Rosette equation

At a certain critical load, the crack spontaneously breaks through to the free surface (the cut-through ), usually with additional crack depth increase D, and changes into a well developed semicircle (solid-line semicircle). This transformation may also be induced in another, stable, manner, e.g., by the action of rosette type stresses around the strain region while loading the indenter before the cut-through . The model given in Fig. 6.2.8 is described by the equation... 

The form of the orbit is, as in every multiply-pcriodic central motion, a rosette. Its equation is easily found. In order to derive it we again introduce the co-ordinates r, ifs in the orbital plane. By (12), 21, we obtain then for the differential equation of the orbit ... 

With the introduction of the rosette sampler and the echo sounder, choosing the depth at which a sample is to be taken is a simple exercise in chart reading. Samples can be taken at any specified depth or in any specified water mass. Using much less sophisticated equipment on a cruise in the South Pacific [167], we were able to take water samples in the Antarctic Intermediate Water from 63 °S almost to the Equator, in order to demonstrate a horizontal continuity and vertical discontinuity in organic particulate content associated with a particular water mass. 

The difference between the latter two sets of equations can lead to very erroneous values of stress when attempting to use an electrical strain gage rosette to determine the state of stress experimentally. In Eqs. 2.25 the traditional symbol e with mixed indices has been used to identity tensorial... 

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