Estimating the strength of single-ended dislocation sources in micron-sized single crystals

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Abstract
Three-dimensional (3D) discrete dislocation dynamics simulations were used to calculate the effects of anisotropy of dislocation line tension (increasing Poisson's ratio, ν) on the strength of single-ended dislocation sources in micron-sized volumes with free surfaces and to compare them with the strength of double-ended sources of equal length. Their plastic response was directly modelled within a 1 µm3 volume composed of a single crystal fcc metal. In general, double-ended sources are stronger than single-ended sources of an equal length and exhibit no significant effects from truncating the long-range elastic fields at this scale. The double-ended source strength increases with ν, exhibiting an increase of about 50% at ν = 0.38 (value for Ni) as compared to the value at ν = 0. Independent of dislocation line direction, for ν greater than 0.20, the strengths of single-ended sources depend upon the sense of the stress applied. The value for α in the expression for strength, τ = α(L)µb/L is shown to vary from 0.4 to 0.84 depending on the character of the dislocation and the direction of operation of the source at ν = 0.38 and L = 933b. By varying the lengths of the sources from 933 to 233b, it was shown that the scaling of the strength of single-ended and double-ended sources with their length both follow a ln(L/b)/(L/b) dependence. Surface image stresses are shown to have little effect on the critical stress of single-ended sources at a length of ∼250b or greater. This suggests that for 3D discrete dislocation dynamics simulations of the plastic deformation of micron-sized crystals in the size range 0.5–20 µm, image stresses making the surface traction-free can be neglected. The relationship between these findings and a recent statistical model for the hardening of small volumes is discussed.