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استخراج توابع هسته تئوری الاستیسیته غیرمحلی برای کریستالهای fcc و hcp و کاربرد آن در مسایل نابه جایی
شه وقار اصل، سیلدا Shahvaghar Asl, Silda
Nonlocal Kernel Functions for fcc and hcp Crystals with Application to Dislocation Problems
Shahvaghar Asl, Silda | 2021
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- Type of Document: Ph.D. Dissertation
- Language: Farsi
- Document No: 54718 (09)
- University: Sharif University of Technology
- Department: Civil Engineering
- Advisor(s): Mohammadi Shodja, Hossein
- Abstract:
- For half a century, the problem of extracting the components of the nonlocal moduli tensor of anisotropic materials has been remained unsolved. In the present work, for the first time, the solution of this problem is proposed and the components of nonlocal moduli tensor are obtained for close-packed crystals, i.e. face center cubic or hexagonal closed packed. To this end, new distinct nonlocal kernel functions which have the characteristics of discrete atomistic Green’s functions in the stress space are obtained through consideration of the nonlocal dispersion relations. Each of dispersion relations are associated with certain directions and are combined with ab initio Density Functional Perturbation Theory (DFPT) calculations of the pertinent phonon frequencies. Since the kernel functions are closely related to both the anisotropy and crystalline symmetries, three new distinct nonlocal kernel functions for fcc crystals and five new distinct nonlocal kernel functions for hcp crystals are obtained. Calculation of the distinct nonlocal kernel functions pertinent to each component of the elastic moduli tensor of the nonlocal continuum theory based on quantum mechanical considerations, is the first of its kind reported in open literature. Moreover, the nonzero components of the classical elastic moduli as well as the equilibrium lattice parameters associated with some fcc and hcp crystals are computed using ab initio Density Functional Theory (DFT) and are compared with the available experimental data. In order to show the importance of the anisotropy of the kernel functions, the nonlocal stress field of both straight screw and edge dislocations inside an infinitely extended fcc or hcp medium examined. Within this theory, the unrealistic singular behavior of the classical stresses at the dislocation core is eliminated. In contrast to the classical anisotropy theory that predicts singular shear stress on the slip plane at the core of the dislocation, the corresponding nonlocal shear stress component predicted by the present theory is zero at the dislocation core. The results show that the normalized nonlocal shear stress distribution and its maximum value are greatly influenced by the anisotropy of the crystalline solids
- Keywords:
- Nonlocal Elasticity Theory ; Ab Initio Calculation ; Face Centered Cubic (FCC)Alloy ; Hexagonal Closed-Packed Crystals ; Discrete Green’s Functions ; Hexagonal Closed-Packed Crystals ; Nonlocal Distinct Kernel Functions ; Screw Dislocation ; Glide Edge Dislocation ; Density Functional Perturbation Theory (DFPT)
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