Improvements Of The Peierls-Nabarro Model And Its Applications

Dislocations are major carriers of plastic deformation in crystalline materials.Of particular interest is dislocation motion in crystallite,which governs many of the macro-scale properties of crystallites during plastic deformation.Peierls stress(?_p),the minimum critical resolved shear stress to move a straight dislocation without thermal activation,is strongly related to the core structure of a dislocation and often used to assess deformability of materials.Quantitative prediction of Peierls stress associated with dislocation glide is of fundamental concern in understanding and designing the plasticity and mechanical properties of crystalline materials.Quantum mechanics based first principles calculations can accurately calculate dislocation core structure,but it is computationally expensive or even impossible for studying Peierls stress because of the finite number of atoms in the model.Molecular dynamics/statics(MD/MS)simulations with empirical potentials is capable for predicting dislocation core structure and Peierls stress associated with a glide dislocation,but reliable empirical interatomic potentials might be unavailable to some complex materials.Peierls-Nabarro(PN)model is an attractive approach to study core structure and Peierls stress of dislocations for its simplicity and efficiency in incorporating the nonlinear feature of the dislocation core into the long range elastic fields.Despite considerable progress has been made in the past few decades to overcome the shortcomings and limitations of the original PN model,application of which to quantitatively predict core structure and Peierls stress for complex structures,and dislocation properties under complex external loading has been a long-standing challenge so far.For instance,general PN models overestimate Peierls stress by one to two orders of magnitude for glide dislocation in face-centred cubic(FCC)metals,atomistic simulations were considered more reliable when empirical interatomic potentials were available.Therefore,improvement of the PN model with broader applicability is of significant importance not only for development of multiscale methods but also for expanding the application field of PN model.In this thesis,substantial improvements of the PN model have been made based on the original semi-discrete variational Peierls-Nabarro(SVPN)framework,by accounting for the large gradient effects and nonlocal atomic interactions in the region around dislocation core.And the improved SVPN model has been validated by applying it to study core structure and Peierls stress for dislocations in FCC and body-centered cubic(BCC)metals,as well as dislocation properties under external loading.MD simulations further validate the improved SVPN model.More specifically,1.An enhanced SVPN model is proposed by incorporating an additional gradient energy term into the energy functional.This gradient energy term is designed to effectively represent the influence of both the discreteness of atoms and the quick variations of the displacement profile in the dislocation core.Using FCC metals as a model system for validation,and by appropriately calibrating the proposed model against the MD simulation on dislocation core structure,the results show that the enhanced SVPN model is capable of accurately predicting the core structure(disregistry profiles),and consequent precise Peierls stress,within a few times the prediction from molecular dynamics calculations.2.A nonlocal SVPN model is developed by incorporating the nonlocal atomic interactions into the semi-discrete variational Peierls framework.The nonlocal kernel is simplified by limiting the nonlocal atomic interaction in the nearest neighbor region,and the nonlocal coefficient is directly computed from the dislocation core structure.The nonlocal SVPN model is capable of accurately predicting the displacement profile,and the Peierls stress,of planar-extended and condensed core dislocations in FCC and BCC metals.3.The nonlocal SVPN model is generalized to a three dimensional one,which is applied to study the effects of the atomic relaxations in the direction normal to the glide plane(vertical direction)on core structure and Peierls stress of dislocations.Calculations shows that,for the dislocations in FCC and BCC metals,the effects of the vertical relaxation can be sufficiently accounted for by the allowing for atomic relaxation in the vertical direction when calculating generalized stacking fault energy surface by atomistic simulations.4.By investigating the variation of Peierls stress of dislocations in FCC crystals with respect to the Escaig stress,the improved SVPN model by the gradient energy term is demonstrated to be an efficient and powerful tool to study dislocation properties under external loading.The Escaig stress is the shear stress perpendicular to the Burgers vector,and it modulates the stacking fault area between two partials of a full dislocation,and in turn,affects the mobility of the dislocation.Calculations shows that Peierls stress pseudo-periodically oscillates and the oscillation gradually damps decreases with the increase of Escaig stress.This pseudo-periodic variation of?_p can be mathematically described by the combination of a sinusoidal and an exponential function,and further accounted for by the variation of the stacking fault width(SFW)between two partials during their movement under applied stresses.MD simulations further examined pseudo-periodic variation of?_p,validating the SVPN model's capability of predicting sophisticated behavior of dislocation under applied stress.Combining the experiment techniques and first principles calculations,the improved SVPN model in the current work could be applied to quantitatively predict Peierls stress for dislocations in more complex crystal structures,and quantitatively study dislocation properties under external loading.