An External Circular Crack in an Infinite Solid under Axisymmetric Heat Flux Loading in the Framework of Fractional Thermoelasticity

Yuriy Povstenko; Tamara Kyrylych; Bożena Woźna-Szcześniak; Renata Kawa; Andrzej Yatsko

doi:10.3390/e24010070

An External Circular Crack in an Infinite Solid under Axisymmetric Heat Flux Loading in the Framework of Fractional Thermoelasticity

Entropy (Basel). 2021 Dec 30;24(1):70. doi: 10.3390/e24010070.

Authors

Yuriy Povstenko¹, Tamara Kyrylych¹, Bożena Woźna-Szcześniak¹, Renata Kawa¹, Andrzej Yatsko²

Affiliations

¹ Department of Mathematics and Computer Sciences, Faculty of Science and Technology, Jan Dlugosz University in Czestochowa, al. Armii Krajowej 13/15, 42-200 Czestochowa, Poland.
² Department of Mathematics, Faculty of Civil Engineering, Environmental and Geodesic Sciences, Koszalin University of Technology, Śniadeckich 2, 75-453 Koszalin, Poland.

Abstract

In a real solid there are different types of defects. During sudden cooling, near cracks, there can appear high thermal stresses. In this paper, the time-fractional heat conduction equation is studied in an infinite space with an external circular crack with the interior radius R in the case of axial symmetry. The surfaces of a crack are exposed to the constant heat flux loading in a circular ring R<r<ρ. The stress intensity factor is calculated as a function of the order of time-derivative, time, and the size of a circular ring and is presented graphically.

Keywords: Caputo derivative; Fourier cosine transform; Hankel transform; Laplace transform; Mittag-Leffler function; fractional calculus; fractional thermoelasticity; generalized Fourier law; stress intensity factor.