Numerical Solution for Crack Phenomenon in Dissimilar Materials under Various Mechanical Loadings

Hamzah, Khairum; Long, Nik Mohd Asri Nik; Senu, Norazak; Eshkuvatov, Zainidin K.

doi:10.3390/sym13020235

Cited by 5 publications

(4 citation statements)

References 25 publications

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“…According to Hamzah et al [7], if the shear stress σ x1 = σ x2 = p and normal stress σ y1 = σ y2 = p then N (z) + iT (z) are defined as follows…”

Section: Bi-materials Platementioning

confidence: 99%

Effect of Mechanical Loadings on Two Unequal Slanted Cracks Length in Bi-Materials Plate

Hamzah¹,

Long²

2022

MJMS

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Although a lot of crack problems in bi-materials plate were previously treated, few solutions are available under mechanical loadings, arbitrary crack lengths and material combinations. In this paper the dimensionless stress intensity factors (SIFs) of two slanted cracks in the upper plate of bi-materials are considered under mechanical loadings with varying the crack length and material combinations systematically. In order to calculate the dimensionless SIFs accurately, the hypersingular integral equations (HSIEs) was formulated by using the modified complex potentials (MCP) function. The details numerical results of the dimensionless SIFs are given in tabular form and graphical presentations. Comparisons with the existing exact solutions show that the numerical results in this paper have high accuracy. Our results are described with clarifying the effect of the mechanical loadings, bi-elastic constant ratio and element size of cracks on the dimensionless SIFs.

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“…According to Hamzah et al [7], if the shear stress σ x1 = σ x2 = p and normal stress σ y1 = σ y2 = p then N (z) + iT (z) are defined as follows…”

Section: Bi-materials Platementioning

confidence: 99%

Effect of Mechanical Loadings on Two Unequal Slanted Cracks Length in Bi-Materials Plate

Hamzah¹,

Long²

2022

MJMS

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“…Hyper-singular integral equations (HSIEs) have found extensive application in various physics and engineering fields, notably in tackling crack-related challenges within fracture mechanics [7][8][9][10]. This method stands out due to its numerous advantages over other commonly employed crack analysis techniques.…”

Section: Introductionmentioning

confidence: 99%

Derivation of hyper-singular integral equations for thermoelectric bonded materials featuring a crack parallel to interface

Mohd Nordin,

Hamzah,

Khashiie

et al. 2023

Math. Model. Comput.

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In this paper, the derivation of hyper-singular integral equations (HSIEs) for thermoelectric bonded materials (TEBM) featuring a crack parallel to interface subject to in-plane shear stress τ∞xy was intensively studied. Generally, stress intensity factors (SIFs) were calculated using HSIEs with the help of modified complex stress variable function (MCSVF), and continuity conditions of the resultant electric force and displacement electric function. The unknown crack opening displacement (COD) function, electric current density, and energy flux load are mapped into the square root singularity function using the curved length coordinate method as the right-hand term. This unknown function is then used to compute the dimensionless SIFs in order to determine the stability behavior of TEBM featuring a crack parallel to interface subject to in-plane shear stress τ∞xy. Numerical results of the dimensionless SIFs at all the crack tips are presented. Our results are totally in good agreement with those of the previous works. It is observed that the dimensionless SIFs at the crack tips depend on the elastic constants ratio, the crack geometries, the electric conductivity, and the thermal expansion coefficients.

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“…Recent decades saw an increasingly extensive interest in crack problems in multilayered elastic media due to their wide range of applications, including a stability analysis of construction for safety design [1][2][3][4][5], characterization of fractured porous media to optimize transport efficiency [6][7][8][9][10], and hydraulic-fracturing simulation for economic development of unconventional reservoirs [11][12][13][14][15], which has motivated the related works intensively in the latest decade [16][17][18][19][20]. The core component of hydraulic-fracturing simulation is well accepted to be the ability to model elastic response of a pressurized crack that intersects a number of layers, each of which is assumed to be homogeneous and isotropic individually [21][22][23][24][25].…”

Section: Introductionmentioning

confidence: 99%

A Boundary-Element Analysis of Crack Problems in Multilayered Elastic Media: A Review

Lan,

Zhou,

et al. 2023

Mathematics

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Crack problems in multilayered elastic media have attracted extensive attention for years due to their wide applications in both a theoretical analysis and practical industry. The boundary element method (BEM) is widely chosen among various numerical methods to solve the crack problems. Compared to other numerical methods, such as the phase field method (PFM) or the finite element method (FEM), the BEM ensures satisfying accuracy, broad applicability, and satisfactory efficiency. Therefore, this paper reviews the state-of-the-art progress in a boundary-element analysis of the crack problems in multilayered elastic media by concentrating on implementations of the two branches of the BEM: the displacement discontinuity method (DDM) and the direct method (DM). The review shows limitation of the DDM in applicability at first and subsequently reveals the inapplicability of the conventional DM for the crack problems. After that, the review outlines a pre-treatment that makes the DM applicable for the crack problems and presents a DM-based method that solves the crack problems more efficiently than the conventional DM but still more slowly than the DDM. Then, the review highlights a method that combines the DDM and the DM so that it shares both the efficiency of the DDM and broad applicability of the DM after the pre-treatment, making it a promising candidate for an analysis of the crack problems. In addition, the paper presents numerical examples to demonstrate an even faster approximation with the combined method for a thin layer, which is one of the challenges for hydraulic-fracturing simulation. Finally, the review concludes with a comprehensive summary and an outlook for future study.

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Numerical Solution for Crack Phenomenon in Dissimilar Materials under Various Mechanical Loadings

Cited by 5 publications

References 25 publications

Effect of Mechanical Loadings on Two Unequal Slanted Cracks Length in Bi-Materials Plate

Effect of Mechanical Loadings on Two Unequal Slanted Cracks Length in Bi-Materials Plate

Derivation of hyper-singular integral equations for thermoelectric bonded materials featuring a crack parallel to interface

A Boundary-Element Analysis of Crack Problems in Multilayered Elastic Media: A Review

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