Hysteresis Loop Counting

The total damage is the sum of individual damages (see Sect. 8.3). If the spectrum of Fig. 8.14 is repeated m times, then damages cumulate and the total one becomes 

Note that cycle 3 is the only one to have a positive mean stress. In all other cycles mean stress is negative and then ineffective. 

---

Not counting the systems with irreversible sorbent s deformation when hysteresis loop is observed in aU range of relative pressure, the LPH has its origin above all in the kinetic effects associated with overcome the potential barrier at the open end of fine pores. As was shown in the work by Jakubov and Mainwaring [81], the behavior of the potential field at the open end of sufficiently narrow pores always exhibits the existence of potential barriers not only for inward diffusion, but also for outward diffiision. In addition, these barriers, generally, are unequal in magnitude. Moreover, the contraction of adsorbent that often occurs at low relative pressure may gives birth to the barrier for outward diffusion for pores, which have not had the barrier for inward diffusion. 

Finally, from point 1 there will be the last unloading to the origin. Let s count the applied cycles by using the rain flow rule (see Sect. 8.2.4). The procedure outlined in Fig. 8.13 is shown in Fig. 6.40. In the loading time history of Fig. 6.37 three independent cycles can be identified and separated, namely cycle (a), cycle (b) and cycle (c). These three cycles correspond to hysteresis loop 2-3-2, 1—4-5 and 0-1-0 of Fig. 6.39. The same cycles can be identified and separated using the rain flow procedure, as schematized in Fig. 6.41. Let s apply the SWT method to evaluate the allowable number N of cycles using Eq. (6.22) and the damage... 

Fig. 8.14 Relationship between rain flow counting and hysteresis loops...

---