Low-Cycle Fatigue of Pre-Strained Pure-Aluminium

Abstract

The effect of pre-strain on the behavior of lattice defects during cyclic straining was analysed theoretically. In order to ascertain the propriety of the results obtained, wires of cold worked aluminium were further cyclically strained in torsion with a constant strain amplitude at 77K or R. T.
The dislocation density during cyclic straining was given as a function of cumulative strain by
ρ_m=(1-f)ρ_pre+f(α₂/β₂)²[1-(1-ρ_pre^1/2β₂/α₂)e^-β₂γ/2]2 0≤f≤1
where ρ_m: mean dislocation density, ρ_pre: mean dislocation density in pre-strained metal, α₂, β₂: constants.
A detailed model for cyclic peak stress vs. cumulative strain response was developed from this equation, on the assumption that the amount of strain hardening is proportional to square root of the mean dislocation density. For cyclic straining with the condition of ρ_pre>(α₂/β₂)², the dislocation density decreases gradually with the number of cycles to(α₂/β₂)². Metals therefore show the behavior of fatigue softening.
The concentration of point defects C_i in pre-strained metal during cyclic straining at low temperatures such as 77K, is as follows:
C_i=C_s[1-1-ρ_pre^1/2β₂/α₂/K₂-β₂/2(K₂e^-β₂γ/2-(β₂/2-ρ_pre^1/2K₂β₂/α₂/1-ρ_pre^1/2β₂/α₂)e-^K₂γ)]
C_s=K₁α₂/K₂β₂
where K₁, K₂: constants.
The density of lattice defects calculated from the above equations agreed with that estimated through resistivity measurements on fatigued specimens at 77K.