4.3 Cyclic Softening and Fatigue Life
The cyclic softening behavior is also essential for the isotropic parameter identification (c and d in Eq. (8))1-3,49 in Chaboche UVP model and even damage parameters62. Thus, the measured peak stress evolutions versus fatigue lives (N ) for both SSFS and MTP tests subjected to saw-tooth and dwell-type loadings are compared in Fig.12. Similar to SSFS fatigue test, significant cyclic softening is observed in MTP specimens with different magnitude levels and rates, as the primary mechanism of cyclic softening in the investigated material is low angle boundary dislocation annihilation63,64. In general, the trends of the measured peak stress evolutions in every cycle in the MTP specimens under saw-tooth loading are similar to that of in SSFS specimen. However, cyclic softening and fatigue lives of MTP specimens exhibit a strong geometry dependency. For example, MTP-3 with the weakest geometry constraint effect gives the closest fatigue life comparing with the SSFS test subjected to saw-tooth loading, while MTP-2 is the intermediate case. The shortest fatigue life can be observed in MTP-1 due to the strongest geometry constraint effect. The measured peak stress evolution subjected to saw-tooth waveform in Fig.12 is consistent with the peak stress evolution as predicted in Fig.8c, which further confirm the feasibility of the testing methodology and FE analysis used in this work. The fatigue life of MTP-3 subjected to dwell-type loading is significantly lower than the test under saw-tooth loading because the hold dwell effect can aggravate the damage accumulation, which is consistent with our previous experimental observations on the investigated material1,3,63,64. Table 4 tabulates the comparison of fatigue lives (Nf ) for all the tests within this test program.