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

Three-dimensional (3D) discrete dislocation dynamics simulations were used to calculate the effects of anisotropy of dislocation line tension ( increasing Poisson's ratio, nu) 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 mu m(3) 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 nu, exhibiting an increase of about 50% at nu = 0.38 ( value for Ni) as compared to the value at nu=0. Independent of dislocation line direction, for nu greater than 0.20, the strengths of single-ended sources depend upon the sense of the stress applied. The value for alpha in the expression for strength, tau = alpha(L)mu b/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 nu = 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 similar to 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 mu m, 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.