Fatigue plastic strain range

For low-cycle fatigue of un-cracked components where (imax or iCT inl am above o-y, Basquin s Law no longer holds, as Fig. 15.2 shows. But a linear plot is obtained if the plastic strain range defined in Fig. 15.3, is plotted, on logarithmic scales, against the cycles to failure, Nf (Fig. 15.4). TTiis result is known as the Coffin-Manson Law ... 

Example 5. An example of modeling coupled failure mechanisms is the failure behavior model for components subjected to the coupling of fatigue and creep (Collins et al. 2009). For components subjected to only low-cycle fatigue, a Coffin-Manson model will approximate the failure behaviors quite well (Equation (14)). In equation (14), Ay is the TTF in cycles, A/ is the plastic strain range and both m and C are constants associated with material properties. 

One additional parameter shown on this graph is the transition life, 2A,. This represents the life at which the elastic and plastic strain ranges are equivalent and can be expressed by Eq. (1.23). The transition life provides an accepted demarcation between low-cycle fatigue (LCF) and high-cycle fatigue (HCF) regimes. 

Isothermal fatigue predictions using the Coffin-Manson relationship have also been developed, but categorized according to the plastic strain levels to which the solder is exposed [88]. Guo et al. developed two equations to predict cycles to failure at 0.5 Hz, based upon a 50% load reduction criterion. The equations refer to two, tension-compression plastic strain ranges, Asp (%) ... 

Increasing the strain range decreases the number of cycles to fatigue failure in materials. Such data for bulk 96.5Pb-3.5Sn solder is given in Fig. 15 for temperatures from 5°C to 100°C. The tensile plastic strain range is plotted vs. TVf on log-log scales. There was no hold in the cycle and the ramp time of the saw-toothed cycles varied from 0.1 to 2.5 sec. On the scale plotted, there is very little difference in the numbers of cycles-to-failure over this range of ramp time. The data were best fit by two straight lines with a break at about 0.3% plastic strain except for — 5°C where there were few data points. The empirical Coffin-Manson relation, = C (P and C are... 

FIG. 22 Effects of In content and plastic strain range on the fatigue life of the Sn-3.5 Ag-In solder. 

Nominal composition in weight % and characteristics 0-2% proof stress (min) (MPa) Tensile strength (MPa) Elongation (min) m Young s modulus (typical) (GPa) Fatigue limit % of T.S.) Bend radius on 2 mm Density (g/cm ) Stress for O 1% total plastic strain in 100 h (MPa) Production range... 

Low-Cycle Fatigue Properties. Results of low-cycle fatigue experiments under strain control on as-worked W plate material at 815 °C are shown in Fig. 3.1-172. Low-cycle fatigue tests of pure W were performed in the temperature range between 1650 °C and 3300 C [1.184]. A relationship Afaiiure = exp(—aT) was found to be valid up to test temperatures of 2700 °C [1.185]. In all cases the failure mode was intercrystalline. Similar results were also obtained at a test temperature of 1232 °C [ 1.186]. The deformation behavior of Nb and Nb IZr under plastic-strain control at room temperature was investigated and cyclic stress-strain curves published [1.182]. 

Considering smooth specimens, the ranges of applied stress or plastic strain control the fatigue or CF responses of metals for HCF and LCF conditions, respectively. For HCF, smooth specimen CF hfe increases with decreasing elastic stress range, at cycles in excess of the transition fatigue life, Nj-, according to the Basquin equation... 

If fee loading process shown in Fig. 1.28 is reversed again from to then a hysteresis loop will result such as feat shown in Fig. 1.29. The hysteresis loop defines a single fatigue cycle in fee strain-life method. After a number of cycles the hysteresis loop stabilizes. The stability occurs normally in less than 10% of the total life. Tlie hysteresis loop is often characterized by its stress range. Act, and strain range, Ae. The strain range may be split into an elastic part, Ae, and a plastic part, Ae. 

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