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

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.

Acknowledgements

The authors acknowledge use of the 3D DDS code, ParaDiS, which was developed at Lawrence Livermore National Laboratory by the ParaDiS team. The work of M. Tang is performed under the auspices of the United States Department of Energy by the University of California. This work was supported by the AFOSR, and by a grant of computer time from the DOD High Performance Computing Modernization Program, at the Aeronautical Systems Center/Major Shared Resource Center. The work was performed at the US Air Force Research Laboratory, Materials and Manufacturing Directorate, Wright-Patterson AFB.