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The combined effects of crystallographic orientation and stacking fault energy (SFE) on the cracking behaviors of twin boundaries (TB) under low-cycle fatigue (LCF) tests were studied in pure Cu, Cu-Al and Cu-Zn alloys. A new approach, called the slipping morphology method, based on the crystallographic characteristics of Sigma 3 TB in face-centered cubic materials, was developed to determine the grain orientations by studying the twin-slip morphology characteristics on the sample surfaces after LCF tests. Through analyzing the dislocation TB interaction and the damage this causes to TBs, a new parameter, defined as the difference of Schmid factors (DSF), was proposed to describe the effects of crystallographic orientation on the LCF cracking behaviors of TBs. A semi-quantitative relationship was established among DSF, SFE, dislocation slip mode and the critical conditions of TB cracking by systematically studying more than a hundred post-fatigue surface morphologies of pure Cu, Cu-Al and Cu-Zn alloys. It is interesting to find that the TB cracking relies strongly on the cooperation of both DSF and SFE. Furthermore, taking into account the interactions between slip dislocations and different boundaries, the fatigue cracking possibilities of several typical interfaces were compared and discussed. The results demonstrate that low-angle grain boundaries (GBs) are the strongest in resisting fatigue cracking, high-angle GBs are the weakest, and TBs are in between, which contributes the most to the final fatigue performance of materials. This new finding will help understanding of the interfacial properties under cyclic loading and may be beneficial to the design of high-performance materials with optimal fatigue properties in the future. (C) 2012 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.