Abstract
The interaction between a screw dislocation and an elastic semi-cylindrical inhomogeneity abutting on a rigid half-plane is investigated. Utilizing the image dislocations method, the closed form solutions of the stress fields in the matrix and the inhomogeneity region are derived. The image force acting on the dislocation is also calculated. The results were used to study the interaction between a screw dislocation and a rigid wedge inhomogeneity with an elastic circular inhomogeneity at the tip by means of conformal mapping. The results show that an unstable equilibrium point of the dislocation near the semi-cylindrical inhomogeneity is found when the inhomogeneity is softer than the matrix. Moreover, the force on the dislocation is strongly affected by the position of the dislocation and the shear modulus of the semi-circular inhomogeneity. Positive screw dislocations can reduce the SIF of the rigid wedge inhomogeneity (shielding effect) only when it located in the lower half-plane. The shielding effect increases with the increase of the shear modulu of both the matrix and the inhomogeneity and increases with the increase of the wedge angle. The shielding effect (or anti-shielding effect) reaches the maximum when the dislocation tends to the wedge inhomogeneity interface.
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Abbreviations
- σ 31, σ 32 :
-
stress components
- μ :
-
shear modulus of the material
- b :
-
Burgers vector of the screw dislocation
- k :
-
parameter related to the shear modulus of the materials
- R :
-
radius of the circular inhomogeneity
- K III :
-
mode III stress intensity factor
- F 1, F 2 :
-
force components on the dislocation
- \(\stackrel{\frown}{\sigma} _{13}\), \(\stackrel{\frown}{\sigma} _{23}\) :
-
perturbation stress components at the dislocation
- α :
-
radian of the rigid wedge inhomogeneity
- m :
-
parameter related to the radian of the rigid wedge inhomogeneity
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Song, HP., Gao, CF. The interaction between a screw dislocation and a rigid wedge inhomogeneity with an elastic circular inhomogeneity at the tip. Meccanica 47, 1097–1102 (2012). https://doi.org/10.1007/s11012-011-9495-0
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DOI: https://doi.org/10.1007/s11012-011-9495-0