A Formulation for the Characteristic Lengths FCC in First Gradient Elasticity Via Sutton-Chen Potential

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Tehranchi, Ali | 2008

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Type of Document: M.Sc. Thesis
Language: Farsi
Document No: 39174 (09)
University: Sharif University of Technology
Department: Civil Engineering
Advisor(s): Mohammadi Shoja, Hossein
Abstract:
The usual continuum theories are inadequate in predicting the mechanical behavior of solids in presence of small defects and stress concentrators; it is well known that such continuum methods are unable to detect the change of the size of the inhomogeneities and defects. For these reasons various augmented continuum theories and strain gradient theories have been proposed in the literature. The major difficulty in implication of these theories lies in the lack of information about the additional material constants. For fcc metals, for calculation of the associated characteristic lengths which arise in first strain gradient theory, an atomistic approach based on Sutton‐‐Chen interatomic potential function is proposed. For validity of the computed characteristic lengths, the size effect pertinent to the fcc (111) plane containing a nano‐size circular void subjected to a uniform far‐field tension is examined via comparing the strain gradient theory and a lattice theory solutions. Moreover, by reconsideration of the Kelvin problem it is shown that a commonly employed variant of the first strain gradient theory is only valid for a few fcc metals
Keywords:
Strain Gradient Elasticity ; Size Effect ; Sutton-Chen (Sc)Potential Function ; Charachteristic Length