Compressive stresses, pressure

CompoundShrinka.g e. In its simplest form (Fig. 8a) compound shrinkage consists of machining the inner radius of an outer component I, (Qp so that it is smaller than the outer radius of an inner component II, The difference between the two is known as the radial interference 5. To assemble the cylinders, outer component I is heated and/or inner component II cooled so that the outer component can be sHpped over the inner as shown in Figure 8b. When the temperature of the assembly returns to ambient, a compressive stress (pressure) is generated across the interface which simultaneously compresses the inner and expands the outer component and, in so doing, displaces radius (r/j by Uj and radius ( jj by U, Unfortunately, it is difficult to carry out this operation without setting up stresses in the axial direction (32). 

During pressure sintering, interiDarticle compressive stress, approximated by the externally applied stress and nonnalized by the relative density of the compact p, supplements the surface tension driving force for pore shrinkage ... 

If it is assumed that uniform tensile stress, like uniform compressive stress (7), has no significant effect on yield, then the yield pressure of a cylinder subjected solely to an internal pressure may be calculated from... 

Fig. 3.2. Common slates of stress, tension, compression, hydrostatic pressure and shear.

The information presented in this work builds upon developments from several more established fields of science. This situation can cause confusion as to the use of established sign conventions for stress, pressure, strain and compression. In this book, those treatments involving higher-order, elastic, piezoelectric and dielectric behaviors use the established sign conventions of tension chosen to be positive. In other areas, compression is taken as positive, in accordance with high pressure practice. Although offensive to a well structured sense of theory, the various sign conventions used in different sections of the book are not expected to cause confusion in any particular situation. 

Fig. 5.11. The study of shock compressibility of pressure-sensitive magnetic alloys was carried out with the quartz gauge impact technique. Loading was either with the specimen material or a quartz gauge. Resulting stress pulses were recorded with a quartz gauge (after Graham et al. [67G01]).

The maximum compressive stress will occur when the vessel is not under pressure = 7.4 + 61.1 = 68.5, well below the critical buckling stress. 

The original solids-conveying model developed by Darnel and Mol [7] assumed that the pressure (or stress) in the solid bed is isotropic. This assumption was made to simplify the mathematics and because of the lack of stress data for solid bed compacts. Previous research, however, showed that stresses in solid compacts are not isotropic [8]. Anisotropic stresses can be represented by the lateral stress ratio. It is defined as the ratio of the compressive stress in the secondary direction to the compressive stress in the primary direction, as shown in Fig. 4.7 and Eq. 4.1. 

The creep stress was assumed to be shared between the polymer structure yield stress and the cell gas pressure. A finite difference model was used to model the gas loss rate, and thereby predict the creep curves. In this model the gas diffusion direction was assumed to be perpendicular to the line of action of the compressive stress, as the strain is uniform through the thickness, but the gas pressure varies from the side to the centre of the foam block. In a later variant of the model, the diffusion direction was taken to be parallel to the compressive stress axis. Figure 10 compares experimental creep curves with those predicted for an EVA foam of density 270 kg m used in nmning shoes (90), using the parameters ... 

For an externally applied pressure, a compression-compression stress field is obtained with a thick-walled sphere. If the sphere wall is thin, a biaxial field is produced. If the pressure is applied internally, a triaxial tension-tension-compression state is generated. A nearly uniform stress field is produced over the entire specimen. The supporting tube is surrounded with a low modulus material to avoid stress concentration and... 

Sharma (90) describes an apparatus which uses a tubular specimen which may be strained longitudinally with internal pressurization. Loading rate can be varied, and strains are measured by clip gages. This device permits characterization of propellant-like materials in various biaxial tension-tension and biaxial tension-compression stress fields. A schematic of the apparatus is shown in Figure 24. 

In a recent attempt to bring an engineering approach to multiaxial failure in solid propellants, Siron and Duerr (92) tested two composite double-base formulations under nine distinct states of stress. The tests included triaxial poker chip, biaxial strip, uniaxial extension, shear, diametral compression, uniaxial compression, and pressurized uniaxial extension at several temperatures and strain rates. The data were reduced in terms of an empirically defined constraint parameter which ranged from —1.0 (hydrostatic compression) to +1.0 (hydrostatic tension). The parameter () is defined in terms of principal stresses and indicates the tensile or compressive nature of the stress field at any point in a structure —i.e.,... 

When rotated into the principal coordinates, all the shear stresses vanish, and it is reasonable to think of the average normal compressive stress as a pressure. It is apparent from Eq. 2.183, however, that the average compressive stress is not equal to the thermodynamic pressure p as evaluated from an equation of state. Stokes made this interesting observation and recognized its concomitant dilemma in his famous 1845 paper. He hypothesized that the dilemma could be resolved by assuming that... 

The transformation can be influenced by an applied stress. As seen in Fig. 24.13, the stress-free transformation to martensite results in a decrease in specimen length. Data in Figs. 24.14 and 24.15 were obtained by applying a series of constant uniaxial stresses at constant ambient pressure, P. The data show that the transformation temperature increases approximately linearly with applied uniaxial compressive stress. This dependence of transformation temperature on stress state follows from minimization of the appropriate thermodynamic function. For a material under... 

The more usual case, both in applications and experiment, is where it is assumed that there is complete absence of slip, stress and strain are not uniform throughout the test piece and barrelling takes place on compression. The pressure distribution over the flat ends of the test piece under these circumstances has been investigated by Hall97. 

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