Evaluation of the period of subcritical growth of a high-temperature creep crack in the wheel of a steam turbine
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EVALUATION OF THE PERIOD OF SUBCRITICAL GROWTH OF A HIGHTEMPERATURE CREEP CRACK IN THE WHEEL OF A STEAM TURBINE O. E. Andreikiv1, 2 and N. B. Sas1
UDC 539.4:536.543
The computational model of propagation of high-temperature creep cracks in metallic materials proposed earlier is used to develop a method for the evaluation of residual life of the wheels of steam turbines. Examples of annular and disk-shaped wheels are analyzed. Keywords: residual life, period of subcritical growth, creep, stress intensity factor, creep crack.
As one of important problems encountered in the process of operation of power-generating equipment, especially at thermal and nuclear power plants, we can mention the problem of evaluation of the residual life of its elements weakened by cracks. This is explained as follows: It is well known [1] that, in most cases, the materials of structural elements contain cracklike defects. They appear both in the process of manufacturing of the materials and elements and as a result of their long-term operation. In these elements, under the conditions of long-term static loading at high temperatures, we observe the formation of high-temperature creep cracks. These cracks propagate and finally attain their critical sizes as a result of which the structures suffer catastrophic failures. In order to predict and prevent these failures, it is necessary to compute the residual service life of the critical (loadbearing) elements (the period of subcritical growth of these cracks). The present work is devoted to the solution of problems of this sort. Thus, in particular, we determine the residual service life of the wheels of steam turbines. Evaluation of the Residual Service Life of the Annular Disk of Steam Turbine Weakened by a Crack Consider a disk (ring) of a steam turbine with inner r1 and outer r2 radii whose specific mass is denoted by and the angular velocity of rotation by (Fig. 1). By using the well-known results from [2], we arrive at the following relations for the stresses formed in the disk:
(0) r (r) =
(0) (r) =
1 r 2r 2 (3 + μ) 2 r12 + r2 2 1 22 r 2 , 8 r
1 r 2r 2 2 ( 3 + μ ) r12 + r2 2 + 1 22 ( 1 + 3μ ) r 2 , 8 r
(1)
(2)
where r and are polar coordinates and μ is Poisson’s ratio. 1 2
Franko Lviv National University, Lviv, Ukraine. Corresponding author; e-mail: [email protected].
Translated from Fizyko-Khimichna Mekhanika Materialiv, Vol. 46, No. 3, pp. 16–22, May–June, 2010. Original article submitted November 12, 2009. 1068-820X/10/4603–0297
© 2010
Springer Science+Business Media, Inc.
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O. E. ANDREIKIV
(a)
AND
N. B. SAS
(b) Fig. 1. Annular () and solid (b) disks of a steam turbine.
For the engineering practice, it is of interest to analyze the case of a disk containing a surface crack (Fig. 1) of length l0 and heated to a temperature which may lead to the formation of high-temperature creep in the process zone near the crack contour and, hence, to crack growth and, as a final result, to the failure of the disk.
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