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Multi-scale Analysis of Dislocation Emission for Nano-crystalline Structures

Fattahi Faradonbeh, Mehran | 2016

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  1. Type of Document: M.Sc. Thesis
  2. Language: English
  3. Document No: 49092 (53)
  4. University: Sharif University of Technology, International Campus, Kish Island
  5. Department: Science and Engineering
  6. Advisor(s): Khoei, Amir Reza; Jahanshahi, Mohsen
  7. Abstract:
  8. In this study, a new multi-scale hierarchical technique has been employed to investigate the role of edge dislocation on nano-plates with hex atomic structure in large deformation. Two multiscale hierarchical atomistic/molecular dynamics (MD)–finite element (FE) coupling methods are proposed to illustrate the influence of temperature on mechanical properties of Magnesium in large deformation. The atomic nonlinear elastic parameters are obtained via computing second-order derivative of Representative atom’s energy and RVE’s strain energy density with respect to deformation criterions (deformation gradient and Green strain tensor) to bridge between atomistic and continuum level, the mechanical characteristics are captured in the atomistic level and transferred to the continuum level directly by functions of strains. Furthermore, comparing the numerical results of the present multiscale method with MD simulation results, discloses that the suggested techniques produce promising results with small amount of error in large deformation. Different number of primary edge dislocations is considered and the temperature is 0 K. Primary edge dislocations are created by proper adjustment of atomic positions to resemble discrete dislocations (DD’s) and then the application of equations of motion to the relaxed configuration of this adjustment. The interatomic potential used for atomistic simulation is Finnis-Sinclair Embedded-Atom-Method (FS-EAM) as many-body interatomic potential and the Nose-Hoover thermostat has been implemented to adjust the modulation of temperature. Total potential energy of different representative volume elements (RVEs) under biaxial and shear loadings have been provided by fitting a fourth-order polynomial in atomistic level. Linear elastic constants are obtained by computing the second derivative of potential energy per unit volume with respect to strain. To calculate the bulk modulus, a linear combination of elastic constants has been carried out. Then, the variation of yield stress, elastic constants, and bulk modulus for nano-crystalline RVE’s at different number of primary edge dislocations and temperature levels have been obtained. In order to provide a relation between various quantities in nano-scale to their counterparts in macro-scale, computed material properties from molecular dynamics simulation have been transferred to each gauss points of finite element mesh using appropriate hyperelasticity functions. The numerical results clearly show the behavior of material in the presence of primary dislocations.
    The analysis of structure of crystal defects such as dislocation and grain boundaries requires consideration of inharmonic effects on the scale of lattice. Molecular dynamic based on interatomic interaction provide a powerful and accurate tool of analysis on this scale. Dislocations are one of the most important classes of defects in crystals. They have significant effects on the physical properties of crystals. They could be primarily created during the formation of a crystal or during the loading specimen. Since dislocation is a change in perfect crystal structure it is possible to identify in the molecular level. However the high computation cost of the MD level has led researchers to use the multi-scale methods in dislocation studies. Example of application of these techniques might be found in the work of Tedmor.et.al[53].
    The future study will be focused on the development of multi-scale technique to control of dislocation emission to investigate the plasticity behavior of nano-Crystalline structure
  9. Keywords:
  10. Molecular Dynamics ; Periodic Boundary Condition ; Representative Volume Element ; Large Deformation ; Mechanical Behavior ; Multiscale Hierarchical Analysis ; Edge Dislocation ; Dislocation Emission

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