Gradient crystal plasticity modelling of anelastic effects in particle strengthened metallic thin films

It is now a well known phenomenon that thin films are susceptible to size effects, which can be captured adequately by gradient plasticity theories. Besides the scale dependency, metal thin films also exhibit time dependent behavior: anelasticity (deformation recovery over time following elastic spring back upon load removal) and creep (permanent deformation developed over time at constant loads). This work focuses on the extension of a strain gradient crystal plasticity (SGCP) model (Int J Solids Struct 43:7268–7286, 2006; Phil Mag 87:1361–1378, 2007; J Mech Phys Solids 52:2379–2401, 2004; Int J Solids Struct 41:5209–5230, 2004), previously developed for the scale dependent behavior of pure fcc metals, so that it can be exploited for the description of the scale and time dependent mechanical behavior of thin films that are made of metal alloys with second phase particles. For this purpose, an extended physically based slip law is developed for crystallographic slip in fcc metals by considering the deformation mechanisms that are active within the grains. In doing so, the interaction of dislocations with other dislocations and with second phase particles is taken into account. Three types of dislocation–particle interactions are considered: (i) the Orowan mechanism, (ii) the Friedel mechanism, and (iii) dislocation climb. Finite element simulations of the bending of a single crystalline beam show that at low stress levels, the plastic slip rate is controlled by dislocation climb within the presented model. Provided that a considerable lattice diffusion occurs and sufficiently large back stresses exist in the material, the extended SGCP model predicts a noticeable time dependent recovery, reducing the residual deformation after unloading. The magnitude and the characteristic time scale of the anelastic recovery are controlled by dislocation glide limited by climb.