Effect of Mean Stress

The level of mean stress also has an effect on the occurrence of thermal failures. Typically, for any particular stress 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. 

For design purposes it is useful to have a relationship between Oa and Om, similar to those used for metals (e.g. the Soderberg and Goodman relationships). It is suggested that the equation of a straight line joining points W and Z in Fig. 2.76 would be best because it is simple and will give suitably conservative estimates for the permissible combinations of Oa and to produce failure in a pre-selected number of cycles. Such an equation would have the form 

Example 2.21 A rod of plastic is subjected to a steady axial pull of SO N and superimposed on this is an alternating axial load of 100 N. If the fatigue limit for the material is 13 MN/m and the creep rupture strength at the equivalent time is 40 MN/m, estimate a suitable diameter for the rod. Thermal effects may be ignored and a fatigue strength reduction factor of 1.5 with a safety factor of 2.5 should be used. 

Solution The alternating stress, is given by Alternating load 4 x 100 

So applying the fatigue strength reduction factor and the factor of safety 

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. 

Oc is the creep rupture strength at a time equivalent to N cycles 

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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. 

SAXS patterns, taken at minimum displacement, have been examined in PS specimens as a function of the R ratio, where R = e. /e If the volume fraction of the fully-loaded PS craze is taken as the usual 0.25 value, the SAXS results indicate that, as R is reduced from 1 to 0.5, v rises to 0.28 and the fibrils contract about 10 4 and as R is further reduced to 0.125, v rises to 0.63 and the fibrils contract about 60% It was also noted that as R was increased from zero to 0.6 the log of the cycles to fatigue fracture increased in a linear manner and a more rapid increase occurred for higher R values. It is interesting to note that, in a prior study of the effects of mean stress on the fatigue life of PS a linear increase in log Nf with R was also found over a wide range of R values from --1 to about 0.4 and, here too, a transition occurred to a more rapid rate of increase at higher R values. 

The maximum stress G ax has an effect on fatigue only in that the higher it is the lower the amplitude Ga of alternated stress that leads to failure. This last statement was delineating the effects of mean stress g on fatigue (see 3.2) ... 

If the independence of the ratio EjEp of is restored it introduces an effect of mean stress in the plastic domain that experience does not confirm. As to the Morrow correction (6.17), Walcher, Gary and Manson [20] observed that in alloys like Ti-6Al-4 V the fatigue strength coefficient a fCm be so high as to mask the mean stress effect. Therefore, they proposed a correction to the fatigue strength coefficient of the type... 

Wener, T., Fatemi, A. Effect of mean stress on fatigue behavior of hardened carbon steel. Int. J. Fatigue 13(3), 241-248 (1991)... 

The next step is to consider the effect of mean stress cr . Using the Gerber criterion, Eq. (5.47) with n — 2, the fatigue limit will be... 

Findley, W.N. A theory for the effect of mean stress on fatigue of metals under combined torsion and axial load or bending. Trans. ASME, J. Eng. Industry 81, 301-306 (1959)... 

Figure 1.33 The effect of mean stress on the strain-life curve.

The Basquin equation can also be remodified as Equation 4.10 to include the effect of mean stress. 

Fig. 17. Effect of mean shear stress on the fatigue strength of EN25 for life of 10 cycles (92). To convert MPa to psi, multiply by 145.

Creep behaviour is a commonly used and very important measure of the effect of mechanical stress on plastics, but it is less used as a means of monitoring degradation due to environmental agents. At shorter times, the measured creep is predominantly due to physical effects and it is only at longer times that environmental effects will be apparent. It can be noted that creep tests use the same test piece at successive time intervals which is advantageous from the point of view of reproducibility. 

Nowhere is the effect of anthropogenic stress felt more than in the development of natural resources of the Earth. Natural resources are varied in nature and often require definition. Eor example, in relation to mineral resources, for which there is also descriptive nomenclature (ASTM C294), the terms related to the available quantities of the resource must be defined. In this instance, the term resource refers to the total amount of the mineral that has been estimated to be available ultimately. The term reserves refers to well-identified resources that can profitably be extracted and utilized by means of existing technology. In many countries, fossil fuel resources are often classified as a subgroup of the total mineral resources. 

Phase transition in gels can be affected by applying uniaxial stress. With increasing stress in the region below 1 x 104 N m 2 at gelation, the effects of uniaxial stress was qualitatively described by the mean field theory. The present results clearly indicate the possibility of a uniaxial stress-induced phase transition of gels. 

A most ingenious use for soap films has been discovered by Griffith and Taylor.1 The equations representing the deformation under torsion of an elastic, solid bar of any cross-section are of the same form as those for the displacement of a soap film stretched over a hole in a flat plate, the hole being of the same shape as the section of the bar. The mathematical solution of these equations may be difficult, but it is easy to measure the displacement of the soap film hence by forming a soap film on a box, in the lid of which is a hole of the same shape as the bar, and measuring the contour lines of the film when pressure is applied inside the box, by means of a spherometer, the effect of torsional stress on bars of the most complicated section may be ascertained. 

If we use the approach just described, we expect the stress field in the substrate to be of the type shown in Figures 18.4 and 18.5 then the mean stress forms a single surface as shown in Figure 18.6. What effect will such a nonuniform pattern of mean stress have on the distribution of components A and B ... 

Effects of stress due to different NaCl concentrations on the DF intensity and Pn of rice were studied. The results show that there is good correlation between the DF intensity and Pn, and that DF intensity can quantify the change of plant photosynthetic physiological status more accurately and faster under different NaCl concentration conditions. Therefore, it is likely that the DF technique will provide a potentially useful approach for non-invasive and real-time monitoring of the effects of NaCl stress on plant growth and photosynthetic metabolism and a powerful means in the selection of salt-tolerance of plants. 

It s possible that fetal overexposure to stress hormones causes physiological programming that endures through childhood and adulthood. Animal experiments demonstrate that prenatal stress hormone excess reduces birth weight and causes lifelong postnatal hypertension, hyperglycemia, and behavioral abnormalities.57 In fact, the scientific literature cites many animal experiments on the effects of maternal stress on fetal development, but it s difficult to interpret what these results mean for human fetal development.58... 

In all the above mentioned experiments, hydrostatic (i.e. isotropic) pressure was applied to materials. In high-pressure experiments, this is usually assumed to be the case, but it is true only when the stress environment is purely hydrostatic. In other cases the stress state of the sample should be described by stress tensors, which are very difficult to determine. The mean pressure could be some average of the normal stress components over the sample, but one cannot neglect the effects of shear stress, differential stress, and stress inhomogeneity on many physical properties [191]. Influence of different conditions of compression on has been studied in detail on the bcc to rhombohedral phase transition in vanadium. Under a non-hydrostatic compression the phase transition occurred at 30 GPa at ambient temperature and at 37 GPa at 425 K. Under quasi-hydrostatic compression in the Ar pressure medium, Ptr increased to 53 GPa. When Ne was used as the medium, Ptr increased to 61.5 GPa, still short of the ideal value of 65 GPa [192]. 

Equipment support legs should be braced unless their dimensions warrant departure from this recommended practice. Resonance should be avoided and, in some cases (e.g. for core internals for which it is difficult to avoid resonance by means of modifying the design), the vibration characteristics of the reactor building s internal structure itself may be modified to prevent resonance effects. If systems are made stiffer, the effects of thermal stresses, other dynamic loads and differential motions of the supporting points should be considered. 

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