Cross tie

Ataiiiv iLi use LPI ahiliiy to cross-tie systems to provide additional redundancy... 

By the principles outlined in the examples, gas pipe line systems may be analyzed, paralleled, cross-tied, etc. 

Use either a 40-in. l.D. header for these three compressors (two running or equivalent with three) or bring in two parallel headers, cross tied, of about half the flow area each, which equals (5,210) (3.408)/ (2,000) (2) or 4.53 fti. This corresponds to a pipe diameter of 2 ft, 5 in., say 2 ft, 6 in. This is still a large pipe, and space arrangements may dictate which is preferred. If this header is coming to the compressors from a great distance, the pressure drop must be checked to be certain that the system drop will ensure specified pressure at the suction of the cylinders. In some cases, the header size can be made slightly smaller if the pressure... 

PLACE A 21/4 TO 21/2 LB CHARGE BENEATH THE RAIL AND COVER WITH BALLAST IN EVERY OTHER CROSS TIE SPACE TO COVER A DISTANCE OF 16 ... 

Initially it was thought that MRAMs would offer a great advantage in cell size over FRAMs however, this prediction was based upon the assumption of raw matrix (cross-tie) arrays. In reality, the problem of cross-talk or halfselect disturb pulses is as acute with MRAMs as with FRAMs, and in each case a space-consuming architecture must be employed with pass-gate transistor isolation of each bit. 

The deformation of the polymer within a thin active zone was originally represented by a non-Newtonian fluid [31 ] from which a craze thickening rate is thought to be governed by the pressure gradient between the fibrils and the bulk [31,32], A preliminary finite element analysis of the fibrillation process, which uses a more realistic material constitutive law [36], is not fully consistent with this analysis. In particular, chain scission is more likely to occur at the top of the fibrils where the stress concentrates rather than at the top of the craze void as suggested in [32], A mechanism of local cavitation can also be invoked for cross-tie generation [37]. 

The craze is modeled by an elastic anisotropic medium with Young s moduli i and 2 corresponding to the stiffness of the cross-tie and the main fibrils ( 1 2). As the strip thickens along the direction 2 (Fig. 4b), the elastic energy density W is stored so that the energy release rate at failure... 

Fig. 4 Description of a craze (a) with a Dugdale zone, and the local analysis (b) as a long strip representing the anisotropic craze structure made of main fibrils oriented along direction 2, connected with lateral cross-tie fibrils along direction 1...

Fig. 6. A schematic showing the parameters which describe the cra2B fibril microstructure, including the cross-tie fibrils...

A simple model for the formation of the cross-tie fibrils follows directly from the discussion of the formation of fibril surfaces given above. In that discussion it was assiuned that all the strands in the entanglement network which span the plane of separation must either break or disentangle. For most of the strands this statement is correct. However, occasionally several polymer strands may be strongly stretched on the void interface simultaneously so that they can not be broken as shown schematically in Fig. 7 a. Under such circumstances, it will be energetically favorable for the... 

Hg. 7a-c. A schematic of the advancing craze-interface showing a A pile-up of entangled strands on the void ceiling, b A stretched cross-tie fibril produced by convolution, and c A cross-tie fibril after the polymer strands relax and concomitantly pull the main fibrils out of alignment... 

In view of the fact that the cross-tie fibrils contain some of the entangled strands that were imagined to either break or disentangle in the development of Eqs. (15) and (20), one can ask how accurate these formulae are given the cross-tie fibril microstructure of a typical craze. From the meridonal LAED reflections, Miller estimated that the cross-tie fibrils comprised only at most about 15% of the volume of the main fibrils and therefore that the corrections required to Eqs. (15) and (20) for the cross-tie fibrils are negligible. 

Finally, the effect of the cross-tie fibril structure on craze breakdown is unknown. We have emphasized here a very simplified picture of the fibril breakdown process in which the nucleation event of a breakdown is the failure of a single transfer length of a main load-bearing fibril. Yet we have excellent evidence that cross-tie fibrils exist and that they can transfer stress between main fibrils. These cross-tie fibrils may have to be considered in developing more exact models of craze fibril breakdown. 

The above definition thus includes the classical fibrillar crazes (formed on surfaces, in thin films or in the bulk at lower or higher temperatures in preoriented or isotropic material, in the presence or absence of a solvant or diluant) as well as those crazes which contain so many voids and cross-ties within the heavily deformed craze matter that it becomes difficult to identify individual fibrils. The Editor is extremely grateful to all authors of this volume and to Dr. G. H. Michler for frequent discussions on the above subject and for their constructive comments which led to the above Jointly proposed definition. 

It is interesting to note that foamed composites are suitable sandwich core materials for FRP boats (8). Cross-ties (or sleepers) for railroads, especially for use in tunnels and subways, are very promising applications. Japanese National raUways carried out a long-term test in a tunnel, and the results were excellent. 

The ratio C66/C22 depends only on the craze microstructure and the elastic properties of the fibrils, i.e. the spacing L between cross-tie fibrils which bridge between one main fibril and the next as well as the distance, d, between main fibrils. Estimates of C66/C22 based on the micromechanics of the craze microstructure can be found in [54]. For crazes in PS, L 60 nm and d 20 nm, leading to an estimate for C66/C22 of 0.02. 

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