tip of the screw is controlled by setting the hydraulic back pressure at the shank end of the screw. The pressure at the tip is calculated from the hydraulic back pressure and the process intensification factor as follows ... 

Tees Tees may be cast, forged, or hot- or cold-formed from plate or pipe. Tees are typically stocked with both header (run) ends of the same size. In general, run ends of different sizes are not typically stocked or specified however, occasionally run ends of different sizes are specified in threaded or socket-welded sizes. Branch connections may be full size or reducing sizes. Branch reductions two sizes smaller than the header are routinely stocked, and it is not typically difficult to purchase reducing tees with branches as small as those listed in ASME B16.9 (i.e., approximately one-half the header size). Economics, stress intensification factors, and nondestructive examination requirements typically dictate the branch connection type. 

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