Stress magnitude

Avoid stresses (magnitude and type) and environmental conditions that lead to stress-corrosion cracking, corrosion fatigue or fretting corrosion. 

ABS is another polymer in which the associated thermal effects can become quite large even at modest stress levels and frequencies. In this polymer, in tests made at 27.6 MPa, it has been noted that AT increases linearly with frequency, in accord with Eq. (5), from a value of about 2.5 °C at 2 Hz to a value above 25 °C at 21 Hz. The influence of stress magnitude on the temperatiare rise, for a constant frequency of 21 Hz, is shown for two different polymers, PSAN and ABS, in Fig. 5. In PSAN over the whole stress range investigated, and in ABS in the range where thermal equilibrium is achieved, AT varies approximately as the square of the stress, as predicted by the preceding equations. It may also be noted from the figure that the associated thermal effects are much more severe for the rubber-modified polymer than for the unmodified PSAN. 

Etheridge M. A. (1983) Differential stress magnitudes during regional deformation and metamorphism upper bound imposed by tensile fracturing. Geology 11, 213-234. 

The claim that the rheology follows from Sq is supported if the rheological properties of a dispersion only depend on the effective packing fraction, if particle size is taken account of properly. Obviously, appropriate scales for frequency, shear rate and stress magnitudes need to be chosen to observe this see Sect. 6.2. The dependence of the rheology (via the vertices) on Sq suggests that sets the energy scale... 

The interior of a continuous sample contains many small volumes and small areas, on any of which attention can be focused. A small internal area has the property that, across it, the material on one side exerts a normal force and a tangential force on the material on the other side. Let the normal force be F and the area A then the ratio F/A approaches a limit as the size of A approaches zero. Thus we define the magnitude of the normal stress at a point across an infinitesimal area of a particular orientation. If we set up Cartesian coordinates so that the orientation of the area can be specified by the direction of its normal then, at a point, for every direction vector there is a normal-stress magnitude. The stress may be compressive or tensile, and in this text we treat compressions as positive. 

It is possible to imagine a universe where space itself has an attribute of left-handedness or right-handedness, or where space does not but materials do. But if we set these possibilities aside and use ordinary ideas about symmetry, it follows that at any point where stresses exist inside a continuum, there are three orthogonal planes across which the tangential stress is zero these planes suffer only normal stresses. The planes themselves are principal planes, their normals are the three principal directions at the point and the normal-stress magnitudes are the principal stress magnitudes. (See Figure 6.1.)... 

The purpose of this chapter is to continue the unification that was begun in Chapter 8. There, first and second derivatives of normal stress with respect to orientation were used we now examine the idea that the chemical potential of a component at a point can be a multivalued direction-dependent scalar like the normal-stress magnitude, and that it too can have a gradient with respect to orientation. 

Comparison of the two situations. The sequence of compressive stress magnitudes normal to the slot that affect a wafer as it slides sideways is exactly the same in the two situations—the specifications were devised to make this so. Then if the process of assigning an associated equilibrium state to a plane is valid, we have to assign the same sequence of associated equilibrium states to successive points, regardless of which path we are following. Then further, if the gradient down a sequence of associated... 

The reason that / can sometimes be safely ignored is illustrated by the two interface problems just discussed. Inside one homogeneous phase, gradients in stress magnitude from point to point can develop only to a limited extent introducing a phase boundary immediately changes the situation and opens up the possibility of almost infinite gradients in and... 

If a small harmonic variation in a material s composition exists along some direction, this equation shows how large a harmonic variation in transverse compressive stress magnitude we can expect to exist at the same time. 

To form expectations about the material composition, we have to consider its stress state. In Chapter 13, it is established that if the initial state is hydrostatic, with compressive stress equal to everywhere, then introducing the strain rate has two effects first, the stress magnitude... 

The preexponential stress magnitude formerly designated A is here designated H to avoid confusion with component A.) Then the mean stress [Pg.158]

The relevant illustration is Figure 16.9 and the feature of interest is the step or mismatch in stress magnitude at the interface in Figure 16.9b. We wish to estimate a constriction rate that, if imposed uniformly, would eliminate this step. Again the objective is to make just a preliminary approach to orders of magnitude. 

The two stress magnitudes that fail to match have been designated Sg and s. Either of these is given by an equation of type (16.2). As already discussed, this equation is not reliable when the denominator approaches zero but if we go to conditions where the denominator is not close to zero (where the factor l/N is the dominant factor), the equation resembles eqn. (15.2). This equation is illustrated numerically on page 146, where it appears that if l/N dominates the denominator, s must be 100 MPa or less. If both Sg and are of the order of 100 MPa, their difference must be somewhat less strictly for purposes of illustration, let us suppose that = 0.7Sg and the difference = 0.3Sg—for example, 30 MPa or less. 

Figure 18.3 Stress magnitudes in and around the cylindrical inclusion, in absence of diffusion. In (a) stress magnitudes are shown by means of profiles drawn on lines through the inclusion s centerline along the x-direction and the z-direction. In (b) stress states are shown by means of ellipses. As with the strain state, conditions are homogeneous inside the inclusion, and again homogeneous with different principal values at points remote from the inclusion.

Figure 18.6 Mean stress magnitudes in the inclusion, as represented by a single mean-stress surface. Except for the effects of diffusion, the conditions specified give plane strain hence the mean stress is close to -I- CTji)/2.

H the governing stress magnitude in a term He that describes an... 

Sq a stress magnitude that is uniform through space... 

Fig. 8.4. Effect of a uniaxial stress along the [100] axis of a Si As sample with 3 x 101B cm 3 on its LHeT absorption spectrum. The propagation vector k of the radiation is parallel to [Oil]. The dotted lines are the zero-stress positions (after [123]). The estimated stress magnitude is 15 MPa. Reproduced with permission from the Institute of Physics...

Linear viscoelasticity is the simplest viscoelastic behavior in which the ratio of stress to strain is a function of time alone and not of the strain or stress magnitude. Under a sufficiently small strain, the molecular structure will be practically unaffected, and linear viscoelastic behavior will be observed. At this sufficiently small strain (within the linear range), a general equation that describes all types of linear viscoelastic behavior can be developed by using the Boltzmann superposition principle (Dealy and Wiss-brun, 1990). For a sufficiently small strain (yo) in the experiment, the relaxation modulus is given by... 

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