Hydrostatic limits

Fig. 3. When subjected to non-hydrostatic pressure, the width of the R-lines increases [113, 139], and this has been used to determine the hydrostatic limits of a number of pressure transmitting fluids. An extensive review of ruby at high pressures has recently been written by K. Syassen [142].

The best medium with regard to hydrostatic conditions found by Piermarini et al. (1973) was a 4 1 methanol-ethanol mixture. In this case hydrostatic conditions were maintained up to a pressure of around 10 GPa. Other common media are a 16 3 1 mixture of methanol-ethanol-water with a hydrostatic limit of 14.5 GPa (Fujishiro et al., 1982), argon or neon with limits of 9 GPa and 16 GPa, respectively (Bell and Mao, 1981) or helium with a maximum value of 70 GPa (Eremets, 1996). 

Single-crystal X-ray diffraction with laboratory sources can yield the most precise high-pressure unit-cell parameter data, and modem DACs allow the routine attainment of pressures of 10 GPa, the hydrostatic limit of the 4 1 methanol ethanol mixture commonly used as a pressure medium because of its ease of use. With other pressure media... 

Because structural phase transitions are often ferroelastic or coelastic in character it is essential to have a well-defined stress applied to the crystal at high pressures. In effect, this means that a hydrostatic pressure medium must be used to enclose the crystal. A 4 1 mixture by volume of methanol ethanol remains hydrostatic to just over 10 GPa (Eggert et al. 1992) and is convenient and suitable for many studies. If the sample dissolves in alcohols, then a mixture of pentane and iso-pentane which remains hydrostatic to 6 GPa (Nomura et al. 1982), or a solidified gas such as N2, He, or Ar can be employed. Water appears to remain hydrostatic to about 2.5 GPa at room temperature, just above the phase transition from ice-VI to ice-VII (Angel, unpublished data). The solid pressure media such as NaCl or KCl favoured by spectroscopists are very non-hydrostatic even at pressures below 1 GPa and have been shown to displace phase transitions by at least several kbar (e g. Sowerby and Ross 1996). Similarly, the fluorinert material used in many neutron diffraction experiments because of its low neutron scattering power becomes significantly non-hydrostatic at -1.3 GPa. Decker et al. (1979) showed that the ferroelastic phase transition that occurs at 1.8 GPa in lead phosphate under hydrostatic conditions is not observed up to 3.6 GPa when fluorinert was used as the pressure medium. At pressures in excess of the hydrostatic limit of the solidified gas and fluid... 

Much less is known about the low temperature hydrostatic limits of pressure media. The flow and deformation properties of cryogenic gas and solid media are hkely not significantly altered at low temperature. Low temperature can, however, be expected to promote sohdification and lower the hydrostatic limit of hquid media. Few quantitative studies of this effect have been reported [70, 124]. In practice,most investigators indirectly assess the onset of non-hydrosta-tic stresses at low temperature and hmit experiments to P, T conditions that are sufficiently hydrostatic for their purposes. The linewidth of fluorescence lines or X-ray diffraction peaks of the pressure calibrant used in an experiment provide a quahtative measure of hydrostaticity. Non-hydrostatic stresses lead to inhomogeneous broadening and an increase in linewidth. A discontinuous increase in hnewidth with pressure is an indication that solidification of a hquid pressure medium has occurred and that significant non-hydrostatic stresses are present. 

Usually, it is assumed that pressure effects under the hydrostatic limit are isotropic, which causes a proportional decrease of all distances in the lattice without a change in the local symmetry of the Ln ion. As the result, a standard assumption is that angular factors C (0, (j>) in the crystal-field Hamiltonian are pressure independent and that the only pressure-sensitive parameters are the Slater integrals, spin-orbit coupling, and radial crystal-field parameters (R)- Then, in most cases, pressure causes small linear shifts of the sharp-lines luminescence related to f-f transitions in the Ln " and Ln ions. 

Piermarini GJ, Block S, Bamnett JS (1973) Hydrostatic limits in liquids and soUds to 100 kbar. J Appl Phys 44 5377... 

Otto JW, Vassiliou JK, Frommeyta G (1998) Nonhydrostatic compression of elastically anisotropic poly crystals. L Hydrostatic limits of 4 1 methanol-ethanol and paraffin olL Phys... 

Angel RS, Bujak M, Zhao J, Gatta GD, Jacobsen SD (2(X)7) Effective hydrostatic limits of pressure media for high-pressure crystallographic studies. J Appl Cryst 40 26... 

The a-7 phase boundary of RDX was also determined by optical polarizing microscopy of single crystals of RDX in a quasihydrostatic environment. Fig. 12 shows two single crystals of RDX at about 3.5 GPa at room temperature in a Fluoroinert (chemically inert fluorinated hydrocarbon) pressure transmitting medium which provides a hydrostatic environment up to about 4.0 GPa at room temperature. At constant pressure, as the temperature is increased the hydrostatic limit increases because temperature reduces the viscosity of the liquid. This... 

When constmction is complete, the pipeline must be tested for leaks and strength before being put into service industry code specifies the test procedures. Water is the test fluid of choice for natural gas pipelines, and hydrostatic testing is often carried out beyond the yield strength in order to reHeve secondary stresses added during constmction or to ensure that all defects are found. Industry code limits on the hoop stress control the test pressures, which are also limited by location classification based on population. Hoop stress is calculated from the formula, S = PD/2t, where S is the hoop stress in kPa (psig) P is the internal pressure in kPa (psig), and D and T are the outside pipe diameter and nominal wall thickness, respectively, in mm (in.). 

Gla.ss Ca.pilla.ry Viscometers. The glass capillary viscometer is widely used to measure the viscosity of Newtonian fluids. The driving force is usually the hydrostatic head of the test Hquid. Kinematic viscosity is measured directly, and most of the viscometers are limited to low viscosity fluids, ca 0.4—16,000 mm /s. However, external pressure can be appHed to many glass viscometers to increase the range of measurement and enable the study of non-Newtonian behavior. Glass capillary viscometers are low shear stress instmments 1—15 Pa or 10—150 dyn/cm if operated by gravity only. The rate of shear can be as high as 20,000 based on a 200—800 s efflux time. 

In the large-diameter vertical cylindrical tanks, because hoop stress is proportional to diameter, the thickness is set by the hydrostatic hoop stresses. Although the hydrostatic forces increase proportionally with the depth of Hquid in the tank, the thickness must be based on the hydrostatic pressure at the point of greatest depth in the tank. At the bottom, however, the expansion of the shell owing to internal hydrostatic pressure is limited so that the actual point of maximum stress is slightly above the bottom. Assuming this point to be about 1 ft (0.305 m) above the tank bottom provides tank shells of adequate strength. The basic equation modified for this anomaly is... 

Each test has specific limitations and may pass defects of various sizes and orientations. The specific limitations for a particular technique must be understood for correct interpretation of results. For example, hydrostatic tests and air-underwater tests may pass defects that run 70% of the wall thickness. Hydrostatic tests may pressurize a defect in such a way that leaking does not occur in the test but can in service. 

If a design limit test is included in the test run (such as a hydrostatic test) and it exceeds safe operating limits, consider writing a special procedure for this part of the test. 

A strength value associated with a Hugoniot elastic limit can be compared to quasi-static strengths or dynamic strengths observed values at various loading strain rates by the relation of the longitudinal stress component under the shock compression uniaxial strain tensor to the one-dimensional stress tensor. As shown in Sec. 2.3, the longitudinal components of a stress measured in the uniaxial strain condition of shock compression can be expressed in terms of a combination of an isotropic (hydrostatic) component of pressure and its deviatoric or shear stress component. 

Figure 9-3. Hydrostatic analogy for a pathway with a rate-limiting step (A) and a step with a AG value near zero (B).

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