Closed form solution for a semi-infinite crack moving in an infinite orthotropic material with a circular crack breaker under antiplane strain. (English) Zbl 1495.74059
Summary: This study investigates the influence of a circular crack breaker on mode-III deformation behavior of a semi-infinite crack in a homogeneous, elastic orthotropic material subjected to longitudinal shear loads. The Galilean transformation is employed to convert the governing wave equation to Laplace’s equation which is time independent, rendering the problem amenable to analysis within the realm of the classical theory of two-dimensional elasticity. Considering the geometrical configuration of the problem, the analytical solution of the problem is possible if the problem is transformed using the appropriate mapping function. Our construction of a holomorphic function that maps the circular hole into a straight line with the edge terminating at the origin is a novelty which enables the use of integral transform method to obtain an analytic solution of the displacement, leading to closed-form expression for mode-III stress intensity factor, \(K_{111}\). The asymptotic values of the fields are obtained and shown to depend on the radius of the crack breaker. A parametric study shows that, for a fixed loading interval, a crack breaker of larger radius leads to increased stress intensity factor.
MSC:
| 74R10 | Brittle fracture |
| 74H10 | Analytic approximation of solutions (perturbation methods, asymptotic methods, series, etc.) of dynamical problems in solid mechanics |
| 74H35 | Singularities, blow-up, stress concentrations for dynamical problems in solid mechanics |
| 74S70 | Complex-variable methods applied to problems in solid mechanics |
| 74E10 | Anisotropy in solid mechanics |
Keywords:
stop hole; longitudinal shear load; mode-III stress intensity factor; wave equation; Laplace equation; mapping holomorphic function; integral transform methodReferences:
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