Failure mode in first-principles computational tensile tests of grain boundaries: Effects of a bulk-region size, dominant factors, and local-energy and local-stress analysis

A first-principles computational tensile test (FPCTT) is a powerful tool to investigate intrinsic strength and failure processes of grain boundaries (GBs), according to atomic and electronic behaviors based on density-functional theory, while careful interpretation is required in comparison with experiments, because of ideal conditions used in FPCTTs. We observed serious effects of a bulk-region size in FPCTTs of the {0 0 1} -5 GB in Al. For a GB supercell with enough thick bulk regions, the energy-strain curve shows spontaneous failure with catastrophic energy release just after the maximum stress point, which we name Type-A failure. For a GB supercell with thin bulk regions, the energy increases gradually even after the maximum stress and continuously becomes that of relaxed fracture surfaces, which we name Type-B failure, although the stress-strain curves are almost common until the maximum stress point in both the supercells. The peculiar failure of Type B occurs by the lack of accumulated strain energies for creating fracture surfaces even after the maximum stress point, because the accumulated strain energy is nearly proportional to the bulk-region size. We clarified that the failure mode in a FPCTT depends on the relationship among the three factors; the accumulated strain energy depending on the bulk-region size, the work of separation (the formation energy of fractured surfaces into a GB), and the maximum stress of the GB (the GB strength). We showed that the failure mode of previous FPCTTs of Al tilt GBs with segregated impurities can be reinterpreted from this viewpoint, by considering the changes of the work of separation and the GB strength by impurities. We should be aware of the distinction of the failure mode in FPCTTs, because experimentally Type-B failure does not occur except for special cases. Finally, we applied ab initio local-energy and local-stress analysis to the FPCTT of the {0 0 1} -5 GB in Al, and discussed how to extract local energy-strain or energy-separation relations independent of the bulk-region size to be combined with meso- or macroscopic simulations.