A Crack Originating from an Angular Corner of a Semi-infinite Plate With a Step

Hasebe, Norio; Ueda, Mikito

doi:10.1299/jsme1958.24.483

Cited by 9 publications

(3 citation statements)

References 1 publication

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“…One of the main merits using a rational mapping function is that stress functions achieved are exact ones for the geometrical shape represented by the rational mapping function. A rational mapping function of a sum of fraction expressions is also applied to any complicated configuration in principle (Hasebe and 1978; Hasebe and Ueda, 1981a;Hasebe and Inohara, 1981b). The technique can be also applied to a crack problem directly to calculate stress intensity factor.…”

Section: Mapping Functionmentioning

confidence: 99%

Magnetic field and magneto elastic stress in an infinite plate containing an elliptical hole with an edge crack under uniform electric current

Hasebe

2010

International Journal of Solids and Structures

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a b s t r a c tTwo-dimensional solutions of the electric current, magnetic field and magneto elastic stress are presented for a magnetic material of a thin infinite plate containing an elliptical hole with an edge crack under uniform electric current. Using a rational mapping function, the each solution is obtained as a closed form. The linear constitutive equation is used for the magnetic field and the stress analyses. According to the electro-magneto theory, only Maxwell stress is caused as a body force in a plate which raises a plane stress state for a thin plate and the deformation of the plate thickness. Therefore the magneto elastic stress is analyzed using Maxwell stress. No further assumption of the plane stress state that the plate is thin is made for the stress analysis, though Maxwell stress components are expressed by nonlinear terms. The rigorous boundary condition expressed by Maxwell stress components is completely satisfied without any linear assumptions on the boundary. First, electric current, magnetic field and stress analyses for soft ferromagnetic material are carried out and then those analyses for paramagnetic and diamagnetic materials are carried out. It is stated that the stress components are expressed by the same expressions for those materials and the difference is only the magnitude of the permeability, though the magnetic fields H x , H y are different each other in the plates. If the analysis of magnetic field of paramagnetic material is easier than that of soft ferromagnetic material, the stress analysis may be carried out using the magnetic field for paramagnetic material to analyze the stress field, and the results may be applied for a soft ferromagnetic material. It is stated that the stress state for the magnetic field H x , H y is the same as the pure shear stress state. Solving the present magneto elastic stress problem, dislocation and rotation terms appear, which makes the present problem complicate. Solutions of the magneto elastic stress are nonlinear for the direction of electric current. Stresses in the direction of the plate thickness are caused and the solution is also obtained. Figures of the magnetic field and stress distribution are shown. Stress intensity factors are also derived and investigated for the crack length and the electric current direction.

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Section: Mapping Functionmentioning

confidence: 99%

Magnetic field and magneto elastic stress in an infinite plate containing an elliptical hole with an edge crack under uniform electric current

Hasebe

2010

International Journal of Solids and Structures

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“…One of the greatest merits of using a rational mapping function is that the obtained stress functions are exact ones for the geometrical shape represented by the rational function. A rational mapping function of a sum of fractional expressions can in principle also be applied to any complicated configuration (Hasebe and Iida, 1978;Hasebe and Ueda, 1981;Hasebe et al, 1984) as well as directly to a crack problem to calculate the stress intensity factor.…”

Section: Mapping Functionmentioning

confidence: 99%

Heat conduction and thermal stress induced by an electric current in an infinite thin plate containing an elliptical hole with an edge crack

Hasebe

Bucher

Heuer

2010

International Journal of Solids and Structures

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a b s t r a c tA uniform electric current at infinity was applied to a thin infinite conductor containing an elliptical hole with an edge crack. The electric current gives rise to two states, i.e., uniform and uneven Joule heat. These two states must be considered to analyze the heat conduction problem. The uneven Joule heat gives rise to uneven temperature and thus to heat flux, and to thermal stress.Using a rational mapping function, problems of the electric current, the Joule heat, the temperature, the heat flux, the thermal stress are analyzed, and each of their solutions is obtained as a closed form. The distributions of the electric current, the Joule heat, the temperature, the heat flux and the stress are shown in figures.The heat conduction problem is solved as a temperature boundary value problem. Solving the thermal stress problem, dislocation and rotation terms appear, which complicates this problem. The solutions of the Joule heat, the temperature, the heat flux and the thermal stress are nonlinear in the direction of the electric current. The crack problems are also analyzed, and the singular intensities at the crack tip of each problem are obtained. Mode II (sliding mode) stress intensity factor (SIF) is produced as well as Mode I (opening mode) SIF, for any direction of the electric current. The relations between the electric current density and the melting temperature and between the electric current density and SIF are investigated for some crack lengths in an aluminum plate.

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“…A rational mapping function of a sum of fractional expressions is also applied to any complicated configuration in principle (for examples, [3,7,8]). The technique can be also applied directly to a crack problem to calculate the stress intensity factor.…”

Section: Mapping Functionmentioning

confidence: 99%

Heat Conduction and Thermal Stress Analyses of a Strip with Semi-Elliptical Notch Under Electric Current

Hasebe¹

2010

Journal of Thermal Stresses

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An electric current is applied in a thin strip conductor with an edge crack or a semi-elliptical notch. The electric current gives rise to two states, i.e., uniform and uneven Joule heat. The Joule heat gives rise to the temperature, and thus the heat flux and also free thermal expansion. Using a rational mapping function, problems of the electrical current, the Joule heat, the temperature, the heat flux and the thermal stress are analyzed and their each solution is obtained as a closed form. The heat conduction problem is solved as a temperature boundary value problem. The distributions of the electric current, the Joule heat, the temperature, and the heat flux are shown in figures. After a free thermal expansion is obtained and a support condition is given, the stress components are calculated. The crack problems are analyzed for the problems of the electric current, joule heat, heat flux and stress. The expressions for intensity of the electric current, the heat flux and the Joule heat at the crack tip are derived. The exact expression of the temperature at the crack tip (notch tip) is also given. The notch problems are analyzed, and the approximate expressions of the concentration are given for each problem, of which error is a few percent. The relations between the electric current density and the melting temperature and between the electric current density and Joule heat are investigated for some crack lengths of aluminum strip. The intensity of the Joule heat relates to the creation of the blow hole.

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A Crack Originating from an Angular Corner of a Semi-infinite Plate With a Step

Cited by 9 publications

References 1 publication

Magnetic field and magneto elastic stress in an infinite plate containing an elliptical hole with an edge crack under uniform electric current

Magnetic field and magneto elastic stress in an infinite plate containing an elliptical hole with an edge crack under uniform electric current

Heat conduction and thermal stress induced by an electric current in an infinite thin plate containing an elliptical hole with an edge crack

Heat Conduction and Thermal Stress Analyses of a Strip with Semi-Elliptical Notch Under Electric Current

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