PSI - Issue 52

Jan Sladek et al. / Procedia Structural Integrity 52 (2024) 133–142 Author name / Structural Integrity Procedia 00 (2019) 000–000

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are affected too. The crack opening displacements are reduced significantly for larger values of micro-thermal length scale parameter.

Fig. 5: Crack opening displacements for various T l parameters at time instant

10 1 10 s    

4. Conclusions A possibility of the crack arrest by the Joule heating is investigated in this paper. The gradients of heat flux and strains are significant at the crack tip vicinity. Therefore, both these gradients are included into the thermal potential and free energy density in gradient theories for heat transport and thermoelasticity, respectively. The uncoupled thermoelasticity is considered here, where thermal fields are not affected by mechanical ones. Since, the thermal response is much slower than the response of elastic and electric fields, the quasi-static approximation is justified for both the electric and elastic fields. General 2D boundary value thermo-electro-elastic problems with cracks under an electric current load are analysed in the gradient theory of the heat transport and thermoelasticity. The mixed FEM formulation has been developed for both uncoupled problems. Some numerical results are presented for the plate with a central crack. After switching-on the electric current, the crack closure is starting due to the compressive stresses generated by the Joule heating. The influence of the micro-thermal length scale parameter on the crack closure is investigated. The crack opening displacements are reduced significantly for larger values of micro-thermal length scale parameter. Acknowledgements The authors acknowledge the support by the Slovak Science and Technology Assistance Agency registered under number SK-UA-21-0010 and VEGA-2/0061/20. References Aifantis, E.C., 2003. Update on a class of gradient theories. Mechanics of Materials 35, 259-280. Allen, P.B., 2014. Size effects in thermal conduction by phonons. Physical Review B 90, 054301. Cai, G.X., Yuan, F.G., 1999. Electric current-induced stresses at the crack tip in conductors. International Journal of Fracture 96, 279–301. Eringen, A.C. 1976. Non-local polar field theory, in Continuum Physics vol. 4, Academic Press, New York. Lazar, M., Kirchner, H.O.K., 2007. The eshleby stress tensor, angular momentum tensor and dilatation flux in gradient elasticity. International Journal of Solids and Structures 44, 2477-2486. Sladek, J., Sladek, V., Repka, M., 2021. The heat conduction in nano-sized structures. Physical Mesomechanics 24, 611-617.