Signatures of long-range elastic interaction in textured materials

2000 ◽  
Vol 62 (9) ◽  
pp. 5265-5269
Author(s):  
T. Lookman ◽  
A. Saxena ◽  
D. A. Dimitrov ◽  
A. R. Bishop ◽  
R. C. Albers
Keyword(s):  
Long Range ◽  
Elastic Interaction ◽  
Textured Materials

A Numerical Scheme for Generalized Peierls-Nabarro Model of Dislocations Based on the Fast Multipole Method and Iterative Grid Redistribution

2015 ◽  
Vol 18 (5) ◽  
pp. 1282-1312 ◽  
Author(s):  
Aiyu Zhu ◽  
Congming Jin ◽  
Degang Zhao ◽  
Yang Xiang ◽  
Jingfang Huang
Keyword(s):  
Boundary Conditions ◽  
Long Range ◽  
Numerical Scheme ◽  
Fast Multipole Method ◽  
Dislocation Core ◽  
Elastic Interaction ◽  
Epitaxial Thin Films ◽  
Fast Multipole ◽  
Multipole Method ◽  
Grid Points

AbstractDislocations are line defects in crystalline materials. The Peierls-Nabarro models are hybrid models that incorporate atomic structure of dislocation core into continuum framework. In this paper, we present a numerical method for a generalized Peierls-Nabarro model for curved dislocations, based on the fast multipole method and the iterative grid redistribution. The fast multipole method enables the calculation of the long-range elastic interaction within operations that scale linearly with the total number of grid points. The iterative grid redistribution places more mesh nodes in the regions around the dislocations than in the rest of the domain, thus increases the accuracy and efficiency. This numerical scheme improves the available numerical methods in the literature in which the long-range elastic interactions are calculated directly from summations in the physical domains; and is more flexible to handle problems with general boundary conditions compared with the previous FFT based method which applies only under periodic boundary conditions. Numerical examples using this method on the core structures of dislocations in Al and Cu and in epitaxial thin films are presented.

ON THE MECHANISM OF WORK HARDENING IN f.c.c. METALS

1967 ◽  
Vol 45 (2) ◽  
pp. 631-661 ◽  
Author(s):  
Helmut Kronmüller
Keyword(s):  
Flow Stress ◽  
Single Crystals ◽  
Long Range ◽  
Work Hardening ◽  
Slip Line ◽  
Elastic Interaction ◽  
Stress Fields ◽  
Internal Stresses ◽  
Transmission Microscopy ◽  
Magnetic Methods

A review of the methods applied for the investigation of long-range stresses in deformed single crystals is given. The results found by magnetic methods are discussed in some detail; slip-line data and transmission microscopy are mentioned briefly. The effect of internal stresses on the flow stress is discussed and it is shown that the elastic interaction between the primary dislocations determines the flow stress almost completely. Secondary dislocations are found to be incapable of relaxing the stress fields of the primary dislocations appreciably.

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