Dislocation Properties Study On FCC Metal Aluminum At Finite Temperature

Dislocations are the major carriers of plastic deformation in crystalline materials,the emergence and movement of which are the chief mechanisms of plastic deformation in crystals.The movement of dislocations are severely depends on the core structure.Within the classical P-N model,the planar dislocation is described by the continuum mismatch field,which in the inelastic dislocation core,can only provide an approximate atomistic description.Under the continuous translational symmetry,dislocations will be move freely in an invariant shape.However,in the real crystal,instead of the continuous form,the discrete translational symmetry will destroy the invariability of the dislocation shape during its movements.Additionally,a dislocation cannot move through crystal unless the applied stress exceeds a critical value that is referred to as Peierls stress ?_p.Because the Peierls equation is invariant under continuous translation transformation,the dislocation shape does not change as it moves.In order to overcome the shortcoming of the traditional theoretical model,recently,the lattice theory of dislocation,which is on the basis of the lattice dynamics,has been developed.Meanwhile,an improved P-N equation considering the correction terms of the discrete effects,has been established to deal with the structure of the dislocation core.Furthermore,a full-discrete theory of dislocation is presented in a model-independent way is proposed.Over the years,the various theoretical models of dislocation have not include the temperature effects.As we know,the lattice vibration will be more and more intense with the increase of the temperature and the intensity will exert significant influence on the core structure,movements and other dislocation properties.In view of these points,it is meaningful and essential to study the temperature related dislocation properties.Based on the improved Peierls-Nabarro?P-N?model,we propose a theoretical formalism for investigating the properties of dislocation at finite temperature.With the help of this formalism,the temperature related dislocation properties of 1/2<110>{111}dissociated edge dislocation in Aluminum is studied.Theoretically,it is assumed that the entropy associated with the elastic field is the same for the dislocations and usual strained lattice,since the only differences in the elastic fields occur in a small region near the dislocation core,and these differences are accounted for the calculations of generalized stacking fault energy?GSFE?.Meanwhile,the reconstruction and kink excitation are not be considered.As mentioned above,the two-dimensional?2D?improved P-N equations can be investigate all straight dislocations including the temperature effect,while the parameters such as the lattice constant,elastic modulus,GSFE surfaces at finite temperature are calculated by the first principle approach.Because the 2D improved dislocation equations are a set of nonlinear integro-differential equations which are hard to be solved,by introducing a new semi-analytical and semi-numerical method,we obtain an approximate solution of the 2D improved dislocation equations.Furthermore,within the framework of the full-discrete lattice theory of dislocation,the uniform shear stress method is adopted to calculate the Peierls stress.In addition,the variation of the FCC metal A1 1/2<110>{111} screw dislocation energy and structure with the external stress and the temperature are investigated.To be specific,the main contents of this thesis are listed below:?1?Proposing a semi-analytical and semi-numerical method to solve the 2D improved dislocation equations.In this thesis,on the basis of the improved 2D dislocation equations,we investigate the properties of FCC metal A1 1/2<110>{111}dissociated edge dislocation within the intrinsic frame.It is found that,under the one dimensional approximation,the dislocation can be described well enough by the structure parameters of the dislocation core which are accurate to first order.However,as for the decomposition dislocation which is much more complicated,the higher order terms.namely cn??n =1,2,3?,cn??n=1,2?,must be as well taken into account.The additional higher order terms greatly increase the difficulties in calculation and make the fully analytic calculation quite hard to be completed.In view of these,in this thesis,an automated high-efficiency parallel calculation program is completed,by which one can accomplish the complicated calculations,involving the stated above high order terms,under different truncation conditions.It is noted that,due to that no prior hypothesis related to the core structure are adopted,this program is also applicable to solving the general equations.?2?The studies on the properties of 1/2<110>{111} dissociate dislocation in Aluminum at finite temperature.In this thesis,the temperature-dependent properties of 1/2<110>{111} edge dislocation in Aluminum are investigated with the help of the improved P-N equation and the first-principles calculations.For the sake of establishing a 2D dislocation equation involving the effects of temperature,on the basis of the Density Function Theory?DFT?and the Density Function Perturbation Theory?DFPT?which is under the Quasi-harmonic Approximation?QHA?,the first principles quasi-static approach is employed to calculate the lattice geometry,elastic modulus and Generalized Stacking Fault Energy?GSFE?at finite temperature.Our results show that the width of the equilibrium separation will be more narrow when the temperature increase with the variation of d_eq being less than 0.32b,which reveals weak dependence of the dislocation on the temperature.As a crosscheck,our results,d_eq = 2.12b coincide with the one of DFT simulation from A.Hunter et.al,2.0±0.5b and the available experimental measurements 2.8b.In addition,we find that the ratio ?I/?U is inversely proportional to the width of the equilibrium separation distance.Our results also show a linear relationship between the width of the equilibrium separation distance d_eq/b and the normalized intrinsic SFE ?I/?b.Moreover,the energy associated with the activation of dislocation with increasing temperature,indicating that the dislocation has become increasingly unstable with temperature.This approach provides a valid solution to investigate the properties of dislocation at finite temperature,and be quite helpful to further study the thermodynamic mechanism for the reconstructions of dislocation core and the kink excitation of dislocation.?3?The studies on the properties of 1/2 1/2<110>{111} screw dislocation,by the uniform shear stress method based on the full-discrete lattice theory of dislocation.First,taking the contribution from the external stress into consideration,the variational method is employed to derive a full-discrete energy function of dislocation.Furthermore,a uniform shear stress method is introduced to analyze the response of the dislocation energy,shape and core position to the external stress and to calculate the Peierls stress ?_p.It is found that,when the external stress becomes bigger,the energy of dislocation will decrease,the Peierls barrier descend significantly?even disappear?,the width of the dislocation increase and the core position moves along the direction of Burgers vector.As a crosscheck,our results,?_p=331Mpa coincide with the one from an approximate method which directly relates to the physical constant of a material,358Mpa and that from the simulation result undissociated core structure 355Mpa.?4?The studies on the impacts of temperature on the properties of the 1/2<110>{111}screw dislocation in aluminum.In this thesis,combining the full-discrete dislocation equation and the phonon spectra from the first principle calculation based on the density function perturbation theory?DFPT?,we study the impacts of temperature on the properties of the 1/2<110>{111} screw dislocation in aluminum.Meanwhile,with the help of the uniform shear stress,the variation of the critical shear stress ?r and ?_p,which are responsible for the free momvement of the straight dislocation across the Peierls barrier in the crystal are investigated.Our results show that,without external shear stress,the Peierls barrier will rise,while the characteristic width of dislocation will be more narrow,when the temperature increase.In addition,it is found that,at different temperatures,when the dislocations are in the initial position,the energy valley and the barrier top,their corresponding energy varies linearly all the time as the external shear stress changes.Meanwhile,we find that the characteristic width is broadened at low temperature with the increase of the shear stress,while at high temperature,this variation is less than 0.01b and the shape of the dislocation will keep unchanged during the movement.At last,as the temperature goes up,the Peierls stress obtained by the uniform shear stress method increases.When employing the natural units,the value of the Peierls stress at T = 900KTis 2.5 times bigger than that at T =0K,which demonstrates that the impact of the temperature on the dislocation can not be ignored.