Isometrics

Fig. 2.10 Isometric projection of the electron density around formamide.

Fig. 5.1 Variation in the energy of pentane with the two torsion angles indicated and represented as a contour diagram and isometric plot. Only the lowest-energy regions are shown.

Many developers of software for finite-element analysis (18) provide drafting of pipelines and associated flow analysis. These companies include Algor, McAuto, MacNeal-Schwindler, and ElowDesign. In software, in-house developed pipe fittings are modularized and isometric views of the piping systems with three-dimensional detailing are now commonplace. 

Fig. 7. Spht screen viewing of designed parts, (a). Top view (b), isometric view (c), front view (d), right-side view.

Pettyjohn and Christiansen Chem. Eng. Prog., 44, 157-172 [1948]) present correlations for the effect of particle shape on free-settling velocities of isometric particles. For Re < 0.05, the terminal or free-setthng velocity is given oy... 

The first five methods are apphcable only after rigorous circuit analysis and when piping layouts and isometric drawings or scale models are available for quantity takeoff (e.g., pipe size, length, and specification, flanges and valve count, etc.). 

Strain and constant time can give respectively isometric stress-log time curves and isochronous stress-strain curves Figure 9.10). Whilst not providing any new information, such alternative presentations of the data may be preferred for certain purposes. 

Figure 9.10. Presentation of creep data sections through the creep curves at constant time and constant strain give curves of isochronous stress-strain, isometric stress-log (time) and creep modulus-log (time). (From ICI Technical Service Note PES 101, reproduced by permission of ICI...

Long-term deformation such as shown by creep curves and/or the derived isochronous stress-strain and isometric stress-time curves, and also by studies of recovery for deformation. 

Design Methods for Plastics using Deformation Data Isochronous and Isometric Graphs... 

As indicated above, the stress-strain presentation of the data in isochronous curves is a format which is very familiar to engineers. Hence in design situations it is quite common to use these curves and obtain a secant modulus (see Section 1.4.1, Fig. 1.6) at an appropriate strain. Strictly speaking this will be different to the creep modulus or the relaxation modulus referred to above since the secant modulus relates to a situation where both stress and strain are changing. In practice the values are quite similar and as will be shown in the following sections, the values will coincide at equivalent values of strain and time. That is, a 2% secant modulus taken from a 1 year isochronous curve will be the same as a 1 year relaxation modulus taken from a 2% isometric curve. 

As before, a similar result could have been achieved by taking a section across the creep curves at 1.5% strain, plotting an isometric graph (or a 1.5% modulus/time graph) and obtaining a value for modulus at 1 year (see Fig. 2.8)... 

This is a stress relaxation problem and strictly speaking stress relaxation data should be used. However, for most purposes isometric curves obtained from the creep curves are sufficiently accurate. By considering the 1.5% isometric curve shown in Fig. 2.8 it may be seen that the initial stress is 16 MN/m2 and the stress after 1 week is 7 MN/m2. 

Accurately performed relaxation tests in which the strain in the material was maintained constant and the decaying stress monitored, would give slightly lower values than those values obtained from the isometric data. 

Isometric data from the creep curves may also be superimposed on the creep rupture data in order to give an indication of the magnitudes of the strains involved. Most plastics behave in a ductile manner under the action of a steady load. The most notable exceptions are polystyrene, injection moulding grade acrylic and glass-filled nylon. However, even those materials which are ductile at short times tend to become embrittled at long times. This can cause... 

It may be seen from Fig. 2.71 that in most cases where the failure is ductile the isometric curves are approximately parallel to the fracture curve, suggesting that this type of failure is primarily strain dominated. However, the brittle... 

This is a stress relaxation problem but the isometric curves may be used. 

From the 0.417% isometric curve, the stress after 1 year is 1.45 MN/m ... 

Then from a 1.6% isometric taken from the creep curves it may be determined that the stress after 10 seconds is 15.1 MN/m and after 1 year it is 5.4 MN/m. ... 

Figure 13.17 shows isometrics of mechanical shaking, reverse air, cartridge, and pulse-jet types of bag filter units. 

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