ABSTRACT
Density evolutions of dislocations and atomic vacancies in copper single crystals subjected to cyclic loadings are numerically evaluated by combining theoretical models for vacancy generation and dislocations’ behaviour during plastic slip deformation. Parameters for the model of dislocation movement, accumulation and annihilation are set so as that they mimic dislocation movement in regions without or with dislocation substructure in crystals. Cyclic stress–strain curve, evolutions of statistically stored dislocations and atomic vacancies are examined in detail. Atomic vacancy densities after 15 cycles of tensile/compressive loading of ± 3% axial strain amplitude reach 1024–1025 m−3, depending on the dislocations’ mean free path and aspect ratio of dislocation loops. Results agree well with experimentally obtained data in the literature.
Disclosure statement
No potential conflict of interest was reported by the authors.
ORCID
Tetsuya Ohashi http://orcid.org/0000-0002-7195-8924
Notes
1 Deformation twin is not taken into account either. If deformation twin generates under some conditions for temperature, strain rate, additive elements and others, additional phenomena will be induced accordingly. This is an interesting area of study, but is beyond the scope of the present paper.
2 Apart from the increase rate, the increment of vacancy from the deformation stage S28 to S30 is approximately 7.67 PPM and the increment of cumulative plastic shear strain is approximately 24% as shown in (b). Because the increment of cumulative plastic shear strain for the case of strain range Δγ = ±1% is 4%, the increment of vacancy concentration for the case of strain range Δγ =±1% could be evaluated as 1.28 PPM/cycle. This is close to the value we obtained from the increase rate and when the cumulative plastic shear strain was 3.