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Stacked Screw Dislocation Arrays in an Anisotropic Two‐Phase Medium
Author(s) -
Chou V. T.,
Barnett D. M.
Publication year - 1967
Publication title -
physica status solidi (b)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.51
H-Index - 109
eISSN - 1521-3951
pISSN - 0370-1972
DOI - 10.1002/pssb.19670210123
Subject(s) - moduli , physics , isotropy , shear modulus , dislocation , prime (order theory) , phase (matter) , condensed matter physics , anisotropy , modulus , matrix (chemical analysis) , materials science , crystallography , combinatorics , mathematics , optics , thermodynamics , composite material , quantum mechanics , chemistry
Abstract The distribution of screw dislocations under an applied stress in uniformly stacked pileups against a second phase is determined. The number of dislocations, n , in each pileup decreases as the separation h between pileups decreases and as the ratio of the shear moduli of the second and the matrix phases ( G ″/ G ′ in the isotropic case) increases. The stress field produced in the second phase is quantitatively described. For L/η′ ≫ x/η″, the intensity of the stress field at a distance x from the tip of each pileup varies as \documentclass{article}\pagestyle{empty}\begin{document}$ \left({\tanh \frac{{\pi L}}{{\eta \prime h}}/\tanh \frac{{\pi x}}{{\eta \prime \prime h}}}\right)^\lambda $\end{document} where L is the length of the pileup, η′ and η″ are respectively functions of the elastic constants of the matrix and the second phases, and λ is a monotone decreasing function of the ratio of the shear moduli, varying in the range 1 > λ > 0 as the ratio varies between 0 and ∞. The stress concentration near the tip thus decreases as h decreases and as the modulus ratio increases. A number of special cases derived from the general solution are discussed.