Stress range

It has been observed [4], that the effect of mean stress on the damage rate is much smaller than that of the stress range when delamination is the dominant failure mode. 

Figure 8 Stage IIAE count rate as a function of stress range...

The Stress-Rang e Concept. The solution of the problem of the rigid system is based on the linear relationship between stress and strain. This relationship allows the superposition of the effects of many iadividual forces and moments. If the relationship between stress and strain is nonlinear, an elementary problem, such as a siagle-plane two-member system, can be solved but only with considerable difficulty. Most practical piping systems do, ia fact, have stresses that are initially ia the nonlinear range. Using linear analysis ia an apparendy nonlinear problem is justified by the stress-range concept... 

For the above, the total allowable stress range (for 7000 cycles or less) is as follows ... 

Fanning friction factor non dimensional stress-range reduction factor... 

Sa metals, excluding factor E, or bolt design stress Allowable stress range for MPa Idp/im (ksi)... 

However, if the sum of longitudinal stresses enumerated is less than their stated limit S/, the difference may be added to the term 0.25S/, in the equation hmiting the stress range ... 

To assure that a system meets these requirements, the computed displacement-stress range Se shall not exceed the allowable stress range [Eqs. (10-93) and (10-94)], the reaction forces [Eq. (10-105)] shall not be detrimental to supports or connected equipment, and movement of the piping shall be within any prescribed hmits. 

Values of thermal-expansion coefficients to be used in determining total displacement strains for computing the stress range are determined from Table 10-52 as the algebraic difference between the value at design maximum temperature and that at the design minimum temperature for the thermal cycle under analysis. 

The allowable stress range for displacement stresses and permissible additive stresses shall be as specified in Eqs. (10-93) and (10-94) for systems primarily stressed in bending and/or torsion. For pipe or piping components containing longitudinal welds the basic allowable stress S may be used to determine S. (See Table 10-49, Note 13.)... 

Allowable stress range and permissible additive stresses shall be computed in accordance with Eqs, (10-93) and (10-94),... 

R = range of reaction forces or moments (derived from flexibility analysis) corresponding to the full displacement-stress range and based on E, Ibf or in lbf (N or N mm)... 

Of all the piezoelectric crystals that are available for use as shock-wave transducers, the two that have received the most attention are x-cut quartz and lithium-niobate crystals (Graham and Reed, 1978). They are the most accurately characterized stress-wave transducers available for stresses up to 4 GPa and 1.8 GPa, respectively, and they are widely used within their stress ranges. They are relatively simple, accurate gauges which require a minimum of data analysis to arrive at the observed pressure history. They are used in a thick gauge mode, in which the shock wave coming through the specimen is... 

When material is subjected to a mean tensile stress (i.e. ct, > 0) the stress range must be decreased to preserve the same according to Goodman s Rule (Fig. 15.5)... 

Here Acto is the cyclic stress range for failure in Nf cycles under zero mean stress, and Acr m is the same thing for a mean stress of a .) Goodman s Rule is empirical, and does not always work - then tests simulating service conditions must be carried out, and the results used for the final design. But preliminary designs are usually based on this rule. 

Act = tensile stress range AeP = plastic strain range AK = stress intensity range N = cycles Nf = cycles to failure Cj, C2, a, b, A, m = constants = tensile mean stress ujg = tensile strength a = crack length. 

The second failure mode to consider is fatigue. The drum will revolve about once every second, and each part of the shaft surface will go alternately into tension and compression. The maximum fatigue stress range (of 2 x 56 = 112 MPa) is, however, only a quarter of the fatigue limit for structural steel (Fig. 28.5) and the shaft should therefore last indefinitely. But what about the welds There are in fact a number of reasons for expecting them to have fatigue properties that are poorer than those of the parent steel (see Table 28.1). 

Figure 28.6 shows the fatigue properties of structural steel welds. The fatigue limit stress range of 120 MPa for the best class of weld is a good deal less than the limiting range of 440 MPa for the parent steel (Fig. 28.5). And the worst class of weld has a limiting range of only 32 MPa ...

Fig. 28.5. Fatigue data for a typical structural steel in dry air. Note that, if the fatigue stress range is less than 440 MPa (the fatigue limit] the component should last indefinitely. The data relate to a fatigue stress cycle with a zero mean stress, which is what we have in the case of our tail drum.

Stress-rupture data are often presented in a Larson-Miller eurve, whieh indieates the performanee of an alloy in a eomplete and eompaet graphieal style. While widely used to deseribe an alloy s stress-rupture eharaeteristies over a wide temperature, life, and stress range, it is also useful in eomparing the elevated temperature eapabilities of many alloys. The Larson-Miller parameter is... 

Fig. 2.2. The characteristic stress pulses produced by shock loading differ considerably depending upon the stress range of the loading. The first-order features of the stress pulses can be anticipated from critical features of the stress-volume relation. In the figure, P is the applied pressure and HEL is the Hugoniot elastic limit. Characteristic regimes of materials response can be categorized as elastic, elastic-plastic, or strong shock.

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