Stacked Screw Dislocation Arrays in an Anisotropic Two‐Phase Medium

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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}$ \left({\tanh \frac{{\pi L}}{{\eta \prime h}}/\tanh \frac{{\pi x}}{{\eta \prime \prime h}}}\right)^\lambda $ 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.
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