Basquin line

Comparison with the monotonic curve of Fig. 5.18 indicates that the material undergoes cyclic hardening. The cyclic hardening exponent is n = 1/6 = 0,165. Therefore, the b exponent of the Basquin line using the Morrow expression (3.32) is 

The Basquin line is shown in Fig. 5.21 by the full curve. Note that, the Basquin curve is not a line because we have not been using a log-log scale, but a single log one. Also in this case a correction must be applied to take into consideration the surface finish and the size effect multiplying the value of the fatigue limit oy times factors Cs and C z obtaining the dashed curve of Fig. 5.21. 

---

True Strain-True Stress. Basquin Line... 

Figure 5.15 shows this bi-linear S-N diagram obtained with the Haibach correction. The Basquin line provides the simplest way to build the S-N diagram, provided that the slope b is known. However, it must be remembered that only the elastic component of the stress amplitude enters in the Basquin Eq. (5.22). 

Therefore, the Basquin line approximate the Wohler curve only in the high cycle fatigue regime, as shown in Fig. 5.15. When the plastic component of the strain cannot be neglected and this happens in general below 10" -10 cycles, the Basquin component must be integrated with the Mason-Cofi n component, as it will be shown in the next chapter. 

Figures 6.5 and 6.6 show the so called transition point Nt where elastic and plastic components intersects. Beyond A, it is the elastic component of strain that dominates and control the fatigue life of the material whereas below N, the plastic strain prevails. This actually means that beyond Nt high cycle fatigue becomes the dominant failure mode and the Basquin line may sufficiently well represent the S-N fatigue behavior of the material. Below N instead, low cycle fatigue is the failure mode of the material and Mason-Coffin relationship based on strain amplitude is needed. In the surroundings of N, it is necessary to consider both components. It is worth noting how for the softer steel Man-Ten the transition Nt from plastic to elastic behavior can be placed at about 2 10" cycles while for the harder steel RQC-100 it already happens at about 10 cycles. At 10" cycles the plastic component of strain is only a mere 1/30 of the elastic one. For the aluminum alloy this transition occurs even earlier at about 100 cycles. At about 10 cycles the total curve coincides with the elastic component. The coordinates of Nt can be found by putting Ep = and recalling Eq. (6.10) it yields...

S-N curve in terms of stress amplitude. The Basquin line contain a parameter, the fatigue strength coefficient a f, that is the true stress at failure (see Sect. 5.2.2). Its value is normally measured with standard specimens of 10 mm diameter and 10 cm length. Therefore, its process volume, that we will assume as reference volume, is Vref — 7853 mm. Therefore... 

In a double-logarithmic plot, the S-N curve of many metals is a straight line for a wide range of the number of cycles (see figure 10.18). This line can be described by the Basquin equation [14]... 

Large numbers of cycles (hcf) can only be reached with a small stress amplitude so that the amount of plastic deformation is small. The total strain thus corresponds mainly to the elastic part of the strain. The line can be described using the Basquin equation, re-written with the help of Hooke s law ... 

Fig. 10.22. S-N diagram of Si3N4 at different temperatures (measured in bending at ii = — 1) [113]. The dashed line is a fit according to the Basquin equation, common to temperatures of 20°C and 1000°C, whereas the dotted line is valid at 1200°C...

Once the analytical expression of the hysteresis loop has been derived, the following step is to infer the equation of the entire e-N curve or Wohler s curve. To this purpose, it is necessary to separate the two component of deformation, the elastic and the plastic one, as already done in Eq. (6.1). As to the elastic component Eg, it has been said in Sect. 5.2.2 that in 1910 Basquin [7] found a power law relationship with the cycles to failure N, see Eq. (5.22), so that in a log-log scale the elastic component of the S-N curve is a line. Later in the 50, Manson and Coffin [8-11] independently found that also the plastic component of the cyclic strain was related to life cycles N through a power law function, known as the Manson-Coffin relationship... 

---