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

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 $\tau^\infty_{xy}$ 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 $\tau^\infty_{xy}$.  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.

thermoelectric
bonded materials
single crack
hyper-singular integral equations
stress intensity factors
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