| Recent improvements in the dislocation dynamics modeling of work hardening has triggered a new interest in the calculation of the cross-slip activation energy, which is responsible for the dynamic recovery in f.c.c. metals. Early attempts to model cross-slip, which were based on either continuum theory or atomistic modeling, had varying degrees of success in the prediction of the reaction path and activation energy, Thus, methods based on classical continuum theory with concept of the Volterra dislocations were limited to describing the strain field outside of the dislocation core due to the singularity problem of the elastic solution. On the other hand, atomistic models are still limited by the use of ad-hoc potentials, which are at the present time unable to reliably predict the energies for atomic displacements far from equilibrium. Therefore, a very critical shortcoming in both elasticity-based and atomistic (MD) models is that both do not include quantum mechanics into their calculations. This aspect limits their use to situations where the material parameters are all known, and does not allow for studies of the influence of local chemistry (e.g. presence of impurities and solutes) on cross-slip.;The objective of the present work is to develop a cross-slip model that takes into account most of the atomistic characteristics of the cross-slip mechanism, and is capable of simulating any complex 3-dimensional configuration without the computational cost of current atomistic models. Thus, a hybrid ab-initio continuum approach is developed for the determination of the dislocation cross-slip configuration and the energy barrier for cross-slip in f.c.c. metals. Quantum mechanics information is introduced into the model through the lattice restoring force calculated using ab-inito methods (gamma-surface). Thus, this force is balanced against the elastic interaction force on the dislocation configuration, which is obtained from a full 3-dimensional interaction. All dislocation configurations are approximated by a network of cubic parametric splines with tangent continuity.;The first approximation of cross-slip activation energy for zero stress was performed by using a non-singular dislocation theory with a core parameter determined from an atomistic method (Peierls-Nabarro approach). An energy barrier of 1.9 [eV] is determined for Cu at the saddle point, which is in good agreement with values determined by other models, including those of Puschl and Escaig. Furthermore, a refinement of the proposed model is developed by representing the Shockley partials with fractional dislocations and adding lattice restoring forces to the dislocations, which are determined from ab-initio methods. Thus, this calculation gives a value of 1.43 [eV] for the cross-slip activation energy, which is in excellent agreement with the activation energy determined from the Bonneville-Escaig experimental value of 1.11 +/- 0.37 [eV]. Finally, a cross-slip scenario with pile-up dislocations on the glide plane is simulated to show the versatility of the proposed model for more realistic dislocation arrangements. |
