Brittle fracture, fracture gradient deformation criterion, Cauchy problem, the Heaviside function, regularization of the initial temperature distribution, the logarithmic potential range.

In [1], we propose a new criterion of destruction coming from the assumption that brittle fracture occurs when the deformation modulus of the gradient reaches the limit. In this study, shown in more detail that the module temperature gradient, and hence the deformation becomes significant in a thin boundary layer, where there is a sharp change in temperature. The solution of the new thermoelastic problem of a sharp change in temperature in a circular area. And it turned out that in the case of chilled curved border region E2, where E2 - Euclidean plane failure criterion is complicated and takes the form of a limit value of the sum of the gradient module main strains, or simply the sum of the principal stresses. The destruction will be determined by the criterion, which is less than the advance. It is also shown: in the case of a heated circular area in E2 criterion of brittle fracture continuum medium will limit the amount of principal strain gradient module. Presented preliminary results of an experiment with samples of the sudden change in temperature.

Mirsalimov Vagif e-mail: mir-vagif@mail.ru, Doctor of Physical and Mathematical Sciences, Professor, Azerbaijan Technical University, Institute of Mathematics and Mechanics of NAS of Azerbaijan, Baku, Azerbaijan.