Density evolution of atomic vacancies in copper single crystals during initial stage of fatigue deformation

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.

KEYWORDS:

• Cyclic deformation
• vacancies
• dislocation mechanics
• modelling
• plasticity of metals
• fatigue damage
• cumulative deformation

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 Figure 14(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.

Additional information

Funding

This work was partly supported by the Council for Science, Technology and Innovation (CSTI), Cross-ministerial Strategic Innovation Promotion Program (SIP), ‘Structural Materials for Innovation’ (Funding Agency: Japan Science and Technology Agency). This work was also partly supported by JSPS KAKENHI grant numbers JP17H01333 and JP18H03848.