Issue 43

B. Saadouki et alii, Frattura ed Integrità Strutturale, 43 (2018) 133-145; DOI: 10.3221/IGF-ESIS.43.10 140 Plastic strain energy Many researchers have used the cyclic plastic strain energy as damage criterion in low cycle fatigue. The dissipation of the mechanical energy is initially caused by the cyclic plastic strain connected, at microscopic level, to the dislocation movement and then, by the stress which relates to these dislocations resistance of displacement. If we consider ΔW the mechanical energy per cycle as design parameter, the law of simple damage consists in supposing that there will be a failure when the total energy W f has reached a critical value. Halford [25] proposed a relation for measurement of the area under the hysteresis loop (Fig. 9), provided that the stress and the plastic strain are measured from the tip of the loop. Figure 9 : Area under hysteresis loop [26]. In the majority of cases, the difference between the energy measured directly from the hysteresis curve by a planimeter and that calculated by Eq. (7) is less than 10%.               1 ' 1 ' p n W n (7) where n’ is the cyclic hardening coefficient. The total energy to failure W f is defined by the Eq. (8):    f f W N W (8) Fig. 10 shows a significant decrease in mechanical energy ΔW per cycle when the number of cycles increases. Practically this energy does not vary during a test since Δε and Δσ evolve inversely. The experimental points are placed around a curve corresponding to the following relation:    0.44 0.364 R W N (9) On the other hand, there is an increase in the total energy to failure W f when the number of cycles increases (Fig. 11). Figure 10 : Evolution of mechanical energy per cycle in terms of fatigue lifetime.