A screw dislocation near a semi-infinite crack partially penetrating an elastic inhomogeneity of arbitrary shape. (English) Zbl 1486.74124
Summary: A novel yet simple method is proposed to derive an analytical solution to the interaction problem of a screw dislocation inside an elastic inhomogeneity of arbitrary shape partially penetrated by a semi-infinite crack. The two analytic functions characterizing the elastic fields of stresses and displacement in the two-phase composite are readily obtained. Furthermore, we derive explicit expressions for the mode III stress intensity factor at the crack tip and the image force acting on the screw dislocation. Several specific examples are presented to demonstrate the obtained solution. An analytical solution to the case in which the screw dislocation is located in the cracked matrix is similarly derived.
MSC:
| 74R10 | Brittle fracture |
| 74G70 | Stress concentrations, singularities in solid mechanics |
| 74S70 | Complex-variable methods applied to problems in solid mechanics |
| 74G10 | Analytic approximation of solutions (perturbation methods, asymptotic methods, series, etc.) of equilibrium problems in solid mechanics |
| 74E05 | Inhomogeneity in solid mechanics |
| 74B05 | Classical linear elasticity |
Keywords:
analytical stress function; series solution; two-phase composite; mode III stress intensity factorReferences:
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