Gradient-dependent deformation of two-phase single crystals

In this work, a gradient- and rate-dependent crystallographic formulation is proposed to investigate the macroscopic behaviour of two-phase single crystals. The slip-system-based constitutive formulation relies on strain-gradient concepts to account for the additional strengthening mechanism associated with the deformation gradients within a single crystal with a high volume fraction of dispersed inclusions. The resulting total slip resistance in each active system is assumed to be due to a mixed population of forest obstacles arising from both statistically stored and geometrically necessary dislocations. The non-local theory is implemented numerically into the finite element method and used to investigate the effect of the relevant microstructural (i.e., size and volume fraction of precipitated inclusions) and deformation-gradient-related length scales on the macroscopic behaviour of a typical nickel-based superalloy single crystal. An analytical framework to link the strain-gradient effects at the microscopic level with the macroscopic behaviour of an equivalent homogeneous single crystal is also proposed.