Engineering Mechanics

Proceedings Vol. 24 (2018)

ENGINEERING MECHANICS 2018

Copyright © 2018 Institute of Theoretical and Applied Mechanics of the Cech Academy of Sciences, Prague

 

Kartvelishvili T., Yumashev M.
pages 365 - 368, full text

The object of investigation of this work is brittle materials under conditions of rapid local heating, which leads to large temperature gradients in the sample and in turn to large mechanical stresses that can cause cracking of the sample and a significant deterioration in its strength and wear resistance. In this problem, an approximate method for calculating unsteady temperature fields is considered, when there is a rapid and intensive heating of a solid sphere by the action of a heat flux, described by its density, which is constant in time. The existence of the fusion front is not taking into account. The method of approximate solution of the linear heat equation is based on the idea of a thermal front. Analytic formulas are obtained that determine the temperature dependence on the coordinate and on time. Then the comparison of the approximate and numerical solution of the heat conductivity equation is made. Investigation of the stress field is carried out to determine the most probable areas of the occurrence of cracks. Analytic expressions are obtained in the case of an elastic material.

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