Stress equivalent

The distance from the crack tip, along the X-axis, at which the von Mises equivalent stress falls below the yield stress, defines the size of the plastic zone, r. For the plane stress case of unconstrained yielding, which corresponds to the free surface of the specimen in Figure 4, this gives... 

Maximum Allowable Working Pressure -As defined in the construction codes for pressure vessels, the maximum allowable working pressure depends on the type of material, its thickness, and the service conditions set as the basis for design. The vessel or equipment may not be operated above this pressure, or its equivalent stress at any other metal, temperature. However, ANSI B31.3, Petroleum Refinery Piping Code, permits variations above the maximum allowable working pressure, as follows ... 

Note that the ratio of the ratio of the hoop stress (pR/h) to the axial stress (pR/lh) is only 2. From the data in this question the hoop stress will be 8.12 MN/m. A plastic cylinder or pipe is an interesting situation in that it is an example of creep under biaxial stresses. The material is being stretched in the hoop direction by a stress of 8.12 MN/m but the strain in this direction is restricted by the perpendicular axial stress of 0.5(8.12) MN/m. Reference to any solid mechanics text will show that this situation is normally dealt with by calculating an equivalent stress, Og. For a cylinder under pressure Og is given by 0.5hoop stress. This would permit the above question to be solved using the method outlined earlier. 

Note that this question involved a biaxial state of stress in the material and hence, strictly speaking, the creep curves used are not appropriate. However, creep curves for biaxial states of stress are rarely available, and one possible approach is to calculate an equivalent stress, a , using a van Mises type criterion... 

The yielding of pipe does not occur provided that the equivalent stress is less than the yield strength of the drill pipe. For practical calculations, the equivalent stress is taken to be equal to the minimum yield strength of the pipe as specified by API. It must be remembered that the stresses being considered in Equation 4-54 are the effective stresses that exist beyond any isotropic stresses caused by hydrostatic pressure of the drilling fluid. 

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... 

Fig. 5. The piezospectroscopic behavior of the two ls-like levels of differently oriented, trigonal shallow acceptor complexes, based on the equivalent stress model, (a) Trigonal distortion equivalent to a stress of + 0.205 kbar (tensional). (b) Trigonal distortion equivalent to a stress of —0.810 kbar (compressional). Roman numerals denote the four possible orientations of the complexes. A4 and A5 6 denote the representations of C3v according to which the states transform in the absence of externally applied stress. The energy shifts are shown for externally applied compressional stress under applied tensional stress, the behavior of (a) and (b) is reversed, as explained in the text.

Si Equivalent stress during service condition, / (the higher of Spi and SL) MPa ksi... 

Unlike MOE, there does not appear to be any increase in MOR when wood is subjected to thermal treatment, even for short time periods (Figure 5.7). This is because MOR is actually the equivalent stress in fibres at the point of failure and, as such, is related to the ultimate bending strength of the wood (Dinwoodie, 2000). 

The stresses around the particles are determined to find the maximum von Mises equivalent stress. These calculation show that the mean value of the stress concentrations is a few percent greater than the exact value for a single void in an infinite matrix. The effect of mechanical interaction globally increases the... 

Thus, the presence of the fluctuating turbulent velocity components causes the momentum transfer rate to be different from p X (mean velocity)2 x dA. But in applying the momentum conservation principle to the control volume the presence of additional momentum transfer is the equivalent of an additional force on the face of the control volume in the opposite direction to the momentum transfer. Thus, the additional momentum transfer due to the fluctuating velocity leads to an equivalent stress, i.e., force per unit area, of value pu 2 and this is what is termed the turbulent stress on the face. 

The design of thickwalled components for pulsating pressure is based on the stress calculation with analytical or numerical methods and the determination of the maximum equivalent stress in relation to the admissible stresses at uniaxial conditions. The latter have to be extracted from Woehler-tests with specimen. If the stresses yield too large at load conditions including a safety factor, the design must be optimized by avoiding the major stress concentrations at bore intersections. The avoidance of T-intersections is reducing stresses by factor 2-3 (Fig. Id). 

Such a wavelength will neither grow nor shrink. The fastest growing wavelength is just Aj = /3 A For a material with a non-Newtonian flow law of the form E = Epia/np), where ct and e are the equivalent stress and equivalent strain rate in tension and and Ep are material parameters, d Jo/dx is computed to be... 

As reported earlier, compaction simulators can be equipped to replicate the compression process of a roller compactor. Zinchuk et al. describe how a compaction simulator can be used to produce ribbons and determine the formulation specific compactability relationship (tensile strength vs. solid fraction) (Fig. 27) (4), Since compacts produced under equivalent stress-strain conditions exhibit similar mechanical properties, the ribbon solid fraction and/or tensile strength can be used as a scale-up factor for pilot and eventually commercial scale manufacturing. 

T3) are available in most FEA software packages and stresses are usually averaged by the FEA software packages to provide more accurate stress values when mapped (contoured) on to the mesh. A good first cut to the understanding of analysis results is the use of the von Mises stress (effective or equivalent stress). Fig. 10 shows the von Mises stress contour mapped to the FEA mesh in pounds/square inch (PSI). 

Equivalent stresses (a) and strains (e) were derived from surface shear stresses and strains by means of the Von Mises yield criterion ... 

Convert the stress at any failure probability to the equivalent stress o-js that would have resulted in failure in 1 s, using Eq. (12A.8). 

Equation (12.40), while appearing to be a useful equation to estimate the lifetime of a part, has to be used with caution since it assumes that c, is identical in all samples. And while that is possible in a laboratory setting where well-defined cracks can be introduced in a sample, its usefulness in practice is limited. What is thus needed is a methodology to transform data (i.e., one with a distribution of failure times) to an equivalent stress that would have caused failure in, say, 1 s in other words, a renormalization of the time-to-failure data. 

Or, one can use equivalent stress-based frameworks that deal with the nature of the singularity rather than a maximum stress these approaches use the stress intensity factor, which is essentially the ampUtude of the singularity (see Section 39.3.1.)... 

Figure 1. The equivalent stress distribution on the working surface.

Banabic et al. (2005) proposed a new expression of the plane stress potential. An improvement of this criterion has been implemented in the finite element commercial code AUTOFORM version 4.1 (Banabic and Sester 2012). The equivalent stress is defined by the following formula ... 

Under more general conditions of multi-axial principal stresses a, 02,o the same condition is reached when the equivalent stress a (or defined as... 

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