Geometrical discontinuities

Any material which contains a geometrical discontinuity will experience an increase in stress in the vicinity of the discontinuity. This stress concentration effect is caused by the re-distribution of the lines of force transmission through the material when they encounter the discontinuity. Causes of stress concentration include holes, notches, keyways, comers, etc as illustrated in Fig. 2.62. 

Other factors which promote brittleness are geometrical discontinuities (stress concentrations) and aggressive environments which are likely to cause ESC (see Section 1.4.2). The absorption of fluids into plastics (e.g. water into nylon) can also affect their creep rupture characteristics, so advice should be sought where it is envisaged that this may occur. 

Moulded plastics will also have crack initiation sites created by moulding defects such as weld lines, gates, etc and by filler particles such as pigments, stabilisers, etc. And, of course, stress concentrations caused by sharp geometrical discontinuities will be a major source of fatigue cracks. Fig. 2.72 shows a typical fatigue fracture in which the crack has propagated from a surface flaw. 

During service the impact behaviour of a plastic article will be influenced by the combined effects of the applied stress system and the geometry of the article. Although the applied stress system may appear simple (for example, uniaxial) it may become triaxial in local areas due to a geometrical discontinuity. Fig. 2.78... 

While ideally structures should be designed and fabricated so that environment-sensitive cracking is avoided, in practice it is sometimes necessary to live with the problem. This implies an ability to detect and measure the size of cracks before they reach the critical size that may result in catastrophic failure. Such inspection has important implications for plant design, which should be such as to allow inspection at relevant locations. The latter are regions of high residual stress (welded, bolted or riveted joints) and regions of geometrical discontinuity (notches, crevices, etc.) where stress or environment concentration may occur. 

On a semiconductor electrode, as on a metal electrode, another part of the double layer will be built up by a dipole layer at the surface of the solid. These dipoles again result from the geometrical discontinuity of die lattice at the surface and from adsorption of ions. 

For flow domains involving singularities such as sharp angles and those involving firee surfaces, the geometrical discontinuities are not explicitly taken into... 

It is worthwhile to consider whether the classical theories (or criteria) of failure can still be applied if the stress (or strain) concentration effects of geometric discontinuities (eg., notches and cracks) are properly taken into account. In other words, one might define a (theoretical) stress concentration factor, for example, to account for the elevation of local stress by the geometric discontinuity in a material and still make use of the maximum principal stress criterion to predict its strength, or load-carrying capability. 

A consideration of the local effects (welds, geometric discontinuities). 

A new design approach, taking into account the metallurgical and geometrical discontinuities inherent in weldment, is being piusued. 

The vessels are welded and in hot service it is the behaviour of the various weldments that generally dictates the vessel life. Weldment performance is dominated by the detailed design and subsequent fabrication of these features. The better designs ensure that the metallurgical discontinuity, i.e. weld metal and associated heat affected zones (HAZ), is not coincident with the geometric discontinuity that can often be associated with the joining of the two discrete parts. This factor has been addressed before, (Williamson, Bissell and Cane, 1988), as has the significance of this effect on inlet and outlet nozzle life (Fig. 2.9). 

A thinning of thimble tubes occurred as a result of flow induced vibration. Thimble tube wear had generally been detected at locations associated with geometric discontinuities or area changes along the flow path (such as areas near the lower core plate, the core support forging, the lower tie plate, the upper tie plate, and the vessel penetration). The thimbles are contained and supported over most of the path from the seal table through the fuel assembly. The thimble is unsupported for a short distance from the top of the lower core support plate to the point of entry into the fuel assembly lower nozzle. This unsupported area is most often subject to flow-induced vibration wear. 

The factor 2 in front of the second integral accounts for the fact that two surfaces, each with surface energy Us, are created from the surface S in the reference configuration. Continuum stress and deformation fields near a geometrical discontinuity such as a crack edge are potentially singular. In such a case, the differentiability requirements on these fields for interpretation of the continuum equilibrium equation or the divergence theorem may not be satisfied consequently, a special interpretation is required (Freund 1990). 

Stress, nominal The stress at a point calculated on the net cross section without taking into consideration the effect on stress of geometric discontinuities, such as holes, grooves, slots, fillets, etc. 

Strain, nominal The strain at a point calculated in the net eross section by simple elastic theory without taking into aceount the effeet on strain produced by geometric discontinuities sueh as holes, grooves, filters, etc. 

Outside of a particular layer of a finite thickness (the physical discontinuity surface), the concentrations of water and hexanol in the corresponding phases are constant. These concentrations are, respectively, c[ and c) in an aqueous solution (liquid) and c i and c i in vapor. Within the discontinuity surface, there is a transition between these concentrations either a smooth one or a positive tongue-like one, as shown in Figure 2.1b. In order to determine the excess (or the difference in the composition to be more precise) of a given component in a surface layer, we need to use Gibbs s method and extrapolate these four constant values to the dividing surface (the geometric discontinuity surface located within the physical discontinuity surface). The excess (adsorption) of... 

Another possibility for the presence of inaccessible surfeces is distortions within the fibril, interior surfeces. Some mechanical treatment of wood fibers shows a strong impact on CP/MAS spectra (22). Distortions of the cellulose I structure within the fibril, distributed along the fibril, may also constitute zones of geometrical discontinuities. 

In a sense, accessible fibril surfeces and inaccessible fibril surfaces are both geometrical discontinuities compared to the ciystal lattice of cellulose I. The polyglucan chains at both kinds of surfeces may exist in conformations distinct... 

Welded joints, because they can have elevated stress levels (from residual stress effects and stress concentrations), geometrical discontinuities, complex metallurgical structures, and possible galvanic cells (preferential weld corrosion)... 

---