Growth of creep cracks in structural elements under long-term loading
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GROWTH OF CREEP CRACKS IN STRUCTURAL ELEMENTS UNDER LONG-TERM LOADING O. E. Andreikiv,1,2 I. Ya. Dolins’ka,1 and N. V. Yavors’ka1
UDC 539.375:539.4:536.543
We propose a computational model for the investigation of the process of growth of high-temperature creep cracks under long-term tensile static loads (dynamic mode of operation) and determine the residual service life of a steam pipe under these operating conditions. It is shown that the indicated loads may lead to the unpredicted fractures of structural elements. Keywords: stationary and dynamic modes of operation, residual service life, high-temperature creep, steam pipe.
It is well known [1, 2] that the strength of structural elements under the action of long-term static loads and high temperatures is exhausted as a result of the high-temperature creep of their materials. This phenomenon was studied in numerous works, especially for flawless materials [1, 2]. At present, we know a series of computational models aimed at the evaluation the residual life of structural elements with cracks under the conditions of high-temperature creep [3–5]. However, the cases where some additional factors (concentrated in time) act upon the material parallel with high-temperature creep and long-term static loads are studied quite poorly. Thus, in the present work, we propose a computational model for finding the period of subcritical crack growth in elements of this kind.
Formulation of the Computational Model Consider a structural element (plate) containing a rectilinear crack of length 2l0 (Fig. 1) subjected to the action of high temperature and long-term static loading symmetric about the crack line. The load undergoes n changes for a certain period of time (dynamic mode [6]). It is necessary to determine the residual life of this element with regard for the changes in the load, i.e., the time t = t* for which, as a result of high-temperature creep, the crack grows to the critical size l* , and the structural element fails. To solve this problem, we use the energy approach [7] based on the first law of thermodynamics and the equation of balance for the rates of change in the energy. By using these equations and the fact that the stressed state is symmetric about the crack line, we arrive at the following equation for rate of changes in the crack length:
∂W p(2) (t)/∂t dl , = dt (γ C − γ t − ∂W p(1) (l)/∂l ) 1 2
(1)
Franko Lviv National University, Lviv, Ukraine. Corresponding author; e-mail: [email protected].
Translated from Fizyko-Khimichna Mekhanika Materialiv, Vol. 48, No. 3, pp. 12–17, May–June, 2012. Original article submitted June 6, 2011. 266
1068-820X/12/4803–0266
© 2012
Springer Science+Business Media New York
GROWTH OF CREEP CRACKS IN STRUCTURAL ELEMENTS UNDER LONG-TERM LOADING
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where W p(2) (t) is a part of the work of plastic strains in the process zone near the crack tip under the conditions of high-temperature creep spent for constant crack length and caused by the plate itself (it depends only on time
t ), W p(1) (l) is a part of the wor
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