Poissons Effect

Since a buried pipe movement is resisted by the surrounding soil, a tensile load is produced within the pipe. The internal longitudinal pressure load in the pipe is independent of the length of the pipe. Thus, Poisson s effect must be considered when designing any length of pipe, whether long or short that is part of a buried pipe system. Buried pipes are influenced by friction with their surrounding media. 

In this analysis the designer must consider two conditions and base the pipe design on the one that is worse. One condition is where the temperature differential is one half the difference between the maximum temperature and minimum temperature. The second condition considers the temperature differential between the maximum pipeline temperature at installation and the minimum design temperature. 

For simplicity, the condition considers the conservative case where the pipe acts simply as a support. The normal practice is to solve all these equations simultaneously, then determine the minimum wall thickness that has strains equal to or less than the allowable design strain. Thus, the minimum structural wall thickness is dictated by the longitudinal tensile load. 

The importance of combining longitudinal strain analyses is that it often provides the designer with a minimum wall thickness on which to base the ultimate choice of pipe configuration. For instance, assume that the combined longitudinal analysis indicates a 

There is a method that can be used for this analysis. It is extremely complex so it requires using a computer. In general, equations are generated to determine the moment and thrust created in the invert area of the deflected pipe, where a pressure term is superimposed. This analysis must examine the strains in the outer and innermost fibers of the pipe to verify that its wall structure is adequate and not overstrained. During this analysis the pipe must be examined under conditions of no pressure, minimum pressure, and maximum pressure. 

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For cross-ply laminates, a knee in the load-deformation cun/e occurs after the mechanical and thermal interactions between layers uncouple because of failure (which might be only degradation, not necessarily fracture) of a lamina. The mechanical interactions are caused by Poisson effects and/or shear-extension coupling. The thermal interactions are caused by different coefficients of thermal expansion in different layers because of different angular orientations of the layers (even though the orthotropic materials in each lamina are the same). The interactions are disrupted if the layers in a laminate separate. 

However, some theoretical treatment considers only the special case of friction sliding of a single fiber along a mechanically bonded interface, particularly for some ceramic matrix composites, where the Coulomb friction law applies. See for example Zhou and Mai (1995) and Shetty (1988). Assuming a constant friction at the fiber-matrix interface and neglecting the Poisson effects, Shetty (1988) reported a simple force balance equation for the frictional shear strength, Tfr... 

When a unidirectional CFRP composite specimen is stretched, its longitudinal resistance decreases. This phenomenon (which may be due to both a transverse Poisson effect and carbon fiber piezo-resistivity) is reversible and the resistance returns to its initial value as the load is released. However, if damage occurs, irreversible resistance changes... 

And the shear stress also induces the Poisson effect, so the influence of shear deformation to the normal deformation is. 

Figure 3.43 Thermomechanical cycle in the tension direction for a specimen of T25C25 (step 1 —> pretension to 25% strain at temperatures above Tg, step 2 —> cooling down to room temperature while holding the pre-strain constant, step 3 —> unloading, which completes the first stage of programming. The Poisson effect is due to the second programming in the transverse direction by compression. Step 4 —> free shape recovery). Source [59] Reproduced with permission from the American Society of Civil Engineers...

Basically, Fig. 1.33 iUuslrates the Poisson effect, previously considered in the section on tension and expressed by Eqs. (1.11)—(1.12a) as rewritten below ... 

In the ab directions, the themieil expansion is actually negative up to approximately 400°C with a minimum at 0°C. It is possible that this observed negative expansion is due to internal stress (Poisson effect) associated with the large expansion in the c direction and it has been suggested that, if it were possible to measure the ab thermal expansion of a single atomic plane, this expansion would be positive.i i... 

Moulin, D., and Roche, R.L., Correction of Poisson effect in the elastic analysis of low-cycle fatigue, Int. J. Pressure Vessels Piping, 19, 213-233, 1985. 

The shear stresses developed parallel to the fibre-matrix interface are of prime importance in control ling the fibre-matrix stress-transfer mechanism, as discussed previously. Yet, one should also consider the effect of strains and stresses that develop normal to the fibre-matrix interface. Such strains and stresses may be the result of the Poisson effect, volume changes, and biaxial ortriaxial loading. They may cause weakening of the interface and premature debonding, and may also induce considerable variations in the resistance to frictional slip, which is sensitive to normal stresses. 

Pinchin and Tabor [21,22] considered the first three effects, namely volume change, external pressure and the Poisson effect. They derived a general equation for the load build-up in a fibre, Pf, at a distance A from its edge ... 

A detailed analysis of the Poisson effect alone was presented by Kelly and Zweben [20], For a simple system the normal stress across the interface can be described by Eq. 3,24, assuming that the entire composite undergoes an axial strain e, and using elastic relations for isotropic fibres and the matrix ... 

Kelly and Zweben [20] indicated that although Eq. 3.20 may predict a compressive normal stress due to the Poisson effect, this may not occur in some special cases, in which fibres are being pulled out of a matrix (i.e. a pull-out test, or fibres bridging across a crack in the composite). In these instances, the tensile strain in the fibre as it enters the matrix is high, while that of the matrix is low. At the cracked composite surface (or at the matrix surface in the pull-out test) the matrix is practically stress-free. Therefore, in these regions the normal stress across the... 

Equation (3.32) presentsasimplisticapproach to frictional pull-out resistance, which ignores the Poisson effect. When this effect is considered (Section 3.2,4), more complex and realistic relations can be developed. 

Special effects may occur in low modulus fibres due to the Poisson effect. The pre-tensioning of the fibre to position it in the mould, for specimen preparation, can affect the load-slip curves, as shown in Figure 3.44 for 890 MPa modulus polyethylene fibre [86]. At a relatively low level of pre-tension (0.8% of fibre... 

The stress-strain conditions in the tests specimen should simulate those which occur in the actual composite, that is, mainly tensile stresses in the matrix. Changes in the matrix stresses can affect the interfacial response due to various influences, such as the Poisson effect. This condition is not satisfied in... 

In order to obtain a composite with adequate crack spacing (5 mm or less), they calculated the value of the interfacial shear bond strength, Tfu, from Eq. (10.1), using typical values for the matrix and for the fibrillated polypropylene crmu = 4 MPa, 14 = 0.05, I4n = 0.95, an equivalent fibre width of 2.5 mm and a thickness of 30 /zm. The calculated Tfu value was 0.23 MPa, which can readily be achieved even with monofilaments. Flowever, It was pointed out by Kelly and Zweben [23] and PInchIn [24] that this level of bond may not be attained in practice once cracking is initiated, because of the Poisson effect (see Section 3.5). At the crack, the matrix strain is zero, while the bridging fibre is loaded due to the Poisson effect the fibre will contract and may separate from the matrix, thus eliminating the normal... 

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