Abstract
Pure copper wires with grain size of 7.5, 23.5, and 123.0μm were cyclically strained in torsion with constant strain amplitudes of 0.025 and 0.05 at 77K. The effect of grain size on the behavior of lattice defects was studied by measuring the change in resistivity during fatigue as a function of number of cycles at 77K.
The dislocation density in a fatigued specimem is given by
ρ1/2=α'/β'(1-e-(β'/γ)2)
β'=β+K3/Δγ, β=a+b/d
where ρ is the dislocation density, α'and K3 are constants depending on the grain size of the specimen, γ is the cumulative plastic strain, Δγ is the plastic strain amplitude, d is the grain size, and a and b are constants. The increase in dislocation density was much smaller in the coarser grain size specimen during cyclic straining, and, therefore, a smaller peak torque was attained in this material.
The change in concentration of point defect Ci in the fatigued specimen is represented as follows.
Ci=Cs[1-1/β'/2-K4(β'/2e-k4γ-K4e-(β'/2)γ)]
Cs=K5α'2/K4β'
where K4 and K5 are constants. The concentration of vacancies determined experimentally by isothermal annealing was in agreement with the result calculated from the above equation.
