Maximum shear stress

The maximum shear stress occurs at the bote and is given by... 

Criteria of Elastic Failure. Of the criteria of elastic failure which have been formulated, the two most important for ductile materials are the maximum shear stress criterion and the shear strain energy criterion. According to the former criterion, from equation 7... 

If it is assumed that yield and subsequent plastic flow of the material occurs in accordance with the maximum shear stress criterion, then /2 may be substituted for in the above and subsequent equations. For the shear strain energy criterion it may be assumed, as a first approximation, that the corresponding value is G j fz. Errors in this assumption have been discussed (11). 

Fig. 16. Maximum shear stress at bore vs number of cycles to failure for specimens of EN25 T steel at various k values. +, / = 1.2 Q = 1-4 ...

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... 

Assume the edge dislocation density to be divided into positive and negative populations, N+ and N, moving only on slip planes at 45° (maximum shear stress) to the planar shock front. For a dislocation multiplication (annihilation) rate M, show that conservation of dislocations requires that... 

As we press a flat indenter into the material, shear takes place on the 45° planes of maximum shear stress shown in Fig. 11.4, at a value of shear stress equal to k. By equating the work done by the force F as the indenter sinks a distance u to the work done against k on the shear planes, we get ... 

An example of liquid/liquid mixing is emulsion polymerization, where droplet size can be the most important parameter influencing product quality. Particle size is determined by impeller tip speed. If coalescence is prevented and the system stability is satisfactory, this will determine the ultimate particle size. However, if the dispersion being produced in the mixer is used as an intermediate step to carry out a liquid/liquid extraction and the emulsion must be settled out again, a dynamic dispersion is produced. Maximum shear stress by the impeller then determines the average shear rate and the overall average particle size in the mixer. 

In many cases the pressure gradient is uniform, so that for a pressure drop, F, over a length, L, the maximum shear stress will be at the wall where r = R... 

In this method [89], a single fiber is taken and partially embedded in a drop of uncured resin placed on a holder. The resin is then cured with the fiber held upright. The holder, with resin and fiber, is held in a grip attached to the crosshead and then pulled out from the resin. The force pulling the fiber out of the resin is balanced by shear stress at the resin-fiber interface holding the fiber in place. The maximum shear stress occurs as the embedded length tends to zero and is given by ... 

For brittle materials such as glass or cast iron, the maximum shear-stress theory is usually applied. 

Shear stress-strain data can be generated by twisting (applying torque) a material specimen at a specified rate while measuring the angle of twist between the ends of the specimen and the torque load exerted by the specimen on the testing machine. Maximum shear stress at the surface of the specimen can be computed from the measured torque that is the maximum shear strain from the measured angle of twist. 

A shaft subject to torque is generally considered to have failed when the strength of the material in shear is exceeded. For a torsional load the shear strength used in design should be the published value or one half the tensile strength, whichever is less. The maximum shear stress on a shaft in torsion is given by the following equation ... 

Due to the liquid circulation in stirred tanks which transports all particles with a certain frequency through the impeller zone, they undergo the maximum shear stress. 

The maximum fluid shear rate in the eddy occurs at the radial position R= 1.793 [86] (Fig. 10). Thus, letting cos yt= 1.0, in Eq. (19) gives the maximum shear stress acting on the cell as ... 

The die-swell (extrudate swell) effect describes the significant expansion of the diameter of the fluid column after exiting from a small pipe (Figure 4.3.8(b)). Some polymer fluids can have a swelling of up to two or three times the exit diameter. A simple proposition for the mechanism of the die-swell phenomenon is that while the fluid is inside the exit pipe, it is subject to a velocity shear, similar to the pipe flow with a maximum shear stress at the wall [18]. This velocity shear stretches... 

The maximum shear stress at the point is equal to half the algebraic difference between the principal stresses ... 

Maximum shear stress theory which postulates that failure will occur in a complex stress system when the maximum shear stress reaches the value of the shear stress at failure in simple tension. 

The maximum shear stress will depend on the sign of the principal stresses as well as their magnitude, and in a two-dimensional stress system, such as that in the wall of a thin-walled pressure vessel, the maximum value of the shear stress may be that given by putting (73 = 0 in equations 13.3 and c. 

The maximum shear stress theory is often called Tresca s, or Guest s, theory. 

The maximum shear-stress theory has been found to be suitable for predicting the failure of ductile materials under complex loading and is the criterion normally used in the pressure-vessel design. 

The maximum intensity of stress allowed will depend on the particular theory of failure adopted in the design method (see Section 13.3.2). The maximum shear-stress theory is normally used for pressure vessel design. 

The maximum shear stress will be given by (see Section 13.3.1) ... 

If the maximum shear stress theory is taken as the criterion of failure (Section 13.3.2), then the maximum pressure that a monobloc vessel can be designed to withstand without failure is given by ... 

Manning (1947) has shown that the maximum shear strain energy theory of failure (due to Mises (1913)) gives a closer fit to experimentally determined failure pressures for monobloc cylinders than the maximum shear stress theory. This criterion of failure gives ... 

A high pressure steam pipe is 150 mm inside diameter and 200 mm outside diameter. If the steam pressure is 200 bar, what will be the maximum shear stress in the pipe wall ... 

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