Buckling collapse

Such failure were mainly support structure or tension anchor destruction by reason of its insufficient strengthen and result in overall buckling collapse of the foundation pit, as shown in Figure 3. 

An important factor that governs the design of SP and PIP used in ultra-deep waters is their buckling collapse capacity. The anatomy of a SP is shown in Fig. 18.5. 

Its fuel rod design also follows that of LWRs. The failure modes of fuel rods considered are over-heating, pellet cladding mechanical interaction (PCMI), buckling collapse, and creep rupture at both normal and abnormal transients. 

In LWRs, buckling collapse and creep rupture are not included in the design failure modes, because experimental verifications have shown that these failure modes are not limiting as long as the plastic deformation of the fuel rod is less than 1.0%. The core pressure and temperature of the Super LWR are much higher than those in LWRs, so these failure modes need to be included in the design failure modes. The evaluations of stresses on the cladding are based on ASME Boiler and Pressure Vessel Code Section III as adopted in BWRs for simplified evaluations. 

The principle of fuel rod integrity is summarized in Table 1.9. Four damage modes of the fuel cladding are expected at transients (a) buckling collapse, (b) stress rupture, (c) PCMI, and (d) thermal damage [65]. 

The criterion for buckling collapse is simple the pressure difference on the cladding does not exceed one-third of the buckling collapse pressure. 

No buckling collapse Pressure difference Pressure difference... 

When the fuel rod internal pressure is lower than the external pressure (i.e., the coolant pressure), the pressure difference acts on the cladding. When the radial compressive stress on the cladding exceeds the elastic limit of the cladding, buckling collapse occurs. That is to say, the buckling collapse pressure can be expressed by a function of the modulus of elasticity (Young s modulus) as follows ... 

The fuel rod buckling collapse should not occur when the fuel rod cooling is deteriorated. 

Thermo-mechanical design criteria Pressure difference < 1/3 Buckling collapse... 

Cladding collapse has been excluded in LWR fuel rod design. However, in the Super FR, pressure difference between internal gas and coolant is higher than that of PWRs. Collapse of cladding is kept as one possible cladding failure mode in the Super FR design. The pressure difference is limited by the buckling collapse pressure with a safety factor of 3 as in the Super LWR (see Chap. 2). 

The buckling collapse pressure for a given pressure difference is calculated by... 

When the required cladding thickness against buckling collapse is calculated, the safety factor of 1/3 is applied and 110% of the system pressure of 27.5 MPa and the cladding temperature of 800°C are considered. 

The polyethylene crystals shown in Fig. 4.11 exist as hollow pyramids made up of planar sections. Since the solvent must be evaporated away prior to electron microscopic observation, the pyramids become buckled, torn, and/ or pleated during the course of sample preparation. While the pyramidal morphology is clearly evident in Fig. 4.1 la, there is also evidence of collapse and pleating. Likewise, the ridges on the apparently planar crystals in Fig. 4.1 lb are pleats of excess material that bunches up when the pyramids collapse. 

For short closed vessels, and long vessels with stiffening rings, the critical buckling pressure will be higher than that predicted by equation 13.51. The effect of stiffening can be taken into account by introducing a collapse coefficient , Kc, into equation 13.51. 

Lourie O, Cox DM, Wagner HD (1998). Buckling and collapse of embedded carbon nanotubes. Phys. Rev. Lett. 81 1638-1641. 

Gibson and Ashby (a. 13) propose separate models for elastic collapse by cell edge buckling and plastic collapse by stretching of cell faces. The latter model gave a scaling relationship between the (initial) collapse stress a pi and the relative densities ... 

The compression under which collapse of the films occurs is very variable. In the case of palmitic acid the buckling point occurred between 20 and 45 dynes per centimetre, when the experiments were carried out with fresh water. On the other hand when water with a Ph of about 6 was used, the film, after being allowed to stand for a few days either covered or open to the atmosphere, resisted compression to over 60 dynes per centimetre. 

External pressure implies that the pressure on the outside of the tank or vessel is greater than that in its interior. For atmospheric tanks, the development of an interior vacuum results in external pressure. External pressure can be extremely damaging to tanks because the surface area of tanks is usually large, generating bigb forces. The result of excessive external pressure is a buckling of the shell walls or total collapse. In some cases wind velocities during hurricanes have been sufficient to knock down and collapse tanks. 

Additional compression eventually leads to the collapse of the film. The pressure nc at which this occurs is somewhere in the vicinity of the equilibrium spreading pressure. Figure 7.7 represents schematically how this film collapse may occur. The mode of film buckling shown in Figure 7.7 is not the only possibility head-to-head as well as tail-to-tail configurations can be imagined. The second structure strongly resembles that of cell membranes, which we discuss in the next chapter. 

At very high values of n the monolayer collapses (buckles). Both the cross-sectional area per molecule in the monolayer and the collapse pressure can be determined. For typical fatty acids, regardless of chain length, the area covered is only 0.2 nm2 per molecule indicating that the fatty acid chains are stacked vertically to the surface in the monolayer. The collapse... 

The cross section of the shaft had previously become constricted by sprayed molten Fe, so that the 3rd portion of the chge jammed. This formed a cavity in the furnace in which an expl gas/air mixt accumulated ignited. Calcn showed that a total pressure of 2.9atm developed during the expln. The collapse of the supporting posts, which corresponded to a buckling load of 9 tons, confirmed these calcns. Back pressure forced the gaseous mixt into the blast main, where a 2nd expln destroyed the blower... 

SEM images of the deformation around an indentation in a 90 im thick MWCNT-AI203 composite prepared by in situ formation of CNTs within the regular and very well aligned pores of an alumina membrane, (a) array of the shear bands formed, (b) close up view of lateral buckling or collapse of the CNTs in one shear band. ... 

In many applications materials are subjected to compressive stresses. The macroscopic phenomena of collapse under an axial compression are the well-known shear and kink bands. In polymers they are caused by the buckling of chains, accompanied by changes in the chain conformation. The resistance against buckling is expressed by the yield strength under axial compression, ac max. Northolt (1981) found a relationship between c,max and Tg. 

Kgure 10.2. Schematic view of the three regions of the force-displacement curve of a typical cellular solid I, small deformation of the intact structure II, buckling and fracture of cell walls and III, compaction of what is increasingly collapsed cell wall material. 

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