Stress intensity factor for multiple inclined or curved cracks problem in circular positions in plane elasticity

Rafar, Rahimah Abdul; Long, Nik Mohd Asri Nik; Senu, Norazak; Noda, Nao Aki

doi:10.1002/zamm.201600290

Cited by 12 publications

(3 citation statements)

References 28 publications

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“…Numerous researchers deal the problems of moving crack in various elastic solids having distinct anisotropy and obtained the expressions of SIF with the impact of several dynamic loading conditions. [28][29][30][31][32][33] As per the authors' knowledge, no mathematical investigation has been made till date to examine the propagation of Griffith crack influenced by plane waves in a monoclinic crystalline layer. The present mathematical model is a novel investigation for SIF at the tip of moving Griffith crack associated with plane wave propagation in a crystalline monoclinic layer with moving parallel punch pressure acting on the boundaries of the layer under the impact of mechanical point loading.…”

Section: Introductionmentioning

confidence: 99%

Analytical study on stress intensity factor due to the propagation of Griffith crack in a crystalline monoclinic layer subjected to punch pressure

Kumar

Mahanty

Singh

et al. 2020

Fatigue Fract Eng Mat Struct

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An analytical model is introduced to analyse moving Griffith crack in a monoclinic crystalline layer of finite width and infinite extent with moving parallel punch pressure acting at the bounding surface of the layer because of the propagation of plane waves under mechanical point loading. Formulation of the model includes coupled singular integral equations with Cauchy‐type singularities. The expression of stress intensity factor (SIF) at the tip of moving crack having constant point loading is established in the closed‐form by employing Hilbert transformation. Further, expression of SIF is deduced for some particular cases of the crystalline layer, that is, without punch pressure and anisotropy. For the sake of validation, the obtained results are matched with pre‐established and standard results. Numerical computations and graphical demonstrations have been carried out for crystalline materials with monoclinic symmetry like lithium niobate and lithium tantalate and for isotropic material as well to unravel the effect of punch pressure, crack length, distinct positions of acting point load and the velocity of crack on SIF. Further, influence of anisotropy has been traced out remarkably through comparative study that is one of the pinnacles of the present study.

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Section: Introductionmentioning

confidence: 99%

Analytical study on stress intensity factor due to the propagation of Griffith crack in a crystalline monoclinic layer subjected to punch pressure

Kumar

Mahanty

Singh

et al. 2020

Fatigue Fract Eng Mat Struct

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“…These problems will affect the engineering structures which related to the stability and safety of the materials. A number of works have been discussed to investigate the characteristics of stress intensity factors (SIFs) at all crack tips for the crack problems in an infinite plane [1,2], half plane [3,4] and bonded two half planes [5,6,7]. The nondimensional SIFs for the crack problems in bonded two half planes subjected to the various stresses was calculated by using the body force method with continuous distributions along cracks [5].…”

Section: Introductionmentioning

confidence: 99%

Mode Stresses for the Interaction between Two Inclined Cracks in Bonded Two Half Planes

Hamzah

Long

2020

KEM

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The various mode of stresses for the interaction between two inclined cracks in the upper part of bonded two half planes which are normal stress (Mode I), shear stress (Mode II), tearing stress (Mode III) and mixed stress was studied. For this problem, the modified complex potentials (MCPs) method was used to develop the new system of hypersingular integral equations (HSIEs) by applying the conditions for continuity of resultant force and displacement functions with the unknown variable of crack opening displacement (COD) function and the right hand terms are the tractions along the crack. The curve length coordinate method and Gauss quadrature rules were used to solve numerically the obtained HSIEs to compute the stress intensity factors (SIFs) in order to determine the strength of the materials containing cracks. Numerical solutions presented the characteristic of nondimensional SIFs at the cracks tips. It is obtained that the various stresses and the elastic constants ratio are influences to the value of nondimensional SIFs at the crack tips.

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“…Hypersingular integral equations of order 2 and 3 arise as a consequence of the reduction of boundary value problems associated with Laplace equation when the boundary conditions involving normal derivatives are enforced. The applications of the hypersingular integral equation of the first kind (HSIE I) of orders 2 and 3 are widely available in the literature of fluid mechanics [6,15,16], acoustic waves [14], fracture mechanics [2], crack problem [24] etc. However, involvement of hypersingular integral equations of the second kind (HSIE II) is not so frequent, especially in the literature of linear water waves.…”

mentioning

confidence: 99%

Water Wave Scattering by a Thin Vertical Submerged Permeable Plate

Gayen

Gupta

Chakrabarti

2021

Mathematical Modelling and Analysis

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An alternative approach is proposed here to investigate the problem of scattering of surface water waves by a vertical permeable plate submerged in deep water within the framework of linear water wave theory. Using Havelock’s expansion of water wave potential, the associated boundary value problem is reduced to a second kind hypersingular integral equation of order 2. The unknown function of the hypersingular integral equation is expressed as a product of a suitable weight function and an unknown polynomial. The associated hypersingular integral of order 2 is evaluated by representing it as the derivative of a singular integral of the Cauchy type which is computed by employing an idea explained in Gakhov’s book [7]. The values of the reflection coefficient computed with the help of present method match exactly with the previous results available in the literature. The energy identity is derived using the Havelock’s theorems.

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Stress intensity factor for multiple inclined or curved cracks problem in circular positions in plane elasticity

Cited by 12 publications

References 28 publications

Analytical study on stress intensity factor due to the propagation of Griffith crack in a crystalline monoclinic layer subjected to punch pressure

Analytical study on stress intensity factor due to the propagation of Griffith crack in a crystalline monoclinic layer subjected to punch pressure

Mode Stresses for the Interaction between Two Inclined Cracks in Bonded Two Half Planes

Water Wave Scattering by a Thin Vertical Submerged Permeable Plate

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