Partially insulated cracks in orthotropic materials under steady state thermo-mechanical loadings

An attempt has been made to investigate the cracked composite medium with thermally conducting multiple cracks at its interface of the dissimilar orthotropic media subjected to thermal and mechanical loadings. The present article examines the governing equations, the associated differential constraints and boundary conditions those govern the temperature field and stress field. Fourier integral transforms, together with their corresponding inverses, have been employed to convert the singular integral equations into a set of linear equations by using the concept of orthogonality and completeness. The numerical technique, namely the Schmidt method, which employs a polynomial expansion of the unknown functions, is used to solve algebraic equations to determine the desired temperature and stress fields. The semi-analytical findings of the expressions for heat flux intensity factor (HFIF), stress intensity factor (SIF), and crack displacements have been mentioned in the article. Both mode-I and II types of cracks have been studied to investigate the effect of thermal conductivity. Detailed graphical representations effectively illustrate the numerical results and the interrelations between crack lengths, bonded strip width, and the partial conductivity coefficient of the crack surface. As the thermal conductivity coefficient increases, the temperature difference tends to zero. The results reveal that an increase in thermal conductivity decreases the SIFs.