Pressure yield

As two surfaces are brought together, the pressure is extremely large at the initial few points of contact, and deformation immediately occurs to allow more and more to develop. This plastic flow continues until there is a total area of contact such that the local pressure has fallen to a characteristic yield pressure of the softer material. 

Normally, then, the actual contact area is determined by the yield pressure, so that... 

The mechanism of boundary lubrication may then be pictured as follows. At the unusually prominent asperities, the local pressure exceeds the yield pressure... 

The coefficient of friction for copper on copper is about 0.9. Assuming that asperities or junctions can be represented by cones of base and height each about 5 x 10" cm, and taking the yield pressure of copper to be 30 kg/mm, calculate the local temperature that should be produced. Suppose the frictional heat to be confined to the asperity, and take the sliding speed to be 10 cm/sec and the load to be 20 kg. 

The resistance due to a circular junction is given by / = /2ak, where a is the radius of the junction and k is specific conductivity of the metal. For the case of two steel plates, the measured resistance is 5 x 10" Q for a load of 50 kg the yield pressure of steel is 60 kg/mm, and the specific resistance is 5x 10 Q/cm. Calculate the number of junctions, assuming that it is their combined resistance that is giving the measured value. 

Derive Eq. XII-18. In an experiment using hexadecane and crossed mica cylinders, the circular flat contact area is about 10 cm in diameter and the two surfaces oscillate back and forth to the extent of 1 % of their diameter per second. The separation distance is 10 A and the yield pressure of the glue-backed mica is 0.1 kg/mm. ... 

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... 

Equation 7 predicts the correct yield pressure only if the material is isotropic, the cylinder free from residual stress prior to the appHcation of pressure, and sufftcientiy long, eg, more than five diameters, for there to be no end effects. 

Although a torsion test is simple to carry out, it is not commonly accepted as an integral part of a material specification furthermore, few torsion data exist in handbooks. If, as is usually the case, the design needs to be based on tensile data, then a criterion of elastic failure has to be invoked, and this introduces some uncertainty in the calculated yield pressure (8). 

It may be seen from equation 7 that even if the wall of an initially stiess-fiee cylindei is infinitely thick, k = oo, the yield pressure cannot exceed T. ... 

Partially Plastic Thick-Walled Cylinders. As the internal pressure is increased above the yield pressure, P, plastic deformation penetrates the wad of the cylinder so that the inner layers are stressed plasticady while the outer ones remain elastic. A rigorous analysis of the stresses and strains in a partiady plastic thick-waded cylinder made of a material which work hardens is very compHcated. However, if it is assumed that the material yields at a constant value of the yield shear stress (Fig. 4a), that the elastic—plastic boundary is cylindrical and concentric with the bore of the cylinder (Fig. 4b), and that the axial stress is the mean of the tangential and radial stresses, then it may be shown (10) that the internal pressure, needed to take the boundary to any radius r such that is given by... 

The effect of subjecting a thick-waded cylinder to a pressure greater than the yield pressure and then releasing the pressure is to put the material adjacent to the bore of the cylinder in compression while the outer layers remain in tension. On subsequent repressurization the cylinder wid, to a first approximation, retrace the unloading path BE (see Eig. 3) so that the cylinder withstands elasticady a pressure equal to that appHed originally. 

Collapse and Bursting Pressure. If the pressure is sufficiently large to push the plastic—elastic boundary to the outer surface of the cylinder so that the fibers at that surface yield, then there is nothing to restrain the wad, and the cylinder is said to codapse. With an ideal material which does not work harden the codapse pressure, P, sometimes caded the full plastic flow pressure, the full overstrain pressure or the full thickness yield pressure, would be the bursting pressure of the cylinder. It is given by equation 10 when thus... 

Fig. 9. Yield pressure of multicomponent vessels designed for optimum conditions (34).

Design Criteria. Traditionally the yield pressure has been regarded as an important design criterion because it is the largest pressure to which an initially stress-free cylinder may be subjected without the cylinder suffering any permanent deformation when the pressure is removed. Customarily,... 

Dry Sliding. When two surfaces mb, the real area of contact involves only sufficient asperities of the softer material so that their yield pressure balances the total load (3). As the initial load W increases, the real contact area illustrated in Figure 1 increases proportionately according to the relation... 

Yield pressurep of the asperities is about three times the tensile yield strength for many materials. The real area of contact is frequently a minute fraction of the total area. With a typical bearing contact stress of 3 MPa and a bron2e bearing asperity yield pressure of 500 MPa, for instance, less than 1.0% of the nominal area would involve asperity contact. 

Because shear and compressive strengths s andp depend in a similar way on material properties such as lattice stmcture and bond strength,yis often in a rather narrow range of about 0.20—0.35 for a wide variety of materials. The following are typical data for sliding on steel with bearing materials varying several hundredfold in yield pressure ... 

If the experimental values P and w are closely reproduced by the correlating equation for g, then these residues, evaluated at the experimental values of X, scatter about zero. This is the result obtained when the data are thermodynamically consistent. When they are not, these residuals do not scatter about zero, and the correlation for g does not properly reproduce the experimental values P and y . Such a correlation is, in fact, unnecessarily divergent. An alternative is to process just the P-X data this is possible because the P-x -y data set includes more information than necessary. Assuming that the correlating equation is appropriate to the data, one merely searches for values of the parameters Ot, b, and so on, that yield pressures by Eq. (4-295) that are as close as possible to the measured values. The usual procedure is to minimize the sum of squares of the residuals 6P. Known as Barkers method Austral. ]. Chem., 6, pp. 207-210 [1953]), it provides the best possible fit of the experimental pressures. When the experimental data do not satisfy the Gibbs/Duhem equation, it cannot precisely represent the experimental y values however, it provides a better fit than does the procedure that minimizes the sum of the squares of the 6g residuals. 

FIG. 20-79 Effect of pelleting pressure on axial crushing strength of compacted calcite particles of different sizes demonstrating existence of a critical yield pressure. Inset shows the effect of hardness on critical yield pressure. [Benhow, Enlargement and Compaction of Particulate Solids, Stanley-Wood (ed.), Butteixooiihs, 169 (1.9S3),]... 

It has been a persistent characteristic of shock-compression science that the first-order picture of the processes yields readily to solution whereas second-order descriptions fail to confirm material models. For example, the high-pressure, pressure-volume relations and equation-of-state data yield pressure values close to that expected at a given volume compression. Mechanical yielding behavior is observed to follow behaviors that can be modeled on concepts developed to describe solids under less severe loadings. Phase transformations are observed to occur at pressures reasonably close to those obtained in static compression. 

Values for collapse resistance, internal yield pressure, pipe body, and joint strength for steel grades as in Table 4-141 are given in Table 4-150. Table 4-150 is directly taken from API Bulletin 5C2, 17th Edition, 1980. Formulas and procedures for calculating the values in Table 4-150 are given in Bulletin 5C3 [152] and are as follows ... 

Internal Yield Pressure for Pipe. Internal yield pressure for pipe is calculated from formula 4-133. The factor 0.875 appearing in formula 4-313 allows for minimum wall thickness. 

Internal Yield Pressure for Couplings. Internal yield pressure for threaded and coupled pipe is the same as for plain end pipe, except where a lower pressure is required to avoid leakage due to insufficient coupling strength. The lower pressure is based on... 

Substrate Absolute configuration ee [%i Yield [%] Pressure [bar] TONb)... 

If the pressure in a thick-walled cylinder is raised beyond the yield pressure pei according to the equation (9), the yield will spread through the wall until it reaches the outer diameter [10]. For a perfectly elastic-plastic material the ultimate pressure for complete plastic deformation of the thick wall pCOmpi-pi, also called collapse pressure, can be calculated by equation (4.3-10). As the ductile materials used for high pressure equipment generally demonstrate strain... 

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