Secondary buckling

Perhaps the most noteworthy aspect of the secondary buckling phenomenon illustrated here is that it is accompanied by an energy release rate at the edge of the zone of delamination that varies with position in the y—direction. This provides a mechanism by which a straight-sided delamination zone may develop a wavy shape through buckle-driven delamination, or a circular delamination zone may develop a lobed shape. The consequences of secondary buckling in thin films have not been studied systematically. 

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In order to examine the phenomenon of film buckling and possible subsequent delamination, this section begins with a description of the simplest case of buckling under plane strain conditions. This is followed, in subsequent sections, by analysis of circular buckles, secondary buckling phenomena and buckles with perimeters of other shapes. 

Fig. 5.16. Post buckljiig configurations plotted for a stress level which is approximately nine times the primarily buckling stress, or 1.5 times the secondary buckling stress. These figures show contours of constant values of transverse deflection w x, y) of the film, normalized by the film thickness fif, over a portion of the undeflected film plane. Part (a) shows the mode which is symmetric in the r—direction for fixed y, whereas part ( ) shows the most easily achieved mode in the j/—direction for fixed x.

A rich variety of experimental observations has been reported in the literature on the buckling of compressively stressed thin films on substrates and on the development of secondary buckling phenomena which lead to configurations with reproducible characteristic shapes. Examples of such observations are presented in this section. 

Fig. 5.17. An example of secondary buckling leading to a wrinkled shape in a circular blister in a SiC thin film on a (100) Si substrate, as revealed by Nomarski interference contrast microscopy. Reproduced with permission from Argon et al.

Pressure-time histories caused by explosions may be nonuniform and subject to amplification because of secondary shocks and shock reflections. Current models can provide only one- or two-dimensional histories. Failure modes are typically permanent deformation (plastic deformation/buckling), stable cracking (leaking), and brittle failure. Table 2.3 (Theodore et al., 1989) describes expected damage estimates for humans, structural elements, and process equipment for particular overpressures. 

Fig. 7 Sequential micrographs of the evolution of the damage in a SiO 4.5 wt.% P film deposited on an Al substrate subjected to a tensile test (system C, Figure 6). The black arrows show the tensile direction, (a) Networks of primary and secondary cracks perpendicular to the tensile axis (e = 11%). The white arrows show a secondary crack which stops when getting close to primary cracks, (b) decohesion and buckling of the strips of film. Slip lines are observed on the Al surface under the buckled strips, and (c) transverse rupture of the buckled zones along the directions of maximum shear of the substrate (e = 19%).

Cobalt leads to more rapid drying at the surface of the film than in the lower layers. If the surface dries first, it will buckle or shrivel when the rest of the film contracts as it hardens. For this reason, secondary driers are usually added with cobalt to accelerate the drying of the bulk of the film. The presence of calcium accelerates the loss of unsaturation in the film. When the levels of the two types of drier are balanced , shrivelling does not occur. Manganese is less pronounced in its surface bias, but is also used with secondary driers. 

In the double pool reactor structure, SGs are located adjacent to the primary vessel, which is the primary coolant boundary. If a water leak should occur from the SG tubes, the primary vessel is exposed to the external buckling load. As a result the mitigation stem against sodium-water reaction events is different from other FBRs. In a beyond design basis leak event, quasisteady state pressure of the secondary cover gas is released through the manometer seal structure passively. 

From the preliminary analysis, the increase of the quasi-steady-state pressure of the cover gas in the secondary vessel is about 0 13 MPa and 0 2MPa for a DBL and a BDBL, respectively These values are much less than the external buckling pressure of the primary vessel (0 56MPa), thus the structural integrity of the primary vessel can be secured... 

As all fibres, cellulose fibres can bear higher loads in tension than in compression because the fibres can buckle or kink under compressive loads. The arrangement of the cellulose fibres in the outer and inner layer of the secondary cell wall ensures that they are loaded in tension if the wood as a whole is loaded in compression and thus increase the compressive strength. The compressive strength of wood, however, is about 30 MPa, approximately one third of its tensile strength. 

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