Stress longitudinal

The sum of the longitudinal stress (in the corroded condition) caused by pressure weight or other sustained loadings is not allowed to exceed Where the sum of these stresses is less than the difference between and this sum may be added to the term 0.25 in equation 25. 

Combined longitudinal stresses shall not exceed the limits established in the code (see pressure design of piping components for Sl limitations). 

However, if the sum of longitudinal stresses enumerated is less than their stated limit S/, the difference may be added to the term 0.25S/, in the equation hmiting the stress range ... 

Impact testing is not required if the design temperature is helow —29 C (—20 F) hut at or above —46 C (—50 F) and the maximum operating pressure of the fabricated or assembled components will not exceed 25 percent of the maximum allowable design pressure at ambient temperature and the combined longitudinal stress due to pressure, deadweight, and displacement strain (see Par. 319.2.1) does not exceed 41 MPa (6000 Ibfiin ). 

Figure 9.2 Longitudinal stress-corrosion cracks in a heat exchanger tnbe the broad gap between the crack faces reveals that high-level residual hoop (circumferential) stresses from the tube-forming operation provided the stress component required for SCC.

The shock-induced micromechanical response of <100>-loaded single crystal copper is investigated [18] for values of (WohL) from 0 to 10. The latter value results in W 10 Wg at y = 0.01. No distinction is made between total and mobile dislocation densities. These calculations show that rapid dislocation multiplication behind the elastic shock front results in a decrease in longitudinal stress, which is communicated to the shock front by nonlinear elastic effects [pc,/po > V, (7.20)]. While this is an important result, later recovery experiments by Vorthman and Duvall [19] show that shock compression does not result in a significant increase in residual dislocation density in LiF. Hence, the micromechanical interpretation of precursor decay provided by Herrmann et al. [18] remains unresolved with existing recovery experiments. 

Steady-propagating plastic waves [20]-[22] also give some useful information on the micromechanics of high-rate plastic deformation. Of particular interest is the universality of the dependence of total strain rate on peak longitudinal stress [21]. This can also be expressed in terms of a relationship between maximum shear stress and average plastic shear strain rate in the plastic wave... 

Kumar and Clifton [31] have shock loaded <100)-oriented LiF single crystals of high purity. The peak longitudinal stress is approximately 0.3 GPa. Estimates of dislocation velocity are in agreement with those of Flinn et al. [30] when extrapolated to the appropriate shear stress. From measurement of precursor decay, inferred dislocation densities are found to be two to three times larger than the dislocation densities in the recovered samples. 

Meir and Clifton [12] study shocked <100) LiF (high purity) with peak longitudinal stress amplitudes 0.5 GPa. A series of experiments is reported in which surface damage is gradually eliminated. They find that, while at low-impact velocities the dislocations in subgrain boundaries are immobile and do not affect the dislocation concentration in their vicinity, at high-impact velocities ( 0.1 km/s) dislocations emitted from subgrain boundaries appear to account for most of the mobile dislocations. 

This process of backward dislocation motion produces reverse plastic flow immediately upon reduction of longitudinal stress from the shocked state. A modification of the Orowan equation, (7.1), to the current situation is... 

In Eulerian coordinates x and t, the mass and momentum conservation laws and material constitutive equation are given by (u = = particle velocity,, = longitudinal stress, and p = material density)... 

The longitudinal stress ct in the wall of a cylindrical pressure vessel containing gas at pressure p is given by... 

The critical stress is 64% greater than the longitudinal stress. However, the change in section from a cylinder to a sphere produces something akin to a stress concentration when this is taken into account the failure is accurately predicted. 

Longitudinal stress is the force pulling on the ends of the pipe divided by the cross sectional area of the pipe wall. The pull is p 7r r. The area of the wall is 7f (r+tp 2 7f r t, and the longitudinal stress is given by equation 9.1-3. Ifr t, then = p r/(2 f j, and the longitudinal stress is half the hoop stress (equation 9.1-4). This is the reason why hoop stress dominates over the longitudinal stress. 

Conner has recently extended the longitudinal stress loading investigations of vitreous silica to shear loading, and shown that within the accepted elastic range the materials deformation properties are strongly influenced by shear [88C02]. 

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. 

Another observation on this solution is that if the Poisson s ratios of the fiber and the matrix are not the same (they are likely different), then longitudinal stresses are induced in the fiber and matrix (with a net resultant longitudinal force of zero) with accompanying shearing stresses at the fiber-matrix boundary. Such shearing stresses will naturally arise under some stress states. Thus, this material characteristic cannot be regarded as undesirable or indicative of an inappropriate solution. 

Poison s ratio It is the proportion of lateral strain to longitudinal strain under conditions of uniform longitudinal stress within the proportional or elastic limit. When the material s deformation is within the elastic range it results in a lateral to longitudinal strain that will always be constant. In mathematical terms, Poisson s ratio is the diameter of the test specimen before and after elongation divided by the length of the specimen before and after elongation. Poisson s ratio will have more than one value if the material is not isotropic... 

These are quite different from Equations 1.2 and 1.3, but the general form of the predicted stresses have now been corroborated by FEA calculations [3]. The normal stress 22 was found to be tensile, in agreement with Equation 1.9 (Figure 1.2), while the longitudinal stress fn increased rapidly with increasing shear y, approximately in proportion to y (Figure 1.3). Such profound consequences of the boundary conditions do not appear to have been noted previously. 

For exchangers with fixed tube-plates the longitudinal stresses in the tubes and shell must be checked to ensure that the maximum allowable design stresses for the materials are not exceeded. Methods for calculating these stresses are given in the standards. 

An expression for the longitudinal stress can be obtained by equating forces in the axial direction ... 

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