A discrete dislocation analysis of strengthening in bilayer thin films

Abstract

A two-dimensional (2D) discrete dislocation plasticity framework, which incorporates some three-dimensional mechanisms through constitutive additions, is used to analyse the response to uniaxial tension of nanoscale bilayer thin films. Frank–Read sources, modelled as junction dipoles in 2D, act as sources of dislocations. Infinite, homogeneous medium fields of the discrete dislocations are superposed with a non-singular complementary field that enforces the boundary conditions and accounts for image stresses arising from the difference in elastic properties between the layers. The resulting boundary value problem is solved using the finite element method. Analysis has been carried out for fully coherent bilayer Al/Cu and Cu/Ni films oriented for double slip. The analysis accounts for the effects of three key mechanisms: resistance to dislocation nucleation and motion due to elastic modulus mismatch (e.g. Koehler barrier); single-dislocation bow-out within layers (Orowan process) and slip blocking at interfaces (Hall–Petch mechanism). The relative importance of each mechanism is studied as a function of the bilayer thickness. The results indicate a significant strengthening with decreasing bilayer thickness. Conclusions are drawn regarding the possible causes of the observed strengthening.