Stress effective

Of all the theories dealing with the prediction of yielding in complex stress systems, the Distortion Energy Theory (also called the von Mises Failure Theory) agrees best with experimental results for ductile materials, for example mild steel and aluminium (Collins, 1993 Edwards and McKee, 1991 Norton, 1996 Shigley and Mischke, 1996). Its formulation is given in equation 4.57. The right-hand side of the equation is the effective stress, L, for the stress system. 

Acetal homopolymer resins show outstanding resistance to organic solvents, no effective solvent having yet been found for temperatures below 70°C. Above this temperature some phenolic materials such as the chlorophenols are effective. Stress cracking has not been encountered in organic solvents. Swelling occurs with solvents of similar solubility parameter to that of the polymer (8 = 22.4 MPa ). 

Correspondingly, the effective stress intensity factor range, may be expressed as... 

Wells, S. A. and Dick, R. I. (1993) "Permeability, Solid and Liquid Velocity, and Effective Stress Variations in Compressible Cake Filtration," Proceedings, American Filtration Society Conference on System Approach to Separation and Filtration Process Equipment, Chicago, Illinois, May 3-6, pp. 9-12... 

For most practical purposes, the onset of plastic deformation constitutes failure. In an axially loaded part, the yield point is known from testing (see Tables 2-15 through 2-18), and failure prediction is no problem. However, it is often necessary to use uniaxial tensile data to predict yielding due to a multidimensional state of stress. Many failure theories have been developed for this purpose. For elastoplastic materials (steel, aluminum, brass, etc.), the maximum distortion energy theory or von Mises theory is in general application. With this theory the components of stress are combined into a single effective stress, denoted as uniaxial yielding. Tlie ratio of the measure yield stress to the effective stress is known as the factor of safety. 

A cylindrical steel pressure vessel (AlSl SAE 10.85, cold rolled) with a wall thickness of 0.1 in. and an inside diameter of 1 ft is subject to an internal pressure of 1,000 psia and a torque of 10,000 ft-lb (see Figure 2-30). What is the effective stress at point A in the wall What is the factor of safety in this design ... 

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. 

Alixant, J-L., Real-time Effective Stress Evaluation in Shale Pore Pressure and Permeability Estimation, Ph.D. dissertation, Louisiana State University, p. 210, December 1989. 

It could be shown (see Sect. 6) that in stirred vessels with baffles and under the condition of fully developed turbulence, particle stress can be described by Eqs. (2) and (4) alone. The turbulent eddys in the dissipation range are decisive for the model particle systems used here and many biological particle systems (see Fig. 2), so that the following equation applies to effective stress ... 

Certain types of corrosion are selective. Thus, corrosion cracking is observed primarily in the case of alloys and only when these are in contact with particular media. Corrosion is often enhanced by various extraneous effects. Stress corrosion cracking can occur under appreciable mechanical loads or internal stresses corrosion fatigue develops under prolonged cyclic mechanical loads (i.e., loads alternating in sign). 

Through the photoelastic effect, stress will modify the refractive index of silicon according to the relations... 

Hydrostatic (single-phase fluid) Archimedes buoyancy. Effective stress - established at the boundary. Alters interparticle electrical forces (repulsion, van der Waals attraction, hydration). 

To close the set of governing equations, additional constitutive relations must be introduced. Following the general effective stress principle, one finds... 

Introducing Bishop s stress tensor cr", called also effective stress tensor,... 

Gray, W.G. and Schrefler, B.A. (2001) Thermodynamic approach to effective stress in partially saturated porous media, Eur. J. Mech. A/Solids 20, 521-538... 

It is unlikely, however, that the lithification of chalk will go on without consolidation, in which the volume of chalk material is reduced in response to a load on the chalk. Consolidation can lead to a reduction in porosity up to about 40%, and an increase in the effective stress (Jones et al., 1984). The increased effective stress is required to instigate the process of pressure solution. Pressure solution provides Ca2+ and HCO3 for early precipitation of calcite cement in the chalk. However, the inherently low permeability of chalk would inhibit the processes of consolidation and pressure solution/cementation unless some permeable pathways are opened up to permit the dissipation of excess pore pressure created by the filling of pore space by calcite cement. Pressure solution will cease if the permeable pathways are blocked by cement. Thus, it appears that the development of fractures, open stylolites and microstylolitic seams (Ekdale et al., 1988) is necessary to permit pressure solution to continue and lead to large rates of Ca2+ and HC03 mobilization. 

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