Explicit solutions of magnetoelastic fields in a soft ferromagnetic solid with curvilinear cracks

Lin, Cheng‐Jian; Chen, Shin-Cheng; Lee, Jui-Lin

doi:10.1016/j.engfracmech.2009.04.017

Cited by 12 publications

(5 citation statements)

References 15 publications

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“…where μ 0 is a universal constant denoting the absolute permeability of vacuum and μ 0 = 4π × 10 −7 T m/A; μ r = 1 + χ stands for the relative magnetic permeability with χ being the magnetic susceptibility of the material; μ = μ 0 μ r = μ 0 (1 + χ) is the magnetic permeability of the material. Furthermore, the components of Maxwell stress ( σ M x x , σ M yy , τ M xy ) and the magnetoelastic stress ( σ x x , σ yy , τ xy ) in the associated magnetoelastic field are given as [11,14]…”

Section: Problem Descriptions and Formulationsmentioning

confidence: 99%

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Periodically spaced collinear cracks in a soft ferromagnetic material under a uniform magnetic field

Gao

Chen

2020

Acta Mech

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This paper aims at a fundamental perspective of multiple cracks' interaction on the fracture behavior of magnetoelastic materials. A theoretical study is performed on a soft ferromagnetic solid weakened by an array of periodic cracks under an in-plane magnetic loading. By using the conformal mapping technique and the analytic function boundary value theory, a rigorous analytical solution of the magnetic and stress fields is obtained, and the closed-form expressions for the field intensity factors are presented. Numerical examples of magnetically impermeable and permeable cracks are studied to reveal the relationship of the mode-I stress intensity factor with the period ratio of the cracks, the surrounding medium, and the applied magnetic loading. The analytical solution in this study can serve as a theoretical benchmark for the fracture problem of a magnetoelastic solid containing multiple defects.

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Section: Problem Descriptions and Formulationsmentioning

confidence: 99%

“…Notable and recent researches on this topic can be found in Refs. [8][9][10][11][12][13], especially the investigations on the magnetoelastic problems of cracks with irregular shapes [14,15]. Important breakthroughs are also achieved on the interface crack problems between bonded dissimilar magnetoelastic materials [16,17].…”

Section: Introductionmentioning

confidence: 99%

Periodically spaced collinear cracks in a soft ferromagnetic material under a uniform magnetic field

Gao

Chen

2020

Acta Mech

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“…These cracks are primarily caused by factors such as material fatigue, corrosion, excessive strain, or stresses, which can result in the structure weakening and eventually failing. A lot of researchers have dealt with and analyzed the crack problems in elastic materials [1,2], thermal materials [3][4][5][6], magnetoelastic materials [7,8], and thermoelectric materials [9][10][11][12].…”

Section: Introductionmentioning

confidence: 99%

Numerical Solution for A Curvilinear Crack Phenomenon in Thermoelectric Bonded Materials Subjected to Mechanical Loadings

Muhammad Haziq Iqmal Mohd Nordin,

Khairum Hamzah,

Nik Mohd Asri Nik Long

et al. 2024

ARAM

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In this study, a curvilinear crack phenomenon laying in the upper part of thermoelectric bonded materials subject to mechanical loadings is considered. A curvilinear crack problem in thermoelectric bonded materials subjected to shear stress is formulated. The modified complex potential (MCP) function method is used to formulate this crack phenomenon into the hypersingular integral equations (HSIEs) with the help of the continuity conditions of the resultant electric force and displacement electric function. The normal and tangential traction along the crack segment serves as the right-hand side of the integral equation. The HSIEs are solved numerically for the unknown crack opening displacement (COD) function, electric current density, and energy flux load using the appropriate quadrature formulas. The numerical solution presented the behavior of the dimensionless stress intensity factors (SIFs) at the crack tips which depend on the elastic constant’s ratio, the position of the crack, the electric conductivity, and the thermal expansion coefficients.

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“…Many researchers have been drawn to investigate the stability behavior of structures or materials subject to remote stress by considering the types of materials such as infinite [1][2][3], finite [4,5], half plane [6][7][8], and bonded materials [9][10][11][12][13]. These types of materials have several conditions such as elasticity [14][15][16], thermoelasticity [17][18][19], magnetoelasticity [20][21][22], and electricity [23][24][25]. One of the important structures in manufacturing are thermoelectric materials.…”

Section: Introductionmentioning

confidence: 99%

Formulation for Multiple Cracks Problem in Thermoelectric-Bonded Materials Using Hypersingular Integral Equations

et al. 2023

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New formulations are produced for problems associated with multiple cracks in the upper part of thermoelectric-bonded materials subjected to remote stress using hypersingular integral equations (HSIEs). The modified complex stress potential function method with the continuity conditions of the resultant electric force and displacement electric function, and temperature and resultant heat flux being continuous across the bonded materials’ interface, is used to develop these HSIEs. The unknown crack opening displacement function, electric current density, and energy flux load are mapped into the square root singularity function using the curved length coordinate method. The new HSIEs for multiple cracks in the upper part of thermoelectric-bonded materials can be obtained by applying the superposition principle. The appropriate quadrature formulas are then used to find stress intensity factors, with the traction along the crack as the right-hand term with the help of the curved length coordinate method. The general solutions of HSIEs for crack problems in thermoelectric-bonded materials are demonstrated with two substitutions and it is strictly confirmed with rigorous proof that: (i) the general solutions of HSIEs reduce to infinite materials if G1=G2, K1=K2, and E1=E2, and the values of the electric parts are α1=α2=0 and λ1=λ2=0; (ii) the general solutions of HSIEs reduce to half-plane materials if G2=0, and the values of α1=α2=0, λ1=λ2=0 and κ2=0. These substitutions also partially validate the general solution derived from this study.

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Explicit solutions of magnetoelastic fields in a soft ferromagnetic solid with curvilinear cracks

Cited by 12 publications

References 15 publications

Periodically spaced collinear cracks in a soft ferromagnetic material under a uniform magnetic field

Periodically spaced collinear cracks in a soft ferromagnetic material under a uniform magnetic field

Numerical Solution for A Curvilinear Crack Phenomenon in Thermoelectric Bonded Materials Subjected to Mechanical Loadings

Formulation for Multiple Cracks Problem in Thermoelectric-Bonded Materials Using Hypersingular Integral Equations

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