Cracked plates subjected to out-of-plane tearing loads

Smart structures are components used in engineering applications that are capable of sensing or reacting to their environment in a predictable and desired manner. In addition to carrying mechanical loads, smart structures may alleviate vibration, reduce acoustic noise, change their mechanical properties as required or monitor their own condition. With the latter point in mind, this article examines the scattering of flexural waves by a semi-infinite crack in a non-ferrous thin plate that is subjected to a constant current aligned in the direction of the crack edge. The aim is to investigate whether the current can be used to detect or inhibit the onset of crack growth. The model problem is amenable to exact solution via the Wiener-Hopf technique, which enables an explicit analysis of the bending (and twisting) moment intensity factors at the crack tip, and also the diffracted field. The latter contains an edge wave component, and its amplitude is determined explicitly in terms of the current and incidence angle of the forcing flexural wave. It is further observed that the edge wave phase speed exhibits a dual dependence on frequency and current, resulting in two distinct asymptotic behaviours.

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“…There is some variation in the definition of the stress intensity factors (cf. [20,21]); however, the following definitions are used herein…”

Section: Kirchhoff Stress Intensity Factorsmentioning

confidence: 99%

Scattering of flexural waves by a semi-infinite crack in an elastic plate carrying an electric current

Abrahams

Lawrie

2011

Mathematics and Mechanics of Solids

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“…Path independent J 1 -and I Ã 1 -integrals are employed for the determination of the stress intensity factor (SIF) at the tip of a crack in mode I or II in a linear isotropic or orthotropic material. Young and Sun [13,14] presented methodologies based on both classical and Reissner-Mindlin theories for computing G for a through-thickness crack in an infinite plate subjected to out-of-plane uniform bending moment and out-of-plane tearing loads using the virtual crack extension and the variation of potential energy. It is shown that SERR obtained using Reissner-Mindlin theory approaches the classical plate solution as the ratio of plate thickness to crack size becomes infinitesimally small.…”

Section: Introductionmentioning

confidence: 99%

“…The strain energy release rate and the virtual crack extension techniques require two runs of analysis for evaluating SERR. Considering the merits and demerits of these techniques, it is observed that for LEFM problems, MVCCI technique in combination with FEM is an efficient tool [13,14,21] for evaluating SERR from which SIF can be calculated. Further, it is observed from the literature that the MVCCI technique can be effectively used for the fracture analysis of cracked plates subjected to combined tensile, bending and shear loads.…”

Section: Introductionmentioning

confidence: 99%