Stress-life diagram

Fig. 6.6 Fatigue life diagram for the tension-tension fatigue of unidirectional SiCf/Si3N4 at 1000°C and a stress ratio (o /cr, ) of 0.1. Fatigue run-out (5 x 106 cycles) was observed when the maximum stress was below apt. After Holmes et al.43...

Ml 679 Constant-life diagram (10 cycles, axial stress)... 

Their stress-cycle diagram consists of the straight line portion only, representing the finite life region FL (curve 3 in Fig. 7.12). 

Times-to-failure are normally presented as creep-rupture diagrams (Fig. 17.9). Their application is obvious if you know the stress and temperature you can read off the life if you wish to design for a certain life at a certain temperature, you can read off the design stress. 

Figure 4.41 shows the Stress-Strength Interference (SSI) diagrams for the two assembly operation failure modes. The instantaneous stress on the relief section on first assembly is composed of two parts first the applied tensile stress,. v, due to the pre-load, F, and secondly, the torsional stress, t, due to the torque on assembly, M, and this is shown in Figure 4.41(a) (Edwards and McKee, 1991). This stress is at a maximum during the assembly operation. If the component survives this stress, it will not fail by stress rupture later in life. 

To ensure that blade stress levels are within the fatigue life requirements of the eompressor, it is usual praetiee to strain-gauge the blading on one or two prototype maehines, measure the stress levels, and generate a Campbell diagram showing the plotted test data. To measure data, an impeller ean also be mounted on a shaker table with a variable frequeney output (0-10,000 Hz). Aeeelerometers ean be mounted at various positions on the... 

In order to explain the linkages between strategy and stress response reference will be made to Fig. lb which depicts the patterns of seasonal change in shoot biomass associated with the full spectrum of primary strategies (Fig. la). For simplicity, this diagram refers to the patterns observed in herbaceous plants in a temperate zone situation with a sharply defined growing season. However, the principles adduced can be applied to any life-form or biome. 

Plot of stress, S, vs. number of cycles, N, required to cause failure of similar specimens in fatigue test. Data for each curve on the S-N diagram are obtained by determining fatigue life of a number of specimens subjected to various amounts of fluctuating stress. The stress axis may represent stress amplitude, maximum stress, or minimum stress. A log scale is usually used, especially for the N-axis. 

The plotted characteristic numbers of cycles to fracture were determined by the Weibull method [21]. Each point represents a test series of ten specimens. In the diagram it can be seen clearly that fretting fatigue leads to a distinct deterioration of the specimen strength and life time. The higher the maximum Hertzian stresses the clearer the decline of the strength and life time is. 

In Figure 10 the number of fracture cycles and the characteristic number of fracture cycles for the respective test series is plotted against the maximum principal stress on the tensile loaded side of the specimens. The characteristic number of fracture cycles was determined by the method developed by Weibull [21]. In the Woehler diagram it can be seen clearly that fretting fatigue leads to a distinct deterioration of the life time. The higher the maximum stresses the clearer the decline of life time is. At Fn = 10 N (Pmax = 2311 MPa) the life time decreases at a maximum base load of OR.max = 210 MPa for about 80%. at Fn = 20 N (pmtx -2912 MPa) the life time decreases for about 91% compared to to life time under the same maximum base loading. 

One of the key limitations of the S-N curve is its inabUity to predict lifetimes at stress ratios different from those under which the curve was developed. To predict the lifetime of a certain component, a more useful presentation of fatigue life test data is the modified Goodman diagram. 

It is worth restoring the Goodman diagram concept to appreciate its use. Essentially, the emphasis of Goodman s work was on tensile-mean stress with respect to fatigue life. The stress required to produce failures during a specified number of cycles is directly related to tensile strength, as indicated schematically in Fig. 7.47. 

A more accurate answer could be obtained directly if the data for a stress-strain time diagram such as Fig. 4-7 were available at a range of temperature. If the curve were available at one temperature with the constants for the WLF equation, it could be generated at the minimum design temperature and the calculation for strain at the design life done directly. 

The S-N diagram plots the life time of a material at constant stress amplitude and R ratio. It is, however, not possible to assert the life time, using the diagram, if the load amplitude changes. The most obvious way to determine the life time in this case is to simulate the service load history in the laboratory. Unfortunately, this is a rather involved procedure that is not feasible in most cases. It would be helpful if it were possible to estimate the life time directly from the S-N curves. One way to do this is to use Miner s rule (also known as Palmgren-Miner rule) [99] that will be explained now. The rule is rather simple and thus easy to employ, but it has some disadvantages, discussed at the end of this section. 

The cylinder is subjected to a repetitive stress by the hydraulic pressure. Approx. 40 strokes are performed per hour so that after an assumed life of the press of 30 years, and two 8-hour shifts per working day, and 300 working days per year, the number of load alternations = 30 X 300 X 2 X 8 X 40 = 5,760,000 is attained. Therefore, the fatigue limit has to be calculated as per Wohler s diagram. 

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