Stress mean

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. 

A more important effect of prestressiag is its effect on the mean stress at the bore of the cylinder when an internal pressure is appHed. It may be seen from Figure 6 that when an initially stress-free cylinder is subjected to an internal pressure, the shear stress at the bore of the cylinder increases from O to A. On the other hand, when a prestressed cylinder of the same dimensions is subjected to the same internal pressure, the shear stress at the bore changes from C to E. Although the range of shear stress is the same ia the two cases (distance OA = CE), the mean shear stress ia the prestressed cylinder, represented by point G, is smaller than that for the initially stress-free cylinder represented by point H. This reduction in the mean shear stress increases the fatigue strength of components subjected to repeated internal pressure. 

Stress concentration Kis defined (1) as local stress/mean stress in a particle and calculated according to if = 1 + 2 LR) length and R is the radius of the crack tip. 

Fig. 15.5. Goodman s Rule - the effect of a tensile mean stress on initiation-controlled fatigue.

These two laws (given data for a, b, Cj and C2) adequately describe the fatigue failure of unnotched components, cycled at constant amplitude about a mean stress of zero. What do we do when Act, and ct , vary ... 

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. 

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.

If we assume that the maximum stress applied is +3cr from the mean stress, where this loading stress value eovers 99.87% those applied in serviee ... 

The mean stress, /i, ean be approximated by substituting the mean values for eaeh variable into the original stress funetion, where ... 

In addition, there is a mean tensile stress aeting on the shaft eross-seetional area. This effeet means stress equates to... 

For convenience, in the previous sections it has been arranged so that the mean stress is zero. However, in many cases of practical interest the fluctuating stresses may be always in tension (or at least biased towards tension) so that the mean stress is not zero. The result is that the stress system is effectively a constant mean stress, a superimposed on a fluctuating stress a a- Since the plastic will creep under the action of the steady mean stress, this adds to the complexity because if the mean stress is large then a creep rupture failure may occur before any fatigue failure. The interaction of mean stress and stress amplitude is usually presented as a graph of as shown in Fig. 2.76. 

This represents the locus of all the combinations of Ca and Om which cause fatigue failure in a particular number of cycles, N. For plastics the picture is slightly different from that observed in metals. Over the region WX the behaviour is similar in that as the mean stress increases, the stress amplitude must be decreased to cause failure in the same number of cycles. Over the region YZ, however, the mean stress is so large that creep rupture failures are dominant. Point Z may be obtained from creep rupture data at a time equal to that necessary to give (V cycles at the test frequency. It should be realised that, depending on the level of mean stress, different phenomena may be the cause of failure. 

The level of mean stress also has an effect on the occurrence of thermal failures. Typically, for any particular sUess amplitude the stable temperature rise will increase as the mean stress increases. This may be to the extent that a stress amplitude which causes a stable temperature rise when the mean stress is zero, can result in a thermal runaway failure if a mean stress is superimposed. 

Fig. 2.76 Relationships between stress amplitude and mean stress...

Stress amplitude = mean stress = To allow for mean stress use... 

For freely suspended bioparticles the most likely flow stresses are perceived to be either shear or normal (elongation) stresses caused by the local turbulent flow. In each case, there are a number of ways of describing mathematically the interactions between turbulent eddies and the suspended particles. Most methods however predict the same functional relationship between the prevailing turbulent flow stresses, material properties and equipment parameters, the only difference between them being the constant of proportionality in the equations. Typically, in the viscous dissipation subrange, theory suggests the following relationship for the mean stress [85] ... 

Mean stress to produce rupture at 105 h at the design temperature 1.5 1.5 1.0... 

---