Strength of thin-walled structural elements with cracks under the conditions of creep
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STRENGTH OF THIN-WALLED STRUCTURAL ELEMENTS WITH CRACKS UNDER THE CONDITIONS OF CREEP O. E. Andreikiv and N. B. Sas
UDC 539.4:536.543
By using a computational model of growth of high-temperature creep cracks in metallic materials formulated by the authors somewhat earlier [Fiz.-Khim. Mekh. Mater., 42, No. 2, 62–68 (2006)], we develop a procedure for the construction of the diagrams of ultimate stresses for cracked plates. This procedure forms the basis of a method used for the evaluation of high-temperature strength of thin-walled structural elements weakened by cracks. The accumulated numerical results are compared with the experimental data available from the literature.
The strength analysis of structural elements of (such as steam boilers, steam pipelines, steam and gas turbines, etc.) subjected to long-term loads at high temperatures fundamentally differs from the short-term strength analysis. This is explained by the fact that the fracture of these elements as a result of creep is studied for hightemperature strength and, as a rule, under the assumption of defectless materials with creep in the classical sense [1–3]. However, for the evaluation of the high-temperature strength of elements, it is also necessary to take into account the development of cracklike defects (see, e.g., [4, 5]). The number of works devoted to the investigation of this problem is insignificant. As a rule, these are experimental works and the accumulated results are used to construct approximate equations for the description of the process propagation of high-temperature creep cracks (see, e.g., [2, 6, 7]. In [8–10], the energy approach to the evaluation of the subcritical period of growth of high-temperature creep cracks is formulated on the basis of the first law of thermodynamics. In the present work, this approach is used to develop a procedure for the analysis of high-temperature strength of thin-walled structural elements with cracks. Plate Containing an Arbitrarily Oriented Crack Consider an infinite perfectly elastoplastic plate containing a rectilinear macrocrack of initial length 2l0 and stretched at infinity in mutually perpendicular directions by uniformly distributed forces with intensities p and q at a certain angle to the crack line (Fig. 1a). High temperatures cause high-temperature creep in the plastic zones formed near the crack tip. We now determine the parameters of the external force p = p * ( t* ) and q = q* ( t* ) for which the residual service life of the plate does not exceed the prescribed value t = t* . The posed problem is inverse to the problem of finding t* = t* ( p* , q* ). Therefore, we first consider the direct problem. On the basis of the energy approach formulated in [8 – 10], this problem is reduced to the solution of the following system of differential equations: ∂Wpl( 2 ) 1 , V = γ f − γ t ∂t
(1)
Franko Lviv National University, Lviv. Translated from Fizyko-Khimichna Mekhanika Materialiv, Vol. 43, No. 2, pp. 33–39, March–April, 2007. Original article submitted September 13, 2006. 174
1068–82
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