Equivalent elastic stress

The utility of K or any elastic plastic fracture mechanics (EPFM) parameter to describe the mechanical driving force for crack growth is based on the ability of that parameter to characterize the stress-strain conditions at the crack tip in a maimer which accounts for a variety of crack lengths, component geometries and loading conditions. Equal values of K should correspond to equal crack tip stress-strain conditions and, consequently, to equivalent crack growth behavior. In such a case we have mechanical similitude. Mechanical similitude implies equivalent crack tip inelastic zones and equivalent elastic stress fields. Fracture mechanics is... 

Fig. 1.11 Representation of the total strain excursion Ae, effectively applied to the fatigue specimen and its conversion into the equivalent elastic stress excursion Aa, ei obtained by linearizing the material behavior...

Failure can be considered as an actual rupture (stress-rupture) or an excessive creep deformation. Correlation of stress relaxation and creep data has been covered as well as a brief treatment of the equivalent elastic problem. The method of the equivalent elastic problem is of major assistance to designers of plastic products since, by knowing the elastic solution to a problem, the viscoelastic solution can be readily deduced by simply replacing elastic physical constants with viscoelastic constants. 

Creep and stress relation Creep and stress relaxation behavior for plastics are closely related to each other and one can be predicted from knowledge of the other. Therefore, such deformations in plastics can be predicted by the use of standard elastic stress analysis formulas where the elastic constants E and y can be replaced by their viscoelastic equivalents given in Eqs. 2-19 and 2-20. 

In this expression, k is a constant equal to about 0.5 nm, corresponding to a mean intermolecular distance when only physical interactions (dispersive and acid-base interactions) are involved and Ef are the elastic moduli of the matrix and the fiber, respectively. This model is equivalent to that of Gent and Schultz [3,4] for a cylindrical geometry and in the case of pure elastic stress transfer between both materials. It is very well verified experimentally for various fiber-matrix systems. The infiuence of the formation of interfacial layers exhibiting mechanical behavior completely different from that of the bulk matrix has also been examined [31]. 

These stresses and equivalent elastic properties, calculated by classical lamination theory, can then be used in the following equations to calculate the strains in the shell ... 

Elastic Stress Analysis and Equivalent Stresses. This is based off of the pre-2007 Section VIII, Division 2 methodology. Stress ranges will be the output values using this analysis. 

Elastic Stress Analysis - Simplified Elastic-Plastic Method. This method may be used in the case where the method indicated above shows the Pr + Pb + Q stress limits are not satisfied, but indicates that the Pl + Pb + Q range and excluding thermal effects must be less than Sps- Additionally, the effective alternating equivalent stress amplitude must include the fatigue penalty factor, ICej, which is based off of the simplified elastic-plastic criteria from the pre-2007 Section VIII, Division 2. Finally, a thermal stress ratcheting assessment must be made. 

The value of alternating stress taken from the fatigue curve is subject to other factors given hy the ASME Code. The ultimate allowable stress for a given number of cycles should be adjusted for these factors as follows (for elastic stress analysis and equivalent stresses ... 

Both Eqs. (11.1) and (11.2) account for the effect of transverse strain on plastic strain intensity factor characterized by the modified Poisson s ratio, V. In Eq. (11.1), this is accounted for by the ratio Sy/Sa, whereas in Eq. (11.2) the ratio Eg/E serves the same purpose as will be shown later. The modified Poisson s ratio in each case is intended to account for the different transverse contraction in the elastic-plastic condition as compared to the assumed elastic condition. Therefore this effect is primarily associated with the differences in variation in volume without any consideration given to the nonlinear stress-strain relationship in plasticity. Instead the approaches are based on an equation analogous to Hooke s law as obtained by Nadai. Gonyea uses expression (rule) due to Neuber to estimate the strain concentration effects through a correction factor, K, for various notches (characterized by the elastic stress concentration factor, Kj). Moulin and Roche obtain the same factor for a biaxial situation involving thermal shock problem and present a design curve for K, for alloy steels as a function of equivalent strain range. Similar results were obtained by Houtman for thermal shock in plates and cylinders and for cylinders fixed to a wall, which were discussed by Nickell. The problem of Poisson s effect in plasticity has been discussed in detail by Severud. Hubei... 

I. Displacement-Traction Relationships. Displacement-traction relationships, in terms of Fourier transformed quantities, on the surface of a half-space, under plane strain conditions, are derived in Sect. 7.1 and given by (7.1.15) for steady-state uniform motion. A similar relationship between the Fourier transform of the displacement and tearing stress is given by (7.1.23) for tearing mode fracture, along the line of the crack. These have the same form as the equivalent elastic relations, with moduli replaced by complex moduli, as required by the Classical Correspondence Principle. 

With this linear elastic stress analysis, the correlation between crack initiation and stress distribution has been established. The interfacial cracking occurs at sites sustaining high peel stresses, while the bulk cracking results from the concentration of the equivalent stress. Thus, enhancing either the adhesion to the component or the bulk strength of the ICA joint will help to improve its reliability. 

The maximum elastic stress range that can be achieved through prestressing techniques is equivalent to two times the yield condition, since the bore of the vessel can only be prestressed to the compressive yield strength value. 

Fig. 1.12 S-N curve obtained for two carbon steels type A 201 and A 302 B, respectively. S is the equivalent ideally elastic stress amplitude...

Fig. 1.14 Difference between S-N curve derived using the equivalent ideally elastic stress procedure solid curve and conventional S-N curve obtained directly in stress controlled tests...

The equivalent elastic modulus, Gip, for the mechanically interlocked interphase is calculated by assuming an isostress condition for the interphase, illustrated in Pig. 23.13. In other words, the adhesive and the adherend surface (projections) are subjected to the same level of shear stress, tjp, at the interphase, while the composite interfacial shear strain, yjp, is a volumetric weighted average of the adhesive and adherend strains, that is,... 

In this constant-load-amplitude method, crack length is measured visually or by an equivalent method as a fimction of elapsed cycles, and these data are subjected to numerical analysis to establish die rate of crack growth. Crack growth rates are ttien expessed as a function of crack tip stress intensity range AAT, which is calculated from expressions basal on linear-elastic stress analysis. 

The referential formulation is translated into an equivalent current spatial description in terms of the Cauchy stress tensor and Almansi strain tensor, which have components relative to the current spatial configuration. The spatial constitutive equations take a form similar to the referential equations, but the moduli and elastic limit functions depend on the deformation, showing effects that have misleadingly been called strain-induced hardening and anisotropy. Since the components of spatial tensors change with relative rigid rotation between the coordinate frame and the material, it is relatively difficult to construct specific constitutive functions to represent particular materials. 

Elastic Strength Pressure (ESP). The gas pressure that will produce an equivalent stress (based on distortion-energy criteria) at some point in the gun that is equal to the min elastic limit of the material at ambient temp... 

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