Simulation Studies on the LongRange Interaction Between Twin Boundaries and Dislocations and Its Effect on Mechanical Properties of Nanoscale Materials
孿晶界與位錯的長程相互作用及其對納米材料力學性能影響的模擬研究
Student thesis: Doctoral Thesis
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Award date  20 Sept 2023 
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Permanent Link  https://scholars.cityu.edu.hk/en/theses/theses(1d0678a1e9a64d089153aeb1359b96bc).html 

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Abstract
Strength and ductility are two main mechanical properties of structural materials, however, there exist some tradeoff between these properties in most cases, so it has been an important problem in the area of structural materials to fabricate materials with both high strength and good ductility. Ever since the combination of superior strength and terrific ductility in nanotwinned materials was found in 2004, nanotwinned materials have attracted much research interests in the areas of materials and mechanics.
The good combination of strength and ductility in nanotwinned materials is rooted in the interaction between dislocations and twin boundaries (TBs), including the sliptransfer of dislocations at TBs and the longrange interaction between dislocations and TBs. Most of the previous works are focused on the observation and theoretical modelling of the motion and reaction mechanisms, and the parameters in these theoretical models are usually fitted according to the macroscopic mechanical properties of materials. According to the point view of bottomup multiscale modelling, parameters at larger scales can be derived from the analysis at finer scales, however, related works are seldom seen, and this hinders the development of numerical methods about the prediction of macroscopic mechanical properties and the optimization of microscopic structures. Thus, it is the aim of this work to quantitatively study the interaction between TBs and dislocations.
An improved algorithm is proposed to study the activation process of dislocations. The plastic deformation of materials at macroscopic scales originates from the nucleation and motion of dislocations at microscopic scales, and the transition path of different microscopic states is usually calculated with the NEB (Nudged Elastic Band) method. However, the NEB  II  method is not efficient when the reaction path is quite long or there exist complicated configuration changes near the critical state. To solve this problem, the FENEB (FreeEnd NEB) algorithm and the ANEB (Adaptative NEB) algorithm are proposed based on the idea of localizing the calculated reaction path, however, in practical applications it is found that the FENEB algorithm is not robust enough and the ANEB algorithm is not accurate enough. The reasons of these problems are analyzed and it found that the low robustness is related to the fact that the forces exerted on the ending nodes of the state chains are dependent on the spring stiffness and the low accuracy of the ANEB algorithm is related to the constraint of the ending nodes of the state chains. An improved scheme with respect to the original FENEB algorithm is proposed and it is combined with the adaptation strategy of the ANEB algorithm to form the FEANEB algorithm. Examples about the nucleation of dislocation at material surfaces, migration of twin boundaries and crossslip of screw dislocations all shown that the proposed FEANEB method is more efficient than the original algorithms in the calculation of reaction paths and transition states.
The intrinsic interaction between TBs and screw dislocations is studied by using an atomcontinuum coupling model with high accuracy. Simulation results show that the longrange interaction between TBs and screw dislocations are much weaker than the interaction between two screw dislocations with the same Burges vector, and the magnitude of former is about 10^{−3} of the latter. From the point view of numerical calculations, the longrange interaction between TBs and screw dislocations can be neglected in the simulation of nanotwinned dislocations. The strong repulsion to screw dislocations from the TBs claimed in a former similar work is actually from the pinning effect from the fixed boundaries to dislocations, and this pinning effect is obvious when the simulated sample is in nanoscale.
The interaction between TBs and general dislocations is studied and the physical origin of the TBdislocation repulsion from TBs to dislocations observed in experiments is revealed. The longrange interaction between TBs and dislocations is related to the Burgers vectors of dislocations, and for the same magnitude of the Burgers vectors, the minimum of this interaction corresponds to the case of screw dislocations and the maximum of this interaction corresponds to edge dislocations. However, even in the case of edge dislocations, the atomcontinuum coupling simulation shows that the magnitude of interaction force between TBs and dislocations is much lower than that between two dislocations. Further simulations about dislocation pileups show that the experimentally observed repulsion from TBs to dislocations is actually from the dislocationtype defects on TBs.
The hindering effect of TBs to surface dislocation nucleation is studied. Surfaces are the dominating sources of dislocations for nanoscale devices, and surface dislocation nucleation is the main reason of plastic deformation and failure. Simulations show that TBs located several atomlayers underneath the surface cause obvious increase of yield strength by effectively hindering the nucleation of dislocations. Further calculation of reaction path of the dislocation nucleation process shows that TBs underneath surfaces causes obvious increase of activation energy of dislocation nucleation. Key Words ： nanotwinned materials; minimum energy path; intrinsic interaction; dislocation pileup; atomcontinuum coupling analysis; molecular dynamics simulation
The good combination of strength and ductility in nanotwinned materials is rooted in the interaction between dislocations and twin boundaries (TBs), including the sliptransfer of dislocations at TBs and the longrange interaction between dislocations and TBs. Most of the previous works are focused on the observation and theoretical modelling of the motion and reaction mechanisms, and the parameters in these theoretical models are usually fitted according to the macroscopic mechanical properties of materials. According to the point view of bottomup multiscale modelling, parameters at larger scales can be derived from the analysis at finer scales, however, related works are seldom seen, and this hinders the development of numerical methods about the prediction of macroscopic mechanical properties and the optimization of microscopic structures. Thus, it is the aim of this work to quantitatively study the interaction between TBs and dislocations.
An improved algorithm is proposed to study the activation process of dislocations. The plastic deformation of materials at macroscopic scales originates from the nucleation and motion of dislocations at microscopic scales, and the transition path of different microscopic states is usually calculated with the NEB (Nudged Elastic Band) method. However, the NEB  II  method is not efficient when the reaction path is quite long or there exist complicated configuration changes near the critical state. To solve this problem, the FENEB (FreeEnd NEB) algorithm and the ANEB (Adaptative NEB) algorithm are proposed based on the idea of localizing the calculated reaction path, however, in practical applications it is found that the FENEB algorithm is not robust enough and the ANEB algorithm is not accurate enough. The reasons of these problems are analyzed and it found that the low robustness is related to the fact that the forces exerted on the ending nodes of the state chains are dependent on the spring stiffness and the low accuracy of the ANEB algorithm is related to the constraint of the ending nodes of the state chains. An improved scheme with respect to the original FENEB algorithm is proposed and it is combined with the adaptation strategy of the ANEB algorithm to form the FEANEB algorithm. Examples about the nucleation of dislocation at material surfaces, migration of twin boundaries and crossslip of screw dislocations all shown that the proposed FEANEB method is more efficient than the original algorithms in the calculation of reaction paths and transition states.
The intrinsic interaction between TBs and screw dislocations is studied by using an atomcontinuum coupling model with high accuracy. Simulation results show that the longrange interaction between TBs and screw dislocations are much weaker than the interaction between two screw dislocations with the same Burges vector, and the magnitude of former is about 10^{−3} of the latter. From the point view of numerical calculations, the longrange interaction between TBs and screw dislocations can be neglected in the simulation of nanotwinned dislocations. The strong repulsion to screw dislocations from the TBs claimed in a former similar work is actually from the pinning effect from the fixed boundaries to dislocations, and this pinning effect is obvious when the simulated sample is in nanoscale.
The interaction between TBs and general dislocations is studied and the physical origin of the TBdislocation repulsion from TBs to dislocations observed in experiments is revealed. The longrange interaction between TBs and dislocations is related to the Burgers vectors of dislocations, and for the same magnitude of the Burgers vectors, the minimum of this interaction corresponds to the case of screw dislocations and the maximum of this interaction corresponds to edge dislocations. However, even in the case of edge dislocations, the atomcontinuum coupling simulation shows that the magnitude of interaction force between TBs and dislocations is much lower than that between two dislocations. Further simulations about dislocation pileups show that the experimentally observed repulsion from TBs to dislocations is actually from the dislocationtype defects on TBs.
The hindering effect of TBs to surface dislocation nucleation is studied. Surfaces are the dominating sources of dislocations for nanoscale devices, and surface dislocation nucleation is the main reason of plastic deformation and failure. Simulations show that TBs located several atomlayers underneath the surface cause obvious increase of yield strength by effectively hindering the nucleation of dislocations. Further calculation of reaction path of the dislocation nucleation process shows that TBs underneath surfaces causes obvious increase of activation energy of dislocation nucleation. Key Words ： nanotwinned materials; minimum energy path; intrinsic interaction; dislocation pileup; atomcontinuum coupling analysis; molecular dynamics simulation
 nanotwinned materials, minimum energy path, intrinsic interaction, dislocation pileup, atomcontinuum coupling analysis, molecular dynamics simulation