Solid cylinder surface ring-shaped crack development under thermal influence

Аuthors

Kirichek V. A.

Taganrog institute named after A.P. Chekhov (Branch of the Rostov State University of Economics), Initsiativnaya str., 48, Taganrog, 347936, Russia

e-mail: Zhornik_Victoria@mail.ru

Abstract

The problem of nonstationary thermoelasticity for a continuous unbounded cylinder, with a ring-shaped crack on the surface propagating under cooling is considered. The cylinder is enclosed in a thin shell modeling a coating with a sliding sealing of its surface. Two limiting cases concerning the elastic properties of the shell are analyzed. In the first case, it is considered that the shell is extremely «hard», in the second one — extremely «soft». The temperature field is assumed to be radial; therefore, the crack does not affect the heat propagation in the cylinder. Therefore, the solution of the problem is represented as the sum of two solutions. The first one, considered assuming the crack absence, satisfies all the thermoelasticity problem conditions, except for the one of the ring-shaped crack banks, which are loaded with an axial load. To eliminate this load, a second solution of the isothermal elasticity theory problem for a semi-infinite cylinder with an extremely «rigid» shell was required. It was reduced to the Fredholm equation of the second kind with respect to a certain function determining the stress intensity factor (SIF), which controls the surface ring-shaped crack development in the cylinder under cooling. The successive approximations method is used for the integral equation solving, and the solution for SIF is obtained in a polynomial form with respect to the dimensionless ring-shaped crack front radius (the ratio of the crack front radius to the cylinder radius). Therefore, when the crack depth decreases, the dimensionless radius of the crack front tends to unity and the solution for the SIF gives a large error. However, in the case of small cracks, a cylinder with a surface ring-shaped crack may be represented as a half-space with an edge transverse crack equal to the ring-shaped crack depth. The data available in the literature for SIF, transformed in relation to the case under consideration, are used. Numerical calculations are carried out and the dependences of the behavior of deep and shallow cracks for cylinders with extremely «soft» and extremely «hard» shells are given. It is shown that in a certain crack depths interval these solutions coincide. The time dependences of SIF are obtained for various sizes of ring-shaped cracks, and it is shown that if an ring-shaped crack begins to grow, then it first grows abruptly to some intermediate value, and then relatively slowly, as temperature gradients develop, and finally stops before reaching the cylinder axis (the cylinder burst from the surface).

Keywords:

two-layer cylinder, thermal impact, thermoelasticity, ring-shaped crack, stress intensity coefficient

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